Citation
Multi-objective optimization model for macroscopic land allocation

Material Information

Title:
Multi-objective optimization model for macroscopic land allocation
Creator:
Kundu, Reema
Publication Date:
Language:
English
Physical Description:
xv, 390 leaves : ; 28 cm

Subjects

Subjects / Keywords:
Land use ( lcsh )
Landscape assessment ( lcsh )
Land use ( fast )
Landscape assessment ( fast )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaves 386-390).
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Reema Kundu.

Record Information

Source Institution:
|University of Colorado Denver
Holding Location:
|Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
464227357 ( OCLC )
ocn464227357
Classification:
LD1193.E53 2009d K86 ( lcc )

Full Text
MULTI-OBJECTIVE OPTIMIZATION MODEL
FOR
MACROSCOPIC LAND ALLOCATION
by
Reema Kundu
B.E., Osmania University, Hyderabad, India, 1995
M.S., University of Kentucky, 2001
A thesis submitted to the
University of Colorado at Denver/Health Sciences Center
in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
Civil Engineering Department
2009


2009 by Reema Kundu
All rights reserved.


This thesis for the Doctor of Philosophy
degree by
Reema Kundu
has been approved
by

Lynn Johnson
XJ A;
(0L4*£3jz-.
Bruce N. Janson
U a / i
kT
Brian Muller
Rajagopalan Balaji
A rVy
Arunprakash Karunanithi
25 April 2009
Date


Kundu, Reema. (Ph.D., Civil Engineering)
Macroscopic Land Allocation Model For Multi-objective Optimization
Thesis directed by Professor Dr. Lynn Johnson
ABSTRACT
This study proposes a land use allocation model based on genetic principles and spatial
characteristics of a landscape. The proposed land allocation model is developed to aid in
optimizing competing and complimentary objectives. An independent tool, MLUSOT
(Macroscopic Land Use Spatial Optimization Tool) that seamlessly integrates with ArcGIS
software package is developed to enable spatial analysis. The research study involves
understanding of spatial elements in land use system, their interactions and influence on
allocation of land uses. It focuses on evaluation of land use alternatives to accommodate
community needs and protect future resources. This study encompasses an intense
literature review to identify state-of-the art methodologies and current practices. Major
short comings including lack of assessment of spatial interactions in the current practices
are identified. A land use allocation model based on genetic principles and spatial
interactions is devised to enhance current practices and address existing deficiencies in
existing land use models.
In order to implement and test the proposed land allocation methodology extensive data
was collected from various sources including federal, state and local agencies. Different
sets of data were analyzed and finalized for calibration and validation of the allocation
model. For calibration, 1998 and 2003 datasets were used. And for validation 2003, 2010,
and 2025 datasets were used. The proposed model, MLUSOT is calibrated and validated
using different datasets within the Front Range urban corridor of Colorado. Three cases
studies are demonstrated to understand various application of MLUSOT. The findings from
these case studies were satisfactory considering the proposed allocation model is a
preliminary land use allocation model. The findings from all the case studies were
compared with DRCOG (Denver Regional Council of Governments) obtained future land
use maps. Only the findings from case study three were compared with IDRISI findings
and DRCOG future land use plans. In all the case studies green areas and residential


development were mostly over predicted. Overall, the findings were satisfactory and could
be used as an input in advanced land use allocation models.
This abstract accurately represents the content of the candidates thesis. I recommend its
publication.
Signed

-
>

Lynn Johnson


DEDICATION PAGE
I dedicate this work to my best friend, and my husband, Mohan. A widely respected
engineer known for his brilliant mind, who among many things has taught me the true
meaning of simplicity and made me a broad-minded and positive thinker.


ACKNOWLEDGMENT
I would like to whole heartedly thank my advisor Dr.Lynn Johnson for his sage advice,
friendly ear, invaluable guidance and insightful directions that helped me throughout my
thesis. I am very grateful to each of the members of my doctoral committee for their
support during the completion of the thesis. A special thank you to the Department of Civil
Engineering for providing me with financial support that helped me throughout the course
of my study.
I would like to acknowledge my parents without whose prayers and encouragement this
thesis would not have been possible. Finally I would like to acknowledge the efforts of my
husband, Mohan whose moral support, patience and guidance has been instrumental in
the completion of my thesis.


TABLE OF CONTENTS
Figures ...............................................................................xi
Tables ...............................................................................xiv
1 Introduction........................................................................1
1.1 General Overview..............................................................1
1.2 Current Issues Related to Land Use Allocation.................................6
1.3 Aims of Research Effort.......................................................7
1.4 Contribution of Thesis........................................................8
1.5 Scope and Limitations.........................................................8
1.6 Thesis Overview...............................................................9
2 Review of land use allocation modeling...........................................10
2.1 Spatial land use models......................................................15
2.2 Economic land use models.....................................................17
2.3 Integrated Land Use Model....................................................19
3 Literature review..................................................................24
3.1 General Overview.............................................................24
3.2 Review of State of the Art Land Use Allocation Technique.....................25
3.2.1 IDRISI Kilimanjaro....................................................... 26
3.2.2 Integrated Regional Modeling..............................................29
3.3 Overview of Available Multi-Objective Multi-Criteria Optimization Techniques:
Conceptual Grounding................................................................32
3.3.1 Analytical Hierarchy Process..............................................33
3.3.2 Equal Weight Averaging Model..............................................37
3.3.3 Goal Programming..........................................................37
3.3.4 Integer Programming.......................................................39
3.3.5 Non-linear Combinatorial Optimization.....................................40
3.3.6 Fuzzy Multi-Objective Programming.........................................41
3.3.7 Multiobjective Generalized Sensitivity Analysis.......................... 43
3.3.8 Multi-criteria Approval-Stochastic Multi-criteria Acceptability Analysis..46
viii


3.3.9 Cellular Automata..........................................................48
3.3.10 Simulated Annealing.....................................................49
3.3.11 Genetic Algorithm.......................................................49
3.4 Past and Present Land use Allocation Techniques.............................51
3.5 A Brief Review of Fragmentation Techniques.................................112
4 Proposed land use allocation model...............................................118
4.1 Overview...................................................................118
4.2 Basic Land Use Allocation Principles.......................................119
4.3 Land Use Allocation Design.................................................125
4.3.1 Identification of design parameters.......................................126
4.3.2 Development of design parameters..........................................129
4.3.3 Building initial framework for the allocation modeling....................132
4.3.4 Evaluation of the design phase of the land use allocation process.........135
4.4 Proposed Land Use Allocation Methodology...................................140
4.4.1 General Mathematical Concept..............................................141
4.4.2 Spatial Representation of NSGA............................................156
4.4.3 Integrated Mathematical-Spatial Conceptual Model..........................164
4.4.4 Land Use Allocation Software Development..................................192
4.5 Land Use Allocation Analysis and Evaluation................................210
5 Data collection..................................................................211
6 MLUSOT calibration and validation................................................234
6.1 Calibration Parameters and Methodology.....................................234
6.2 Calibration MOEs...........................................................244
6.3 Calibration Analysis and Results...........................................246
6.4 Land Use Allocation Model Validation Analysis..............................267
6.1 Conclusion.................................................................329
7 Conclusions and recommendations..................................................330
Appendix
A. Sample Python Programming Code.................................................332
B. MLUSOT Model Screen Captures.....................................................347
C. Model Prediction and Analysis Maps / IDRISI Analysis...........................355
ix


Bibliography
386
x


FIGURES
Figure
1.1 Land Use & Land Cover (USGS)......................................................3
1.2 Downtown Denver in 1885 & 2007 respectively (Historic Colorado)...................4
2.1 Land Use System (ILUTE Model)......................................................11
2.2 Land Use System (ILUTE Model)......................................................12
2.3 Land Use System (ILUTE Model)......................................................13
2.4 Land Use Models (ILUTE Model)..................................................... 14
2.5 Spatial Model Basic Structure (ILUTE Model).......................................16
2.6 Economic Model Basic Structure (ILUTE Model)....................................18
2.7 Integrated Model Basic Structure (ILUTE Model)....................................20
3.1 Integrated Regional Model (Denver Regional Council of Governments)................30
3.2 Fuzzy Multi-objective Algorithm (Foulds)..........................................42
3.3 Multiobjective Generalized Sensitivity Analysis Flowchart (Foulds)................45
3.4 LUCC Modeling framework (Land-Use and Land-Cover Change)..........................64
4.1 Flowchart Representing Genetic Algorithm (Goldberg)...............................145
4.2 Demonstration of Pareto Efficiency (Goldberg).....................................152
4.3 Flowchart Representing Non-Dominated Sorting Genetic Algorithm (Goldberg).........155
4.4 Representation of Spatial Data Types (ESRI)......................................158
4.5 Representation of Spatial Features on Raster Dataset (ESRI)......................159
4.6 Representation of Raster Dataset with Cell Values (ESRI).........................160
4.7 Summary of Steps Involved in Proposed Land Use Allocation Process.................166
4.8 Flowchart Illustrating Spatial process in Creating Factor Raster Dataset..........168
4.9 Flowchart Illustrating Assignment of Dummy Fitness Values.........................169
4.10 Flowchart Illustrating Computation of proximity of..............................171
4.11 Flowchart Illustrating Spatial Niche Count Method...............................173
4.12 Flowchart Illustrating Spatial Reproduction Method..............................175
4.13 Flowchart Illustrating Spatial Mutation Method..................................178
4.14 Illustration of Detailed Iteration Procedure for Mutation Method................181
4.15 Spatial Representation of Population Termination Criterion......................184
4.16 Mathematical Representation of Population Termination Criterion.................188
4.17 Constraint, Restricted, Other land use terminating condition flow chart.........190
4.18 Application Linking.............................................................194
4.19 Application Architecture........................................................199
4.20 Application Iterative Development Process.......................................200
4.21 Application Calibration and Validation..........................................202
4.22 Main Frame- Components of Main Window in an Interactive Display.................203
4.23 Input Entry Window..............................................................204
XI


4.24 Need a figure demonstrating the three sub-menus under Tools menu..............205
4.25 GA Process Window, associated sub-windows......................................206
4.26 Rank window....................................................................207
4.27 Fragmentation Window...........................................................208
4.28 Statistics Window..............................................................209
4.29 Help Menu......................................................................210
5.1 Front Range Urban Corridor of Colorado...........................................213
5.2 USGS & DRCOG 2001 Land Use Distribution..........................................218
5.3 Land use classification of DRCOG 2003 dataset (Denver Regional Council of
Governments)..........................................................................221
5.4 USGS Land use classification sample (USGS).......................................222
5.5 Calibration Output Dataset.......................................................223
5.6 Calibration Output Dataset Land use Distribution.................................224
5.7 Calibration Input Dataset........................................................225
5.8 Calibration Input Dataset Land use Distribution..................................226
5.9 Validation Input Dataset.........................................................229
5.10 Validation Input Dataset Land Use Distribution.....................230
5.11 Validation Output Dataset.......................................................231
5.12 Validation Output Dataset Land Use Distribution.................................232
6.1 Calibration Input Dataset........................................................249
6.2 Model Predicted Land Use Map 1...................................................250
6.3 Model Predicted Land Use Map 2...................................................251
6.4 Model Predicted Land Use Map 3...................................................252
6.5 Calibration Observed Dataset.....................................................253
6.6 Calibration Output 1 Pixel-Pixel Standard Deviation..............................255
6.7 Proximity of Observed Development Areas to.......................................261
6.8 Proximity of Predicted Development Areas to......................................262
6.9 Proximity of Predicted Development Areas to......................................263
6.10 Proximity of Predicted Development Areas to.....................................264
6.11 Validation Input Dataset........................................................268
6.12 Validation Output Dataset.......................................................269
6.13 Pixel-Pixel Standard Deviation of Validation Case 1............................274
6.14 Pixel-Pixel Standard Deviation of Validation Case 1............................275
6.15 Proximity of Observed Developed Areas to Conservation Areas....................283
6.16 Proximity of Predicted Development Areas to Conservation Areas.................284
6.17 Proximity of Observed Developed Areas to Conservation Areas....................285
6.18 Proximity of Predicted Development Areas to Conservation Areas.................286
6.19 Pixel-Pixel Standard Deviation of Validation Case 2............................291
6.20 Pixel-Pixel Standard Deviation of Validation Case 2............................292
6.21 Proximity of Observed Development Areas to Conservation Areas for Validation Case
2 Output 1 (2010).....................................................................300
6.22 Proximity of Predicted Development Areas to Conservation Areas for Validation Case
2 Output 1 (2010).....................................................................301
6.23 Proximity of Observed Development Areas to Conservation Areas for Validation Case
2 Output 1 (2025).....................................................................302
xii


6.24 Proximity of Predicted Development Areas to Conservation Areas for Validation Case
2 Output 1 (2025)....................................................................303
6.25 Pixel-Pixel Standard Deviation of Validation Case 3.............................309
6.26 Pixel-Pixel Standard Deviation of Validation Case 3.............................310
6.27 Pixel-Pixel Standard Deviation of Validation Case 3.............................311
6.28 Pixel-Pixel Standard Deviation of Validation Case 3.............................312
6.29 Proximity of Observed Development Areas to Conservation Areas...................322
6.30 Proximity of Predicted Development Areas to Conservation Areas..................323
6.31 Proximity of Predicted Development Areas to Conservation Areas..................324
6.32 Proximity of Observed Development Areas to Conservation Areas...................325
6.33 Proximity of Predicted Development Areas to Conservation Areas..................326
6.34 Proximity of Predicted Development Areas to Conservation Areas..................327
xiii


TABLES
Table
3-1 Relative Importance of Pair of Criteria ranked on 1-9 Intensity Scale..............34
3- 2 Weight Calculation Example.......................................................35
4- 1 Summary of Land Use Model Elements...............................................136
4-2 Roulette Wheel Selection Demonstration.............................................149
4-3 Demonstration of Pareto Optimality..................................................152
4-4 Spatial Functions Associated with an Raster Dataset...............................162
4-5 Spatial Functions Associated with an Raster Dataset (Cont.).......................163
4- 6 Spatial Functions Associated with an Raster Dataset (Cont.).......................164
5- 1 List of Data Collected............................................................214
5-2 List of Data Collected (Cont.)......................................................215
5-3 List of Data Collected (Cont.)......................................................215
5-4 Calibration Input and Output Dataset................................................227
5- 5 Validation Input and Output Dataset...............................................233
6- 1 Land Use Codes....................................................................239
6-2 Land Use Codes (Contd.).............................................................240
6-3 Participants Response to Hypothesis 1 Model Input Parameters.....................241
6-4 Participants Response to Hypothesis 2 Model Input Parameters.....................242
6-5 Participants Response to Hypothesis 3 Model Input Parameters.....................242
6-6 Participants Response to Hypothesis 3..............................................243
6-7 Calibration Model Input parameters.................................................247
6-8 Calibration Ranks (Objectives Vs. Factors).........................................248
6-9 Difference in Calibration Output 1 Predicted Areas and.............................256
6-10 Difference in Calibration Output 2 Predicted Areas and............................257
6-11 Difference in Calibration Output 3 Predicted Areas and............................258
6-12 Tabulated Predicted Areas of Observed Dataset Vs. Calibration Output 1.........259
6-13 Tabulated Predicted Areas of Observed Dataset Vs. Calibration Output 2.........260
6-14 Tabulated Predicted Areas of Observed Dataset Vs. Calibration Output 3.........260
6-15 Effective Mesh Size of Calibrated Outputs........................................266
6-16 Validation Model Input parameters for Case 1 ......................................270
6-17 Validation Model Input parameters for Case 1 (Contd.)..............................271
6-18 Validation Ranks (Objectives vs. Factors) for Case 1.............................272
6-19 Land Use Codes for Validation Input Dataset........................................272
6-20 Land Use Codes for Validation Input Dataset (Contd.)...........................273
6-21 Difference in Predicted Areas of Validation Casel .................................276
6-22 Difference in Predicted Areas of Validation Casel .................................277
6-23Difference in Predicted Areas of Validation Casel..................................277
6-24 Difference in Predicted Areas of Validation Casel ................................278
XIV


6-25 Tabulated Predicted Areas of Validation Casel Output 1 (2010)..................279
6-26 Tabulated Predicted Areas of Validation Casel Output 2 (2010)..................280
6-27 Tabulated Predicted Areas of Validation Casel Output 1 (2025)..................281
6-28 Tabulated Predicted Areas of Validation Casel Output 1 (2025)..................282
6-29 Effective Mesh Size of Validation Casel Outputs (2010)...............................287
6-30 Effective Mesh Size of Validation Casel Outputs (2025)...............................287
6-31 Validation Model Input parameters for Case 2........................................289
6-32 Validation Ranks (Objectives vs. Factors) for Case 2................................290
6-33 Difference in Predicted Areas of Validation Case 2 Output 1 (2010) vs.............293
6-34 Difference in Predicted Areas of Validation Case 2 Output 2 (2010) vs.............294
6-35 Difference in Predicted Areas of Validation Case 2 Output 1 (2025) vs.............295
6-36 Difference in Predicted Areas of Validation Case 2 Output 2 (2025) vs.............295
6-37 Tabulated Predicted Areas of Validation Case2 Output 1 (2010).......................296
6-38 Tabulated Predicted Areas of Validation Case2 Output 2 (2010)..................297
6-39 Tabulated Predicted Areas of Validation Case2 Output 1 (2025)..................298
6-40 Tabulated Predicted Areas of Validation Case2 Output 2 (2025)..................299
6-41 Effective Mesh Size of Validation Case2 Outputs (2010)..........................304
6-42 Effective Mesh Size of Validation Case2 Outputs (2025)..........................304
6-43 Validation Model Input parameters for Case 3........................................306
6-44 Validation Ranks (Objectives vs. Factors) for Case 3................................307
6-45 Difference in Predicted Areas of Validation Case3....................................313
6-46 Difference in Predicted Areas of Validation Case3....................................314
6-47 Difference in Predicted Areas of Validation Case3....................................315
6-48 Difference in Predicted Areas of Validation Case3....................................316
6-49 Tabulated Predicted Areas of Validation Case3 Output 1 (2010)..................317
6-50 Tabulated Predicted Areas of Validation Case3 Output 2 (2010)..................318
6-51 Tabulated Predicted Areas of Validation Case3 Output 1 (2025)..................319
6-52 Tabulated Predicted Areas of Validation Case3 Output 2 (2025)..................320
6-53 Effective Mesh Size of Validation Case2 Outputs (2010)..........................328
6-54 Effective Mesh Size of Validation Case2 Outputs (2025)..........................328
xv


