Computers, Environment and Urban Systems 49 (2015) 114

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Computers, Environment and Urban Systems

journal homepage: www.elsevier .com/locate /compenvurbsys

A land-use spatial optimization model based on genetic optimizationand game theory

http://dx.doi.org/10.1016/j.compenvurbsys.2014.09.0020198-9715/ 2014 Elsevier Ltd. All rights reserved.

Corresponding author at: School of Resource & Environment Science, WuhanUniversity, 129 Luoyu Road, Wuhan 430079, China.

Yaolin Liu a,b,, Wei Tang a, Jianhua He a,b, Yanfang Liu a,b, Tinghua Ai a,b, Dianfeng Liu a,ba School of Resource & Environment Science, Wuhan University, 129 Luoyu Road, Wuhan 430079, Chinab Key Laboratory of Geographic Information System, Ministry of Education, 129 Luoyu Road, Wuhan 430079, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 20 May 2013Received in revised form 5 August 2014Accepted 4 September 2014Available online 22 September 2014

Keywords:Land-use spatial optimizationGenetic algorithmLocal land-use competitionGame theory

Land-use patterns can be considered as a consequence of competitions between different land-use types.How to coordinate the competitions is the key to land-use spatial optimization. In order to improve theability of existing land-use spatial optimization models for addressing local land-use competitions (thecompetitions on land units), a loosely coupled model based on a genetic algorithm (GA) and game theoryis constructed. The GA is repeatedly executed to separately optimize the spatial layout of each land-usetype. The land-use status quo is overlaid with the optimization results to find local land-use competi-tions. The concept of land-use competition zones is introduced in this study. Using the competition zonesas the basic units, the model utilizes multi-stakeholder games and the knowledge of land-use planning tocoordinate the local land-use competitions. The final solution is obtained after the land-use coordination.Gaoqiao Town, Zhejiang Province is selected as the study area to verify the validity of the model. Theexperimental results confirm that the model is feasible to undertake land-use spatial optimization andto coordinate the competitions between different land-use types.

2014 Elsevier Ltd. All rights reserved.

1. Introduction

Land-use spatial optimization is a complicated spatial decision-making problem with multiple conflicting objectives. How to coor-dinate land-use competitions is the key to land-use spatial optimi-zation. The quantitative constraints of land resources and theirmulti-suitability are the main reasons for these competitions(Chen, 2007; Liu, Wang, & Long, 2008). From the spatial perspec-tive, land-use competitions can be considered as a scramble forland units between multiple land-use types; however, in essencethese competitions are a conflict of interest between multiplestakeholders (Zhang, Li, & Fung, 2012).

Many researchers have performed extensive research in thefield of land-use optimization. The existing optimization modelscan be roughly divided into the following three categories: linearprogramming models, cellular automata models, and models basedon intelligent algorithms. Linear programming models can quicklydetermine the optimal land-use structure according to specificobjectives and constraints (Arthur & Nalle, 1997; Chuvieco, 1993;Sadeghi, Jalili, & Nikkami, 2009); however, these models are unableto change the land use of parcels and to undertake spatial optimi-zation (Sant-Riveira, Crecente-Maseda, & Miranda-Barrs, 2008).

Cellular automata models are based on land-use conversion rulesfor local areas and can generate different land-use patterns underdifferent conditions using a bottom-up approach (Li & Yeh, 2000,2002). Irrational land use in local areas can be adjusted usingwell-designed land-use conversion rules. However, optimizationobjectives and other important macroeconomic factors cannot beeasily incorporated into cellular automata models.

Land-use spatial optimization is a complicated combinationaloptimization problem. The computational intensity increases expo-nentially as the scale of the problem increases when using anexhaustive search to solve the problem (Xiao, 2008). For manyreal-world applications, numerous spatial variables are involved,and many spatial and non-spatial constraints need to be handled.Conventional mathematical models are not able to find the optimalsolution within an acceptable timeframe (Aerts, Eisinger, Heuvelink,& Stewart, 2003). Therefore, as a compromise between the time-frame and the optimality of the final solutions, various intelligentalgorithms for land-use spatial optimization have been developed,such as simulated annealing algorithms (Aerts & Heuvelink, 2002;Sant-Riveira, Boulln-Magn, Crecente-Maseda, & Miranda-Barrs, 2008), particle swarm algorithms (Liu, Li, Shi, Huang, & Liu,2012; Liu, Liu, Liu, He, Jiao, et al., 2012; Liu, Wang, Ji, Liu, & Zhao,2012), ant colony algorithms (Li, Shi, He, & Liu, 2011; Liu, Li, et al.,2012), and genetic algorithms (GAs). While these algorithms maynot be able to obtain the optimal solution for every case, near-opti-

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2 Y. Liu et al. / Computers, Environment and Urban Systems 49 (2015) 114

mal solutions are often good enough to support decision-making forregional land-use planning. Geographic information systems (GISs)play an important role in the application of the intelligent algo-rithms to land-use spatial optimization (Wu & Grubesic, 2010).These algorithms and GIS can be loosely coupled through theexchange of data files. GIS are utilized to process and visualize spa-tial data for these algorithms. Moreover, for open GIS, part of GISfunctions can be reused in the development of these intelligentalgorithms.

