[ieee 2011 fourth international workshop on advanced computational intelligence (iwaci) - wuhan,...

6
AbstractIntegrating optimization techniques with GIS has recently been a rapid expansion of interests and researches in the area of spatial decision support (SDS) and resource allocation. Land use planning or allocation (LUP or LUA), as one of main resource allocation issues, refers to the optimal allocation of multiple sites of different land uses to an area, which not only relates to the conditions and quantity of land, but also should consider the spatial relation of sites and other influences. Recent developments in this field focus on the design of allocation plans that utilize mathematical optimization techniques. In this paper, we firstly describe LUP with mathematics and formulate a multi-objectives optimization model for it, and then demonstrate how genetic algorithm (GA) can be used to solve this non-linear and multi-objectives spatial optimization problem. The objectives of optimization model consider both planning cost and spatial pattern of the land use. The method is applied to a case study in China. I. INTRODUCTION AND use planning or allocation (LUP or LUA), as one of main resource allocation issues, may be defined as the process of allocating different competitive land uses or activities, such as agriculture, forest, industries, recreational activities or conservation, to different units of a landscape to meet the desired objectives of land managers(Aerts, et al, 2002). As a typical non-linear and multi-objectives spatial optimization problem, LUP require input from extensive spatial databases and involve complex decision-making problems. Recently, much attention has been paid to solving resource allocation problems with multi-criteria decision-making (MCDM) techniques in a geographic information system (GIS) environment. There are two basic MCDM techniques suitable for implementation in a GIS (Aerts, et al, 2002). The first is multi-criteria analysis (MCA), which involves the evaluation of a relatively small set of allocation alternatives. These alternatives, usually about three to five and rarely more than ten, are defined beforehand and are simply evaluated against each other. Furthermore, in LUP a set of allocation alternatives is not available and difficult to define. Hence, research in this field has changed focusing to techniques that generate an optimal allocation alternative using optimization techniques (Chuvieco 1993, 1997; Aerts 2001; Aerts and Heuvelink 2002). These so-called design techniques form the second branch of basic MCDM techniques. Design Manuscript received Sept. 21, 2011. This work was supported in part by the Zhejiang Provincial Natural Science Foundation of China under Y5080259. Ren zhouqiao is with the Zhejiang Academy of Agricultural Sciences, Hangzhou 310021 CHINA, phone:86-571-86419079; fax:86-571-86404270; e-mail: [email protected]. Lu xiaonan is with the Zhejiang Academy of Agricultural Sciences, Hangzhou 310021 CHINA; e-mail: [email protected]. techniques generate an optimal solution from a much possibly infinite set of alternatives. In the past, numerical optimization techniques such as linear integer programming (LIP) are used for this purpose, and these are assembled under the term multi-objective mathematical programming (MMP). There are many examples that use MMP in combination with GIS (Cova and Church 2000), but the application of MMP techniques in a spatial context is far from straightforward. One major difficulty is the large dimensionality of the problems. Furthermore, some of the criteria involved non-linearities. For instance, in land use planning, large and compact areas of the same land use are preferred, instead of small and broken. The use of MMP techniques for LUP problems is limited to areas with a much reduced spatial resolution or restricted grid size. (Aerts, et al. 2002). Then non-classical heuristic approaches, such as simulated annealing, greedy growing algorithms, and tabu search, were also found applicable to this problem. However, they do not guarantee the optimal solution. Recently, Genetic algorithm (GA), biological evolution-based heuristic approaches, has been found suitable enough to tackle this problem. GA can make a remarkable balance between exploitation and exploration of a search space. Matthews et al. (2000) explored the potential of applying GA to spatially integrated land-use management problem. Stewart et al. (2004) used a GA, along with a goal reference point approach, to another spatially integrated problem, involving two objectives: minimization of cumulative cost, and compactness of areas under each land-use. The main objective of this paper is to model an optimization tool for solving non-linear and high-dimensional land use planning problems. In the next section we will provide a mathematical formulation for the land use planning problem, which includes multiple conflicting and spatial related objectives. This formulation gives rise to a nonlinear combinatorial optimization problem, for which a specific GA is developed in Section III. And in Section IV , the methodology is applied to a practical land use planning problem in China. II. LAND USE PLANNING AS A MULTI-OBJECTIVE OPTIMIZATION PROBLEM Land use planning as defined above, is an optimization problem, where different objectives of land managers are to be optimized, subject to the restrictions imposed on the selection of an effective land use for a unit. Every unit of a landscape has different suitability to perform different functions, and Land use planning should depend on the proper evaluation of the suitability of land to sustainability support many services that a society needs. However, in the traditional methods, much more attention is paid to the Using GA for Land Use Planning Zhouqiao Ren and Xiaonan Lu L 64 Fourth International Workshop on Advanced Computational Intelligence Wuhan, Hubei, China; October 19-21, 2011 978-1-61284-375-9/11/$26.00 @2011 IEEE

