【正文】 Figure 4. Semicode for describing the counter for defining the pactness objective function.半碼用于描述限定緊湊的目標(biāo)函數(shù)的計(jì)數(shù)器。宗地土地使用類型是ci的地塊j的一般適用性可以定義：where w1 to w9 are the weights given to the factors. The weights are defined such that其中w1至W9是考慮到的因素的權(quán)重。適宜性可以通過一系列不同的因素來解釋，它是程序依賴（庫門和史迪威2007，lagore 2008）。對(duì)于依賴標(biāo)準(zhǔn)，如兼容性，采用德爾菲法生成矩陣。兩個(gè)半徑之間的兼容性和依賴目標(biāo)函數(shù)的影響從1減少到0的距離的函數(shù)。方程（10）的第二部分是最大化布置的最小相容性。應(yīng)當(dāng)指出的是，當(dāng)目標(biāo)想要最大化所有鄰域土地的總兼容性，那么就降低一些可以簡單被其他一些高兼容性鄰域進(jìn)行補(bǔ)償?shù)募嫒菪浴Ｄ繕?biāo)函數(shù)兼容性的距離效果。更具體地說，兼容性函數(shù)可以定義：其中，函數(shù) 定義了距離的影響，并被等式（9）計(jì)算。AHP方法詳細(xì)解釋在很多資料中提供參考，例如金等。通過德爾福法，土地用途的兼容性級(jí)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(qiáng)不相容（ HI） 。第一輪包括調(diào)查表的設(shè)計(jì)，響應(yīng)的分析，以及制備兼容性草案矩陣。德爾菲法是一個(gè)迭代過程，旨在實(shí)現(xiàn)達(dá)成共識(shí) 在一組特定的主題（阿德勒和1996年Ziglio ， Skulmoski等，2007 ）專家。. 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(biāo)函數(shù)每個(gè)土地利用類型與其鄰里的不同的土地利用類型有一個(gè)水平的兼容性。顆粒在下一步驟中的運(yùn)動(dòng)是由個(gè)體極值和GBEST啟發(fā)。第一，初始種群是選定的，每個(gè)粒子開始在搜索空間中移動(dòng)。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(dá)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。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(gè)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(gè)數(shù)。所有的參數(shù)是和方程（3）中相同的，除rep(h)是從作為一個(gè)領(lǐng)袖的非主導(dǎo)的檔案得到的值。每個(gè)單元顯示在這個(gè)空間的一個(gè)超立方體（科埃略科埃略等人，2004）。在二維搜索空間中，超立方體是正方形。下面是該方法的簡要說明。許多方法已被用于這個(gè)目的（雷耶斯 Sierra和科埃略科埃略2006年， Parsopoulos和Vrahatis 2010 。PSO變種面臨的主要挑戰(zhàn)是每個(gè)目標(biāo)函數(shù)的正確的操作信息，這些信息是為了引導(dǎo)粒子走向帕累托最優(yōu)的解。. 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 and Vrahatis 2010。此外，所有粒子在整個(gè)空間的最佳位置（Gbest）和在先前的粒子的最佳運(yùn)動(dòng)位置（Pbest）將被存儲(chǔ)。每個(gè)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(gè)動(dòng)作。 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。因此，存在不能保證絕對(duì)最佳辦法可以解決。 ，M}（1）?至少在一個(gè)目標(biāo)上答案xi比xj更好，那就是，