GAs are widely used among the aforementioned intelligent algo-rithms (Goldberg, 1989; Zhou & Sun, 1999). This technique has beenapplied to solve common spatial optimization problems, e.g., facilitylocation (Brookes, 1997, 2001; Li & Yeh, 2005), forestry planning(Ducheyne, De Wulf, & De Baets, 2006; Fotakis, Sidiropoulos,Myronidis, & Ioannou, 2012), water resource allocation (Fotakis &Sidiropoulos, 2011), and land-use optimization (Holzkmper &Seppelt, 2007; Lautenbach, Volk, Strauch, Whittaker, & Seppelt,2013; Porta et al., 2012; Stewart, Janssen, & van Herwijnen, 2004).Pareto front based methods are often integrated with GAs to illus-trate the trade-off among conflicting optimization objectives, whichassists planners in addressing regional-scale land-use competition(Balling, Taber, Brown, & Day, 1999; Bennett, Xiao, & Armstrong,2004; Cao et al., 2011; Morio, Schdler, & Finkel, 2013). However,these GA-based optimization models do not consider local land-use competitions (the competitions on land units). The genetic oper-ators have been improved from the random search techniques tobeing combined with the knowledge of land-use planning in previ-ous studies (Cao, Huang, Wang, & Lin, 2012); however, the combina-tion is simple. These operators lack an effective game-basedcoordination mechanism for local land-use competitions. Theimportant role of interest factors is ignored in the coordination,

Fig. 1. Model f

which may lead to difficulty in implementing the coordinationresults.

Game theory can simulate the decision behavior of variousstakeholders in a conflict of interest and assist them in makingthe most favorable decision (Rasmusen, 2001; Zhang, 2004). Rele-vant studies have applied game theory to monitor land-usechanges (Wu, Wu, & Shen, 2005), allocate water resources (Liu,Sun, Gu, & He, 2002), cope with multi-objective optimization(Lee, 2012), and solve land-use conflicts (Hui & Bao, 2013). How-ever, game theory methods are usually applied in isolation andhave been rarely coupled with land-use optimization models. Inconsideration of the difficulty in coupling the genetic operatorswith game theory methods, a loosely coupled model based on agenetic algorithm and game theory is constructed in this study.The model is intended to improve the ability of existing land-usespatial optimization models for addressing local land-use competi-tions. The second part of this study provides the details of themodel. The third part introduces the study area and relevant data.The corresponding experimental results are described and ana-lyzed in the fourth part, and the relevant conclusions are given inthe final part.

2. The land-use spatial optimization model

The land-use spatial optimization model in this study consistsof two parts (Fig. 1). In the first part, an improved GA is repeatedlyexecuted to separately optimize the spatial layout of each land-usetype. In the second part, the land-use status quo is overlaid withthe optimization results from the first part to find local land-usecompetitions. The concept of land-use competition zones is intro-duced in this study (see Section 2.2). Using the competition zones

ramework.

Y. Liu et al. / Computers, Environment and Urban Systems 49 (2015) 114 3

as the basic units, the model utilizes multi-stakeholder games andthe knowledge of land-use planning to coordinate the local land-use competitions. Interest factors are introduced into the coordina-tion process through multi-stakeholder games (see Section 2.3.1).Different game models can be constructed according to the charac-teristics of different competition types. The knowledge of land-useplanning ensures the rationality of the coordination results. In thismodel, the local land-use competitions are roughly divided intotwo categories: agricultural land competition and competitionbetween agricultural land and development land. The former cate-gory is the competition between agricultural lands, e.g., farmlandversus garden and farmland versus forest. The latter category isfurther subdivided into two types: agriculture (status quo)-devel-opment land competition and development (status quo)-agricul-ture land competition.

The land-use coordination is a multiple stakeholder game. Dif-ferent stakeholders and interest demands are involved in differentlocal land-use competition types. In this study, solving the agricul-ture-development land competition problem is used as an example;a game model that simulates the negotiations between farmers andthe government is constructed to coordinate this competition type.The other local land-use competition types are solved using guid-ance from land-use planning knowledge.

2.1. Genetic optimization

2.1.1. Chromosome structure and initializationThe vector chromosome and the grid chromosome are the most

commonly used structures in land-use spatial optimization(Balling et al., 1999; Cao et al., 2011). The grid chromosome isselected in this study because of the effective representation ofthe study area and the convenient manipulation of land units. Eachexecution of the GA focuses on optimizing that spatial layout ofonly one land-use type. Through repeated executions of the GA,the model separately optimizes the spatial layout of each land-use type (Fig. 1). Therefore, the grid cells (namely genes) in a chro-mosome are all binary variables. When a cell is allocated to thefocused land-use type, its value is 1; otherwise, the cell has a valueof 0. The land-use patterns in the chromosomes are too fragmentedwhen the random strategy for initialization is utilized. Therefore,each chromosome in the population is initialized to the land-usestatus quo (Fig. 2). The two initialization strategies are comparedin Section 4.1.