Upload: xiaonan

Post on 02-Mar-2017

212 views

Category:

Documents


0 download

TRANSCRIPT

Abstract—Integrating optimization techniques with GIS has recently been a rapid expansion of interests and researches in the area of spatial decision support (SDS) and resource allocation. Land use planning or allocation (LUP or LUA), as one of main resource allocation issues, refers to the optimal allocation of multiple sites of different land uses to an area, which not only relates to the conditions and quantity of land, but also should consider the spatial relation of sites and other influences. Recent developments in this field focus on the design of allocation plans that utilize mathematical optimization techniques. In this paper, we firstly describe LUP with mathematics and formulate a multi-objectives optimization model for it, and then demonstrate how genetic algorithm (GA) can be used to solve this non-linear and multi-objectives spatial optimization problem. The objectives of optimization model consider both planning cost and spatial pattern of the land use. The method is applied to a case study in China.

I. INTRODUCTION

AND use planning or allocation (LUP or LUA), as one of main resource allocation issues, may be defined as the process of allocating different competitive land uses or

activities, such as agriculture, forest, industries, recreational activities or conservation, to different units of a landscape to meet the desired objectives of land managers(Aerts, et al, 2002). As a typical non-linear and multi-objectives spatial optimization problem, LUP require input from extensive spatial databases and involve complex decision-making problems.

Recently, much attention has been paid to solving resource allocation problems with multi-criteria decision-making (MCDM) techniques in a geographic information system (GIS) environment. There are two basic MCDM techniques suitable for implementation in a GIS (Aerts, et al, 2002). The first is multi-criteria analysis (MCA), which involves the evaluation of a relatively small set of allocation alternatives. These alternatives, usually about three to five and rarely more than ten, are defined beforehand and are simply evaluated against each other. Furthermore, in LUP a set of allocation alternatives is not available and difficult to define. Hence, research in this field has changed focusing to techniques that generate an optimal allocation alternative using optimization techniques (Chuvieco 1993, 1997; Aerts 2001; Aerts and Heuvelink 2002). These so-called design techniques form the second branch of basic MCDM techniques. Design

Manuscript received Sept. 21, 2011. This work was supported in part by the Zhejiang Provincial Natural Science Foundation of China under Y5080259.

Ren zhouqiao is with the Zhejiang Academy of Agricultural Sciences, Hangzhou 310021 CHINA, phone:86-571-86419079; fax:86-571-86404270; e-mail: [email protected].

Lu xiaonan is with the Zhejiang Academy of Agricultural Sciences, Hangzhou 310021 CHINA; e-mail: [email protected].

techniques generate an optimal solution from a much possibly infinite set of alternatives.

In the past, numerical optimization techniques such as linear integer programming (LIP) are used for this purpose, and these are assembled under the term multi-objective mathematical programming (MMP). There are many examples that use MMP in combination with GIS (Cova and Church 2000), but the application of MMP techniques in a spatial context is far from straightforward. One major difficulty is the large dimensionality of the problems. Furthermore, some of the criteria involved non-linearities. For instance, in land use planning, large and compact areas of the same land use are preferred, instead of small and broken. The use of MMP techniques for LUP problems is limited to areas with a much reduced spatial resolution or restricted grid size. (Aerts, et al. 2002).