1 Introduction
1.1 General Overview
Winston Churchill once said, Plans are of little importance, but planning is essential. Over
the decades planning has been a significant activity in our lives, from preparing a simple
list to sophisticated five year urban or transportation or economic plans. A major part of
planning is creating plans to use and secure our resources. Usually planning ranges from
informal or specific individual plans to local or federal government scientific plans. The
basic need for planning is to secure resources, for example lets consider land use
planning, which is done to secure economic resources, social development resources,
physical (soil, hydrology) resources and so on. This thesis deals with land use planning
concepts and associated analysis. Lets discuss land use planning in detail but at first what
is land use planning? Over the years there have been several definitions of land use
planning published but the fundamental goal is the same. Land use planning is defined as
creating plans, dealing with various procedures or methods to make use of the land in
order to meet specific community needs. This elementary definition hosts a lot of questions
in mind such as, what is land use? Why is land use planning so important? What role does
it play in community development?
We use land for several purposes or activities such as housing, traveling, farming,
developing technology and so on. The term land use refers to the land which is used for
activities or human activities. The activities relate to economic and cultural activities, which
are exercised in a specific physical place. These human activities need not necessarily be
visible (such as recreational activities) in that they are land use documentations such as
residential practices, commercial practices, agricultural practices and so on. Thus these
documentations could be derived and need not need to be determined from satellite
imagery. A land could be used for one activity such as residential or multiple activities such
as upland areas used for farming and recreation purposes. Every type of land is unique
and suitable for specific activity or activities. For example, typically grasslands are not
suitable for crop production or agricultural purposes. Generally there are several land use
1


classifications but this thesis uses Anderson classification system (1976), which is followed
by United States Geological Survey (USGS). According to Anderson classification system
there are in general nine types of land uses, which are as follows,
a) Urban or builtup land
b) Agriculture
c) Rangeland
d) Forest land
e) Water
f) Wetland
g) Barren land
h) Tundra
i) Perennial snow on ice
The above each of the land use is further broken down into three levels of detailed
classification, which is explained in Data collection chapter. In the above discussion term
grassland is used, which in strict sense is referred to as land cover by the scientific
community. Land cover is the natural landscape or the physical cover or material at the
surface of the earth, which can be captured only either by satellite imagery or field survey.
Land cover includes water, forest, vegetation (wetlands), rocks, urban areas (constructed
materials at the earth surface), woodlands, grasslands and soils. Usually many scientific
papers and articles use land cover and land use interchangeably but in this thesis
documentation these two words are treated separately. Land use is represented by human
settlements and activities on a specific type of land cover. Thus land use is a well-founded
link between human activities and land cover. Figure 1.1 represents a general outline of
land use and land cover of USA. From the figure below we can observe atleast five types
of land use/land cover representing Colorado, they are forest, farming, mines (gold & Zinc)
and oil/natural gas deposits.
2


-
l <>wtisr
-t&utrf; '
MA
JM4 If 14
Off4\
£ £<& /I
^ lip ^
A
* a
(HHI Figure 1.1 Land Use & Land Cover (USGS)
Now that we are cognizant of land use/land cover and differences between them a basic
question comes to mind that why is land use/land cover changes important? Land use and
land cover changes play a vital role in community development, economic growth, social
development, environmental consequences, food production and so on. There have been
significant land use/land cover changes in Colorado during the past century, which has
lead to economic and cultural development at the same time ante up problems such as
natural vegetation loss, loss of open spaces, urban sprawl, decline in wildlife habitat and so
many more. This thesis deals with land use changes in Colorado, so lets focus more on
changes in land use in Colorado. Over past ten years there has several land use changes
observed in such as conversion of Denver Stapleton International Airport to urban
neighborhood with mixed housing types and greenways, changes in the South Platte River
basin incited the coexistence of irrigated farmland and urban centers, highlands ranch
converting open spaces to large residential areas and many more such land use changes.
On the positive side above developments have contributed to economic development and
social/cultural developments improving the quality of life. Below s Figure 1.2 showing
downtown Denver in 1885 and 2007 in that it is clear that over more than a decade there
3


has been extensive development. From the figures below it is evident that today the
residential, commercial land uses are more compact or closely spaced and there is hardly
any open space or public land visible indicating potential of human activities to cause
alterations in land surface leading to socio-economic consequences.
Figure 1.2 Downtown Denver in 1885 & 2007 respectively (Historic Colorado)
Changes in land use/land cover concerns not only individuals or land owners but the whole
community as well. The way we use the land determines state of natural resources,
activities such as movement from place to place (transportation uses) and our future. For
example in past few years the farmlands in northeastern Colorado have reduced to 30%
due to shortage of water created by increase in urban land areas. Most of the open lands
are auctioned away, land uses/land cover such as forests and pastures are being
converted to farmlands in order to offset the losses to urbanization. Over the past few
years there has been increase in fragmented land uses due to lack of proper land use
planning and lack of proper allocation of residential and commercial development. The
bucolic view of northern Colorado, especially Loveland, Johnstown till Windsor and Fort
Collins is replaced by extensive residential and commercial development. This is an
example of unplanned growth and a compromised land use planning where the social and
environmental objectives are under-achieved. These changes in land uses are affecting us
at individual and community level. Thus a robust strategic land use planning is required in
order to protect the green belt, meet social, economical and environmental objectives and
improve the quality of life.
4


Over the last decade decision makers have invested significant dollar amount in land use
planning and related activities. Colorado State Land Board have invested approximately
$120,000 dollars to study and plan open spaces near Craig to help restore the lands after
the land has been used for natural gas drilling and sheep grazing (Denver Rocky Mountain
News). Similarly Great Outdoors Colorado (GOCO) along with Colorado State University
(CSU) has invested approximately $200,000 to map open spaces in Colorado for better
land use planning for the future (Denver Rocky Mountain News) Many counties especially
Jefferson and cities such as Arvada, Golden, Lakewood, Westminster and Wheat Ridge
have conducted Fairs for the community to understand and get involved in land use
planning. Recently in 2006 Urban Land Institute conducted a land use planning meeting in
Los Angeles to discuss the importance of land use planning and robust land use planning
techniques. In Central Colorado near Parker in order to save natural resources such as
water, land developers are changing their community and landscaping designs, calling the
community "Prairie New Urbanism". Thus in order to minimize loss of land cover/land use
and preserve natural resource, maintain sustainability and most of all build a environmental
friendly community we need strong plans. Planning helps in decision making process in
order to keep harmful externalities such as water/air pollution away from the communities.
Land use planning helps in understanding thoroughly the problem, externalities and risks,
basically help us to look into all aspects of the problem. For example, land use planning in
Colorado has helped identify preservation lands, which are added every year to the Bureau
of Land management (BLM), U.S. Fish and Wildlife Service, U.S. Forest service and
National Park Service (NPS) domain and now these organizations have more than 33.6
million acres of preservation land in their domain (Denver Rocky Mountain News). Also
land use plans helped identify the key agricultural lands in Weld, Washington and Morgan
counties, where agricultural lands contribute about 20% of the economy (Denver Rocky
Mountain News). Overall agricultural lands in Colorado contribute 1% to states economy
thus some of the non-critical agricultural lands have been in the past allocated to other land
uses (Denver Rocky Mountain News). Therefore, land use planning helps to identify gaps
and areas that might otherwise be neglected and there is a need for a robust technique in
order to allocate land uses effectively and create optimal land use plans. The main
objective to this thesis is creating basic elemental land use plans for the Front-Range
region of Colorado taking into account environmental constraints and spatial constraints
5


such as compactness and contiguity, which will be discussed in the later sections and
chapters in detail.
1.2 Current Issues Related to Land Use Allocation
As mentioned and demonstrated in the previous section land use allocation and planning
plays a very important role for community development by maintaining environmentally
safe and sustainable living. A principal element of land use planning is land use allocation
process. Land use allocation process involves allocating various land uses to a potential
land areas based on user or decision maker specified objectives and constraints.
Land use encompasses all kinds of land use types varying from intense urban areas,
branched out sub-urban development and sundry agricultural areas. The spatial
organization of these land uses are always changing with circumstances thus a scientific
assessment of uses of various land types are required to adopt best land use practices.
Multitudinous top-down procedures are fundamental part of land use planning and
development. Land use planning and management comprises of systematic assessment of
spatial elements such as forests, rivers, streams residential areas and so on dong with
evaluation of various land use alternatives to accommodate public needs and protect future
resources. Thus allocation of available space to various land uses is a complex iterative
process dictated by real worlds dynamic circumstances.
Due to the dynamic nature of land use changes allocation of fixed land bases deals with
competing and complimenting issues. Over the recent years there has been considerable
interest in developing GIS applications to accommodate dynamic nature of spatial pattern
of land uses. This thesis concerns with spatial allocation problem. A meta-heuristic
approach is proposed to deal with spatial land use allocation taking into account
topographical relationships. Spatial allocation deals with allocating characteristics of spatial
attributes such as land use type or land cover to various spatial entities such as polygon,
raster cells and so on. The computational complexity further increases for a multi-objective
spatial allocation problem. In a multi-objective problem typically the objectives are either
competing or concordant thus making the exercise a complex optimization task. In order to
achieve a solution that optimizes all objectives, in this case spatial attributes, a complex
6


formulae based on decision heuristics is used to locate a single raster cell for allocating a
particular spatial attribute. The whole process of spatial optimization is an iterative process,
where after locating a potential single raster cell for allocating a spatial attribute the
adjacent cells are evaluated for allocation purposes.
1.3 Aims of Research Effort
Land use allocation process is a complex task, which involves systematic assessment of
various factors, including economic, social, and environmental factors. The allocation of
various land use types to available spaces is achieved by evaluating future economic
impacts, population growth, surrounding environment impact and interrelated spatial
elements such as residential areas, non-residential areas, agricultural areas and
conservation areas. Thus, a robust allocation process ensures sustainable community
development and protection of natural resources. In order to ensure an effective and
efficient land use allocation it is essential to model the allocation process appropriately.
The principal goal of this research study is to develop a macroscopic land use allocation
model based on genetic algorithm principles and demonstrate the influence of spatial
factors of the allocation process. The objectives of this research study are as follows:
1. Examination of spatial characteristics of land use system.
2. Data collection to develop a macroscopic allocation model, calibrate and validate
the model.
3. Develop the macroscopic land use allocation model based on genetic algorithm
principles and spatial characteristics of land use system, which produces various
sustainable land use alternative plans.
4. Compare the proposed model land use plan outputs to the state-of-the art model
results.
5. Calibrate and validate the proposed land use optimization model by using
measures of effectiveness including pixel-pixel standard deviation, total area
predicted, location of predicted land use with respect to neighboring land use types
and fragmentation.
7


6. Study various complex land allocation cases dictated by dynamic real world
circumstances by running the proposed allocation model.
1.4 Contribution of Thesis
The thesis explores innovative methods for prediction and optimization of land uses for
small and large scale communities. The thesis proposes a unique method of optimizing
competing goals to arrive at a set of solutions to suit a variety of needs. These competing
objectives include land development, preservation of natural habitat and allocation of
certain quotas for specific land use types. The resultant optimized scenarios could be
employed to realize balanced growth patterns that better suit the needs of the community
while preserving cherished assets and values which are not possible with the use of
traditional linear land use forecasting techniques. The proposed methodology also allows
for definition of unlimited number of goals and constraints that helps in development of a
family of solutions which could be implemented in a phased fashion to realize the ultimate
potential of a community.
1.5 Scope and Limitations
The scope of this research study is to demonstrate the effectiveness of the land use
allocation model by exploring land use spatial interactions and its effects on land
allocation. This study encompasses an intense literature review to identify state-of-the art
methodologies and current practices. Major short comings including lack of assessment of
spatial interactions in the current practices are identified. A land use allocation model
based on genetic principles and spatial interactions is devised to enhance current practices
and address existing deficiencies in existing land use models. The proposed land
allocation model is developed to aid in optimizing competing and complimentary objectives.
An independent tool that seamlessly integrates with ArcGIS software package is developed
to enable spatial analysis. The research study is limited to preliminary land use prediction
tool that involves understanding of spatial elements in land use system, their interactions
8


and influence on allocation of land uses. It focuses on evaluation of land use alternatives to
accommodate community needs and protect future resources. The findings are based on
case studies illustrated in this study and should not be assumed for other geographic
locations.
1.6 Thesis Overview
This thesis contains seven chapters. The second chapter reviews principles of land use
allocation. It also examines the spatial and non-spatial elements of land use system. The
factors contributing in development of the land use allocation model are assessed in
second chapter. The third chapter focuses on literature review related to state of the art
land use models and current land use practices. The comprehensive literature review
presents a wide range of mathematical land use models, spatial models and census based
allocation models. Also mathematical principles of several land use allocation models are
presented. Finally Chapter 3 presents a brief review of fragmentation techniques. Chapter
4 demonstrates a detailed explanation of basic land use principles implemented in the
proposed model, the model design and methodology of the proposed land allocation
model. It describes the genetic algorithm concepts, and spatial concepts used in
development of the allocation model. Chapter 4 also describes in detail the development of
the land use allocation tool. Chapter 5 demonstrates the data collection technique used in
development of the model. A detailed description of data collected from various sources,
analysis of datasets for calibration and validation tests are described. Chapter 6 illustrates
the calibration and validation of the land allocation model. The measures of effectiveness
for calibration and validation of land use allocation model are described in detailed.
Chapter 6 also demonstrates comparison of the model outputs and state of the art model
results. Chapter 7 focuses on summarizing the research study and recommendations for
further enhancement of land use allocation models.
9


2 Review of land use allocation modeling
Land use allocation models forecast the layout of an area by determining various uses of a
land. These models evaluate the existing conditions of an area and determine the amount
of land that can be dedicated to a particular activity or land use type. Land use models can
be used either in evaluating a larger regional area or local area depending upon the
requirements of the given problem and data availability. Land use models help understand
the existing land use patterns, dynamics of land use changes and predict the future land
use patterns. Land use pattern indicate the layout or the land use design of an area, which
usually consists of a collection of land use types.
Figure 2.1, Figure 2.2, and Figure 2.3 below represent a typical land use system.
As explained in the Introduction chapter there is several land use types including
residential, commercial, agricultural, transportation and bare land. Few of the existing land
uses such as agricultural lands, wetlands, and water bodies, are constraint to the allocation
of developed activities including residential areas, commercial areas and transportation
facilities. Under these constraints the correlated land uses compete for a favorable land.
Land use models simplify the use of multiple constraints, conditions and interaction
between various land uses easily understandable.
10


Land Use and Land
Cover System
Bare Exposed Rock
Note: -Level 1 & Level 2 of LU Classification
Transitional Areas <
Mixed Barren Land ^
Figure 2.1 Land Use System (ILUTE Model)
11


Figure 2.2 Land Use System (ILUTE Model)
12


Note: -Level 1 & Level 2 of LU Classification
Figure 2.3 Land Use System (ILUTE Model)
In order to analyze the land use interactions and factors affecting the future development of
a land, allocation models are used. Since early 19th century several researchers and land
use planners have developed many models to determine the use of land in different
locations based on transportation activities, economic impacts, and environmental impacts.
Also there has been extensive use of land use design or the layout of existing land uses in
modeling future allocation of land uses. Land use allocation models, regional or local can
be categorized into three general models as follows (Figure 2.4).
13


2.1 Spatial land use models
2.2 Economic land use models (also includes wide variety of policies)
2.3 Comprehensive or Integrated land use models
Land Use Models
Spatial Models Economic Models
(Regional & Local Scale) (Global, Regional, & Local
Scale)
i
i
jL
Integrated Models
(Global, Regional &
Local Scale)
Combined Model
Land Use Allocation
(CLUE, PLACE3S, UPLAN)
Land Use Assessment
(GTAP, AgLU)
Land Use Allocation
(Several Models, every
state has their own regional
model)
Figure 2.4 Land Use Models (ILUTE Model)
14


2.1 Spatial land use models
Spatial or geographic land use models are based on dynamics of land use system. In
spatial modeling actual land use structure and the layout of existing land use systems is
considered. The historical and existing land use systems, which represent the underlying
human and biophysical driving factors, are quantified to explore future land use changes.
Spatial patterns, connectivity between various land uses, and distances to specific
constraint land uses such as transportation, forest and conservation land uses are
considered in predicting possible future land uses. Connectivity is the key influencing factor
or the driving force in spatial analysis of land use allocation process. Various land uses in
land use system are either spatially connected or have related land use characteristics. A
land is always connected to another piece of land by some distance, which could be of any
scale (global, regional or local). Thus, a land area cannot be analyzed for allocation
independently, which gives rise to the need for considering neighborhood land uses.
Connectivity also represents underlying biophysical and human driving factors. Lets
consider an example, the Chatfield reservoir in Colorado discharges into the South Platte
River. The water from the catchment contains eroded soil and other materials due to the
rains and human settlements, which has increased the sediment in the river. This increase
in the sediment is caused due to the biophysical and the human settlements (transportation
activities). Therefore, connectivity represents the underlying biophysical and human
factors and plays an important role in spatial analysis of land use allocation process.
Connectivity is usually quantified by measuring distances to various constraint and related
land uses. The other driving factors considered in spatial allocation model are high level
processes or the influence of the existing land use structure on the allocation, changes in
land use characteristics due to disturbances such as natural disasters and economic
changes, and non-spatial factors.
15


Spatial Factors
Historic Land Use
Structu e
Existing Land Use
Structure
Accessibility Variables Neighborhood characteristics

_________4__________
Land Use Allocation
Figure 2.5 Spatial Model Basic Structure (ILUTE Model)
Allocation of a land use to a potential land area is influenced by the existing (global or
regional scale) or neighboring land uses (local scale). High level processes define the
dynamics of a land use system. High level or hierarchical processes represent changes in
the existing land uses, which has a high impact on social, economic, and ecological
structure of the society. The allocation of land uses, which are low level processes, affect
the high level process and eventually impact the economy. For example, an industrial
development adjacent to existing residential community would impact the living conditions
and thus leading to changes in the landscape. Therefore, a spatial allocation process
involves assessment of connectivity and high level processes before an allocation of a land
use can be determined. The hierarchical processes can be measured by creating buffer
zones around the area of interest and evaluate every land use characteristics within the
16


buffer zone before allocation is determined. Spatial allocation models should include
interactions between various land uses and their characteristics at every scale, global,
regional and local scales.
Determining driving factors for a spatial allocation model is very difficult process since land
use system is complex and depends upon wide range of spatial, social, economic and
ecological factors at various scales. The driving factors should be chosen in such a way
that it should account for long term stability of the land use system. There are few spatial
allocation models including CLUE (Conversion of Land Use and it's Effects), PLACE3S
(PLAnning for Community Energy, Environmental, and Economic Sustainability), and U-
PLAN, which use accessibility to constraint and other significant land uses (transportation
land use), connectivity, hierarchical processes, overlay of multiple maps, historical and
existing land uses to determine allocation. Other than spatial factors most of the spatial
allocation models use non-spatial factors to determine the land use demand. The most
common non-spatial factors are demographic characteristics, economic factors, and
policies.
2.2 Economic land use models
Compared to spatial land use models economic models disregard spatial characteristics of
the land use system. Economic models are more focused on economic & policy issues
(trade policy) of a land use. Initially economic land use models were designed to focus on
economic changes and interactions of agricultural and forest land uses. But recently the
economic models are designed for assessment of market structure of residential land use
development. In order simulate land use changes economic theories work around market
supply and demand management. Supply from the land use resources are estimated to
match the demand to reach the equilibrium. Supply and demand variables in the economic
model are converted to land area, which is used in land use management. Actually,
economic models are used for land use assessments and with consideration of spatial
characteristics the economic analysis can be used in allocation of land uses. These kinds
of models are usually categorized as integrated models.
17