2.1.2. ObjectivesLand-use suitability S and compactness C are the objectives con-

sidered in the spatial layout optimization of each land-use type.Improving the suitability is conducive to the rational use of landresources. Compact land use is important for achieving sustainableeconomic development, especially considering the deficiency of

Fig. 2. The initialization str

land resources. The two objectives are integrated together usinga weighted sum. The landscape shape index is selected as the met-ric for determining land-use compactness. The relevant formulasare as follows:

S PM

i1PN

j1sij uijPMi1PN

j1uij; 1

C XHh1

Ph4

ffiffiffiffiffiAh

p ; 2

Maximize : F w1 f SnormS w2 fCnormC: 3

In Formula (1), sij is the suitability of the focused land-use type inthe cell indexed by i and j. Moreover, uij is a binary-state variablethat is 1 if the cell indexed by i and j is allocated to the focusedland-use type; otherwise, the value is 0. In Formula (2), H is thenumber of patches in the chromosome, Ph is the perimeter of apatch, and Ah is the area of a patch. A patch is a set of cells thatare contiguous with each other and are allocated to the focusedland-use type. Smaller values of Formula (2) correspond to bettercompactness. Formula (2) favors the chromosomes with compactand fewer patches. In Formula (3), f Snorm and f

Cnorm are utilized to nor-

malize the objective values (see Section 4.1 for details). Moreover,w1 and w2 are the weights of objective S and objective C. Theseweights satisfy the following constraints: (1) w1 + w2 = 1, (2)0 6 w1 6 1, and (3) 0 6 w2 6 1.

2.1.3. Land-use constraintsLand-use conversion is not random and is subject to constraints

from multiple aspects, such as the economy, society, and ecology.Violations of the constraints often lead to irrational allocation ofland resources. We divide the constraints into two types: (1) areaconstraints and (2) spatial constraints. The area constraints macro-scopically control the use of regional land resources (Cao et al.,2012). These constraints are utilized to maintain a rational land-use structure in land-use spatial optimization, such as the mini-mum farmland area and the maximum development land area.The spatial constraints restrict land-use conversion within specificgrid cells (the land-use data are provided in a raster format). Forexample, land use in a nature reserve should remain unchanged.To satisfy the area constraints, a penalty method is introduced intothe fitness evaluation of chromosomes (see Section 4.1). The spa-tial constraints are considered in the execution of the mutationoperator (see Section 2.1.4).

2.1.4. Genetic operatorsThe random search adopted in the conventional crossover and

mutation operations leads to arbitrary land-use conversion andgenerates irrational land-use patterns. The conventional crossover

ategy of chromosomes.

Fig. 3. Schematic representation of the mutation operation.

Fig. 4. The structure of a competition zone and its neighborhood.

4 Y. Liu et al. / Computers, Environment and Urban Systems 49 (2015) 114

and mutation operations have been improved in some studies.Knowledge of land-use planning is incorporated into the new oper-ators. When changing the value of a gene, both land-use con-straints and the land use in the neighborhood of the gene areconsidered (Cao et al., 2012; Fotakis et al., 2012).

In this study, the crossover operator randomly selects oneCN CN window in the study area and subsequently swaps the landuse in the windows in the two chromosomes. The number of theselect and swap operations executed on the two chromosomesin one iteration of the GA is N1, which is a model parameter. Themutation operator randomly selects two 3 3 windows in thestudy area. The average suitabilities of the focused land-use typein the two windows are individually calculated. The window witha better suitability is labeled H. The other window is labeled L.The mutation operator moves the land use in window L to win-dow H (Fig. 3). The cell values in window L are changed from 1 to0, while the cell values in window H are changed from 0 to 1. How-ever, the number of value-changed cells in window L should beidentical to the number of value-changed cells in window H. There-fore, the moving process terminates if either of the two followingconditions is reached. First, the cell values in window L are all 0(Fig. 3(a)). Second, the cell values in window H are all 1 (Fig. 3(b)).The spatial constraints are incorporated into the mutation operator.If the land-use conversion on a cell (the cell value changes from 1 to0 if it is in window L and from 0 to 1 if it is in window H) violates anyof the spatial constraints, the conversion is withdrawn. This cell isnot considered in the moving process. The number of the selectand move operations executed on one chromosome in one itera-tion of the GA is N2, which is also a model parameter. Roulette wheelselection is utilized as the selection operator.

2.2. Definition of land-use competition zones

The same land-use competition type typically occurs withinseveral contiguous grid cells. Therefore, we introduce the conceptof competition zones into the model to promote land-use coordi-nation. Based on an 8-neighbor structure, a competition zone iscomposed of cells that are contiguous with each other and havethe same land-use competition type. According to the aforemen-tioned competition classification, competition zones can also bedivided into three types: agricultural land (AA), development-agri-culture (DA), and agriculture-development (AD) competitionzones. The structure of a competition zone and its correspondingneighborhood is shown in Fig. 4.

2.3. Mechanism for land-use coordination

Different coordination strategies are adopted for different land-use competition types. The agricultural land competition and the

development-agriculture land competition are solved using knowl-edge of land-use planning. For an AA competition zone (see Section2.2 for the definition of AA), the priority degree PD for each agricul-tural land type is separately calculated. The formula is as follows:

PDi Ci Di; 4

where Ci is the area of land-use type i in the competition zone andits neighborhood on the land-use status quo map. Moreover, Di isthe area of land-use type i in the competition zone on its optimizedspatial layout map. The land-use type with the highest PD isselected as the new land-use type of the competition zone. All cellsin the competition zone are allocated to the new land-use type,which is helpful for compacting land use in local areas.