Then non-classical heuristic approaches, such as simulated annealing, greedy growing algorithms, and tabu search, were also found applicable to this problem. However, they do not guarantee the optimal solution. Recently, Genetic algorithm (GA), biological evolution-based heuristic approaches, has been found suitable enough to tackle this problem. GA can make a remarkable balance between exploitation and exploration of a search space. Matthews et al. (2000) explored the potential of applying GA to spatially integrated land-use management problem. Stewart et al. (2004) used a GA, along with a goal reference point approach, to another spatially integrated problem, involving two objectives: minimization of cumulative cost, and compactness of areas under each land-use.

The main objective of this paper is to model an optimization tool for solving non-linear and high-dimensional land use planning problems. In the next section we will provide a mathematical formulation for the land use planning problem, which includes multiple conflicting and spatial related objectives. This formulation gives rise to a nonlinear combinatorial optimization problem, for which a specific GA is developed in Section III. And in Section IV , the methodology is applied to a practical land use planning problem in China.

II. LAND USE PLANNING AS A MULTI-OBJECTIVE OPTIMIZATION PROBLEM

Land use planning as defined above, is an optimization problem, where different objectives of land managers are to be optimized, subject to the restrictions imposed on the selection of an effective land use for a unit. Every unit of a landscape has different suitability to perform different functions, and Land use planning should depend on the proper evaluation of the suitability of land to sustainability support many services that a society needs. However, in the traditional methods, much more attention is paid to the

Using GA for Land Use PlanningZhouqiao Ren and Xiaonan Lu

L

64

Fourth International Workshop on Advanced Computational Intelligence Wuhan, Hubei, China; October 19-21, 2011

978-1-61284-375-9/11/$26.00 @2011 IEEE

t j

i

Fig. 1. Model for a landscape

U11 U12 U13 U14

U21 U22 U23 U24

U31 U32 U33 U34

U41 U42 U43 U44

economic return, but the environment impaction and social efficiency is ignored. Generally, mathematical programming generally provides the optimum area for each land use type, which is often termed as quantity structure optimization techniques, but does not indicate the geographic location of the area, with the exception of the integer programming models. It can be applied complementarily with MCA, using the results of one mathematical programming model as input variables of a MCA, but it will not always compatible due to the complexity of land use (Li Jun 2006). It also is called ‘two steps’ method. Based on this, we put forward to design a multi-objective mathematical model combined the quantity structure and the spatial pattern to achieve the synchronized goal.

A. Basic Mathematical D escript for LUP For the ease of

mathematical analysis, a landscape can be represented by atwo-dimensional grid, as shown in Fig.1 by i and j axes of the three-dimensional matrix, where each grid represents a unit of thelandscape. Then a unit can be identified by its location (i, j) in the landscape. The third axis of the matrix, the t- axis as shown in Fig.1, represents the time-scale of a unit over a planning horizon. In practice, the time-scale often ishandled simply with base-time (current) and target-time (planning). Let iju be the land use allocated to the cell (i, j).For convenience, let us suppose that possible land uses are labeled from 1 to K, so that

'kuij � , � �Kk ,...,2,1' �A land use map is an allocation of a land use to every grid

cell in the region with I Rows and J Columns, and our aim is to identify the land use map which best achieves the decision maker’s objectives. It is useful to express the land use map interms of I×J×K binary variables ijkx , such that 1�ijkx if

kuij � , and 0�ijkx otherwise. With this formulation it is recognized that the selection of a land use map is an integer programming problem involving I×J×K binary variables. By definition we would require the condition as below.