Economic Factors
Market Supply &
Demand
Land Use Economics
Employment
Policy
Household Level Data (Expenditures &
Income)
Land Use Assessment
Figure 2.6 Economic Model Basic Structure (ILUTE Model)
The drivers of land use changes in economic land use models include market demand or
commodity demand and production, population growth, income growth, taxation policy,
trade policies and land use densities or development densities. In few of the economic land
use models such as AgLU (Agriculture and Land Use) the land use changes are modeled
by evaluating carbon emissions corresponding to each major land use in the study area.
The supply and demand concept of economics is used in AgLU. The supply variables
included crop supply, livestock, biomass energy and forest products corresponding to
appropriate land uses. These supply variables were estimated based on biomass price
and were used in determination of emissions. Similar to supply parameters demand
variables included crop demand, livestock and forest products, which were estimated from
population and income corresponding to land use system of the study area. The market
supply and demand outputs were compared in terms of local price, which also included
18


consideration of local taxes and subsides. Usually economists represent geographic space
as economic units to assess land use changes. The other commonly used economic land
use model is GTAP (Global Trade Analysis Project) based on economic policy analysis.
GTAP uses trade patterns, commodity demand and green house gas emissions in
assessment of land use changes. In order to allocate land uses these economic models
are combined with spatial analysis, which are usually defined as integrated land use
models.
2.3 Integrated Land Use Model
Unlike spatial and economic land use models, integrated land use models simulate
interactions between demographic, economy, policies and spatial aspects of the land use
system. Integrated land allocation models include supply and demand interactions between
land development, location choices, land use activities and transportation land use system.
Transportation system plays a key role in integrated allocation models. Interaction between
transportation system, ecosystem and human sub-system is incorporated into the model.
The spatial interactions in integrated models include distances of transportation system to
other land uses in a study area. Spatial modeling is not as extensive as spatial allocation
models in integrated methodologies. Integrated models are also used extensively in study
impacts of land use changes including rate and location of land use changes. Integrated
models are designed mostly for global and regional spatial scales.
Integrated models are basically a network of several models, which are either
endogenously or exogenously modeled. Mostly the endogenously variables include
economic parameters, demographic parameters and government policies. Although there
are few models, which use just demographic and spatial parameters as endogenous
variables. Commonly used exogenous variables are area supply and demands, crop
prices, population growth, production of agricultural commodities including crops and
livestock, and climate data. In a typical integrated model the exogenous variables include
the outputs from economic model, policy model and transportation planning model. These
outputs along with environmental and economic impacts are modeled to find a suitable
land for allocation.
19


In addition to the exogenous variables the typical inputs or endogenous processes include
demographic (zonal population & employment projections) characteristics of the study
area, land use spatial distribution, spatial interaction model, travel demand model, and
vehicle ownership model. Figure 2.7 illustrates a typical integrated model.
Figure 2.7 Integrated Model Basic Structure (ILUTE Model)
20


The integrated model determines a potential land area for a land use by not only
considering the economic, policy and demographic factors but social factors such as crime
rate of the study area and social character of the area. In addition to social factors other
driving parameters are, physical factors such as accessibility to the potential land area and
neighboring land uses (although this is a spatial factor), accessibility to transit, area of the
potential site, private and public developments around the potential site, and future costs of
the development for the potential land. Integrated models usually include several policy
related variables, which are taxation, subsidies, environmental impact reviews, zoning
incentives, public housing provisions and servicing land (gas, cable, transportation)
provisions. Another significant driving factor in integrated model are economic demand of
the study area at every spatial scale including local, regional and global scales. To sum up
integrated models require several exogenous variables, which are resultant of various
models in allocation of land uses as compared to spatial and economic models.
As discussed earlier, spatial models or spatially explicit models exhibit real world
conditions more closely as compared to non-spatial models. Land use allocation decisions
depend greatly on spatial heterogeneity features of landscape. Economic models unlike
spatial models fail to represent spatial features of a heterogeneous landscape of a region.
Economic models focuses more on demand and supply relationships of a region or more
specifically flow of population and employment in a region. The spatial features of a region
or a landscape are ignored in economic models. Spatial features or a complex chain of
spatial patterns such as heterogeneity, agglomerations or contiguous landscape, and
compact network of parcels are most significant factors that contribute towards allocation
of land use.
The above mentioned spatial patterns are not explained in economic models. Economic
models consider space as a featureless plane and distances to central business district
(CBD) is a determining factor for land use changes. In spatial models neighboring land
uses and their functionalities play a significant role in making allocation decisions.
Neighborhood development areas including commercial land uses, industries and business
district impacts the nearby conservations areas such as wetlands, sensitive habitats and
parks. Allocation of land use in spatial models is influenced by existing land use for
adjacent parcels such as constraint parcels (conservation areas), development areas
(commercial areas and residential zones) and transportation areas. Thus there is a need to
21


consider spatial heterogeneity variables and variables representing spatial characteristics
for allocating land uses to potential spaces. The other spatial characteristics that are
considered in spatial modeling are clusters or agglomerations, land use spillovers and
spatial externalities such a social interactions of network of parcels in a region. By
modeling these spatial characteristics in a model the direct and indirect impacts of
neighboring land uses, and effect of allocation on various habitats and conservation areas
are taken into consideration, thus ensuring efficient functioning of a geographic region. The
agglomerations or cluster of parcels isolate various dependent habitats from each other,
which gives rise to fragmented parcels. Similarly, land use spillovers could lead to cluster
or contiguous parcels. Hence, allocation of a land use to a potential geographic space is a
complex process and depends mainly on spatial characteristics of that region. In addition
to spatial characteristics, social interactions between neighboring parcels also play a
significant role on allocation process. Social interactions of a network of parcels or a
community represent the community health and economic growth, in sum the efficient
functioning of a community. Therefore, modeling allocation of land uses require several
spatial and temporal variables at various spatial scales before considering the input of
economic variables. Spatial models vary in scale from a microscopic local scale to a
macroscopic global scale. For a microscopic scale allocation model, distance from streets,
highways, residential communities, parks, commercial, industrial and shopping areas have
a marked influence on the outcome of the land use allocation as compared to regional
scale macroscopic model that does not deal with the intricate local resources while
determining/allocating land use. In summary, spatial characteristics or variables play a
significant role in land use allocation.
Generally, economic models divide a region into various zones of household and
commercial or industrial zones connected via transportation network. Whereas spatial
models consider a region as network of various land use types represented by parcels,
which are physically connected to each other. Spatial models include ecological and
environmental land use models. Commonly, when modeling land use allocation, spatial
model is initially used in land use allocation analysis. Main reasons for using spatial model
is it is an inexpensive method compared to economic or integrated model and a spatial
model explores a range of possible spatial or geographic locations of future land uses.
These range of possible spatial allocation solutions are further explored at economic and
22


policy level using an integrated model. An integrated model is basically combination of
spatial and economic models, which also includes some level of policy analysis. Integrated
models should not be used in initial analysis of land use allocation as they have high
degree of uncertainty and model errors due to large amount of exogenous variables.
Integrated models also require huge amounts of resources, which include large amount of
data ranging from spatial data, economic data to policies. Integrated models are generally
customized based on state or federal policies. These models are expensive in terms of
data availability, data collection, model development, and execution. Also calibration and
validation of integrated models are difficult and consume a lot of time compared to spatial
models. Thus, a spatial model for the initial analysis of land use allocation is more practical
and then based on the output of the spatial model decision on resources required for
further analysis can be invested.
The land use allocation model developed in this thesis research is a spatial model, which
has its potential use in preliminary land use allocation analysis. Since simulation is the
most inexpensive and fast method of investigating allocation of land uses a spatial
simulation model is developed in this thesis research. The allocation model developed as a
part of the thesis research is based on strong mathematical principles. Genetic algorithms,
which is based on mechanics of natural selection is used as a framework to develop the
spatial model. This genetic spatial allocation model is developed at a macroscopic scale,
which generates several possible allocation outputs. The allocation solutions from the
model can be further explored by using them as a set of input data in integrated models.
Before getting into details of development and implementation of genetic spatial allocation
model lets go through few past researches conducted on spatial models, especially the
mathematical spatial models. The next chapter, Chapter 3 explores several spatial,
economic, integrated models and mathematical techniques used over the past few years to
develop land use allocation models.
23


3 Literature review
3.1 General Overview
Over the years there has been an ongoing debate on allocation of specific land use types
to available physical spaces. Past few years land use trends show increase in developed
land spread out all across cities, towns and suburbs. Thus resulting in a diverse land-use
pattern expanded across all regions in the nation. Land use allocation in general is a
complex task especially when considering urban areas due to conflicts between allocation
of residential areas, industrial areas or any kind of development areas and preservation of
biodiversity and heterogeneous landscapes. There are several top-down procedures
documented and implemented to address land use allocation problem. This chapter
examines several optimization approaches to multi-objective multi-criteria land use
allocation problem, which deals with identification of multiple potential sites, optimal
allocation of future developments and conservation of environmental sensitive areas within
or around developed areas. Also in this chapter an attempt is made to examine the
benefits and drawbacks of various land use allocation quantitative and qualitative
procedures implemented over the past ten years.
There are several multi-criteria optimization techniques proposed to solve land use
allocation problems in past years. The research efforts related to incorporation of multi-
criteria optimization mechanism in geographic information systems has been very well
documented. The idea is to find a procedure or a technique which is economical, time
efficient and practically possible. This chapter consists of detailed review of land use
allocation techniques used over past few years. This chapter is divided into five sections of
literature review including this section. In the next section, Section 32 two state of the art
techniques used in Colorado are reviewed, of which one of them is used in comparing the
results obtained from the proposed thesis model. Section 3.3 is a compilation of review of
various mathematical techniques used in land allocation process over the past few years.
24


In Section 3.4 all the land use techniques used over the past few years have been
reviewed and critiqued. Also Section 3.4 illustrates the application of various mathematical
techniques, which are summarized in Section 3.3. The last section of this chapter, Section
3.5 contains a brief review of fragmentation techniques, of which one of them have been
adopted and used in the thesis problem. The following section reviews two state of the art
techniques, which are popular and used by various public and private sectors, researchers,
educational institutions and various other scientific communities.
3.2 Review of State of the Art Land Use Allocation Technique
Traditionally, there are several methods used by decision makers and accredited
researchers in nation and all over the world to model land allocation but only few methods
are widely recognized as state-of the-art techniques. IDRISI and Integrated Modeling
techniques are two commonly used state-of the-art techniques in various states in US and
internationally recognized. IDRISI is well-established GIS software broadly used all over
the world by decision makers to model land use allocations, especially multi-objective and
multi-criteria scenarios. Whereas, integrated regional modeling technique was used by
Denver Regional Council of Governments (DRCOG) to predict and map future land use
patterns for the state of Colorado, which is published as "Metro Vision in the DRCOG
website. The other city decision makers using integrated modeling are California, Ohio and
Oregon Department of Transportation (ODOT), Texas (San Antonio, Dallas and Houston),
Seattle (Washington) and many other cities. Furthermore, IDRISI and integrated modeling
are unique, reliable and widely recognized land use allocation techniques, which could be
used as a standard of comparison with the allocation method proposed in this thesis. The
results of the proposed land allocation methodology presented in Chapter 5 of thesis report
are compared with the results of the standard procedures mentioned above, which is
explained in detail in the later chapters. The proposed land allocation model serves as a
lens through which projected future land use changes or plans are analyzed and evaluated
in order to examine whether they address the changes proposed in Metro Vision Plans.
Thus this section deals with the review of current state-of the-art techniques used in urban
and regional planning by public sector, private sector and accredited researchers. This
25


section presents a brief overview and summary of the concepts of two state-of the-art
techniques, IDRISI and Integrated Regional Model (IRM).
3.2.1 IDRISI Kilimanjaro
IDRISI Kilimanjaro or in short IDRISI was developed by Clark Labs in 1987, founded by a
Geography Professor Ron Eastman (Eastman). This Clarks Lab software is Windows
based, which is used mostly by university researchers for educational purposes, by local
governments and management of resource allocation by planners and decision makers. In
an overall IDRISI is used for resource allocation especially land allocation purposes in
approximately 170 countries. IDRISI has many features but is mainly used for analysis and
mapping of spatial information in digital form. IDRISI has total of 200 modules of which the
GIS Analysis Menu, which contains approximately eight sub-modules is used to conduct
spatial data analysis (Eastman). Of the eight sub-modules, the specific sub-module of
interest is Decision Support, which is used to conduct multi-objective, multi-criteria land
allocation analysis. There are fourteen modules under the sub-module Decision Support, of
which four modules, WEIGHT, MCE, RANK and MOLA are used in allocation process
(Eastman).
Land use modeling in IDRISI Kilimanjaro is divided into two main parts of evaluation, multi-
criteria evaluation (MCE) and multi-objective evaluation. Multi-criteria evaluation is
conducted by choosing any of the following three processes,
a) Boolean overlay
b) Weighted Linear Combination (WLC)
c) Ordered Weighted Average (OWA)
Before choosing the above techniques all the input data, factor maps and constraint maps
in ESRI raster format, are entered into the IDRISI module to convert into IDRISI data
format. Initially the MCE module normalizes all the factor maps by assigning criterion
scores in byte scale, 0 &1 or 0& 255, where 1 or 255 is assigned for the most suitable
area depending on constraints and objectives (Eastman). Then all factor maps are
assigned certain weights to account for trade-offs thus creating suitability maps. These
suitability maps are further evaluated for multi-objective criteria. The main aim of the MCE
26


process is to give a decision maker an opportunity to choose between alternatives
corresponding to specific objectives.
In IDRISI, criteria are defined as set of factors and constraints, where a factor improves
suitability of a specific alternative and a constraint define restrictions to the alternative
selection process. All the data, factor maps and constraint maps are represented in IDRISI
grid data format. Each and every factor map is initially assigned a criterion score based on
constraints and objectives. For example, if the objective is to allocate commercial type
activity then a score of 1 is assigned to the area say a radius of 10 km (constraint) away
from a preservation area. The score assignment depends on constraint and the objective.
After all factor maps are standardized, a pairwise comparison between factor maps is
conducted so that criterion weights are assigned to each factor maps. The pairwise
comparison is done using a method called Analytical Hierarchy Process (AHP), which is
explained in detail with examples in next few paragraphs. IDRISIs WEIGHT module
performs AHP in order to assign weights to the factor maps. The WEIGHT module
computes a set of optimal weights for a pairwise comparison matrix of factors in a multi-
criteria model based on eigenvector principal. The main principle of the WEIGHT module is
that the pairwise comparison of all possible combinations of all potential criteria is
conducted by creating a matrix of eigenvalues and then finding the optimum set of weights
by computing the principal eigenvector (Eastman). The weights are assigned in such a way
that the sum of all weights is always equal to one. The final stage of MCE is evaluation of
the factor maps using any of the above mentioned three procedures, Boolean Intersection,
WLC and OWA.
A user can choose any of the three processes mentioned above to create factor maps. The
first method is Boolean overlay, which is carried out by overlaying criteria map layers and
combining the criteria layers using logical operators such as AND (intersection) and OR
(union) (Eastman). The final suitability map of Boolean operation contains 1 and 0 values,
where 1 represents most suitable for an alternative and 0 not suitable for a particular
alternative (Eastman). The second method, WLC computes and generates a suitability
map by multiplying each factor map by their weights and then summing them, such that the
sum is equal to one. The WLC suitability map is finally multiplied with constraint map to
account for unsuitable areas. The OWA technique is very similar to WLC, only difference
being weights of each pixel are compared and evaluated instead of factor weights. The
27


OWA procedure assigns weights at pixel level instead of assigning weights to the factor
maps thus called order weights. A pixel value of a factor map is compared to a pixel value
at the same location of another factor map and so on. A pixel to pixel comparison is
conducted and weights are reassigned to each pixel based on hierarchy order of pixel
values. For example, lets consider three factor maps of equal factor weights having single
pixel values (all at same location) of X=105, Y=115 and Z=100. The order weights are Z=1
(minimum value), X=2 and Y=3 (maximum value). After the assignment of order weights
all the factor maps are evaluated similar to WLC procedure to produce a single suitability
map. It is the choice of the user to use any of the above mentioned MCE techniques. The
three methods above create suitability maps corresponding to specific objective based on
constraints.
There are two kinds of objectives encountered in a multi-objective problem, complementary
and conflicting type. In the case of complementary objectives, the suitability maps
generated corresponding to specific objective are evaluated by assigning weights to
objectives and linearly combing all the factor maps. But this logic is not applied to
conflicting objectives, where objectives compete against each other. To deal with
conflicting objectives initially the suitability maps corresponding to each objective is created
and ranked accordingly. Then an iterative process of land allocation is conducted until an
optimal solution is reached. During each teration process all allocation conflicts are
checked and suitability maps are re-ranked such that future conflicts are reduced.
The above IDRISI Kilimanjaro process is widely recognized process of land allocation used
in various fields, education, public and private sector. Although the land allocation
methodology used in IDRISI is of spatial in nature and a widely recognized AHP is used,
the following are the drawbacks,
a) All input data, factor maps and constraint maps needs to be converted to IDRISI
data format, which is very tedious process. Also IDRISI does not use ESRI data
format.
b) The suitability map created by IDRISIs MCE module does not account for non-
linear relationship across factor maps or constraint maps. All the three procedures,
Boolean, WLC and OWA create suitability maps by linear combination of input
variables
28


c) The IDRISI MCE module/process creates suitability maps favorable to each
objective at a time and then the multi-objective land allocation (MOLA) process
compares each of the objective suitability maps for conflicts and resolves the
conflicts. This systematic process of land allocation where a suitability map
favorable to each objective is not only unrealistic but includes or excludes pixel
areas that are not correctly represented thus increasing the model uncertainty.
Also the primary disadvantage of MOLA process is that the effects of factor
weights are unknown until the compromise solution has reached
d) In order to solve a multi-criteria, multi-objective land allocation problem using
IDRISI, one has to go through tedious range of modules
The drawbacks b and c can be eliminated by using a stochastic technique such as genetic
algorithms. The next state-of the-art technique reviewed in this section is Integrated
Regional Modeling, which is used by Denver Regional Governments to model land use
changes.
3.2.2 Integrated Regional Modeling
Integrated models have been in use since 1980s to analyze and model various fields and
their relationships such as, economic activities, transportation activities and land use
changes. There are many kinds of integrated models related to land use changes or
involving land use as a main component in the model. The most common kind of integrated
land use models integrate economic concepts, transportation changes, environmental
changes and demographic history to model iiture land use changes. The IRM used by
DRCOG for modeling regional land use changes is based on sectoral-land use integration
(Denver Regional Council of Governments). The sectoral part of the integration model is
based on analysis and relationship between various economic sectors such as commercial
activities, residential activities, agricultural activities and transportation facilities. Whereas
the land-use part of the integration model is based on analysis of spatial relationship
between various land uses such as commercial, residential, transportation and agricultural.
Thus the sectoral-land use integration model is an econometric model, which is the basic
concept supporting DRCOGs Integrated Regional Model. In many regions such as Salt
Lake City, Houston, Portland, Sacramento and Denver, Integrated models are used for
regional planning and considered as state-of the-art land use planning model. DRCOG
29


used an Integrated Regional Model (IRM) to forecast future land use plans, which could be
viewed in a report named Metro Vision. The logic supporting IRM can be explained by the
following figure below.
Exogenous
variables
(distance to
major
transportation
facilities &
residential
areas, historical
development
trends,
economic
variables)
Regional
Economic
Model (Input)
Economic based Demographic
Location Model based Location
(Sectoral Model) Model
Work
\^
Exogenous
variables
(distance to
work,
commercial
areas and
schools,
demographic
related
variables)
Modal Choice, Tour
based models; checking
the accessibility to
various locations
Transportation
Supply &
Demand Model
Figure 3.1 Integrated Regional Model (Denver Regional Council of Governments)
30