The appearance of the development-agriculture land competi-tion is primarily due to the sporadic emergence of developmentland in large tracts of agricultural land. The sporadic emergenceof development land is unfavorable to the scale management ofagricultural land. The strategy for solving this competition type isto convert development land to agricultural land. When the entireneighborhood of a DA competition zone is agricultural land (seeSection 2.2 for the definition of DA), the area of each agriculturalland type in the neighborhood on the land-use status quo map iscalculated. The new land-use type of the competition zone is theone with the largest area. All cells in the competition zone are allo-cated to the new land-use type.

The agriculture-development land competition is solved usingnegotiations between farmers and the government. On one hand,it is necessary for the government to expropriate some agriculturalland for economic development. The government must fully con-sider the location and the developmental value of the agriculturalland for expropriation and the compensation to the land-lost farm-ers. On the other hand, agricultural land is the primary source offarmers income. Their life will be largely affected if they lose their

Y. Liu et al. / Computers, Environment and Urban Systems 49 (2015) 114 5

land. In the negotiation process, farmers safeguard legitimaterights and personal interests.

2.3.1. A game model simulating negotiations between farmers and thegovernment

A game model simulating negotiations between farmers and thegovernment is constructed. Whether the agricultural land in an ADcompetition zone is expropriated is determined by the result of thegame model (see Section 2.2 for the definition of AD). If the ADcompetition zone is expropriated, all cells in the zone are con-verted to development land. We execute the game model sepa-rately for each AD competition zone. Details regarding the gamemodel processes in an AD competition zone are provided below.

In the game model, farmers and the government take action inturn. When the government plans to expropriate the agriculturalland in an AD competition zone, the farmers must decide whetherto agree to the expropriation after comparing their agriculturalincome with the compensation. If the farmers reject the expropri-ation, the government can choose to negotiate with the farmers orsimply give up. When negotiations are adopted, the farmers mustdecide whether to agree to the new compensation. If the farmersreject the expropriation, the government either renegotiates withthe farmers or gives up. The process continues back and forth.The two sides can play the game for a long time; however, thegame cannot go on indefinitely. More specifically, let N be the larg-est number of rounds for the game. If the farmers reject the expro-priation in the Nth round of the game, the government will chooseto give up the expropriation. The entire game process can be rep-resented through a game tree (Hui & Bao, 2013). An example of agame tree in which N equals 3 is shown in Fig. 5.

The following formula is applied to calculate the farmers totalincome I from agricultural production in the coming M years:

I M X

i

S Pi Fi; 5

where S is the area of the AD competition zone, Pi is the percentageof agricultural land-use type i in the competition zone, and Fi is theannual income per unit area.

Let T be the initial compensation. As the game continues, thecompensation to the farmers increases; however, the incrementalamount of compensation in one round gradually decreases. Thischange is modeled using a decreasing geometric progression. Thefirst term is W, while the common ratio is q. The farmers compen-sation amount is S T after the 1st round of the game, S T + Wafter the 2nd round, and S T + W + W q after the 3rd round.The farmers compensation after the nth round is calculated usingthe following formula:

Cn S T W 1 qn1

1 q : 6

In Formula (6), W = p S T and 0 < p, q < 1.The government determines the lease price of the AD competi-

tion zone according to its future usage, e.g., industrial develop-ment, commercial and residential development, or developmentfor public interests. The lease price differs widely among theseusages. In this study, we cannot foresee the future usage of thecompetition zone. Therefore, an average lease price for AD compe-tition zones is introduced. We modify the average lease price toobtain the final lease price of the competition zone based on loca-tion conditions. The percentage of the development land in theneighborhood of the competition zone is utilized to evaluate thelocation conditions. A high percentage indicates a high lease price.If Q is assumed to be the average lease price and V is the govern-ments revenue from land leasing, the governments net revenueRn if the agricultural land is obtained in the nth round of the gamecan be calculated using the following formulas:

V k SDSnei

u Q S; 7

Rn 1 e V Cn: 8

In Formulas (7) and (8), Snei is the area of the neighborhood, SD is thearea of the development land in the neighborhood, k and u are theinfluence coefficients of the location conditions (0 < k < 1, u > 1),and e represents the cost the government should bear to makethe competition zone ready for development (0 < e < 1). The formercomponent of the tuples in Fig. 5 is the farmers income; the lattercomponent is the governments net revenue.

The negotiations between the farmers and the government aremodeled as a dynamic game. The game model hypothesizes thatboth the farmers and the government are rational. The farmersaccept the land expropriation if and only if the compensation Cnexceeds the income I from agricultural production. The govern-ment gives up the land expropriation if and only if the compensa-tion to the farmers becomes sufficiently large such that the profitRn becomes negative. In the game model, both the farmers andthe government are clear that it is time for each side to make adecision; they each even know the exact node where the decisionis made. This property is known as complete and perfect informa-tion (Rasmusen, 2001). With this property, backward induction canbe utilized to find the sub-game perfect Nash equilibrium of thegame (Zhang, 2004). Each participant in dynamic games has hisown strategy set, and a strategy is a complete action guide forthe participant. The word complete means that a strategy of aparticipant can provide advice to the participant on how to act atall his decision nodes in the game tree. The sub-game perfect Nashequilibrium is a strategy combination that indicates the strategiesparticipants should adopt. At each decision node of the farmers, thestrategy for the farmers indicated by the sub-game perfect Nashequilibrium chooses the action that brings a higher profit betweenagreeing and disagreeing with the land expropriation. Similarly, ateach decision node of the government, the indicated strategy forthe government chooses the action that brings a higher profitbetween expropriating and not expropriating the land. Accordingto the indicated strategies, a path from the root node of the gametree to one of the leaf nodes can be found. The leaf node of the pathgives the answer to the question of whether the competition zoneshould be expropriated for development. The corresponding profitsof the government and the farmers are also provided.