11

���

K

kijkx MjNi ,...,1,,...,1 ���

B. Objective Functions in LUP Problem 1) Minimization of sum of cost: In many researches,

economic return is a very important objective function in model. It is computed by

��

�K

kkkE exf

1 (1)

where kx , ke are the number and economic value of land use type k, respectively. Obviously, it is correspondingly defined in a certain range when the ranges of total permissible areas under different land uses were provided in the original problem. In fact, the range could be obtained by MMP for land quantity structure optimization. In this paper, economic return is neglected in LUP model, instead the cost is introduced. These ranges have been considered arbitrarily in the present work for illustrative purpose only. Where the cost means how much we should pay off for the allocation, changing current land use type to another. In practice, the planning can be easily taken into practice if the cost is lower, and it will be suspended otherwise, so that there exist minimizing objective of the form:

��� �

�N

i

M

jijcfijcf Cxf

1 11 (2)

where ijcfC is the cost for land use type f applied in unit (i, j)

which is used for c in current. ijcfC in the planning region can be computed using (13) below.

2) Maximization of land use suitability index: Every unit of a landscape has different suitability to different land use type. One of the most important aims of LUP is set a reasonable land use to every unit. The allocation should satisfy the requirement of land use suitability.

���� � �

�K

k

N

i

M

jijkijk sxf

1 1 12 (3)

Where ijks is the result of suitability evaluation of land use k

for the cell (i,j), ijks can be computed by many methods, since in 1976 FAO published A Framework for Land Evaluation which allowed standardization of methodology and terminology. The ijks also be used in land use type change index computation.

3) Maximization of land use k compactness index: Recently, much attention has been paid to spatial pattern of land use, especially with the development of landscape and ecology science, where GIS acts as an important role for quantifying and presenting of spatial pattern. There exist a number of spatial attributes indicating the pattern extent to which the different land uses are connected, contiguous or fragmented across the region, but not every attributes is suitable for LUP. In this paper, the measures of compactness described by Aerts[2] is selected. It can be described in terms of recording for each cell, the number of neighbouring cells which have the same land use. In his sense, the neighbouring cells to (i, j) are the (i-1, j), (i+1, j), (i, j-1) and( i, j+1), In our experiment, the neighbouring is extend to eight, termed as moore neighbouring domain, and the cells (i-1, j-1), (i+1, j+1), (i-1, j-1),( i+1, j+1) are introduced. Formally, let ijkB be the number of neighbouring cells to (i, j) which have land use k. Then

65

� ��� �

� � �

��N

i

M

j kujiijkijkijkk

ij

BxB1 1 ),(

(4)

k is a measure of the compactness of the allocations to get

land use k. k =0 if every cell allocated to k has no much

neighbouring cell allocated to k, while k will tend to the maximum if all cells allocated to the k form a single squareregion. So that we can define a maximizing objective of the form:

��

�K

kkf

13 (5)

C. Constraints in LUP Problem A land use, effective at one location, may be totally

ineffective at another location. For the effective allocation of a landscape, the consequences of variations must be taken into account. One constraint is that every land use type should be controlled in a certain range, which are set not only according to the requirement of social development, but should comply with natural principle. Another constraint is on the choice of land uses which have a major influence on characteristics of land itself. For instance, the change from one type to another is subjected to the land use suitability, but also related with its neighbouring cells status. Apart from these, landscape spatial pattern and diversity are also major issues which are to be taken into care during any planning. In case of resource arrangement, compact and contiguouspatches are always preferred, but in order to improve the landscape vitality, the simple pattern also should satisfy the requirement of diversity. Based on these, the constraints on the problem can be defined as below:

i) The range of number cells of a land use type:�� Kk ,...,1�� (6)

where ��� �

�N

i

M

jijkk xx

1 1

, decision varible ijkx must be 0 or 1

in the model as defined above. kx is the sum of cells which

be allocated with land use k ( minkX , max

kX ) is the range of number of cells allocated to a certain land use type k. They can be obtained by MMP and MCDM.

ii) The land use suitability of a unit: min

kijk Ss � (7)

where ijks is the result of suitability evaluation of land use k

for the cell (i,j), and minkS is the lower bound of it.

iii) The land use type change index of a unit: min

cfijcf pp � (8)

where ijcfp and mincfp are the possibility and the lower

bound of index of land use change from current type c to

planning type f, respectively. ijcfp can be computed using eq.8 below.

iv) The size of a patch of a land use: maxmin

kkk nnn �� (9)

where ( minkn , max

kn ) is the range of size (number of cells) of a patch under land use type k.