The Integrated Regional Model in based on an econometric type integrated model concept,
where the spatial area of interest is divided into zones. Initially inputs from the regional
economic model and few exogenous variables including the future employment and
residential demands are computed. The future demands are used to model marginal costs
or costs of the future residential area development. An equilibrium employment and
residential supply is generated to meet the demand based on economic theory. The future
demand is expressed in terms of population categorized by employment and residential
activities. Within employment sector an equilibrium check is performed to review the
employers-employee ratio. The employment population and household or residential
population are expressed in terms of locations and thus allocating various activities. These
activities are again converted to categorized population to input in a policy simulation
model, where all activities such as work to home, home to work, work to other activities
including shopping are simulated to generate future traffic assignments. The traffic
assignments are checked with the land use activities so that the assignments do not
exceed the demands.
The Integrated Regional Model is implemented in UrbanSim, an open source simulation
model, which analyzes and evaluates interactions between landuse, transportation
planning and related policy issues (Denver Regional Council of Governments). Also a
standard industry software TransCAD is used to model spatial interactions between
various landuse activities used for transportation planning purposes. Thus IRM is a
socioeconomic model which optimizes several land use activities based on microeconomic
principles. Therefore, land use changes are assessed as a function of changes in
demographic variables, economic variables and travel model elements. The main
drawbacks of IRM are as follows,
a) The integrated model has several exogenous variables as inputs, which induces
some amount of variance in the model thus increasing the uncertainty in
predictions
b) Similar to IDRISI, IRM also doesnt account for the nonlinear relationships between
the parameters or the factors used in the allocation process
c) The integrated model combines several state-of the-art models or techniques to
create land use plans, increasing the complexity of the whole integrated system
and thus inflating the model uncertainty
31


d) The integrate model is based on historical data thus doesnt account for dynamic
variables in modeling future land use activities
Although IRM is a robust white-box model it doesnt account for nonlinear relationships
between parameters, which represents a more realistic situation and also there are many
exogenous variables in the model, which increases the uncertainty of predicted results.
The integrated regional model used by DRCOG produces results at an interval of five-year
time period with the base year as 2005, thus producing land use plans for the year 2010,
2015,...,2030 for the front range region of Colorado (Denver Regional Council of
Governments). These land use plans are used to compare with the results obtained from
the proposed allocation model in this research.
Apart from the above models, IDRISI and IRM, there are several mathematical and
statistical techniques available to model land use allocation. In order to understand the
concept of proposed land allocation methodology in this thesis research, there is a need to
be aware of the most commonly used, robust and relatively easy to implement techniques
or concepts used in allocation process. The knowledge of these mathematical and
statistical based concepts are essential to understand the application in various land use
allocation methodologies over the past 10 years, illustrated in the further sections in this
chapter. Next section presents reviews of various concepts in context with land use
allocation process, which would help identify the significance of the proposed land use
allocation technique in this thesis.
3.3 Overview of Available Multi-Objective Multi-Criteria Optimization Techniques:
Conceptual Grounding
This section illustrates various conceptual theories that are exercised to perform land use
allocation. The following basic mathematical/statistical concepts or theories will help us
gain a better understanding of the use of meta-heuristic technique chosen in this thesis to
optimize a complex process such as land use allocation. Optimization is a mathematical
technique typically employed to find the maxima and minima of functions which may or
may not be subjected to constraints (Foulds): An optimization algorithm generates
scenarios by combination of parameters, controls exogenous inputs, evaluates the
performance of the function and directs exploration of optimal solutions in the most
promising direction. Optimization models are typically used in all areas of decision making
32


including, engineering design and financial portfolio selection. In this thesis research a
meta-heuristic evolutionary optimization technique is used to solve a multiple objective land
allocation problem. Several multi-criteria optimization methods have been applied in the
past 10 years which are related to multi-criteria land use allocation analysis. A few of these
methods are:
1. Analytical Hierarchy Process
2. Equal Weight Averaging Model
3. Goal Programming
4. Integer Programming
5. Non-linear Combinatorial Optimization
6. Fuzzy Multi-Objective Programming
7. Multiobjective Generalized Sensitivity Analysis
8. Multi-criteria Approval-Stochastic Multi-criteria Acceptability Analysis
9. Cellular Modeling
10. Simulated Annealing
11. Genetic Algorithm
This section illustrates and critics most of the above techniques and few other multi-criteria
techniques in detail.
3.3.1 Analytical Hierarchy Process
Analytical Hierarchy Process (AHP) is a decision making process, which was originally
devised in 1970s by Dr. Thomas Saaty, supporting, procedures involving multilevel goal
hierarchies (Foulds). AHP is a systematic procedure designed to compare a set of
objectives or alternatives with each other in the form of a series of one-on-one comparison
matrix in order to make both, qualitative and quantitative aspects of decision.
The primary input to the AHP is relative importance between pairs of criterion declared by
decision makers. These relative importance rankings between criterions are termed as
pairwise comparison in AHP. These pairwise comparisons are used to establish weights
for criteria and performance scores for options on different criteria. Lets consider an
example to better understand the AHP concept.
33


Let us assume that a set of criteria has been established. The next step for a decision
maker is to rank relative importance of each pair of criteria. Let us assume that the
responses are cumulated in verbal form and subsequently coded on a nine-point intensity
scale, as in Table 3-1 below. The intermediate index values, 2, 4, 6 and 8 could be used to
represent shades of judgment between five basic assessments (mentioned in Table 3-1). If
the judgment is that B is relatively more important than A, then a reciprocal index value is
assigned. For example if B is Strongly More Important" than A then an index value, 1/5 is
assigned to this judgment. Here the main assumption is that the decision maker is
consistent in making judgments about any one pair of criteria. Considering this assumption
that all criteria will always be ranked equally when compared to themselves then
1/2/7 ?/7 ? 1*! . . .
comparisons are required to establish a complete set of pairwise judgments
for n criteria (Foulds).
Table 3-1 Relative Importance of Pair of Criteria ranked on 1-9 Intensity Scale
Importance of A relative to B Index
Equally Important 1
Weakly More Important 3
Strongly More Important 5
Very Strongly More Important 7
Absolutely More Important 9
Thus considering three criteria the following pairwise matrix could be constructed.
34


? 1 3 7^
?l/3 1 4
91/7 1/5 1?
From the above matrix it is obvious that there is a consistency maintained in the judgment
of any one pair of criteria but there is no consistency between the pairs. Thus the next step
would be to estimate a set of weights that will provide a best fit to the observations
recorded in the above pairwise comparison matrix.
There are many methods available for estimation of weights. Saaty has utilized advanced
matrix algebra for estimation of weights. Saatys method estimates the maximum
eigenvalue of the matrix and then calculates the weights as the elements of the
eigenvector (Foulds). This complex operation can be undertaken effectively by a special
AHP computer package. Another way to calculate weight would be to calculate geometric
mean of each row in the matrix then compute the sum of geometric means and finally
normalize each of the geometric mean. Table 3-2 below illustrates the above mentioned
geometric mean procedure. Both, Saatys method and the geometric mean method yield
similar weights up to three decimal points. Beyond three decimal points there are
significant differences in weights between both methods.
Table 3-2 Weight Calculation Example
Geometric Mean Calculations Weights
Criteria 1 = ?1 ? 3? 7?^ = 2.7589 0.649
Criteria 2 = ?l/3 ? 1 ? 5 =1.1856 0.2789
Criteria 3 = ?l/7 ? l/5 ? 1 ?^ = 0.3057 0.0719
Sum 4.2502 1.00
35


A full implementation of AHP involves not only calculating weights for criteria but pairwise
comparison to establish relative performance scores for each options on each criterion.
This daunting task is automated by computer packages such as Expert Choice.
AHP provides lot of benefits to decision makers such as,
1. AHP helps a decision maker focus on development of a formal structure, which
captures all the important factors needed to differentiate a good choice from a poor
one.
2. Pairwise comparisons provide elative importance of criteria, which are readily
accepted in practice.
3. AHP comfortably fits with the circumstances where judgments are the predominant
form of information.
Despite of above attractions of AHP method there are several drawbacks such as,
1. The axioms on which AHP is based are not clear enough to be empirically
testable.
2. The 1 to 9 scale as mentioned in Table 3-1 has a potential of being inconsistent.
Considering the example above (matrix), a is ranked 3 relative to B and B is
ranked 5 relative to C. Considering consistent ranking system based on 1-9 scale,
rank of A relative to C should technically be 15, which is impossible.
3. There is no theoretical foundation on the link between the points on 1 to 9 scale
and verbal descriptions.
4. Criteria weights are evoked before setting the measurement scales for the criteria.
A decision maker pursues to make statements about relative importance of objects
or items without the knowledge of items being compared.
5. There are changes in the relative ranking of few items of the original options due to
the introduction of new options. This rank reversal phenomenon arises from a
failure to consistently relate scales of measurement to the associated weights.
The above drawbacks of AHP are overcome by using meta-heuristic or stochastic
techniques, which are discussed further below in this section. One technique which is very
common in solving multi-criteria problem is equal weighted technique, described below,
known to outperform AHP.
36


3.3.2 Equal Weight Averaging Model
Andersons weighted averaging model is an algebraic model, where the overall rating of
suitability of a criterion is a weighted average of the suitability of individual characteristics
for a criterion. The weighting of criterion depends on the following characteristics:
1. Negative information is weighted higher than positive information
2. Extreme information is weighted higher than moderate information
3. Non-analytical information mixed in with analytic information leads to more
cautious inferences and weaker impressions.
The integrative measure of a multi-objective problem would be a weighted average score
computed by summing various responses of each indicator weighted by its score. For
example, if indicators for good objective (positive weights) as well as indicators for poor
objective (negative weights) are identified, a weighted average score would reflect the
integrative measure of a multi-objective problem faithfully.
Prior studies indicate that equal-weighted averaging model (EAM) outperforms analytical
hierarchy process (AHP) in terms of predictive performance (Foulds). It is also seen that
attribute weights measured using EAM are similar to AHP. There is lot of complexity
involved in EAM requiring greater number of judgments and more cognitive effort. The
major advantages of EAM are that it is computationally simple and can be used for linear
parameters. The main drawback of EAM is that the methodology is restricted to discrete
variables. Goal programming in combination with some stochastic techniques is known to
be used for allocation problems where the variables are continuous. In terms of linear
techniques to deal with multi-criteria there are a couple of them most widely used, such as
integer programming and goal programming (also used for non-linear problems). Goal
programming has also been used with genetic algorithms to solve a multi-objective, multi-
criteria land allocation problem, which is illustrated in the next section.
3.3.3 Goal Programming
37


Goal Programming (GP) is a multiobjective optimization technique that helps find a
compromise solution when absolute solutions are not possible or meaningful objectives do
not exist. GP is applied to both, linear and non-linear models. GP trades off goals until
most satisfying solution is obtained. In GP, the objectives are changed to constraints by
adding some variables such that a significant deviation from the goal is observed. A simple
Microsoft EXCEL linear programming solver is adequate for solving a linear GP problem.
The two kinds of GP are as follows,
i. Regular GP A decision maker (DM) places a value or price on each unit
deviation from goal.
ii. Pre-emptive GP Used when regular GP cannot be used due to existence
of a conflicting condition where a higher priority goal is much more
important than the next goal but may not be more important than a lower
priority goal (Foulds) Here a hierarchy for goal levels is set by assigning
the first priority to the goal of highest importance and second priority to
goal of second-highest importance and so on.
GP technique is implemented using the following steps:
i. Decision variables of the multiobjective problem are identified and hard
constraints are formulated when using GP techniques.
ii. Goals corresponding to their respective target values are specified. In order to
achieve goals, constraints are created using decision variables and constraints
are converted to goal constraints by including deviational variables.
iii. Deviational variables that have undesirable deviations from goals are
identified. The undesirable deviations are penalized by formulating the
objectives.
iv. Appropriate weights corresponding to the objectives are identified and the
problem is solved.
v. The objective function values are not compared against each other because
iteration gives rise to new weights. The weights are modified and the problem
is again solved ifthe solution is not satisfactory or unacceptable.
The advantages of GP are as follows,
i. GP avoids infeasibilities
38


ii. Management goals are realistically expressed
iii. The deviations from goals are minimized and selected outputs are
optimized
The disadvantages of GP are as follows,
i. Weightings are difficult to set for conflicting objectives such as habitat and
harvest volume
ii. Outcomes may be difficult to interpret as three might be more than one
factor controlling the outcome
iii. Lacks ability to optimize several objectives
The conflicting criteria or objectives as well as multiple objectives are easily tackled using
stochastic approach. But if a solution needs to be integer valued then an optimization
technique such as integer programming is best suited. The most common and popularly
used linear technique in land allocation problems is integer programming, explained below.
3.3.4 Integer Programming
Integer Programming (IP) or Integer Linear Programming (ILP) is an optimization problem
in which the objective problem and constraints are integers. The problem is called Pure
Integer Programming Problem when all the required variables are integers only and the
problem is called as Mixed Integer Programming Problem if some variables are integers
(Foulds). Other problems are called as Pure (Mixed) 01 Programming Problem or Pure
(Mixed) Binary Integer Programming Problem in cases where the integer variables are 0 or
1 (Foulds).
Generally, two kinds of algorithms have been developed in order to solve IP problems. The
first method is the Cutting Plane (CP) method also known as Gomorys method, which
works for Pure Integer Programming Problem only (Foulds). The second method is the
Branch and Bound (B&B) method, which is used in global optimization and also for
continuous functions.
The advantages of IP are as follows,
39


i. IP is more realistic algorithm to solve complex problems such as land use
allocation, as IP allows problems with thousands of variables and
constraints to be solved using computer programs. IP has been applied in
several areas such as inventory design, capacity planning, marketing,
finance, multiple plant location studies, maximizing material utilization, data
development analysis and so on.
ii. IP helps in resolving decision making problems and determining solutions
for unbound cases without violating any constraints. IP also warns if a
problem is improperly formulated.
iii. The variation in results for a problem can be observed very clearly by
changing coefficients, which is also called as sensitivity analysis.
The major drawbacks of IP are as follows,
i. The unimportant variables are ignored in a multi-criteria problem thus
giving rise to less rigorous problem with lower accuracy and certainty.
ii. IP is static in the sense that it doesnt consider changes and evolution of
variables with time.
iii. The values of the variables in an IP problem should be known with
certainty in order to progress in formulation process.
iv. Functions need to be linear in an IP problem, which means that each
decision variable is a separate term having an exponent of one.
The integer programming technique and most the other above techniques mentioned are
used for solving linear problems, although some of them in combination with stochastic
techniques have known to be used to solve non-linear problems. In reality most of the
problems dealing with multiple objectives, factors and constraints are non-linear in nature
and needs a robust technique, which can optimize a nonlinear multi-criteria problem. Some
of the concepts illustrated below are of such nature, which are capable of solving a multi-
criteria nonlinear problem. Lets start with a simple nonlinear technique, non-linear
combinatorial optimization.
3.3.5 Non-linear Combinatorial Optimization
40


A combinatorial optimization is an optimization procedure where the goal is to find the best
possible (optimal) solution such that this set of feasible solutions is discrete or can be
reduced to discrete one. The word combinatorial indicates that only a finite number of
feasible solutions exist. A nonlinear combinatorial optimization problem (NLCOP) is a
combinatorial problem with a nonlinear objective function (Foulds). In most of the prior
studies NLCOP was analyzed by decoupling the combinatorial aspect from the nonlinear
aspect and dealing with these concepts separately.
The main advantages of NLCOP are ease and flexibility of implementation, robustness and
speed of convergence. The drawbacks of NLCOP are that it adds computational burden to
the problem and it cannot guarantee a global optimum. There are couple of techniques,
which are considered best suited for attaining global optimum and one of them is genetic
algorithms, which is dealt later in section. First lets understand few common stochastic
techniques used in solving a complex land allocation problem, one of them is fuzzy
optimization technique considered a powerful technique to model tradeoffs between
various criteria.
3.3.6 Fuzzy Multi-Objective Programming
Fuzzy Multi-Objective (FMO) theory is based on degree of quantitatively measurable
human satisfaction where a problem need not necessarily have any original
commensurability (Foulds). In practice, a decision maker facing a multiobjective problem
has a fuzzy target set such as each objective function could be either below or above a
certain value, which could be quantitatively implemented into each objective function. In
FMO theory an objective function is defined by a membership function, whose value can
be expressed as a degree of satisfaction of a decision maker. Thus an objective function
having no commensurability is treated with the same scale.
A FMO optimization problem is a maximization problem of the combination of membership
functions, which could be combined using any of the three operators: minimum operator,
sum operator and product operator (Foulds). The most common operator used in fuzzy
41


decision set for a multiobjective problem is a sum operator due to the following
advantages,
i. The sum of objective functions gives rise to a reasonable convergence of the
multiobjective problem
ii. The sparseness of the Hessian matrix (square matrix of second partial
derivates) is not affected considering the amount of calculation
iii. The membership function can be easily updated
A conventional FMO optimization problem can be illustrated as shown in Figure 1 below.
Membership functions which are in turn used in construction of objective function are built
using the subjective experience of a decision maker. The parameters in the problem are
then tuned and the membership function is updated until convergence of the problem is
attained.
Objective
Function Value
Trade-off
Ratio
Updating
membership
function
Figure 3.2 Fuzzy Multi-objective Algorithm (Fouids)
42


The advantages of FMO over traditional methods are as follows
1. Human reasoning is implemented in computers thus giving rise to effective
solutions with complex inputs
2. FMO doesnt require prior knowledge of advanced math theory
3. FMO provides the user with great flexibility and developer options
4. FMO handles decision making problems that cannot be defined by
mathematic models.
Despite the above mentioned advantages of FMO theory there are several disadvantages,
such as,
1. Development of the FMO algorithm is very complex
2. FMO requires considerable computing power
3. FMO theory is very difficult to explain to users.
Although FMO is a very robust technique, realistically thinking some of the aims of an
optimization problem is to reduce computational time, easy to implement and easy to
communicate the problem with decision makers. Multi-objective sensitivity analysis is easy
to implement nonlinear optimization technique, capable of dealing with multiple criteria
problems.
3.3.7 Multiobjective Generalized Sensitivity Analysis
Multiobjective generalized sensitivity analysis (MOGSA) is a multi-criteria procedure based
on parameter sensitivity analysis (Foulds). Figure below illustrates the MOGSA algorithm.
43