Although farmers may have incomplete information about thegovernments profit in real-world negotiations, the game modelconstructed in the study is still a dynamic game of complete and per-fect information. The reason for this is that the farmers do not utilizetheir information about the governments profit to maximize theirown profit in the dynamic game. According to the governmentsprofit, the government can be classified as two types: a high profitgovernment and a low profit government. For different types ofthe government, the farmers can put forward different compensa-tion demands. The government can also provide different compen-satory standards in consideration of its profit. If the farmers utilizetheir incomplete information about the governments profit to max-imize their own profit, the negotiations between the farmers and thegovernment cannot be modeled as a dynamic game of completeand perfect information. A dynamic game of incomplete informa-tion may be more suitable for the negotiations. The incompletenessof the farmers information means that they only have the priorprobability of the governments type and do not know which typethe government belongs to. After knowing which compensatorystandard the government selects, the farmers can determine theposterior probability of the governments type using Bayes theo-rem. The dynamic game of incomplete information is more compli-cated than the complete and perfect information. The sub-game

Fig. 5. A game tree representing negotiations between farmers and the government.

6 Y. Liu et al. / Computers, Environment and Urban Systems 49 (2015) 114

perfect Nash equilibrium and backward induction are not applicableto the dynamic game of incomplete information. Applying thedynamic game of incomplete information to land-use coordinationrequires future examination.

The real government in a Chinese town is not merely satisfiedby obtaining a positive profit in land expropriation. The profit fromland expropriation is a considerable addition to local fiscal revenue(Zhou, 2007). The government does their best to maximize theprofit to support local economic development. Occasionally, thegovernment delays the compensation payment and even skimpsor embezzles the compensation to obtain more profit (Zhao,2009). Farmers will resist the infringement of their legitimateinterests through various means. Negotiations with the farmersare an effective way for the government to handle the conflictsfrom land expropriation. Moreover, negotiations help the govern-ment avoid the farmers violent struggle and appeal to higherauthorities for help, which may introduce additional losses to thegovernment (Zhao, 2009). In reality, farmers are typically in a weakposition in the game between farmers and the government. There-fore, the game model constructed in this study pays more attentionto the protection of the farmers interests.

3. Study area and data

Gaoqiao Town is located in Zhejiang Province, eastern China(Fig. 6). The town covers an area of 104.03 km2 and has a popula-tion of approximately 58,000 people. There are a variety of land-forms within the town, e.g., low mountains, hills, basins, andplains. Forests make up approximately 64.2% of the town, 10.98%is development land, and 16.3% is farmland. Gaoqiao Town hasbeen experiencing high-speed economic development, and simul-taneously some undesirable phenomena have appeared, e.g.,excessively rapid expansion of development land and conflictsbetween farmland and development land.

The land-use data of the study area at a 1:10,000 scale werederived from the second nationwide land survey. These data wereconverted to a 546 516 grid with a resolution of 25 25 m. Rel-evant yearbooks, suitability evaluation maps, and topographicmaps were also collected. Both land attributes and the land-usestatus quo were considered in the suitability evaluation. Theresults of the suitability evaluation were divided into four grades:highly suitable (100), suitable (80), marginally suitable (60), andunsuitable (20). This study primarily considers the spatial optimi-zation of (1) farmland, (2) gardens, (3) forests, and (4) developmentland. Paddy fields and upland fields are classified as farmland. Gar-dens are comprised of orchards and tea plantations. Developmentland includes rural settlements, the urban district, and land formining and industry. Transportation land, hydraulic constructionland, water, and scenic areas remain unchanged in theoptimization.

4. Results and discussion

4.1. Spatial layout optimization

The parameter values for the spatial layout optimization of eachland-use type are listed in Table 1. A unary linear regression wasutilized to predict the population in the target year, i.e., 2020,according to the data from 1996 to 2005. The minimum farmlandarea per capita was calculated according to the following formula(Cai, Fu, & Dai, 2002):

Sper capita bGr

P q k ; 9

where b is the self-sufficiency rate of grain. The government plansto raise the rate to 80% in the target year. Moreover, Gr is the grainconsumption per capita. From 1996 to 2005, the grain consumptionper capita declined continuously. For the target year, Gr was set to

Fig. 6. The study area.

Table 1The parameter values for the spatial layout optimization of each land-use type (the unit of the numbers in the parentheses is cell).

Current area Minimum area Maximum area w1 w2 Smin Smax Cmin

Farmland 16.3% (27,067) 14.3% (23,780) 0.5 0.5 20 100 260.28Gardens 6.62% (11,020) 4.1% (6818) 0.5 0.5 20 100 361.12Forests 64.2% (10,6751) 60.7% (100,939) 0.5 0.5 20 100 380.51Development land 10.98% (18,265) 10.98% (18,265) 12.77% (21,235) 0.3 0.7 20 100 253.11

Table 2The parameter values of the GA.

