【正文】 umber of repetitions es to an end and/or the final condition of the algorithm is met. MOPSO算法MOPSO算法可以分為兩大類（雷耶斯 Sierra和科埃略科埃略2006年）。第二類包括為每個(gè)粒子評(píng)價(jià)所有的目標(biāo)函數(shù)，并基于帕累托最優(yōu)概念的方法，產(chǎn)生非支配最佳位置（通常被稱為領(lǐng)導(dǎo)者）來指導(dǎo)的顆粒。 Fan等。第一，在創(chuàng)建初始種群，計(jì)算目標(biāo)函數(shù)的值，與非主導(dǎo)的答案都保存在一個(gè)外部檔案。然后，下面的方法時(shí)，直到重復(fù)次數(shù)玩完和/或算法的最終條件得到滿足。The velocity of any particle in the d dimension can be calculated by the followingequation: where all of the parameters are the same as in Equation (3), with the exception that rep(h) 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 Paretofront.在d維的任何粒子的速度可以通過以下計(jì)算公式： where all of the parameters are the same as in Equation (3), with the exception that rep(h) 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(jià)值主導(dǎo)的檔案作為一個(gè)領(lǐng)袖，如在以下。如在以下。當(dāng)選擇超立方體h后，被選擇的解決方案中的一個(gè)被隨機(jī)作為下一個(gè)運(yùn)行的一個(gè)領(lǐng)導(dǎo)者（REP（h）在公式（5）），并且粒子的新位置被計(jì)算。這包括回答結(jié)構(gòu)的定義，本目標(biāo)函數(shù)和約束條件。一個(gè)粒子的運(yùn)動(dòng)是指在土地用途安排上的小變化。通過顆粒的一步步運(yùn)動(dòng)，最高效的土地利用安排被找到。在這項(xiàng)研究中，兼容性意味著何種程度的兩個(gè)或兩個(gè)以上的土地利用類型共存，沒有重大的負(fù)面影響。這在評(píng)估沒有標(biāo)準(zhǔn)存在的情況下尤其有用（ Talei等。該問卷被送到五個(gè)被選中的德黑蘭直轄市和10個(gè)關(guān)于這個(gè)問題專家的顧問公司。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?yàn)榻o定的算法使用數(shù)值來解決這個(gè)問題，在分析層次分析法（AHP）和結(jié)構(gòu)化的成對(duì)比較法（謝里菲等人。（1989）和Saaty和巴爾加斯（2000），（2004），Bhushan和RAI和Hotman（2005）。為簡單起見，在本研究中，我們假設(shè)β= 1。表示最小的距離在兩個(gè)土地利用，倆類土地利用類型間有最大影響。為了克服這個(gè)問題，目標(biāo)函數(shù)可以改變?nèi)プ畲蠡钚?shù)量的兼容性。方程中沒有這部分，低兼容性相鄰地塊的效果可能會(huì)被高兼容周邊地補(bǔ)償。. 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:。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(jì)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)）。在這項(xiàng)研究中，使用給定的權(quán)重計(jì)算土地的用途的任一方面的一般的適宜性。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。. 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。考慮的因素是面積（A），可達(dá)性（AC），每個(gè)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）。. 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(gè)位置可解釋為一個(gè)特定的使用的適宜性（Steiner2008）。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(gè)標(biāo)準(zhǔn)。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。因此，第一個(gè)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(gè)地塊i的鄰域數(shù)量，n是所有的地塊的數(shù)量。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 pens