44


Figure 3.3 Multiobjective Generalized Sensitivity Analysis Flowchart (Foulds)
The main purpose of MOGSA is to estimate parameter sensitivity of a complex multi-
criteria problem. The main objective is to determine the parameters that significantly
influence a multi-criteria response function (Foulds) These parameters are changed jointly
over the feasible parameter space in order to observe and determine the nature of
variation in the response function. Initially the population is ranked using Pareto ranking
system and divided into two datasets. Pareto ranking is based either on counts or cost. A
parameter is ranked highest in a count Pareto set if a parameter in a dataset occurs many
times or it is ranked the highest in the cost Pareto set if a parameter is highly expensive.
Pareto ranking separates the significant aspects of a problem from the trivial ones. A
Pareto set is considered to be a non-inferior, non-dominated or efficient set or tradeoff
dataset in a multi-criteria problem.
The datasets are divided into behavioral and non- behavioral datasets, which are used to
determine cumulative marginal distributions using Kolmogorov- Smirnov (K-S) method. A
sensitivity analysis is performed if the marginal distributions of the two datasets are
different otherwise they are declared as non-sensitive set. If the differences between two
distributions are below 1% then the farameters are considered to be highly sensitive, if
difference is between 1 to 5% then medium sensitive and if above 5% then the parameters
are declared as low sensitive (Foulds). The datasets are bootstrapped or re-sampled 50 to
200 times for statistical robustness and then tested for stability (Foulds). The MOGSA
algorithm is stopped if the sensitive parameters are determined to be stable in order to
produce a final dataset of sensitive parameters. The above process (figure) is repeated
until stability is attained.
The main advantage of multi-criteria methodology MOGSA is the usage of sensitivity
analysis, which is easy to compute, provides significant information to make a decision and
interaction between parameters are revealed. A few disadvantages of the MOGSA
methodology are as follows,
1. The determination of parameters corresponding to variation in response function
are based upon the best information at the disposal of the analyst
2. MOGSA lacks systematic methodology for combining parameters, which limits the
reliability of the method
45


3. The insensitive parameters are discarded, which causes degradation in the quality
of the model.
Although multi-objective sensitivity analysis technique is easy to implement, the parameter
estimation and analysis needs to be more robust as in genetic algorithm where a fitness
function is used to evaluate the parameters. Another most common stochastic technique
used in allocation analysis is multi-criteria acceptability analysis, which is usually used in
combination with other optimization techniques such as analytical hierarchy process and
integer programming.
3.3.8 Multi-criteria Approval-Stochastic Multi-criteria Acceptability Analysis
Multi-criteria approval (MA) analysis is a process developed to analyze decision making
problems involving multiple criteria. MA is based on a voting scheme and well suited to
analyze severely conflicting criteria or preferences. Stochastic multi-criteria acceptability
analysis (SMAA) is a procedure use to analyze problems associated with uncertainty and
ordinal and cardinal data (Foulds). SMAA is complicated to understand as compared to
MA. In prior studies such as forest planning MA and SMAA are used in developing a multi-
criteria decision support system. MA and SMAA methods complement each other giving
good results. MA is usually used as a first step to identify the nature of the decision
problem such as behavioral and technical aspects and followed by SMAA which is used for
in-depth analyses of the problem. MA-SMAA is typically used to analyze problems with low
quality information (Foulds).
MA is based on approval voting theory, which enables dichotomous evaluations (such as
approved and disapproved) of alternatives with-respect-to decision criteria (Foulds). A
voter votes for as many candidates as he or she approves according to the approval voting
theory. A candidate who gets the maximum number of votes wins the election. This theory
promotes moderate candidates only. In a multi-criteria problem a decision maker is asked
to rank criteria by their importance. Later, alternatives for each criterion are approved
based on a border theory, which is an average evaluation of alternatives with-respect-to
the criterion considered. The voting results are determined after defining the dichotomous
evaluations (Foulds) and the voting results are classified into five categories as follows,
46


1. Unanimous This occurs when only one alternative has been approved with-
respect-to all criteria.
2. Majority This occurs when one alternative has been approved with respect to
most important majority of the criteria.
3. Ordinally dominant This occurs when one alternative is declared superior based
on order of criteria and dichotomous evaluations.
4. Deadlocked This occurs when more than one alternative is approved and
disapproved with respect to the same criteria.
5. Indeterminate This occurs when there is inadequate information on criteria order
and approval or disapproval of an alternative with respect to the criteria is not
possible.
The second procedure, SMAA is based on stochastic assignment of so called acceptability
indices to alternatives and criteria weights representing the preferences that support the
choice of decision alternative (Foulds). SMAA is capable of handling both ordinal and
cardinal data. SMAA is renamed as SMAA-0 (Stochastic Multi-criteria Acceptability
Analysis with Ordinal data) when it deals with ordinal data (Foulds). SMAA-0 is applied in
discrete multi-criteria problems, where criteria are uncertain and the weights corresponding
to criteria are impossible to obtain.
The above mentioned MA and SMAA procedures when applied individually in any multi-
criteria problem are associated with lot of drawbacks but when applied together they
compliment each other. The advantages of MA as described above are self evident. MA
can be used in analyses of severely conflicting criteria problem and is a very good
approach for a problem with low quality information. The main disadvantage of MA is that
this method tends to promote moderate ranking candidates and mostly ignores the low and
high raking candidates. Thus MA fails to maintain diversity in the population. The other
disadvantage of MA is that it ignores cardinal information when mixed information is used
in decision support tasks.
The advantages of SMAA-0 are that it is a good approach for problems with uncertainty
and mixed data (ordinal and cardinal data) and it maintains diversity in the population by
choosing alternatives from different groups of criteria. The main drawback of SMAA-O is
that it is very difficult to understand. SMAA-0 combined with MA helps in elimination of
47


most of the disadvantages encountered while solving a multi-criteria problem through the
use of these methods individually.
Most the above stochastic techniques are either difficult to implement and understand or
could be improved methodologically. The stochastic concepts illustrated below are used
very commonly not only to solve spatial problems but are capable of handling multi-criteria
problems. Cellular Automata is known to be used in raster data analysis and in land
allocation problems.
3.3.9 Cellular Automata
Cellular automaton (CA or Cellular Automata) was originally formulated by Ulam and von
Neumann in the 1940s to assess the behavior of complex and extended dynamic systems,
where space and time are discrete (Foulds). CA is a discrete model, which consists of an
infinite, regular grid of cells, each in one of a finite number of k possible states. The grid
can be in any finite number of dimensions and updated synchronously in discrete time
steps according to a local, identical interaction rule. The state of a cell at t is determined by
the state of neighborhood cells at time t-1. Each time the rules are applied to the grid a
new generation is produced.
Cellular automata are simulated on a finite grid instead of infinite grid, for example, in CA
universe would be considered as rectangular two dimensional plane rather than infinite
plane. The simplest nontrivial CA are the one-dimensional CAs with two possible states per
cell, which implies that a cell is connected to r local neighborhood cells on either side,
where r is a parameter referred to as the radius (Foulds) For example, a cell having 2
neighbors will have a neighborhood of 3 cells and 2 = 8 possible patterns with 2s = 256
possible rules. In a typical two-dimensional CA two types of cellular neighborhoods are
possible. First one with a total of 5 cells (a cell with four immediate neighbors, 4+1=5)
and second one with a total of 9 cells (cell along with its eight surrounding neighbors). For
a one dimensional finite-sized grid, the application of spatially periodic boundary conditions
results in a circular grid whereas for a two dimensional finite grid the resulting grid is a
toroidal. CAs has been applied in the field of communication, computation, construction,
growth, reproduction, competition and evolution.
48


The advantages of CAs are that it provides extremely simple models of common
differential equations such as wave equations and dso provides a discrete model for a
branch of dynamical systems theory. Other advantages of CAs in the area of urban
systems include object-oriented programming, links with geographic information systems
and remote sensing data. Although there are several advantages to cellular automata
modeling it is still very much in its infancy. Drawbacks of CA technique include issues
associated with cellular model calibration such as extensive tuning and testing to get
desired behavior, their capacity to represent top-down processes and the meaning of
transition rule. Applying an applicable rule and updating a single system would require
updating every cell in the system, which is a very time consuming process. Another major
issue is that it is difficult to track the state as everything is updated at a cellular level.
Simulated Annealing, another stochastic technique explained below, although not usually
applied at cellular level is used in raster analysis and to solve multi-criteria land allocation
problems.
3.3.10 Simulated Annealing
Simulated annealing (SA) is a simple Monte Carlo simulation technique, which is a
probabilistic algorithm applied to a global optimization problem for locating good
approximation to the global optimum (Foulds). In the SA algorithm, each point (let the point
be x) in a search space is compared to a state of some physical system and a function f(x),
which is to be minimized is interpreted as internal energy of the system (Foulds). The main
goal of SA is to bring an initial state of a system to a state with minimum energy and to
escape the local minima.
The advantages of SA are that it converges to the optimal solution of a problem and easy
implementation leading to better results for a local search. The drawbacks of SA are that it
converges at infinite time and is slower than other algorithms. In terms of computational
time, genetic algorithm performs better than simulated annealing.
3.3.11 Genetic Algorithm
49


Genetic Algorithm (GA) is a heuristic technique, which means that GA helps find
approximate solutions for difficult-to-solve problems. GA uses principles of evolutionary
biology or biologically derived techniques such as inheritance, mutation, natural selection
and recombination (crossover) (Foulds). GA is different from other heuristic algorithms
including simulated annealing and tabu search. The major differences are that GA is
stochastic in nature and works on a population of possible solutions unlike other heuristic
methods that try to improve a single solution through iterations.
GA is implemented as computer simulation programs that utilize initial population or
chromosomes of candidate solutions to optimize them towards better solutions. Initially the
selection operator chooses the fittest individual. There are various selection techniques
such as roulette, tournament, top percent, best and random selections that could be used
depending on the type of multiobjective problem (Foulds). The key idea is to select the best
initial population for further iteration. The next GA operator is crossover or recombination,
which combines the selected individuals to form a new individual. The last operator,
mutation adds some noise to the individuals so that diversity is maintained. There are
several types of crossover operators and mutation operators, which can be applied
depending on the type of problem.
The main advantages of a simple GA are as follows,
i. The search procedure finds a set of variables that optimizes the fitness of
an individual or whole population, which is not possible by traditional non-
linear solution techniques
ii. Non-linear programming solvers use a type of gradient search technique,
which leads to convergence at local optima which means that true feasible
solutions are not found. The probabilistic nature of GA leads to a global
optimum thus encompassing a range of possible optimal outcomes.
iii. GA can quickly scan a vast solution set
iv. GA finds a solution through evolution
v. GA does not require any rules of the problem as it works with its own
internal rules, which is very effective in the case of complex or loosely
defined problem.
Although there are many advantages to GA, a few drawbacks are as follows,
50


i. There is a risk with GA that it could find a sub-optimal solution. This means
that the algorithm tries to find the best set of solutions, where most of them
are copies of each other. This drawback will be eliminated in the proposed
study by the use of two powerful selection operators which are non-
dominated sorting method and niche method.
The methodology proposed in thesis is based on meta-heuristic technique, which is
basically a hybrid genetic algorithm technique used in order to eliminate some of the
drawbacks mentioned in all the above procedures. The application of most of the above
concepts over the past ten years is demonstrated in the section below to understand the
development of a relatively realistic and a robust land use allocation procedure.
3.4 Past and Present Land use Allocation Techniques
There has been several land use allocation procedures proposed and formulated for more
than a decade. Initially land use allocations were non-spatial analysis and based on
demographic and economic factors. One such research article in 1979 by Goltry et al.
illustrated an industrial land allocation process. Goltry et al. research dealt with the
allocation of physical space to industrial areas (Goltry). The allocation of the industrial land
is dependent on four principal methods. The first method evaluates the industrial
employment corresponding to expected industrial impacts including amount of air and
water pollution and solid waste generated from the industry. The second method takes into
account industrial employment forecasts to translate into land demand for future industrial
development. The third method classifies the available land sites in the study area based
on physical and political characteristics of the land such as slope, depth of bedrock and
zoning respectively. The final fourth method evaluates results from the above three
methods and based on economic cost for the industrial development selects the best site
to allocate the future development. The information gathered for all the above mentioned
four methods for the lowest development cost were from US Government Reports
Announcements, 26, 1979 (Goltry). To summarize the paper describes industrial land
allocation process based on employment forecasts and cost of future industrial
51


development. This allocation process seems to be favorable from economic point of view.
It is not clear how the industrial impacts have been accounted for in the allocation process.
After a gap of about ten years, in 1990 Tomlin et al. illustrated a spatial land use allocation
procedure. Tomlin et al. research article discusses a hypothetical land use allocation
experiment using Geographic Information Systems (GIS) for the study area located in
Illinois (Tomlin). In the same year, Tomlin et al. introduced a land use allocation model
called ORPHEUS, which was used to solve an allocation problem by an terative and
heuristic process made possible by the integrated use of various geo-processing tools
(Tomlin). Although Tomlin et al. research article did not provide adequate information on
land use allocation experiment it is evident that GIS and heuristic techniques were used in
modeling land use allocation when the GIS technology was not as advanced as today.
There were a couple of significant researches on land use allocation based on shape of the
land. For example, in 1991 Benabdallah and Wright demonstrated several discrete
programming models for a small to medium range allocation problem, where the primary
constraint is a particular shape of the future land use parcel (Benabdallah, Shape
considerations in spatial optimization). Most cases discussed in the Benabdallah and
Wrights paper displays a successful land use allocation to a physical space with the
rectangular shape. In the same year, 1991, Benabdallah and Wright also demonstrated a
heuristic algorithm to address a multi-objective land use allocation problem where the land
uses are allocated to parcels with particular shape. A nonlinear discrete optimization model
is used in addressing a districting problem. Benabdallah and Wrights research used shape
of the land parcel as constraint in modeling land use allocation but looking at recent trends
of land use changes it is obvious that allocation of land uses is not a constraint to shape
and size of land parcel. Similar to Tomlin et al. research adequate information on
Benabdallah and Wrights research is not available. However, all the researches stated
above concludes that spatial analysis, heuristic techniques and linear techniques were
used in modeling either a simple land use allocation problem or multi-objective problem.
There were many linear techniques combined with spatial analysis procedures proposed
during the period of 1990 to 2000, which is illustrated further below. In 2000 for the first
time a significant research article by Lam and Sun demonstrated the allocation of
residential areas in an urban area in Hong Kong to available geographic spaces (Lam).
Hong Kong 2006 planning data is used to obtain the population forecasts in order to
52


allocate future residential areas to potential physical spaces. The primary constraints in the
allocation model are land production costs, total development costs and transportation
costs. Genetic algorithm is used to identify the potential spaces for future residential
developments. Since 2000 there has been significant use of genetic algorithms (GA) in
solving multi-criteria land allocation problems with a very scant involvement of spatial
analysis due to complex nature of the combined GA-Spatial technique. Also there has
been increase in usage of demographic and transportation data in the land allocation
analysis. As illustrated by Arasan in 2000, a land allocation procedure was proposed,
where the objective is to obtain a least travel intensity under two major constraints, zonal
population and employment (Arasan). The study area located in Chennai, India, where the
potential land use allocation is considered for the planning period of 1991 to 2011. By
controlling the zonal population values and future employment over an area, various
allocation plans are generated. A linear programming technique is used to analyze the
intensity of travel to work.
Therefore, it is evident that there have been several critical researches conducted to solve
a multi-criteria land allocation problem using a range of techniques from linear to nonlinear.
Also since past couple of years, there has been increase in spatial analysis in connation
with linear or nonlinear techniques to solve land use allocation problems. For example, in
2003 Zhang et al. proposed a linear programming technique in combination with GIS to
allocate land space that promotes grain/horticulture-animal/husbandry forestry (Zhang).
The constraints for the spatial model is obtained from GIS and a set of technical
coefficients form an objective function. The optimal scenarios are generated from linear
programming model (Zhang). Thus the above summary indicates that significant
sophisticated research has been conducted to solve multi-criteria land use allocation
problems. In order to understand the proposed technique in this thesis research it is
essential that some significant research articles be reviewed, which would also lay a strong
foundation for the research conducted in accomplishing thesis goals. Let's understand in
detail the application of various techniques (as mentioned in the previous section of this
chapter) in land allocation problems.
Although there has been some notable research in the area of land allocation in the past,
some of the significant research closely related to this thesis problem as well as thesis
proposed land use allocation technique are demonstrated since 1994. In 1994 Minor and
53