Population size Iteration Crossover rate CN N1 Mutation rate N2

100 10,000 0.9 15 100 0.9 300

Y. Liu et al. / Computers, Environment and Urban Systems 49 (2015) 114 7

the value for 2005. Furthermore, P is the grain yield per hectare.From 1996 to 2005, the grain yield per hectare exhibited a fluctuat-ing yet increasing trend. The average grain yield per hectare for theten-year period was 5499.42 kg/h m2; for the target year, P was setto the 2005 value (7053.1 kg/h m2). Additionally, q is the ratio of thesown area to the total area of farmland; k is the multiple croppingindex. We set q and k to their respective ten-year averages using theperiod from 1996 to 2005. The minimum farmland area in Table 1 isthe product of the population in 2020 and the minimum farmlandarea per capita. The minimum garden and forest areas were set totheir respective minimum values between 1996 and 2005. Thegrowth rate of the urban district of Gaoqiao Town from 1996 to2000 was too fast. The urban district area in the target year (i.e.,2020) was predicted according to the data from 2001 to 2005 usingunary linear regression. The area of rural settlements and the areaof land for mining and industry were individually predicted accord-ing to the data from 1996 to 2005. The maximum area of develop-ment land in Table 1 was set to the sum of the predicted areas of theurban district, rural settlements, and land for mining and industry.The minimum area was set to the area of the existing developmentland. A penalty method was adopted to handle the area constraints.The chromosomes which violated the area constraints were elimi-nated in the iterative process. Two spatial constraints were consid-ered in the execution of the mutation operators. First, the land-usetype of an area where the gradient is greater than 25 should not befarmland due to the conservation of soil and water. Second, theurban district cannot be converted to farmland, gardens, or forestsdue to the large expense of this conversion.

No a priori knowledge is available for determining the objectiveweights. Objective S and objective C were given equal weights inthe spatial layout optimization for farmland, gardens, and forests.For development land, the objective C was emphasized and

assigned a higher weight. Details regarding the normalization ofobjective functions in the spatial layout optimization of farmlandare provided below. The same normalization methods were alsoapplied for gardens, forests, and development land. The suitabilityvalue of farmland ranges from 20 to 100 (see Section 3). Therefore,the maximum value of objective S (Smax) was set to 100 in the spa-tial layout optimization of farmland; the minimum value of objec-tive S (Smin) was set to 20. The following formula was used tonormalize the values of objective S:

f Snormx x xmin

xmax xmin10

We executed the GA only using objective C to optimize the spatiallayout of farmland and to estimate the minimum value of objectiveC (Cmin). However, it is challenging to estimate the maximum valueof objective C. Therefore, the following formula was utilized to nor-malize the values of objective C:

f Cnormx xmin

x: 11

The parameter values of the GA are shown in Table 2. The optimiza-tion problem in this study involves hundreds of thousands of vari-ables. The GA must perform several generations to determine abetter solution because of the extensive search space. It is impossi-ble to greatly improve the quality of chromosomes in one step of

Fig. 7. The values of the objective functions before and after the genetic optimization.

Fig. 8. Convergence curves of the genetic optimization.

8 Y. Liu et al. / Computers, Environment and Urban Systems 49 (2015) 114

the iteration. Therefore, the number of iterations was set to a largevalue. The mutation operation in this study plays an effective role inthe land-use spatial optimization. The mutation rate and N2 werealso set to large values, which contributed to reducing the iterationtime. CN and N1 were determined by trial and error. Several value

Fig. 9. Tradeoff curves of objective function values

combinations of the parameters CN and N1 were utilized to optimizethe spatial layout of each land-use type. There are fluctuations inthe fitness values of the optimization results of the same land-usetype. The optimization result of farmland and the optimizationresult of development land were both satisfactory when CN wasset to 15 and N1 was set to 100.

The model was implemented in C++ on the Windows platform(Microsoft Corporation). An open-source library (Geospatial DataAbstraction Library, GDAL) was utilized to access spatial data.The commercial GIS software (ArcGIS Desktop 9.3, EnvironmentalSystems Research Institute) preprocessed spatial data and visual-ized the results of the model. The spatial layout optimization offarmland required approximately 4.5 h on a Lenovo desktop com-puter with a Pentium(R) Dual-Core CPU E5800 @3.20 GHz and2 GB RAM; 4.1 h, 4.9 h, and 4.2 h were required for gardens, forests,and development land, respectively. The land-use coordinationrequired only 40 s.

Currently, the land-use suitability of the study area is high;therefore, the goal of the genetic optimization is to improve theland-use compactness while minimizing suitability decreases.The values of the two objective functions before and after the opti-mization are shown in Fig. 7. The suitability of farmland and devel-opment land decreases slightly; however, the compactness of thetwo land-use types is largely improved. The compactness of gar-dens is slightly improved. For forests, both the compactness andthe suitability exhibit nearly no changes. The spatial optimization

(normalized) for different weight distributions.

Fig. 10. The spatial distribution of various land-use competitions.

Y. Liu et al. / Computers, Environment and Urban Systems 49 (2015) 114 9

Fig. 10 (continued)

10 Y. Liu et al. / Computers, Environment and Urban Systems 49 (2015) 114

process can also be reflected by the convergence curves (Fig. 8).Similarly, the optimization effect of farmland and developmentland is better than for gardens and forests.

