【正文】 ) is the value obtained from the nondominated archive as a leader, as described in the followings.By assuming m as the number of available solutions in a hypercube, the probability roulette wheel of Equation (6) is applied to choose a hypercube with the h index. In fact, the aim is to choose a hypercube with fewer particles to optimize the density of the Pareto front.所有的參數(shù)是相同的在方程（3），除代表（H）從非得到價值主導(dǎo)的檔案作為一個領(lǐng)袖，如在以下。通過假設(shè)M作為一個超立方體可解的個數(shù)，概率方程輪盤（6）應(yīng)用于選擇與H指數(shù)超立方體。事實上，其目的是選擇用較少的粒子優(yōu)化的帕累托密度超立方體前。所有的參數(shù)是和方程（3）中相同的，除rep(h)是從作為一個領(lǐng)袖的非主導(dǎo)的檔案得到的值。如在以下。通過假設(shè)m作為一個超立方體可解的個數(shù)，概率輪盤方程（6）與?指數(shù)應(yīng)用于選擇超立方體。事實上，其目的是用較少的粒子選擇一個超立方體去優(yōu)化的帕累托解的集合的密度。where mi is the number of particles in the ith hypercube, β is a constant coefficient to control the amount of differentiations in the probability values, and k is the number of all hypercubes.After choosing hypercube h, one of its solutions is chosen randomly as a leader (rep(h) in Equation (5)) for the next run, and the new position of the particles is calculated. The process is continued until the optimization criteria are met. In multiobjective optimization, usually the criterion is to reach a specified number of iteration.其中mi是在第i個超立方體顆粒的數(shù)，β為常數(shù)系數(shù)，控制概率值中的差異量，以及k是所有的超立方體的個數(shù)。當(dāng)選擇超立方體h后，被選擇的解決方案中的一個被隨機作為下一個運行的一個領(lǐng)導(dǎo)者（REP（h）在公式（5）），并且粒子的新位置被計算。該過程繼續(xù)進行直到最優(yōu)化準則得到滿足。在多目標優(yōu)化下，通常情況下準則一定會達到迭代的指定數(shù)量。3. Developed landuse optimization modelIn this section, we first match the MOPSO method with the problem in hand, the optimizationof landuse arrangement. This includes the definition of the answer structure, the objective functions, and the constraints.In the PSO algorithm used here, every possible arrangement of all considered land uses throughout the entire land units can be considered as a potential particle (particle location) in the search space. The algorithm looks for a particle location (an arrangementof land uses) that satisfies the objective functions best. First, initial population of particles is selected and each particle starts to move in the search space. The moving of a particle means small changes in the arrangement of land uses. With any movement of a particle, its fitness regarding objective functions is calculated. At every step, both the best locations experienced by the individual particle (Pbest) and the group of particles (Gbest) are found and stored. The movement of the particle in the next step is inspired by Pbest and Gbest. Through stepbystep movements of the particles, finally the arrangements of land uses with the highest values of fitness are found.3 發(fā)達的土地利用優(yōu)化模型在本節(jié)中，我們首先匹配MOPSO方法的問題在手，優(yōu)化土地使用安排。這包括回答結(jié)構(gòu)的定義，本目標函數(shù)和約束條件。在這里使用的PSO算法，所有土地使用的每一個可能的安排都是通過全部土地單位可被看作是搜索空間上的一個潛在的粒子（顆粒位置）。該算法查找一個粒子的位置（該結(jié)構(gòu)土地用途）最好的滿足目標函數(shù)。第一，初始種群是選定的，每個粒子開始在搜索空間中移動。一個粒子的運動是指在土地用途安排上的小變化。帶有顆粒的任何運動，其目標函數(shù)適應(yīng)度都將被計算。每一步，單個粒子所經(jīng)過的最佳位置(Pbest)和粒子群的最佳位置（ Gbest）被發(fā)現(xiàn)并存儲。顆粒在下一步驟中的運動是由個體極值和GBEST啟發(fā)。