Jacobs research effort dealt with the allocation of potential physical space to solid and
hazardous waste hndfill subjected to conflicting objectives and constraints (Minor and
Jacobs). Potential sites in Orange County, North Carolina were chosen as study area. A
mathematical model was formulated using commercial package, Experimental
mathematical Programming (XMP) software to solve the landfill allocation problem (Minor
and Jacobs) The main objectives of this allocation problem are minimizing land purchase
cost, maximize contiguity and maximize compactness. The following constraints were
considered in the model,
1) Potential sites need to be within city limits and within 100 year flood plan
2) Necessity of water table or bedrock near the potential site surface
3) Accommodation of expected quantity of waste generated by communities
4) Industries within the scope of the planning region and all the variables in the
mathematical model need to be greater than or equal to zero.
The model results as stated in the article indicated a reduction in contiguity in solutions due
to the reduction in compactness. The model solutions also become infeasible for smaller
values of compactness and contiguity. The article also indicates the inclusion of future
factors in the model such as suitability constraints, for example, soil type, water table depth
and flood plain proximity to urban areas. It is not clear what tools were used to measure
the compactness and contiguity. There is also no indication of addressing boundary issues
such as consideration for adjacent environmentally sensitive areas such as water bodies,
parks or habitats and so on. The accessibility to transportation facilities was not
considered. A higher value of compactness and contiguity doesnt necessarily indicate loss
of habitat due to fragmentation thus these measures are not enough for measuring
fragmentation. The methodology demonstrated by Minor and Jacobs in land use allocation
of solid and hazardous waste landfill is not clear, several questions come to mind such as
was there any spatial analysis conducted to model contiguity and compactness? Were
spatial relations such as distance from transportation facilities and residential areas
considered? Since the land use is sensitive to environment, were any policies considered?
Past few years the use of land use policy in allocation problems has become very
common. In 1996 Duerdens research efforts examined types of approaches that can be
adopted for land use allocation based on policies (Duerden). Since the consideration of
land use policies is out of scope of this thesis research, at this point in time Duerden's
54


article is not discussed in detail. Spatial analysis is crucial to this thesis thus most of the
articles reviewed are related to spatial and mathematical /statistical analysis. In 1997 Rens
paper demonstrated a land use allocation model using a software package, Geographic
Information Workshop for Windows (GIWIN) (Ren). GIWIN package contains the GIWIN
software, step-by-step detailed guidelines, GIWIN-LRA model introduction and a case
study database. GIWIN land resource allocation software is written in MS-Visual C/C++
under MS-Windows operating system (Ren). This software package is used as a training
model to demonstrate the role of GIS in decision making process. The package contains
four main elements, data management, GIS analysis, land resource allocation model and
graphic editor. The main objective of the model is to demonstrate the role of GIS in spatial
data analysis and decision process in land resource assessment and allocation. This
objective is accomplished by the model through a seven stage process. Stage 1 includes
defining factors and constraints layers, where the zero value is assigned for most of the
constraint areas. The factors are divided into impact factor layers, which are the criteria for
land use assessment and relevant factor layers, which are used to obtain scores for the
degree of target land use suitability. Stage 2 of model analysis includes coding of relevant
factor layers. The relevant factors layers are coded by using a spatial correlating model,
Four-C model, which was developed by the author in 1995 (Ren). The Four-C model
assigns scores using overlay measurement corresponding to land use categories in the
existing map based on suitability of the objective or target land use. The final product of
stage 2 consists of a raster image with 0 to 100 values representing scores of suitability for
target land use, which will be used again to generate scores for impact factor layers (Ren).
Stage 3 involves assigning weights to relevant factor layers. Analytical Hierarchy Process
(AHP) is adopted for assigning weights to factor layers. Each process compares two layers
and assigns a number (weight) representing the relative importance ranging from 1/9
(extremely less important) to 9 (extremely more important).Stage 4 of the model involves
multi-criteria assessment of the relevant factor layers, which is accomplished by weighted
linear overlay of the factor layers. In Stage 5 the suitability assessment grid generated from
Stage 4 is overlaid again with existing objective land use map to revise the weights and
related scores of relevant factor layers. If the correlation between the suitability grid and
existing objective land use map indicate that the areas with higher suitability scores are
mostly occupied by the target land use then the assessment is considered good. Stage 6
involves allocation of multiple land use types or the objective land use type to highest
55


suitability score areas in the assessment map. Finally the last step, Stage 7 includes
mapping of all the alternative future land use development plans based on the objective/s
of the model. The author demonstrated the GIWIN model by using a case study region
located at Yogyakarta in Indonesia (Ren). A subset of dataset for the Yogyakarta region
was extracted from the regional planning GIS database to conduct the land allocation
analysis. The target land use or the objective of the case study was to allocate wet paddy
fields and new settlement areas to the study area. For the wet paddy fields the relevant
factors chosen to generate suitability grid maps were geology, elevation, slope, soil series
and soil depth. In the case of new settlement areas the relevant factor layers were
population density, accessibility to railway and highways, elevation and slope, where the
population density and distances from railway and highway were computed using GIS
operations. The minimum time required to complete the exercise using GIWIN model was
half a day. There was no consideration of non-linear relationships between the parameters
of the model and also the spatial analysis is restricted to representation of data and data
analysis such as weighted overlay. Thus the GIWIN model assumes a linear trend in
allocation agricultural and residential land uses (Ren).
Another paper in 1997 by Xia demonstrated the use of GIS but extended a bit further by
using remote sensing data, a very high resolution data for land allocation (Xia). Xias paper
presents a sustainable land use allocation model based on three main criteria, (i)
consuming land use resources by maintaining equity between generations, (ii) maintaining
a reasonable amount of economic growth by consuming minimum amount of cultivated
land, and (iii) less fertile land should be given higher preference for commercial
development (Xia). The model is demonstrated using an urban city, Dongguan located in
Guangdong province, People's Republic of China. The main objectives for the case study
area, Dongguan are allocation of urban development, agricultural lands and to control the
encroachment of agricultural lands. Remote sensing data and GIS data were used to
investigate the case study area for available land use resources. GIS modeling technique
based on spatial efficiency was used in allocation of various land uses.
Three main scenarios were established for the allocation model, 1) for the time series,
1988 to 1993 the actual land loss was equal to amount of land provided for the allocation,
2) for the years 1988 to 1993 the amount of land provided for allocation was 9,687.36
hectares and 3) for 1993 to 1998 the amount of land provided was 7,456.10 hectares (Xia).
56


AML was used to develop urban suitability maps and agricultural suitability maps. Slope
and soil types were used in creating agricultural suitability maps. Similarly for urban
suitability maps distance and slope were considered. Cost distance technique was used to
compute the distances, where the closest area to the town or city was considered to be the
best suitable land for urban development. The suitability maps contained scores allotted to
all the grid cells based on field investigation and satellite images. The scores were scaled
from 1 to 7, where 1 being the most unsuitable land for agricultural practices and 7 being
highly suitable for agriculture (Xia). Urban land use allocation was given more weight than
agricultural land use allocation. Tietenbergs dynamic model based on theory of
environmental economics was used in assessing the optimal land use allocation process
over time. Each iteration produced a suitability map, where the urban suitability scores
were altered based on the previous years land use pattern. The neighborhood function
was also considered in assigning scores for the urban suitability map, which included all
urban development, crops and orchard in the neighboring regions of the potential future
land use. The case study lesults generated for the time period 1988 to1993 and 1993 to
1998 indicated that Dongguan had agricultural land loss over the time (Xia). The results
were validated using ERDAS IMAGINE. Xias research article demonstrates a thorough
spatial analysis in allocation of agricultural and urban land uses. Although the objectives of
the model are conflicting more importance is given to urban development compared to
agricultural land use allocation. The suitability score assignment or the fitness of each cell
for land use allocation is judged based on cost distances however, there could be many
other significant variables such as contiguity and compactness, which would have
impacted the suitability scores significantly. It is not clear how the least suitable cell or an
unsuitable area for certain land allocation is evaluated.
The research reviewed so far considered either spatial or non-spatial analysis but a
combination of both type of analysis sometimes results in a sophisticated technique to
analyze land allocation. On similar grounds in 1998 Verburg et al. paper presented a land
use allocation model based on statistical analysis, where a combination of spatial and
aspatial (bio-physical and socio-economical) factors are considered (Verburg and Koning).
The paper describes a modeling procedure for assessment and evaluation of patterns of
land use based on statistical analysis. The model, CLUE (Conversion of Land Use and its
Effects) is a dynamic land use allocation model, which simulates various land use
57


scenarios, accounts for historical and present land use pattern interactions and socio-
economical and bio-physical conditions (Verburg and Koning). CLUE is demonstrated by
illustrating several examples for the region Ecuador from De Koning et al.
The following are the main modules of the land allocation model:
1. Demand module this module computes the changes in demand of agricultural
products at national level based on historical and future trends of food demand,
population growth, changes in import & export and dietary changes.
2. Population module this modules computes the changes in population and
corresponding demographics based on various census projections
3. Yield module this module spatially computes the yield changes of agricultural
cover types over time and corresponding distribution at national level
4. Allocation module this module models the changes in pattern of land cover types
over time
All the above modules simulate various factors on yearly basis. The CLUE model assumes
that the future land use changes can accommodate the future demand. The model
simulates the allocation of land uses at two grid resolutions, coarse and fine scale
resolution. At the coarse scale general trends of land use patterns are computed and at
fine scale the computations from the coarse scale and aspatial constraints are used in
computing the final land use allocation map. The coarse scale was generated by
aggregating grid cells. The scales used for the study region Ecuador are 36*36 km for
coarse resolution and 9*9 km for fine resolution (Verburg and Koning). The grid size for the
study region was selected based on size of administrative units. The factors used in
simulation of land use allocation in Ecuador included census data (if a specific region did
not have census data then surveys were used), bio-physical data from digital or paper
maps, soil conditions and climate.
Both the coarse and fine scale analysis are iterative procedure. The Coarse scale analysis
was conducted by using step-wise regression to assess the impact of bio-physical factor
and socio-economic factor on changes in land use distribution, which indicated a significant
impact at 0.05 level (Verburg and Koning). The estimated regression cover with higher
values was compared with the actual land cover and the highest value cells were selected
for allocation. Values obtained from the difference in the covers were allocated to
58


corresponding cells in the actual cover. The regression map was compared with the
changes in demand and until the demand was meet the step-wise regression procedure
was repeated.
The fine scale analysis involved the regression cover, the output from coarse scale
analysis, demand module, local biophysical and local socio-economic conditions. The fine
scale allocation is also an iterative process, until the changes in demand are meet the
iteration continues. Thus the CLUE model accounts for complex interactions between
biophysical and socio-economic factors at regional and local level. The author discusses
using remote sensing data in CLUE framework for future scenarios.
CLUE modeling has been applied to many other study areas such as Ecuador and China
in regional scale. In order to understand the modeling technique lets review the CLUE
modeling in Ecuador. In 1999 De Koning et al. research article describes CLUE modeling
application with just two main modules, demand module and allocation module for Ecuador
region (Koning and Verburg). The CLUE modeling framework was used in Ecuadorian
region to produce land use maps reflecting agricultural development. For land use
allocation modeling a grid size of 9.25*9.25 km and a cell size of approximately 5*5 min of
the Ecuadorian region was considered (Koning and Verburg). The cell attributes included
biophysical and socio-economical data from census. Factors such as soil type, climate and
altitude were used for the allocation analysis. The baseline map considered for the analysis
was for the year 1991, which included three main agricultural land use types, grassland,
permanent crops and temporary crops. For the coarse scale analysis initially stepwise
regression for each eco-region was used, where land use variables are independent
variables and land use types are dependent variables. After the stepwise, multiple
regression was used to create the regression cover using biophysical, socio-economic and
other variables. The model validation was conducted using a backward calculation of land
use changes from 1991 to 1974 (Koning and Verburg). After the validation future scenario
of agricultural development was created for 2010. The results were found satisfactory
indicating an increase in grassland areas and increase in agricultural areas in coastal
tropical forests, Andean footslopes and the Amazon. It is not clear whether the population
and yield modules were merged with the demand and allocation modules.
59


Another application of CLUE model in 1999 by Verburg et al. demonstrated the use of
three modules at national level. Verburg et al. research demonstrates CLUE modeling
framework applied at national level for China (Verburg and Veldkamp). The paper
describes modeling nation wide land use changes with the emphasis on agricultural land.
In this case the CLUE modeling uses just three modules, demand module, population
module and allocation module. The most challenging aspect of the modeling was data
uncertainties due to under-reporting of cultivated areas and other areas in Statistical
yearbooks. According to the research reports 15% of the total land in China is cropland
and horticultural land, 55% are forests and grasslands, 23% are bare lands, deserts,
glaciers and only 3% of the total area is developed area (Verburg and Veldkamp).
The demand module computes demand changes of agricultural products based on quantity
of import and export products, diet changes and population growth (obtained from
population module). The population module as usual computes population changes and
corresponding demographic characteristics at national level. Three main demographics
considered for the allocation analysis are, agricultural labor, rural population and total
population. The allocation module is a spatial analysis module, which uses demand
module outputs, population module outputs, regression cover and several land use driver
maps. The regression analysis here uses climate data, geomorphologic data and
demographic data. The grid size used in spatial analysis is 32*32 Km, where each cell is
characterized by land use type (Verburg and Veldkamp). The future land use maps were
developed for 2010, where the baseline was 1990 land use map. The results indicated
decrease in cultivated lands and decrease in production capacity of lost arable lands
relative to production capacity of total agricultural lands. To summarize agricultural demand
and future projected population along with few socioeconomic and biophysical variables
are used to allocate various land uses. It is not clear the yield module has been used to
allocate land uses in China at national level.
Verburg et al. CLUE model is a very comprehensive model from socio-economic point of
view. The model has four sophisticated modules based on various exogenous and
endogenous variables thus increasing the uncertainty of the model. The stepwise
regression analysis used at coarse resolution includes or excludes parameters from model
based on statistical significance and also the major drawback is usage of same data to
perform the comparison analysis. The CLUE model doesnt include any spatial interaction
60


between various land uses or consideration of non-linear relationships between
parameters. The model is not dynamic in nature as it is based on historical data. Finally the
CLUE model does not generate a range of land use plans, which is essential in land
allocation modeling analysis as it is always preferable to generate many alternative land
use plans due to varying range of views of decision makers.
In 1998 Johnston et al. paper demonstrated a framework to develop a set of spatial land
use maps. The framework consists of linking commercial urban model, TRANUS (Modeling
Package for transportation and land use policies) to California based GIS land allocation
model, CUFM (California Urban Futures Model) in order to develop land use maps for the
study region, Sacramento, CA (Robert and Barra). The zonal land use projections obtained
from TRANUS are used as an input in CUFM to obtain projected land use maps. TRANUS
uses logit based substitution model, which allows each input activity to choose a location
and land type thus creating a choice set for all input activities. The logit algorithm contains
a cluster of multinomial logit demand equations which simulates all the activities at an
increment of 5 year time period (Robert and Barra). The model converges easily thus the
run times for the calibration is faster. However due to large amount of inputs required for
the sub-models in the calibration process, it takes weeks to complete the calibration. Due
to this complexity the goodness of fit test for the dataset is very difficult to conduct thus
testing of alternatives and obtaining calibration data for more than one base year is
problematic. The evaluation model of TRANUS produces various kinds of policy oriented
ASCII format outputs classified by household income class or type of employment such as
number of trips, vehicle miles of travel by mode and operator, vehicle energy usage and
energy use in various structures (Robert and Barra). This ASCII output from TRANUS can
be feed into other models such as CUFM.
For the study, four-county Sacramento region or the Sacramento Area Council of
Governments (SACOG), which consists of 58 administrative zones, was chosen (Robert
and Barra). For the TRANUS the main inputs were, household income categories,
employment categories based on various land use types, trip purposes and land use
categories (agriculture, industrial, mining, forests, high office density, high residential
density and so on). The future scenarios over 5 year increment produced by the model
consisted of zonal allowable growth categorized by land use type, projected total regional
employment and network changes (Robert and Barra). The year 1990 was chosen as base
61


year and four scenarios at an increment of 5 year period were developed for 2015. The
land use growth projections from TRANUS for 2015 included acreage defined by land use
types, which was fed into the GIS land allocation model. CUFM is a nonlinear model that
allocates residential development based on profitability, which is a function of land process,
accessibility to transportation facilities and local government fees (Robert and Barra). The
land uses suitable for development were produced by overlaying several GIS maps such
as wetlands, land use types, transportation facilities, city boundaries and slope. According
to the results presented in Johnston et al. paper the GIS model created reasonable results,
where the land uses having high values were allocated to high service areas in cities and
near freeway ramps.
Johnston et al. land use allocation research illustrated the use of commercial package to
allocate various urban land uses. The commercial packages are based on multinomial logit
model and non-linear model, which is a very robust technique. Also the model generates
set of land use plans although there is no mention of modeling contiguity and
compactness. Also modeling of spatial relationships between various land uses and
parameters are not mentioned.
A research involving modeling of spatial relationships was carried out by an
interdisciplinary project in 1997 called Land Use and Land Cover Change (LUCC), which is
formed by joint leadership of International Geosphere- Biosphere Programme (IGBP) and
International Human Dimensions Programme (on Global Environmental Change, IHDP)
(Land-Use and Land-Cover Change). The main objectives of this project are as follows:-
a) Understanding the driving forces of global land use and land cover
b) Assessment of land use and land cover temporal and spatial change dynamics
c) Defining the relationship between land use and sustainability
d) Understanding relationships between LUCC, climate and biogeochemistry
The LUCC project developed several methodologies to assess local, regional and global
land use changes and related effects. The project is divided into three main activities or as
LUCC defines it as three focuses of the land allocation project are as follows,
62


a) Land use Dynamics (Focus 1) several land use studies were compared to
understand the decision making process in local, regional and global context.
Several sustainability scenarios were developed.
b) Changes in Land Cover (Focus 2) at this focus or step of the model the land use
changes and their affect on land cover patterns changes were studied. Several
spatial, empirical and analytic land cover change models were developed. The
main variables or land use changes indicators considered in these models were
socio-economic, biophysical and census data. Most of the data were spatial in
nature such as remote sensing, satellite images and raster datasets. Multivariate
statistical analysis was conducted to relate several variables to land cover
changes. Several hot spots (areas reflecting land cover changes) and cold spots
(areas that would be reflecting land cover changes in future) were detected.
c) Regional and Global land use/cover models (Focus 3) here simulation and
process based model were used to link between biophysical, demographic and
economic models developed in Focus 2. Also historical data for the past 300 years
were collected and some of it converted to spatial forms in order to analyze
historical land cover changes.
All the above steps and modeling technique of LUCC is illustrated in Figure 3.4 below. An
international committee of social and natural sciences scientists were brought together to
understand and assess dynamics of land use. There were workshops, conferences and
collaborative projects and research conducted to collect data, synthesize several datasets
such as biophysical, socio-economic and institutional in order to assess land use changes
(Land-Use and Land-Cover Change). According to the LUCC research social, economic
and political forces drive changes in land uses, which in turn impacts land cover.
63


Figure 3.4 LUCC Modeling framework (Land-Use and Land-Cover Change)
Although the LUCC model evaluates spatial relationships between various parameters it is
based on historical data and not dynamic in nature. LUCC model is robust model from
economic modeling point of view but in order to generate an effective land use planning it
is essential that spatial relationships between various land use parcels and spatial
characteristics such as contiguity and compactness need to be modeled.
In the next research article spatial characteristics, especially contiguity and compactness
are used as main criteria in land allocation problem. In 1999 Cova et al. research
demonstrated a theoretical framework for allocating land use to an optimal site based on
neighborhood search technique using spatial criteria such as contiguity and compactness
(Cova and Church). The main idea of Cova et al. paper is to make use of all the properties
of data represented in raster format, where a point to area neighborhood operation,
contiguity and compactness can be effectively addressed. The paper addresses the site
search problem by assuming a raster dataset for theoretical formulation of the problem.
According to Cova et al. complexity of site search problems increases with the increase in
the size of the problem or area of investigation, which in turn adds more decision variables
64


and constraints to the problem (Cova and Church). The paper describes a neighborhood
optimal site search approach where allocation problem is broken down into small local
parcels thus reducing the constraints and decision variables. The main objective of
theoretical problem is to maximize the site suitability. The constraints considered for the
problem are contiguity, site area, maximum diameter, site cost and root cell.
A root cell is a cell in a raster dataset under investigation, which is spatially fixed until the
site search for that particular parcel in which the cell is located is completed. For a solution
to be contiguous the requirement is the immediate cell adjacent to the root cell should
belong to the same site as the root cell, if this is true then the next adjacent cells are
checked and further, thus for any cell to be included in a solution they need to be
contiguous with the previous cell (cell closer to the root cell). For two-dimensional
contiguity measurement, a cell is included in a solution if either of its adjacent cells or both
adjacent cells closer to root cell by Manhattan distance are in the solution (Cova and
Church). According to Cova et al. if the two-dimensional contiguity measurement is
considered as constraint then the solution is always a contiguous solution. Thus each cell
is assessed for the site suitability by the neighborhood search operator and a suitability
map is generated. According to Cova et al. based on the neighborhood search operator the
compactness of the local parcel is increased or decreased. The author also suggests using
linear integer programming commercial packages including CPLEXMIP and UNDO. Finally
the author suggests the use of user interface so that a decision maker can interactively
explore the suitability map.
Cova et al. allocation model is based on contiguity and compactness, the fitness of each
cell in a grid data is judged by the above two spatial criteria but not any other spatial
relationships with other land uses including distance from the transportation facilities and
adjacent environmentally sensitive areas. The theoretical model presented above is not
very realistic as a land allocation models primary criteria is available location and its
relation with other surrounding land uses in local, regional or national scale. Usual practice
of land allocation model suggests modeling based on socioeconomic and biophysical or
inclusion of spatial relationships with other land uses integrated with evaluation based on
contiguity and compactness.
65