Random initialization was tried in the spatial layout optimi-zation of farmland in this study. In each initial chromosome,farmland distributes randomly in the study area and the farm-land area is 27,067 (Table 1). Random initialization was alsotried for development land. The relevant convergence curvesare shown in Fig. 8. The random initial chromosomes are of poorquality, which has significant disadvantageous effects on thequality of the optimization results. Random initialization maynot be suitable for land-use spatial optimization. In this study,the spatial layout of farmland and the spatial layout of develop-ment land were optimized using multiple weight distributions.The tradeoffs between the suitability objective and the compact-ness objective are illustrated in Fig. 9. The compactness objectiveis more susceptive to the weight distribution than the suitabilityobjective. The optimized value of the suitability objective linearlyincreases as its weight increases. Simultaneously, the optimizedvalue of the compactness objective exhibits a nonlinear decreas-ing trend.

The results of the genetic optimization indicate that the currentspatial layout of farmland and development land is partially irra-tional. Forests represent the dominant land-use type in the studyarea. The spatial layout of forests is compact even before the opti-mization (Fig. 6). Therefore, forests do not have much potential forthe genetic optimization.

4.2. Land-use competitions

After the spatial layout optimization of each land-use type,there are 7918 cells within which land-use competitions occur.According to the above definition (Section 2.2), 1940 competitionzones are generated. The spatial distribution of various

land-use competitions can be seen in Fig. 10. Relevant statisticalinformation is listed in Table 3. The conflict between agriculturalland and development land is obvious in the study area. The spatialdistributions of the development-agriculture land competition andthe agriculture-development land competition have many over-laps. Most of the overlaps are concentrated in the southeasternportion of the study area, especially in the border areas of farmlandand development land. However, the spatial distribution of theagricultural land competition is more dispersed.

The agriculture-development land competition is a conse-quence of the rapid economic development and populationgrowth. Farmland and development land are two dominant land-use types in the area marked by the rectangles in Fig. 10(a) and(b). Currently, the spatial layout of the development land in thearea is very fragmented. Therefore, the area will be a hotspot forland-use conflicts; the experimental results confirm the inference.

4.3. Land-use coordination

The knowledge of land-use planning is utilized in the land-usecoordination. The game model that simulates the negotiationsbetween farmers and the government targets the agriculture-development land competition. The parameter values of this gamemodel are listed in Table 4. The area constraints and the spatialconstraints are verified in the land-use coordination. The land-use conversion of a competition zone is withdrawn if the conver-sion violates any of the constraints. The annual income per unitarea from agricultural land is relevant to the farmers managementof agricultural land. However, detailed data for the management ofagricultural land in each AD competition zone is lacking and diffi-cult to obtain. Therefore, the annual income per unit area fromfarmland is assumed to be identical for all of the AD competitionzones. The same assumption is applied to the annual incomes

Y. Liu et al. / Computers, Environment and Urban Systems 49 (2015) 114 11

per unit area from garden and forest areas. We estimated thevalues of the three parameters based on the yearbooks. The aver-age lease price was calculated according to the governments total

Table 3Statistical information regarding land-use competitions.

Agriculture-developmentland competition

Development-agricultureland competition

Agriculturallandcompetition

Cell 3134 1876 2908Competition

zone654 508 778

Table 4The parameter values of the game model.

Annual income per unit area from farmland (RMBa/mub) 2000Annual income per unit area from gardens (RMB/mu) 3000Annual income per unit area from forests (RMB/mu) 2500Land-use term M (year) 30Average land lease price Q (RMB/mu) 160,000Influence coefficients k/u 0.5/4

a RMB is Chinese currency. 1 RMB = about 1/6 U.S. Dollars.b Mu is an area unit in China. One mu = about 666.7 m2.

Fig. 11. The spatial distribution o

Table 5Statistical information regarding the land-use coordination.

New land-use type Agricultural landcompetition (778 zones)

Dc

Farmland 331 4Gardens 199 3Forests 248 3Development land 0 4

revenue from recent land leases and the total area of the leasedland. The coefficients k and u have a substantial effect on the loca-tions of new development land. When k decreases and u increases,the agricultural land surrounded by development land can be moreeasily converted to non-agricultural uses. After several experi-ments, k and u were set to 0.5 and 4, respectively. Numerousrounds are advantageous for farmers to express their compensa-tion demand. Therefore, N was set to 10. To protect the farmersrights and interests, M was set to 30. The maximum compensationamount stipulated by the Land Administration Law is 30 times theannual income from agricultural land. Typically, farmers cannotobtain this much compensation in reality. However, in this study,

Cost e 0.2The largest number of rounds N 10Initial compensation T (RMB/mu) 35,000p 0.4q 0.6

f the new development land.

evelopment-agriculture landompetition (508 zones)

Agriculture-development landcompetition (654 zones)

9 337

53 317

Fig. 12. The relationship between the area of new development land and the initial compensation.

Fig. 13. The final allocation solution.

12 Y. Liu et al. / Computers, Environment and Urban Systems 49 (2015) 114

the farmers can obtain more compensation than the stipulatedmaximum amount through the game model. The parameters pand q were empirically determined. Although the same set ofparameter values was used for all AD competition zones, the farm-ers behavior was different in each zone. The farmers in differentAD competition zones put forward different compensationdemands according to their incomes from agricultural production.The number of rounds in the game varies with the competitionzones; higher compensation demands correspond to more rounds.