III. GA FOR LAND USE PLANNING

The formulation of the previous section generated aconstrained non-linear combinatorial programming problem, which needs to be solved for each set of criteria and goals specified. As seen in literature (sec.II), such a problem is best solvable by non-classical methods, out of which geneticalgorithms (GAs) have been used widely and a number ofdifferent GAs were suggested to solve multi-objective optimization problems. Of them, Fonseca and Fleming’s MOGA, Srinivas and Deb’s NSGA, Deb’s NSGA –II and Horn et al.’s NPGA enjoyed more attention. These algorithms also demonstrated the necessary additional operators for converting a simple GA to a MOGA. In this paper, we extended the NSGA-II by introduce infeasibility to form an improved MOGA, and design a knowledge-informed method for population initialization to satisfy the specific LUP problem.

A. Infeasibility D egree and Operator In NSGA-II, Deb has defined crowding distance and

designed the crowded-comparison operator to solve the selection of individuals in the same Pareto optimal front. However, the infeasible individuals near the optimal front, which cannot satisfy the constraint, may have more important roles in the process of evolution. Furthermore, when the feasible individuals cannot reach the population size, the infeasible individuals also should be considered.

1) Infeasibility degree: The individual’s infeasibility normdegree ( )( kx can be computed by

2/1

1

2

1

2 )))]([)}](,0[min{()( �����

��K

jiki

J

ikik xcxcx (10)

where )( kx is the distance between the infeasible and theindividual and the feasible region. And a threshold of computation formulation is defined as that:

sizepopxT

sizepop

iicrit _/))((1 _

1�

� (11)

where T is similar with the temperature in simulated anneali- annealing, but here T is arising step b y step, which can be looked as the opposite process of annealing, and pop_size is the population size. It is clear that with the process of some evolution, crit is enforced. In other words, the requirement to infeasible individuals is more and more stick with someevolution.

2) Feasible proportion of population: For the importance of infeasible individuals in evolution, the feasible individuals

66

are limited partly by ( in is the number of individual will be selected on this Pareto front): iii rFn � (12)

where iF is the number of individual on No.i Pareto front, iris a proportion factor, )1,0(�ir .

3) Selection Operator based on infeasibility degree: The crowded-comparison operator in NSGA-II is used to guide the selection process for the feasible individuals at the various stages of the algorithm toward a uniformly spread-out Pareto optimal front. Here, we designed the comparison operator to guide the selection process between feasible and infeasible or two infeasible individuals after selecting a certain number of individuals by crowded-comparison operator. Assume that every infeasible individual in the population has the attributes of infeasibility degree ( ifdi ), it has been divided into three forms:

i) p is infeasible individual, and q is feasible one isn isthe number of selected individuals on front i :

Selected( p ) If ( ( iis nn � ) and ( critifdp � ) ) ii) Both p and q are infeasible individual:

Selected( p )

If ( ifdifd Cp � and ( ifdifd Cq � ) and ( jfdifd qp � ) )

OR If ifdifd Cp � and ( ifdifd Cq � )

B. Extended NSGA-II The extended NSGA-II procedure is shown in Fig.2, where is the last pareto set, is the infeasible’s and is the

proportion index. It is simple and straightforward. Compared with NSGA-II, the only difference is about infeasible individual operator in evolution process. After a certain proportion size feasible individuals are selected into crossover pool, the selection operator based on infeasibility degree is started until the new parent 1�tP is formed. The new

population 1�tP of size N is now used for selection, crossover,

and mutation to create a new population 1�tQ of size N.