In the next article the authors illustrated a multi-criteria land allocation model based on
spatial relationships between various land uses at local scale and linear weighted overlay
technique at regional scale. In 2001 Carsjens and Knaap demonstrated an agricultural land
use allocation problem at local and regional scales using multi-criteria techniques. At the
local scale, dairy farms are allocated to optimal sites and at the regional level, pig farms
are allocated to the potential sites (Carsjens and Knaap). Both the local and regional
allocation cases are divided into three main steps or phases as follows,
a) Stepl involves excluding all the restricted areas such environmental conservation
areas, transportation facilities and developed areas ( residential, industrial and so
on)
b) Step 2 involves assessment and evaluation of the remaining areas for suitability
to future agricultural land allocation using multi-criteria evaluation (MCE)
techniques
c) Step 3 involves analyzing and evaluating the allocation results
Both the local and regional allocation projects are modeled using ESRI Arclnfo (GIS
software) at Wageningen University in Netherlands as a part of thesis research (Carsjens
and Knaap). The assumption for the local scale allocation process is that farm buildings
are potential locations for farm allocations due to the high costs involved in relocating farm
buildings. For the suitability analysis parcels for the farmland selected are larger in size
because of the fact that current farmland parceling is continuously changing due to land
ownership and farm management parcels. The larger parcels with boundaries such as
transportation facilities, conservation areas, developed areas and waterways are
considered to be fixed in size for fie planning period of 15 to 30 years (Carsjens and
Knaap).
The local study area is located in south of Netherlands, Leijen, which is approximately 125
sq. km. As mentioned earlier, for the phase 1 restricted areas are excluded. The remaining
potential spaces are divided into larger parcels of farmland, which are further divided into
grid cells of size 625 sq. m (Carsjens and Knaap). Each cell was evaluated for future
allocation, the distance from each grid cell to nearby farms within 2500 m radius were
considered profitable. Each grid cell was assigned a value, which represented suitability for
future allocation of dairy farm. The final value of each grid cell was decided by the distance
from the farmstead or the farm buildings, the nearer the farm buildings to the potential grid
66


cell the more suitable they are for future allocation due to least transportation costs. The
suitability of a cell allocation at local scale is judged by the distance from farmsteads, which
could lead to isolated dairy farms or patchy landscape. Although distance from farmstead
seems very logical step from transportation costs point of view, distance of a potential land
from farms itself would probably reduce fragmentation issues. It is not clear if number of
farm animals per acre or a similar criterion have been considered in the above local model.
The regional model reviewed below is related to allocation of pig farms, where numbers of
animals have been considered as a main criterion.
Regional study area is located in Netherlands in Noord-Brabant province, which is
approximately 5000 sq. km (Carsjens and Knaap). At the regional scale, potential sites are
evaluated to allocate pig farms. Due to reasons such as environmental and spatial
organization the pig farms need to be clustered and these clusters need to be separated
from each other by pig free corridors. Two main criteria for pig farm allocation includes that
the maximum allowed pigs in each duster need to be one million and pig free corridors
should be atleast 1000 m minimum width. In addition to the above two criteria, other factors
are based on socio-economic, biophysical and spatial criteria (Carsjens and Knaap), which
are as follows,
1) Conservation of valuable landscapes
2) Environmentally sensitive areas
3) Production capacity of each farm
4) Number of farm buildings and related industries
5) Environment acidification and problems associated with manure production
Based on all the above criteria the suitable sites for pig farming were established and
evaluated for future allocation. Each criterion were represented by GIS map, they were
assigned a specific weight and finally combined to obtain a suitability map for pig farming.
According to Carsjens and Knaap the larger the area of analysis more variables are
contributed to the multi-criteria analysis thus resulting in longer computational time,
obscure allocation process and fuzzy multi-criteria process. Although the regional model is
robust from perspective of considering several significant criteria, it is not clear if non-linear
relationships have not been modeled.
67


Recently there has been a lot of emphasis given in using sophisticated techniques such as
cellular automata, simulated annealing and genetic algorithms, in land allocation problems.
The framework of these techniques permits a researcher to model non-linear spatial
relationships, which is one of the goals of this thesis research. One such research effort in
2002, Barredo et al. demonstrated a hypothetical assessment of urban land use drivers
and an urban cellular automata model for simulating urban growth at local and regional
scales for an urban city, Dublin (Ireland).
The authors suggest five general groups of land use drivers, which are either constraints or
criteria that could be used in allocation process, they are as follows,
a) Factors related to socio-economic, political and economic development
b) Spatial features such as accessibility of urban cities
c) Environmental characteristics
d) Urban and regional planning policies
e) Neighborhood characteristics with respect to local scale
Barredo et al. describes three main phases involved in understanding urban land use
dynamics at local scale. In phase 1 level all the land use drivers or the factors are fixed
(linearly deterministic) until they are influenced by some external drivers. In phase 2 new
urban land use drivers ( temporally and spatially dynamic due to influence in phase 1) at
local scale are introduced, which in turn induces a non-linear process causing new land
distributions to develop thus allocating various urban land uses. At every phase level the
grid cells in land use is ranked based on the suitability of each cell for future allocation. At
phase 3 the grid cell rankings from phase 1 are evaluated and the suitability of cell is
stochastically modified based on human-related decisions. According to the authors in
reality all the three processes occur simultaneously and due to the different nature of the
processes, linearly deterministic (Phasel), non-linear dynamic process (Phase 2), and
stochastic process (Phase 3) the whole allocation process is very complex iterative
probabilistic system (Barredo and Kasanko).
Barredo et al. proposes cellular automata algorithm to deal with the above complex spatial
temporal land use allocation process. Cellular automata is a process where data is
considered to be in a grid format and the grid cells values are changed based on rules set
by neighboring cell states.
68


The allocation process uses an urban cellular automata model developed by Research
Institute for Knowledge Systems (RIKS) in Netherlands. The allocation model is a
constrained CA model with the following unique qualities,
a) Cell space Each grid cell in CA have 100m*100m space defined by unique
suitability scores (Barredo and Kasanko). The suitability values for each cell are
assigned by combination of various factors such as linear weighted sum of socio-
economic, environmental, physical variables, accessibility, zoning and
neighborhood effects. The suitability maps are fixed in time and space throughout
the simulation run unless a user manually changes the suitability scores.
b) Cell neighborhood The cell neighborhood is defined by a circular space having
0.8 km radius around the central cell (Barredo and Kasanko). In order to capture
neighborhood effects and conduct local spatial processes on the central cell a
radius of eight cells is considered.
c) Cell states CA model uses 22 states of cell, which are categorized as active,
passive, fixed (temporal and spatial) and transition (Barredo and Kasanko). The
active states of the cell are the land uses that are generated from the urban growth
demands. Barredo et al. defines nine such active land uses assigned to cells
including, residential continuous dense, residential discontinuous, residential
discontinuous sparse, industrial, commercial, public, private services and
abandoned land. The passive cell states are land uses that do not participate in
land use dynamics such as arable land, wetlands, forests and shrubs. The fixed
cell states are land uses that do not change spatially or temporally but affect the
land use dynamics such as water bodies, transportation facilities, and artificial non-
agricultural vegetated areas. And finally the transition cell states are construction
sites.
d) Neighborhood effect the neighborhood effect of all the cells surrounding the
central cell is computed by distance form the central cell and state of the cells. The
paper describes about 15 active and passive cell states used in computation of
calibrated weight of each neighborhood cell (Barredo and Kasanko).
e) Transition rules every grid cell is assigned a transition value based on
accessibility, suitability, zoning and neighborhood effect. Then each cell receives a
stochastic coefficient based on extreme value distribution. At each iteration a cell is
69


assigned with a rank based on the cells highest potential to attain a particular
state or land use. During the entire iteration each time a number of cells in a
particular state are checked so that they are equal to cell demands or objective.
f) Land use demands the land use demands for each cell space in CA model is
obtained from activity levels of each cell. The activity levels, which are developed
from general demographic and economic data, are initially converted to
productivity or density variables in order to compute the demand.
Barredo et al. research also demonstrated an urban CA model, which simulated urban
growth over the period of 30 years from 1968 to 1998. Historical datasets from MOLAND
(Monitoring Land use/cover Dynamics) were used to simulate and calibrate the urban
growth CA model. All the simulated results were compared with actual datasets. The above
presented variables such as zoning and suitability values were not used as the datasets as
they were not available. The CA model was evaluated and calibrated using three
techniques as follows,
a) Using matrices method (cell by cell comparison) to compare actual and simulated
datasets
b) Using fractal dimensions to compare actual and simulated datasets
c) Visual comparisons
The comparison results indicated a good visual similarity between simulated and actual
datasets although the simulated results were less fragmented compared to actual datasets.
Some of the grid cells with fixed state such as pastures were replaced by dynamic or active
state such as residential land uses. Although there were some differences in area and
radius plots between simulated and actual datasets, overall the pattern distributions
seemed concordant.
The suitability scores obtained in the phase 1 of the local urban land dynamics model were
generated by linear weighted sum of various factors. Some of the discrepancies in the
results as mentioned above could have been probably avoided by assigning cell fitness
based on non-linear relationships between the factors. Also there seems to be a confusion
between cell states, passive and fixed, where some of the passive cell states or land uses
could be classified under fixed and vice versa. For the neighborhood analysis mentioned
above a radius of 0.8 km was considered as buffered zone for analysis, it is not clear
whether the border cells were included or excluded from neighborhood analysis. The
70


analysis also considered distance from the central cell of the buffered region as a criterion
but it is not clear if adjacent cell states or distance within different cell states of the buffered
area were considered for any analysis. Finally the urban CA model is not dynamic in nature
as it is based on historical data, which could be improved by adding some spatial
parameters. Inspite of above all deficiencies most of the time CA generates satisfactory
results expect that the computational time is relatively large compared to some of the
similar techniques such as simulated annealing and genetic algorithms.
There is one more research effort published in 2002 similar to Barredo et al., is worth
reviewing as it deals with multi-objective land allocation problem similar to this thesis
problem. In 2002 Oliveira et al. research demonstrated goal programming technique for a
multi-objective land allocation problem for the study area, Santa Candida Farm (Parana,
Brazil). Goal programming (GP) is similar to linear programming only the difference being
GP can handle multiple conflicting objectives. The main objective of GP is to minimize the
deviation caused by goals or target values, which is achieved by defining an objective
function equal to weighted sum or vector sum of goals. Oliveira et al. paper describes eight
main goals set to allocate various land uses such as native areas, reforestation areas,
fields, swamps and permanent preservation in Brazilian forest. The study area considered
for GP is for the five year planning period and of 2000 ha in size located in General
Carneiro in Parana (Oliveira and Volpi). The eight goals are as follows,
a) Pine harvest here the goal is to increase pine harvest in reforested areas to meet
the pine plant industry demand
b) Araucaria harvest similar to the above goal, increase in araucaria harvest in
native areas to meet the demand of the araucaria plant industry
c) Erva-mate harvest to meet the demand of erva-mate plant industry an increase
in erva-mate harvest in native areas is required
d) Tourism increase in tourism in the farmlands of General Carneiro as it increases
revenue and thus increase in socio-economic value of the region
e) Pasture increase in pasture lands for buffalo grazing
f) Maintaining employment this goal is intended for the economic growth of the
farmlands
g) Increase in diversity of flora increase in diversity of species for environmental
preservation
71


h) Increase in diversity of fauna similar to flora, increase in diversity of fauna for
environmental conservation an increase in economy due to increase in tourism
Weighted goal programming technique was used in the Brazilian farm allocation problem.
Initially unitary weights were assigned to all the goals thus all goals have same priority.
Theoretical goals or target values were set from previous runs of linear programming for
each objective. Two main constrains in GP were goal (target value) constraints and area
constraints. The results indicated that the target values for the goals, Pine, Araucaria,
Erva-mate, tourism and pasture were met and rest of the goals could not be achieved. GP
was run for various weights 1000, 100 and 10, and the results indicated that as the weights
were increased the production of pine was reduced thus decrease in allocation of
reforestation areas (Oliveira and Volpi). The increase in weights also indicated an increase
in diversity of flora and fauna, thus achieving the environmental diversity goal. Therefore,
the allocation of reforestation areas and environmental diversity objectives were in conflict.
Several solutions were obtained by changing the priority and weights of the goals. Oliveira
et al. paper demonstrated good comparison between objectives by changing weights of the
goals through goal programming.
Goal programming technique used in above research demonstrates trade-offs between
various objectives although several objectives were not achieved. This also illustrates that
GP performs well for two objectives and as objectives increases in number GP fails the
optimization process. Objectives in GP are handled independently meaning they are
optimized one after another and treated as separate entities, whereas in reality in a multi-
objective problem, the objectives are related and have some sorts of correlation or linear or
non-linear relationships between them. A GP model integrated with a stochastic approach
could solve some of the above stated problems. Also for a model to be more realistic it is
essential to include spatial variables or parameters such as distance functions, contiguity
and compactness.
A research in the same year as above i.e. in 2002 demonstrated a multi-objective problem
using integer programming. The research paper by Aerts et al. demonstrated Integer
programming technique to solve multi-use land allocation problem or MULA. In this paper
raster data of size 8*8 cells is used to demonstrate four scenarios of IP to solve a MULA
problem (Aerts and Eisinger). Based on the performance of the four models, two models
were chosen to assess and evaluate to replace a mining area with a suitable land use in
72


Galicia, Spain. In general two main objectives were considered for the IP models,
maximizing compactness and minimizing costs. The main focus of the paper is not only to
simulate a MULA problem but to create a model, which would run faster and is capable of
solving larger problems.
The four models are as follows,
a) Non-linear integer program here two objectives are considered, minimize cost
and maximize compactness. The constraints are there can be only one land use
per grid cell, area restrictions for particular land use and border conditions for
compactness objective (Aerts and Eisinger). Efficient solutions were obtained by
various combinations of parametric weights assigned to each objective function.
b) Linear integer program this model is similar to the above non-linear IP model just
an inclusion of additional integer variables and linear constraints. The
compactness objective modified a little bit in this linear model. Linear IP solver is
used to solve the problem but with more variables as compared to the above non-
linear model.
c) Linear integer program using buffer cells here the compactness is measured by
minimizing buffer cells around the core central area of concern. Every area in this
model is surrounded by a buffer zone equivalent to one parcel area. Thus by
minimizing the buffer cell number the core areas tend to cluster. The objectives are
similar to model 1 and 2 but additional constraints are added to make sure each
core cell is surrounded by buffer cells or another core cell of same land use.
d) Linear integer program using aggregated blocks here the grid cells are converted
into blocks thus the compactness objective is defined as minimizing number of
blocks of same land use type. According to Aerts et al. the block size impacts
allocation process, the larger the blocks more information is lost. The objectives
here are minimizing number of blocks and minimizing costs.
All the model results are evaluated under the following two criteria,
a) Comparing the computational time of each model with the degree of compactness
achieved by each model.
b) Comparing all the models for reliable results or selecting the model with best
global optimum result.
73


The first criterion above was obtained noting the time to obtain optimum results for all the
models and then compare the CPU time. Compactness is measured by computing the sum
of all adjacent cells with same land use, which is referred as standard compactness. The
second criterion was obtained by evaluating each model for non-inferior solutions. Both the
criteria were evaluated for grid size of 8*8cells. Also the models were compared under
single objective condition, where compactness was favored. Then tradeoffs between
objectives, cost and compactness, were evaluated for all the four models. Overall model
3(Linear integer program using buffer cells) and 4 (Linear integer program using buffer
cells) performed well compared to model 2 (Linear integer program) and 1 (Non-linear
integer program).
Model 3 and 4 were applied in the case study area, where a mine area needs to be
replaced by new land use. The case study area is located in northwestern part of Spain,
Galicia, which is of size 25 sq. km (Aerts and Eisinger). The objectives were similar to the
above model, minimizing costs and maximizing compactness. The main constraints were
portion restrictions of various land uses such as, 48% for forests, 26% for water and 26%
for shrubs (Aerts and Eisinger). The study area of 300*300 cells was impossible to
evaluate using model 3 and 4 so the area was reduced to samples of 16*16 and 30*30
cells (Aerts and Eisinger). For 16*16 cell area the results indicated global optimum by
models, 3 and 4 (Aerts and Eisinger). For 30*30 cell area the model 4 did not perform well
thus was eliminated from analysis and model 3 was used to obtain the global optimum
(Aerts and Eisinger).
Thus the models, 1, 2 and 4 could not handle larger areas whereas model 3 could handle
about 50*50 cell area but overall all the models produced similar results indicating global
optimum. The integer programming land allocation problem demonstrated above is a good
illustration of comparisons of computational capacity of various scenarios. Most of the time,
when modeling complex problems such as land allocation, computational times are given
less attention but for the model to be more realistic this criterion should be considered. The
IP models above optimize the two objectives, compactness and costs giving more weight
to one objective at a time, which is less realistic and could be improved by equally
weighing the objectives or a mechanism where none of the objectives dominate over other
like in genetic algorithms and simulated annealing.
74


Before getting into simulated annealing, genetic algorithms and other stochastic based
optimization models lets review one of the most famous linear models, Lowry model,
which deals with urban land allocation problems. In 2002 Jun et al. demonstrated three
kinds of modified Lowry models in order to eliminate the limitations imposed by original
Lowry model. The original Lowry model developed in 1964 by I. S. Lowry is based on basic
economic mechanism of urban areas (Jun). The land uses, industrial, residential and
services are predicted based on the population and service potential of particular areas
under the land use constraints, threshold population and housing densities. Three main
disadvantages of Lowry model listed by the authors are inadequate behavioral or economic
theory, zonal aggregation of employment types and lack of inclusion of urban demand and
supply interactions, as Lowry model is demand driven model (Jun).
In order to overcome the limitations of Lowry model the three modified Lowry models
includes additional coefficients such as basic household trip data and trade flow data within
urban areas (Jun). In order to incorporate interregional urban behavior in the modified
models the authors suggest treating cities as interacting zones. Since trade-flow data is
difficult to obtain the authors also suggest deriving them from gravity models. The three
proposed models by Jun et al. are as follows,
a) Equilibrium model
b) Linear Programming model with land supply constraints
c) Modified dual linear programming model based on economic efficiency
The first model, equilibrium model incorporates multi-zonal urban input-output model,
which includes land use demands by land use types, inter-industrial and interspatial
linkages. The equilibrium model simulates relationships between variables, which are as
follows,
1) Outputs of various land uses including industries and services
2) Employment classified by various land uses
3) Land requirement coefficients of various land uses including commercial,
residential and industrial areas
4) Land use demands
5) Work and shopping trip matrices
6) Commodity flow matrices.
75


