【正文】 ，使其適合于復雜的應用，例如土地利用規(guī)劃。例如，馮和林（ 1999）采用多目標累積遺傳算法（ CGA ）累計產(chǎn)生城市土地不同的場景用來城市規(guī)劃，城市區(qū)域為空間單元。Member等（ 2000 ）使用了主動多目標CGA優(yōu)化三個目標函數(shù)：最小化交通，減少運輸成本，減少土地利用現(xiàn)狀的變化。 Ligmann 杰琳斯卡等。 Cao等。The main objective of this study is to optimize the arrangement of urban land uses in parcel level using MultiObjective PSO (MOPSO) algorithm, considering multiple objectives and constraints simultaneously. In contrast to the abovementioned studies, in this research, the main objectives of landuse arrangement (patibility, dependency, suitability, and pactness) are considered together. In other words, the aim is to optimize the arrangement of urban land uses with respect to all those parameters. This indicates that many objectives have to be considered simultaneously, with a vast search space (many possible arrangements of land uses). The second difference of this research with others is in the usage of PSO for optimization. As indicated in the above literature review, most of the research on multiobjective landuse optimization is based on versions of Genetic Algorithm (GA). The main difference between PSO and GA methods is that PSO does not need genetic operators such as crossover and mutation, which are usually difficult to implement. Moreover, their information sharing mechanism is different: In GA, the information sharing is among all chromosomes, whereas in PSO, only the ‘best’ particle shares its information with others (Parsopoulos and Vrahatis 2010). In general, the main advantage of PSO is the flexibility and simplicity of its operators (Engelbrecht 2006, Van den Bergh and Engelbrecht 2006). The output of the MOPSO is a Pareto front of optimized answers, among which the user can select the most preferable answer based on his/her own priorities. This model proposes several land arrangements to support decisionmaking based on parameters specified by a decisionmaker.本研究的主要目的是在考慮多重目標同時約束下采用多目標粒子群算法（ MOPSO ）用于優(yōu)化城市土地地塊水平線的安排。換句話說，我們的目標是優(yōu)化城市土地利用相對于這些參數(shù)的布置。在上述文獻的回顧表明，大多數(shù)對多目標的土地利用優(yōu)化的研究是基于版本的遺傳算法（GA）。此外，他們的信息共享機制是不同的：在遺傳算法中，信息共享是所有染色體中，而在PSO中，只有39。的顆粒與他人分享它的信息（Parsopoulos和Vrahatis2010）。在MOPSO的輸出是一個帕累托解的集合的優(yōu)化答案，其中，用戶可以選擇基于他/她的自己的優(yōu)先事項的最優(yōu)選的答案。2. Fundamentals of the researchIn this section, the concepts of multiobjective optimization and the algorithms applied in this research are discussed.2 該研究的基本原理在本節(jié)中，討論了適用于這項研究的多目標優(yōu)化算法的概念. Multiobjective optimizationThe purpose of multiobjective optimization problems is to simultaneously optimize several objective functions (Hillier and Liberman 1995。 instead, one can obtain a set of answers called the‘Pareto front of the optimized answers’ or the ‘nondominated answers’ (Deb et al. 2002,Coello Coello et al. 2007). If we assume that f 1, f 2, . . . , fm are the objective functions of a problem, then xi can be a nondominated answer if the following conditions are met (Coello Coello and Lomont 2004, Sivanandam and Deepa 2008):? The answer xi should not be worse than xj in all objectives。因此，還有是不是只有一個答案的問題，反而可以得到一組答案叫“帕累托解的集合的優(yōu)化答案”或“非支配回答，（Deb等人。2007）如果我們假設(shè)F 1，F(xiàn) 2。 。 ，M}（1）?至少在一個目標上答案xi比xj更好，那就是，fk (xi) fk(xj)對于至少一個k∈{1，2。 。因此，存在不能保證絕對最佳辦法可以解決。. PSO algorithmThe PSO algorithm was developed by Kennedy and Eberhart (1995), as one of the AIbased optimization methods. In PSO, a number of particles are placed in the search space of some problem, each evaluating the objective function (fitness) at its location. In other words, the location of each particle is a solution to the problem, which can be evaluated against the objective function. Each particle decides on its next movement in the search space by bining some aspect of the history of its own best (bestfitness) locations with those of some members of the swarm. The next iteration happens when all particles are moved.Gradually, the swarm moves toward the optimum of the fitness function (Clerc 2006). If the dimension of the search space is d, the current location and velocity of the particle at time t are denoted by vectors x and v, respectively. Furthermore, the best position of all particles in the whole space (Gbest) and the best position of the particle in the previous movement experiences (Pbest) are memorized. With these explanations, the equation of the particles’motion for any dimension of d (the dth part of this vector will be indicated with the d index) is (Parsopoulos and Vrahatis 2010):where and are the previous velocity and location of the particle in the dth dimension,respectively。 w is the inertia weight (monly set to 2), r1 and r2 are random numbers generated uniformly in the range [0, 1] and are to provide randomness in the flight of the swarm。在PSO，一些粒子被放置在一些搜索問題的空間，在它的位置上有每個目標的評價函數(shù)。每個粒子結(jié)合其歷史方面的一些最好的（最適宜）的位置和一些群體其它成員的最好位置決定在搜索空間的下一個動作。漸漸地，群走向的適應度最佳的函數(shù)（二零零六年克萊爾奇）。此外，所有粒子在整個空間的最佳位置（Gbest）和在先前的粒子的最佳運動位置（Pbest）將被存儲。權(quán)重系數(shù)c1和c2控制Pbest位置和Gbest位置對于一個粒子速度的相對影響。. MOPSO algorithmMOPSO algorithms can be divided into two categories (ReyesSierra and Coello Coello2006). The first category consists of PSO variants that consider each objective function separately. In these approaches, each particle is evaluated with only one objective function at a time, and the best positions are determined following the standard single objective PSO rules, using the corresponding objective function. The main challenge in these PSO variants is the proper manipulation of information from each objective function,in order to guide particles toward Paretooptimal solutions. The second category consists of approaches that evaluate all objective functions for each particle, and based on the concept of Pareto optimality, produce nondominated best positions (often called leaders) to guide the particles. The determination of leaders is nontrivial, since they have to be selected among a plethora of nondominated solutions in the neighbourhood of a particle. This is the main challenge related to the second category. Many methods have been used for this purpose (ReyesSierra and Coello Coello 2006, Parsopoulos