通過顆粒的一步步運動，最高效的土地利用安排被找到。. Objective functionsIn this research, four objective functions were considered to model the problem: maximization of the landuse patibility, maximization of the landuse dependency, maximization of the landuse suitability, and maximization of the pactness between landuse types. These objective functions are discussed in the following sections. 目標函數(shù)在本研究中，四個目標函數(shù)被考慮進問題的模型：最大化土地使用的兼容性，最大化土地利用相關(guān)性，最大化的土地利用適宜性，土地利用類型之間的緊湊的最大化。這些目標函數(shù)將在以下章節(jié)中討論。. Compatibility objective function Each landuse type has a level of patibility with different landuse types in its neighbourhood. In this research, patibility means the degree to which two or more landuse types coexist without a significant negative impact. To describe the patibility between land uses at parcel level, a patibility matrix between land uses was used. In this research, the Delphi method is used as a framework for constructing detailed patibility matrix. The Delphi method is an iterative process designed to achieve consensus among a group of experts on a particular topic (Adler and Ziglio 1996, Skulmoski et al. 2007). This is especially useful in situations where no standard criteria exist for evaluation (Talei et al. 2007). The activity of this section was based on a tworound Delphi survey. The first round includes the design of the questionnaire, analysis of the responses, and preparation of draft patibility matrix. The questionnaire was sent to five chosen municipalities of Tehran and to 10 consultant panies, expert on the subject. The second round includes distribution of the matrix, reevaluation of the results, and revision of the patibility matrix. This led to a relative and approximate patibility score for detailed landuse types, which were used to construct a detailed patibility matrix. Following the Delphi method, the levels considered for patibility of land uses are: highly patible (HC), moderately patible (MC), low/neutrally patible (NC), moderately inpatible (MI), and highly inpatible (HI). Table 1 shows the results of the Delphi survey on landuse patibility. 兼容性目標函數(shù)每個土地利用類型與其鄰里的不同的土地利用類型有一個水平的兼容性。在這項研究中，兼容性意味著何種程度的兩個或兩個以上的土地利用類型共存，沒有重大的負面影響。描述土地用途地塊水平的相容性，使用的是土地用途之間的兼容性矩陣。在這種研究， Delphi法被用作于構(gòu)建詳細兼容性矩陣的框架。德爾菲法是一個迭代過程，旨在實現(xiàn)達成共識 在一組特定的主題（阿德勒和1996年Ziglio ， Skulmoski等，2007 ）專家。這在評估沒有標準存在的情況下尤其有用（ Talei等。 2007年）。本節(jié)的活動是基于一個兩輪德爾菲調(diào)查。第一輪包括調(diào)查表的設(shè)計，響應(yīng)的分析，以及制備兼容性草案矩陣。該問卷被送到五個被選中的德黑蘭直轄市和10個關(guān)于這個問題專家的顧問公司。第二輪包括矩陣的分布，對結(jié)果的評價，和相容性修正矩陣。得到一個相對詳細的土地使用兼容性評分和近似類型，它被用來建立一個詳細的兼容性矩陣。通過德爾福法，土地用途的兼容性級別是：高度兼容（ HC）適度兼容（ MC ） ，低/中性兼容（NC ），中度不兼容（ MI）和強不相容（ HI） 。表1顯示了德爾菲調(diào)查的結(jié)果Because the given algorithm uses numerical values to solve the problem, the analytic hierarchy process (AHP) and the structured pairwise parison methods (Sharifi et ) are used as a framework for the quantification of the patibility levels that arises from the qualitative assessment mentioned in the previous process. AHP is one of the widely applied multicriteria evaluation methods (Bowen 1993). Detailed explanation of AHP method is provided in many references, such as Golden et al. (1989) and Saaty and Vargas (2000), Bhushan and Ra