【正文】 . Compactness objective functionSome land uses such as residential are preferred to。適合的目標(biāo)函數(shù)定義為：where n is the number of parcels and is the suitability of parcel i for landuse type Ci.其中n是地塊的數(shù)量和是土地使用類型為Ci 的地塊i的適用性。權(quán)重被定義為 The units and concepts of parameters are different. Therefore, they are transferred into parable scales using AHP method and are normalized in the range [0, 1]. The suitability objective function is defined by:參數(shù)的單位和概念是不同的?？紤]的因素是面積（A），可達(dá)性（AC），每個地塊的邊數(shù)（ED），斜率（S），所有制類型（P），噪音污染（SP），空氣污染（AP），電阻的變化（R）之間的差異和邊緣尺寸（De）。在這項研究中，使用給定的權(quán)重計算土地的用途的任一方面的一般的適宜性。. Suitability objective functionThe utility of a location can be interpreted as the suitability for a certain use (Steiner 2008).The suitability can be explained by a range of different factors and it is program dependent (Koomen and Stillwell 2007, Lagore 2008). In this research, the general suitability of each parcel for any of the land uses was calculated using the weights given to the factors. The weights of factors for different land uses were determined by urban planners. Considered factors are area (A), accessibility (Ac), number of edges of every parcel (Ed),slope (S), ownership type (P), sound pollution (Sp), air pollution (Ap), resistance to change(R), and difference between edge sizes (De). The general suitability of parcel j for landuse type Ci can be defined by: 適宜的目標(biāo)函數(shù)一個位置可解釋為一個特定的使用的適宜性（Steiner2008）。類似于兼容性功能，依賴函數(shù)是基于距離被定義為： where iis the calculated dependency for parcels i and j, is the dependencyof two landuse types Ci and Cj extracted from the dependency matrix, and is thedistance function of the dependency (similar to the patibility function). Finally, the dependency objective function is defined by:其中Depij是計算了的地塊i和地塊 j的依賴性，是從相關(guān)矩陣中提取的土地利用類型的Ci和Cj的依賴性，是距離函數(shù)的依賴性（類似的相容性函數(shù)）。有關(guān)土地使用類型間依賴關(guān)系的滿意度是土地利用安排的可接受性的一個標(biāo)準(zhǔn)。. Dependency objective functionUsually, a landuse type needs some other landuse types in its vicinity in order to serve people properly. The amount of satisfaction regarding such dependencies between land use types is a criterion for the acceptability of landuse arrangements. For the dependency criterion, such as patibility, a matrix is generated using Delphi method.Similar to patibility function, the dependency function is defined based on distance:。Figure 3. Between the two radiuses the effect of patibility and dependency objective functionsreducing from 1 to 0 as a function of distance.圖3。方程中沒有這部分，低兼容性相鄰地塊的效果可能會被高兼容周邊地補(bǔ)償。因此，第一個目標(biāo)函數(shù)可以被定義的： where i indicates the parcel under consideration, j represents its neighbours, ni is the number of neighbours for each parcel i, and n is the number of all parcels. The second part of Equation (10) is to maximize the minimum patibility of the arrangement. Not having this part in the equation, the effect of a lowpatible neighbouring parcel might be pensated by a highpatible neighbouring parcel. Similar to this objective function, a similar term is added to dependency and suitability objective functions.其中i表示所考慮的地塊，j代表其鄰域， ni 是每一個地塊i的鄰域數(shù)量，n是所有的地塊的數(shù)量。為了克服這個問題，目標(biāo)函數(shù)可以改變?nèi)プ畲蠡钚?shù)量的兼容性。In Figure 3, the maximum and the minimum distances of the effects are schematically shown.It should be noted that, when the objective is to maximize the total patibility of a land with all its neighbours, then low patibilities with some neighbours can simply be pensated by high patibilities with some other neighbours. To overe this problem, the objective function can be altered to maximize the minimum amount of patibility as well. Following this objective, each land would have an adequate level of patibility with all its neighbours. Thus, the first objective function may be defined by:在圖3中，是最大距離和最小距離的影響示意圖。表示最小的距離在兩個土地利用，倆類土地利用類型間有最大影響。Figure 2. Effect of the distance on the patibility objective function. shows the minimumdistance between two land uses and which two landuse types has the maximum effect on each other in this distance (as shown in y axis it is consider 1 in this research) and the shows the maximum radius of effect between two land uses. β shows the distance effect on patibility.圖2。為簡單起見，在本研究中，我們假設(shè)β= 1。兩個地塊的的兼容性（記為Compij）i和j與土地利用類型ci 和cj，一個彼此間的距離dij被定義為：where Compcicj is the patibility of two landuse types Ci and Cj in the patibility matrix.More specifically, the patibility function can be defined by: in which, the function defines the effect of distance and is calculated by Equation (9). For simplicity, in this study, we assume β=1. The general shape of this function is shown in Figure 2.在pcicj是兩種土地利用類型的Ci和Cj的相容性矩陣。（1989）和Saaty和巴爾加斯（2000），（2004），Bhushan和RAI和Hotman（2005）。 AHP是一個廣泛應(yīng)用的多準(zhǔn)則評價方法（鮑文1993）。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 Rai (2004), and Hotman (2005). Table 2 shows the weights calculated using this method.The patibility (denoted as Compij) of two parcels i and j with landuse types Ci and Cj, at a distance dij to each other is defined by: 因為給定的算法使用數(shù)值來解決這個問題，在分析層次分析法（AHP）和結(jié)構(gòu)化的成對比較法（謝里菲等人。得到一個相對詳細(xì)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(xì)的兼容性矩陣。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。本節(jié)的活動是基于一個兩輪德爾菲調(diào)查。這在評估沒有標(biāo)準(zhǔn)存在的情況下尤其有用（ Talei等。在這種研究， Delphi法被用作于構(gòu)建詳細(xì)兼容性矩陣的框架。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(fù)面影響。這些目標(biāo)函數(shù)將在以下章節(jié)中討論。通過顆粒的一步步運(yùn)動，最高效的土地利用安排被找到。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。一個粒子的運(yùn)動是指在土地用途安排上的小變化。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(biāo)函數(shù)。這包括回答結(jié)構(gòu)的定義，本目標(biāo)函數(shù)和約束條件。在多目標(biāo)優(yōu)化下，通常情況下準(zhǔn)則一定會達(dá)到迭代的指定數(shù)量。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(jī)作為下一個運(yùn)行的一個領(lǐng)導(dǎo)者（REP（h）在公式