C. Chromosome Representation and Population Initialization

1) Chromosome representation: The basic component of GA is chromosome which represents a solution in the search space of an optimization problem. The LUP problem requires a chromosome to encode the information needed to schedule land uses in different units of a landscape. We selected atwo-dimensional grid of genes, similarly with spatial-based representation, where position of each gene (grid) represents a unit of a landscape, and its value determines the land use for that unit.

2) Population initialization: Ordinary, it is no meaning that generating initial population (solutions) randomly in LUP, except for a blank region. In fact, Land use planning must consider the current land use situation or status, and the allocation is governed by some restriction defined by government or natural principle. For instance, one river couldn’t be converted into other uses, and the basic farmland is protected significantly. Thus, we generate the initial solutions under some rules defined beforehand to ensure the individuals in initial population are not far beyond the practical allocation. The first is that some units with fixed use unchanged in GA operation are labeled with same gene code (land use type) in any individuals. Secondly, the allocated land use type is suitable to the unit. The third is that the size of patch must satisfy the minimum size correspondingly.

IV. PRACTICAL APPLICATION

The method is tested in one town’s practical land use planning. There are many low hills and forestry in the region, but the ecological environment is frail for unreasonable development. In its long term planning, it has been defined as an important ecological protection and improvement region. The region is divided into a 50*60 grid, displayed in Fig.3,where 1670 cells in the region and the ‘hollow’ cells out of it, and as many as 7 distinct land use types could be identified in this area.

A. The Objectives All three of objectives defined in Section II were

considered relevant to the current case study. Obviously, 2fand 3f can be computed directly, and ijcfC in 1f is computed using eq.13 below:

Fig. 3. Land use situation map

Qt

F1

F2

F3

… ……Fe

Fifd

rt Pt+1

Rejected population

Infeasible individual operator

Fig. 2. Extended NSGA-II procedure

Pareto Ranking

Rt

Pt

67

RPC cfijcf � /1 (13)

where cfP is possibility index for changing based on land use type, which is in the range of 0 to 1. To every unit of land use,

cfP is different in practice. For convenience, a fixed possibility index table (Table 1) is used for all over the region, instead of computation cfP for every unit. And R is the coefficient for changing based on land use type suitability, which can be calculated with formula FCR � , where C is set with 0.1, 0.3, 0.7, 0.9, while the cell’s suitability for current use type is labed as I, II, III, IV from high to low, and F is set with 0.9, 0.7, 0.3, 0.1, while the cell’s suitability for planning use type is I, II, III, IV. It is clear that with the control of R, the allocation tends to maintain suitable land use situation and change unsuitable land use type to suitable one.

TABLE IPOSSIBILITY INDEX for LAND USE TYPE CHANGING

Current land use type

Plannint land use type

Cul.. Orc.. For… Gra… Con… Wat… Unu…Cultivated 1 0.8 0.9 0.9 0 0 0 Orchard 1 1 0.6 0.5 0.2 0 0 Forestry 0.2 0.5 1 0.8 0.2 0 0

Grass 0.8 0.7 0.7 1 0.1 0 0 Construct 0 0 0 0 1 0 0

Water 0.1 0.1 0 0 0.1 1 0 Unused 0.9 0.8 0.8 0.8 0.9 0 1

B. Constraints Lower and upper bounds for the extent of each land use

type (together with the corresponding values for the current situation), are shown in the Table II, which also indicates minimum desirable cluster sizes separately for each land use type, where the lower bound and upper bound are obtained by researches in optimization the land use quantity optimization, the ecological value as a priori, and the economic return as a priori, respectively. Land uses for 348 out of the 1670 cells were fixed a priori, which mainly are water source and forestry in Northwest and two big construction zones. Finally, there were also restrictions on what changes were permitted, as defined in Section II.