Statistical information regarding the land-use coordination isshown in Table 5. There are 778 competition zones within whichagricultural land competition occurred; the new land-use type isfarmland in nearly half of these zones (42.54%). The develop-ment-agriculture land competition occurred in 508 competitionzones; however, only 55 of these zones (10.83%) were convertedto agricultural land. Most of the DA competition zones did notmeet the requirements for the conversion from development landto agricultural land. Moreover, 49 of the 55 competition zoneswere converted to farmland, three to gardens, and three to forests.

The sporadic emergence of development land was more oftenlocated in farmland, which may have an unfavorable effect onthe scale management of farmland.

Furthermore, 317 of the 654 AD competition zones were con-verted to development land using the parameter values listed inTable 4. The agricultural land surrounded by development landhas a high priority to be expropriated for development if the influ-ence coefficients of location conditions are set to appropriate values.Therefore, the extensive expansion of development land can beavoided (Fig. 11). 337 AD competition zones remained for agricul-tural use. The compensation demand of the farmers was not metin 281 of these zones. In the remaining 56 AD competition zones,the government was not satisfied with its profit and gave up landexpropriation. With the other parameters fixed, the relationshipbetween the area of new development land and the initial compen-sation is shown in Fig. 12. When the government adopted a lowinitial compensation, no agricultural land was converted to develop-ment land. As the initial compensation increased, the area of newdevelopment land increased, then remained steady at a relatively

Fig. 14. The adjustment of local land-use patterns in the final solution.

Fig. 15. The objective function values of the final solution.

Y. Liu et al. / Computers, Environment and Urban Systems 49 (2015) 114 13

high level and ultimately decreased. The reason for this pattern is asfollows. As the initial compensation increases (less than50,000 RMB/mu), the number of cases of farmers rejecting landexpropriation tends to decrease. The area of new development landincreases. However, the governments profit from land expropria-tion is largely reduced if the initial compensation continues rising(more than 50,000 RMB/mu). The government prefers to give upland expropriation in this case, which causes the area of new devel-opment land to decrease. When the initial compensation was set to45,000 RMB/mu, the number of cases of farmers rejecting landexpropriation was 82; however, when the initial compensationwas increased to 50,000 RMB/mu, the number was 0. Therefore,the government must balance the area of the expropriated landand the compensation to farmers. In this study, a reasonable rangefor the initial compensation was from 35,000 RMB/mu to50,000 RMB/mu.

4.4. Final solution

The final solution generated by the model is shown in Fig. 13. Thespatial layout of agricultural land and development land in the solu-tion is more compact relative to the land-use status quo (Fig. 14Aand C). Moreover, the sporadic emergence of development land inagricultural land is substantially decreased (Fig. 14 B). Overall, theland use of the study area became more rational. The objective func-tion values of the final solution are shown in Fig. 15. The land-usesuitability is well maintained. Although the compactness wasdamaged during the land-use coordination, the land-use pattern ofthe solution remains better than that of the land-use status quo,especially for the development land. The percentages of farmland,gardens, forests, and development land in the solution are 15.7%,

6.5%, 63.9%, and 12.0%, respectively, which meet the area constraintsin Table 1. The experimental results confirm that the model is feasi-ble to undertake land-use spatial optimization.

5. Conclusion

A land-use spatial optimization model is constructed in thisstudy, through coupling a genetic algorithm and game theory.The GA is repeatedly executed to separately optimize the spatiallayout of each land-use type. The land-use status quo is overlaidwith the optimization results to find local land-use competitions.The concept of land-use competition zones is introduced. Usingthe competition zones as the basic units, the model utilizesmulti-stakeholder games and the knowledge of land-use planningto coordinate the local land-use competitions. The competitionsare divided into three types to promote the land-use coordination.A dynamic game model of complete and perfect information isconstructed to solve the agriculture-development land competi-tion. The other competition types are solved using guidance fromland-use planning knowledge.

In order to verify the validity of the model, the model was uti-lized to optimize the land resource allocation in Gaoqiao Town,Zhejiang Province. The sporadic emergence of development landin agricultural land is substantially decreased in the final solution.The land-use pattern of the solution is more rational than that ofthe land-use status quo. The dynamic game model of completeand perfect information balanced the interests of farmers and thegovernment in solving the agriculture-development land competi-tion, and helped the government find suitable locations of the newdevelopment land. Through revealing the relationship between the

14 Y. Liu et al. / Computers, Environment and Urban Systems 49 (2015) 114

area of new development land and the initial compensation, thedynamic game model provided a referable range for the initialcompensation. The incorporation of the dynamic game modelimproves the ability of the land-use spatial optimization modelto support decision-making for regional land-use planning.

Local land-use competitions are a complicated problem involv-ing interests of multiple stakeholders. A dynamic game model ofincomplete information for the agriculture-development landcompetition can be constructed in future research. Game modelsfor the other land-use competition types can also be considered.

Acknowledgement

This study was supported by the National Natural Science Foun-dation of China (Grant No. 41371429).

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land-use spatial optimization model based on genetic optimization and game theory1 Introduction2 The land-use spatial optimization model2.1 Genetic optimization2.1.1 Chromosome structure and initialization2.1.2 Objectives2.1.3 Land-use constraints2.1.4 Genetic operators2.2 Definition of land-use competition zones2.3 Mechanism for land-use coordination2.3.1 A game model simulating negotiations between farmers and the government3 Study area and data4 Results and discussion4.1 Spatial layout optimization4.2 Land-use competitions4.3 Land-use coordination4.4 Final solution5 ConclusionAcknowledgementReferences