These variables are used to obtain land demand classified by land use type, which is either
represented by sector or zone. The second model, linear programming (LP) model is an
improvement over the first one as it includes urban supply constraints. Here the objective
function is defined as maximization of regional income under land supply constraints. The
main assumption in the LP model is unlimited labor supply. The input-output model used in
first model is used in LP model to compute wages, interest rate and rents. The land
demands corresponding to land uses, industries, residential areas and services are
determined using four endogenous variables such as total output (summation of output of
various land uses) and number of workers classified by residence, shopping areas and
employment. According to the authors the predetermined land supply constraints in LP
model are major limitations to the allocation results, which do not reflect actual decision
process.
The third model, dual LP model is an improvement over the second and the first model as
it includes land values to determine land allocation areas. Equalizing constraints procedure
is used in the third model, which consists of two main stages, the first stage is to formulate
a dual LP model corresponding to primal formulation and second stage is to modify the
dual LP model by adding constraints such that all shadow prices for land parcel are equal.
These shadow prices corresponding to each land use are obtained from the primal
formulation. The shadow prices specify the marginal social value per unit change of each
land use and when these marginal values are equalized economic efficiency is attained.
The allocation process depends on the marginal value, higher the marginal value of a land,
more land area is allocated to various land use types. According to the authors the dual LP
model is a significant improvement over first two models and the original Lowry model as
the model incorporates more local urban developments to allocate various land uses.
All the three models proposed by Jun et al. are demonstrated using a theoretical dataset
for a metropolitan area with three zones. The sectors 1 and 2 are assumed to be industrial
sectors and sector 3 is assumed to be commercial and service areas. All the three models
are compared corresponding to objectives including total output value, work locations,
shopping locations and residential locations. The dual LP model performs better compared
to equilibrium and LP model. Also all the three models were compared corresponding to
land uses allocated to three sectors. The dual LP model allocated more land parcels (units)
to industrial uses and less land units to residential uses. According to the authors the
76


equilibrium model can be used to study impact of residential and commercial land uses in
an area, LP model can used to study urban development patterns and dual LP model can
used to study land use policies.
All the three modified Lowry models are an improvement over the original Lowry model,
which is based on economic theory. Land allocation Lowry models are developed from only
one perspective, which is economic theory but in order to attain sustainable land use
development it is essential to include environmental related parameters such as
preservation of environmentally sensitive areas. As we know that, the better the land
information more improved the land allocation model gets thus it is essential to include
spatial analysis within allocation framework analysis. Also most of the economic land
allocation model lead to substantially patchy landscape thus an inclusion of spatial analysis
improves the model. Apart from the several linear, integer and goal programming land
allocation models discussed above, in 2002 a simulated annealing land allocation model
was introduced. Since then stochastic based land allocation models have become popular
and have been widely used in modeling various aspects of land use planning. One such
model in 2002 by Aerts et al. demonstrated a multi-use land allocation problem using
heuristic algorithm, Simulated Annealing (SA). SA is used in solving a land allocation
problem in the study area, Galicia, Spain, where a one-time mine area needs to be
restored and an appropriate land use needs to be allocated to that area (Aerts and
Heuvelink). Two objectives were chosen for the SA model, maximizing compactness and
minimizing costs of the land use under constraints, which includes restrictions in the type of
land use to be allocated, compactness and cost restrictions. Earlier in 2002 Aerts et al.
demonstrated a similar model with the similar objectives as above using Integer
programming, which is reviewed above.
Simulate Annealing is a randomized algorithm, which is designed to find global optimal
solutions for a large problems with local maxima and minima. In SA initially large
perturbations are allowed but as the iterations increase (also called cooling phase) the
probability of perturbations are decreased until the solution converges on best local
maximum (Aerts and Heuvelink). According to the authors, SA is capable of handling large
datasets, non-linear functions, and spatial compactness helps in decision making process.
SA is used in the case study for allocating land use suitable for the former mining area.
77


The study area for the SA model is situated in northwestern part of Spain, As Pontes in
Galicia. As Pontes was a lignite mine of total area 25 sq. km., which is divided into two
zones, exploitation area and dump site (Aerts and Heuvelink). The exploitation area has
two pits of 200m to 250 m depth, which are excluded from the restoration process as the
site is considered to be naturally filled with groundwater and convert into lake over time.
The dump site is a waste fill area, which is included in the SA analysis and will be restored
to its original state before the land was used for mining. Thus, land uses will be allocated to
the dumpsite based on minimum costs and maximum spatial compactness.
For the allocation model the study area is divided into 300*300 cells, where each cell is of
25*25 m size (Aerts and Heuvelink). Borland Delphi aid ESRI MapObjects (2001) were
used to analyze and visualize input and output (land use maps) data. The main objectives
considered in the restoration of the dumpsite are lower cost involved in restoration process
and less fragmented areas to promote recreational activities and increase the natural value
of land. Since the main aim of the allocation process is to restore the dumpsite to its pre-
mining state, the constraints considered are area restrictions of specific type of land use
such as 60% of forests, 22% of shrubs and 18% of water (Aerts and Heuvelink). Physical
attributes such as slope and elevation were considered as main contribution to the
restoration costs and elevation was considered to be a crucial criterion in the allocation of
water bodies to the dumpsite. The optimization results indicated that forests were allocated
to flatter slopes, shrubs were allocated anywhere in dumpsite irrespective of any physical
attributes of the area and water bodies were allocated at the areas with lower elevations.
Thus according to the authors, SA was successfully used in the allocation of various land
use types, optimizing spatial compactness, a non-linear objective and cost objective.
Simulated annealing (SA) performs similar to most of the stochastic based techniques and
it is widely used in multi-objective or multi-criteria problems such as one above. The above
case is a good demonstration of SA application the only drawback being the computational
time of SA is significantly higher compared to other stochastic based techniques such as
genetic algorithms. In 2003 a research effort by Almeida et al. demonstrated a land
allocation model using an empirical land use algorithm within a Cellular Automata
framework. The land use allocation model demonstrated using a medium sized town
Bauru, west of Sao Paulo State, Brazil (Almeida and Batty). The model was developed for
the time period 1979 to 1988. The initial (1979) and final (1988), land use maps and all
78


other data were represented in raster format using 100*100m grid size. The data used for
land allocation model were pre-processed using SPRING GIS, which is a Brazilian GIS and
remote-sensing image processing software. The initial data for allocation modeling had
about 316,063 cells (487*649 grid) (Almeida and Batty). The land use data, initial and final
were processed through IDRISI in order to obtain cross-tabulations, which were in turn
used to compute land use transition rates.
The study area is divided into total of eight land uses such as residential, industrial,
services, commercial, institutional, non-urban land uses, mixed use and recreational land
use, of which five land uses were allocated from 1979 to 1988 (Almeida and Batty). A total
of twelve physical and socio-economic factors such as distance to various land uses, areas
served by water supply and so on, were identified to model the land allocation. Initially
these factors were evaluated for inter-dependencies corresponding to particular land use,
using Cramer's statistical test (based on chi-square test) and comparison between factor
map distributions (based on joint uncertainty). There were overall 12 factors evaluated for
inter-dependencies corresponding to five land use transitions. There were some visual
comparisons done between the factor maps. After the initial variable selections, weights
were assigned to the chosen factors based on Bayes rule of conditional probability
(Almeida and Batty). In order to compute transition probabilities, first land use type
corresponding to a particular cell (cell A) in raster data is evaluated for frontier cells, which
are the cells with land use type other than cell A. These frontier cells are considered as
potential cells for allocation. When the neighborhood cells of cell A is surrounded by similar
land use types then the edge of group of cells form frontier. This small patch of cells with
same land use type is called as reduced set. Once a reduced set is identified in the raster
dataset then the transition probability of the cell in question is weighted based on the
amount of land use type in the eight-cell Moore neighborhood. ER Mapper is used to
demonstrate the transition probabilities.
These probabilities are used in allocating land uses and thus iterated until the required
amount of land use type is achieved. The allocation model fitness was assessed using a
technique, where land use distributions are compared at different resolutions. There were
overall three resolutions used for comparison, 3*3, 5*5 and 10*10 cells (Almeida and
Batty). Results indicated a good fit for all the resolutions, the fits were above 0.90. The land
allocation model illustrated by Almeida et al. is based on elementary probabilistic methods
79


within CA framework, where most of the primary and secondary inputs in the model are
obtained from external resources or software packages. Thus there is always a chance of
high uncertainty in the model results. The CA model presented above is a robust model as
it includes statistical inter-relationships between factors, statistical analysis and evaluation
but there is no evidence of spatial correlation analysis. The cell resolution (here, 100 m)
seems to be a lower than usually used in several spatial analyses, which is 30 m, thus
there might be some loss of information. The frontier cell logic seems to prevent patchy
landscape but it is not clear if constraint areas such as environmentally sensitive areas are
excluded from the frontier cell allocation. Finally, the transition probabilities are based on
reserved number of cells belonging to a particular type of land use, which could be
improved by adding some more parameters such eb spatial correlation with other and
adjacent land uses. Overall the CA model produces acceptable results, which are validated
by statistical procedures and multiple resolution fitting procedure.
The next research paper uses a stochastic based approach to model land use allocation
along with spatial analysis. The research effort by Wang et al. in 2003 demonstrated a
multi-objective land allocation model at watershed level using inexact-fuzzy algorithm and
spatial analysis. The inexact algorithm is used in optimizing various economic and
environmental objectives under several constraints (Wang and Yu). The spatial analysis
uses the results from the optimization model, which are recommended optimal land use
changes classified by hydrologic sub-areas. The model is demonstrated using Lake Erhai
basin, China as study area. The total area of the basin is about 2565 sq. km., where 10%
of the basin is covered by Lake Erhai, 45% by forest, 28% by farmland, 16% by barren
land use and only 1% of the basin area is urban and industrial uses (Wang and Yu). The
main objective of land allocation in Lake Erhai basin is to conserve the environment and
economic development of the region. For optimization purposes Lake Erhai basin is
divided into seven sub-areas by the local authorities and experts based on administrative,
hydrological and ecological zones. The modeling is done for the 15 year planning period.
Four objectives (maximize or minimize) are considered for the optimization model, they are
forest cover, soil loss, water quality (especially nitrogen loss, phosphorous loss and COD
discharge) and economic development. Few of the constraints for the fuzzy optimization
model are as follows,
80


a) Activities related to forests
b) Water demand and supply
c) Water quality
d) Soil loss
e) Activities related to industries
f) Tourism activities
g) Agricultural production
h) Land availability
Since the model is formulated using unknown distributions of decision variables,
constraints and objective functions except for few variables whose distributions could be
assumed within a particular range, the model is named as inexact fuzzy multi-objective
model or programming (IFMOP). Every iteration result of IFMOP model is presented to
decision makers for further improvement hence making the optimization model an
interactive approach. The decision makers evaluate the results based on the following
criteria,
a) Accomplishment of objectives and the trade-offs between them
b) Consideration of model constraints
c) Uncertainty level of the optimization model
The optimization model is run for four different environmental-economic trade-offs
scenarios. Two of the scenarios consider water quality as their highest priority objective.
The other two scenarios focus on economic objective and water pollution control objective
respectively. The optimization model results indicate that tourism needs to be maximized
as it has lower potential for pollution and high economic value and increase in forests to
improve the water quality of Lake Erhai (Wang and Yu). The results of the model are
implemented in the spatial land allocation model.
Three factors are taken into account in order to allocate the land uses in the spatial model,
they are existing land use, land conversion rules and land suitability. The study area, Lake
Erhai basin is mostly rural in nature with only 1% attributed to urban land use. Thus the
existing urban land uses were not used in allocation process. In order to allocate future
land uses to the study area land suitability analysis was conducted based on the following
criteria,
81


a) Access to transportation facilities
b) Consideration of physical features such as elevation, slope, flood plain,
groundwater 'aquifer and soil
c) Development costs and benefits
In order to allocate paddy, dry land, vegetable farming, forest industry and urban land uses
slope and distance to water bodies were considered and constraints were set accordingly.
The distances to transportation facilities and other land uses were computed using buffer
function in ESRI Arcview 3.x (Wang and Yu). Overlay function was used to obtain various
constraint and factor layers. There were several criteria set for land allocation such as flat
areas for paddy farming, steeper slopes for forests or dry land or vegetable farming and
areas farther from water bodies for industrial use to reduce environmental impact. The land
allocation analysis was performed using Avenue scripting language in Arcview 3.x. Thus
land allocation maps were generated successfully using the IFMOP and GIS models. The
above illustration of fuzzy optimization model and spatial model together represents a
robust model. The distributions of the decision variables in the fuzzy model are not
assumed but explored and estimated, which makes the model much stronger. The spatial
model includes spatial relationships between various land uses, which are essential in land
allocation models. It is not clear how the inputs from fuzzy model are used in spatial model
and also it seems none of the spatial criteria such as compactness, contiguity or
neighborhood analysis is included in the above model. The model could be improved by
integrating fuzzy concept and conducting tradeoff analysis within spatial framework.
In 2003 there was one more research effort related to neighborhood analysis and other
spatial criteria to study land use patterns. The research article by Verburg et al. analyzes
and suggests a methodology for accounting neighborhood interactions in land allocation
models. The primary focus of Verburg et al. research is to assess and evaluate
neighborhood characteristics of land uses and propose an empirical method to
demonstrate the interaction between neighborhood land uses (P. H. Verburg, A method to
analyse neighbourhood characteristics of land use patterns). Neighborhood in spatial
context can be defined as a cell or set of cells that are a certain distance away from the
central cell (grid cell of concern) a are spatially related to the central cell. The author
defines a term called enrichment factor, which represents the neighborhood characteristics
of a specific land use. Enrichment factor is defined as a proportion of land use type in the
82


neighborhood of a location to the same land use type in the map as a whole. For example,
if the proportion of a land use type of neighborhood of a location is equal to the whole map
average then the enrichment factor is 1. The enrichment factor was computed using C++
programming based on Moore neighborhood. Thus for a particular land use type, the
average neighborhood characteristic is the average of all the enrichment factors
corresponding to each cell belonging to the same land use type. The enrichment factor
was computed for the study area, Netherlands using 1989 dataset, especially for the areas
with prominent land use changes between 1989 and 1996 (P. H. Verburg, A method to
analyse neighbourhood characteristics of land use patterns). The 1989 and 1996 land use
maps were in the raster format of 500*500 m resolution. The land use types for the study
area were aggregated and reclassified from 33 to ten land use types. The enrichment
factor compared with land use changes using logistic regression. The results indicated that
residential, recreational and industrial land use types occur in clusters. Arable land was
always found be in the neighborhood of agricultural lands. A positive enrichment factor was
found for the residential areas when compared with commercial land uses, which indicated
that residential land use is mostly allocated near commercial land parcels.
In addition to studying local neighborhood characteristics, regional variations in
neighborhood characteristics were studied. For studying regional variations the study area
was divided into two regions based on soil types, sandy soils and clayey soils. The
enrichment factors for the two regions were computed separately and compared with the
factors for the whole region. The neighborhood characteristics were also compared at
various scale levels of dataset such as 500*500m and 25*25m resolutions. The results
indicate that neighborhood characteristics of land uses differ by scale, region and time-
period. The authors concluded that for brge scale datasets in addition to studying
neighborhood characteristics, accessibility, spatial policies, and environmental factors are
required to assess and evaluate spatial patterns. Although according to Verburg et al.
neighborhood interactions play an important role in land allocation models, especially
models based on transition probabilities such as Cellular Automata. The research by
Verburg et al. is a good demonstration of studying clusters in landscape and could help
boost any stochastic based spatial models in optimization of land allocation. Neighborhood
analysis, spatial correlation and other spatial analysis are very essential in modeling land
allocation problems. The next research article illustrates land allocation modeling based on
83


spatial analysis using raster data. This thesis research uses raster data to model land
allocation thus it is essential to review work done in similar areas in order to avoid
repetition of research efforts and also to gain more knowledge in improving research work.
The research article by Cromley et al. in 2003 demonstrated a large scale land allocation
problem using Dual Simplex method. A simplex algorithm is a step-by-step iterative
process used in solving a linear programming problem, which analyzes one feasible
solution at a time until an optimal solution is obtained (Cromley). The dual simplex method
illustrated in Cromley et al. research article is used to solve a scale-independent problem,
where only the information of one pixel (one grid cell of raster data) is stored in the memory
at a time. For the dual simplex algorithm to work the land use demands are provided and
suitability scores are computed from the criteria corresponding to the land uses to be
allocated.
In Cromley et al. research dual variables considered were value or rent of the land parcel
and value of each activity. Dual algorithm initially chooses one of the dual values and
computes the other dual value corresponding to each land pixel (Cromley). The following
are the steps explaining the dual simplex technique described in the research article by
Cromley et al.:-
1) Initially the activity value is set to zero
2) Using the suitability weighted scores (specified by the user) and activity value
form stepl the land parcel rent value is computed
3) The grid cell or land pixel corresponding to highest rent is initially chosen to
allocate the corresponding activity
4) The level of primal infeasibility corresponding to each activity is computed by
checking if the total allocated activity exceeded the demand
5) If the allocated activity is more than demand then the solution is primal infeasible
otherwise the allocation is feasible. For primal infeasible solution the activity value
is increased by one value and steps 2 thru step 5 is repeated
Thus the dual simplex method stores suitability score for one pixel at a time and not storing
the information of the complete raster data or all the grid cells.
The dual simplex technique in Cromley et al. research used Von Thunen concept in step 1
and 2 for the first iteration described above (Cromley) Von Thunen model is a technique
84


that determines the location and percentage of various land uses by allocating these
activities (land uses)) to land cover with highest rent value, which is difference between
price of land activity and corresponding production cost (Cromley). The authors describe a
case study to demonstrate the dual simplex technique.
The dual simplex technique is used to allocate five land uses or activities such as
residential, commercial, conservation, farmland and manufacturing in northeastern part of
Connecticut. The raster data contains total of 289,773 pixels, each pixel of 30*30m size
(Cromley) The demand in number of pixels corresponding to each activity is given.
Several criteria corresponding to each activity were specified and data related to these
criteria were converted to suitability scores using score range procedure. The suitability
scores ranged from 0 to 255, where 0 is least suitable and 255 is defined as most suitable
(Cromley) Results indicated that farmland was most valuable activity followed by
manufacturing, commercial, residential and conservation land uses. The algorithm
converged at 97th iteration thus producing an optimal solution. The main disadvantage of
the above method is choosing the rent, a high rent value of a land cover would permit
allocation and lower rent value would prevent the activity allocation. The dual simplex
model uses very few decision variables to allocate land uses and has a major
disadvantage of storing minimum information. Since the model cannot accommodate more
than one pixel information, spatial analysis is out of the picture. Thus the model could be
improved by integration of more statistical and mathematical techniques.
Most of the above research papers reviewed above dealt with land allocation in various
areas other than ecotones. Ecotones are growing problem now-a-days due to the
diminishing sub-urban areas and expansion of patchy urban zones. Ecotone is usually
defined as transition zone between two or more community zones, which could be two
ecosystems where there is a region of rapidly changing species. In 2004 a research article
by Svoray et al. demonstrated an urban land use allocation model in ecotone areas. The
two main objectives of the ecotone research are development of an integrated tool
containing GIS based multi-criteria technique and habitat heterogeneity model and the
second objective is to apply the integrated tool in the study area (Svoray and (Kutiel)),
Maale Adumim city in Israel. Maale Adumim area is considered to be very diverse
containing a wide range of plants, the largest in Israel, it is also a Mediterranean to semi-
arid ecotone area (Svoray and (Kutiel)). Thus the multi-criteria allocation model considers
85