TABLE IIVARIOUS CONSTRAITS for EACH LAND USE TYPE

C. Results As defined above, in this Extended NSGA-II, the

population size is set 100, and the max generation is 100. In this experiment, the algorithm has been executed for 100

generations which has taken about 5 hours with Intel Core 2 Duo CPU 2.10GHZ, RAM 3.0 GB. The result of land use allocation map is shown in Fig.4

In the end, the result is compared with the current land use situation by comparing some kinds of landscape ecological index, such as Shannon Diversity Index, Dominant Degree Index, and Compactness. We can find that the planning solution obtained by this optimization tool can meet the ecological requirement and the land spatial pattern is more compact. And for water system and the forestry in the northwest are pick-up before optimizing, which existed as fixed cells, the result of optimizing shows more protection paid to water and forestry in the region.

V. CONCLUSIONS

As a typical non-linear and multi-objectives spatial optimization problem, allocating land use with traditional ‘two steps’ method will cause incompatible between quantity and spatial allocation. And the traditional optimization algorithms cannot satisfy land use planning for existing multiple and conflict objectives. Hence, an integer programming model is designed for LUP, and an extended genetic algorithm is put forward based NSGA-II to generate optimized solutions for it. The experiment demonstrates that GA can be used in LUP. But the efficiency of this algorithm need be improved, in order to quickly response to the decision-makers’ intention. And LUP is a complex process, this optimizing tool also should be integrated with others to form a decision-making support system, in which user can easily select or modify the objectives, and define the restrictions according to special interesting. This is the main challenge in LUP and other resource allocation problems for the future.

ACKNOWLEDGMENT

The software for this work used the GAlib genetic algorithm package, written by Matthew Wall at the Massachusetts Institute of Technology.

REFERENCES

[1] J.C.J.H. Aerts, M.F. Goodchild and G.B.M.Heuvelink, Accounting for spatial uncertainty in optimization with spatial decision support systems”, Transactions in GIS, vol.7, no.2: pp.211-230, Mar.2003.

Land use type Current situation

Range of areas Minimum cluster size

Lower bound Upper bound

Cultivated 936 909 933 4 Orchard 30 35 50 4 Forestry 463 452 461 3

Grass 7 5 7 2 Construction 89 90 112 4

Water 66 65 73 1 Unused 79 68 75 1

Fig. 4. Land use planning map

68

[2] J.C.J.H. Aerts and G.B.M. Heuvelink, “Using Simulating Annealing for Resource Allocation”, International Journal of Geographic Information Science, vol.16, no.6, pp.571-587, Nov.2002.

[3] P.J. Agrell, A. Stam and G.W. Fischer, “ Interactive Multi - objectives Agro-ecological Land Use Planning: The Bungoma Region in Kenya”, Eur. J. Oper. Res, vol.158, no.1, pp.194-217, Oct.2004.

[4] E. Chuvieco, “Integration of linear Programming and GIS for Land-Use Modeling”, International Journal of Geographical Information System,

,vol.7, no.1, pp.71 83, Jan.1993. [5] T. J. Cova and R. L. Church, “Contiguity Constraints for Single-Region

Site Search Problems”, Geographical Analysis, vol.32, no.4, pp.306329, Oct.2000.

[6] K. Deb, S. Agarwal, A. Pratap and T.Meyarivan, “ A Fast and Elitist Multi-objective Genetic Algorithm: NSGA-II”, IEEE Transactions on Evolutionary Computation, vol.6, no.2, pp.182-197, Apr.2002.

[7] K.Fedra and A. Haurie, “ A Decision Support System for Air Quality Management Combining GIS and Optimization”, International Journal on Environment and Pollution, vol.12,no.2, pp.125-146, Apr.1999.

[8] D. M.Hanink and R. Cromley, “Land-Use Allocation in the Absence of Complete Market Values”, Journal of Regional Science, vol.38, no. 3, pp. 465-480, Aug.1998.

[9] N. Srinivas and K. Deb, “Multiobjective Function Optimization Using Nondominated Sorting Genetic Algorithms”, Evol. Compute,, vol. 2,no.3, pp. 221–248, Sept.1995.

[10] T.J. Stewart, R. Janssen and M.V. Herwijnen, “A Genetic Algorithm Approach to Multi- objective Land Use Planning”, Computers & Operations Research, 31, pp.2293-2313, Dec.2004.

69