【正文】 fk (xi) fk(xj)對(duì)于至少一個(gè)k∈{1，2。2007）如果我們假設(shè)F 1，F(xiàn) 2。 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。在MOPSO的輸出是一個(gè)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(xiàng)的最優(yōu)選的答案。此外，他們的信息共享機(jī)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。換句話說(shuō)，我們的目標(biāo)是優(yōu)化城市土地利用相對(duì)于這些參數(shù)的布置。 Cao等。Member等（ 2000 ）使用了主動(dòng)多目標(biāo)CGA優(yōu)化三個(gè)目標(biāo)函數(shù)：最小化交通，減少運(yùn)輸成本，減少土地利用現(xiàn)狀的變化。帕累托集通常是獨(dú)立的相對(duì)重要的目標(biāo)，使其適合于復(fù)雜的應(yīng)用，例如土地利用規(guī)劃。 （2007年） 。In some other studies, objectives are optimized simultaneously in multiobjective mode focusing on Pareto front. The concept of Pareto front is properly described in Deb et al. (2002) and Coello Coello et al. (2007). The Pareto set is usually independent of the relative importance of objectives, making it suitable for plex applications such as landuse planning. Many studies on landuse optimization are carried out using Pareto front. For example, Feng and Lin (1999) generated different scenarios of urban land uses for urban planners using multiobjective Cumulative Genetic Algorithm (CGA), having the city zones as spatial units. Objective functions were maximizing the suitability of lands for development and maximizing the patibility of neighbouring zones. Member et al. (2000) used an initiative multiobjective CGA to optimize three objective functions: minimizing traffic, minimizing the costs of transportation, and minimizing current landuse changes. In this initiative algorithm, the optimization process was not performed simultaneously。此外，非凸優(yōu)化的解決方案不能被最小化的線性組合來(lái)獲得目標(biāo)（ Cao等2011） 。例如， Shiffa等。因此，許多方法的開(kāi)發(fā)，以多重目標(biāo)轉(zhuǎn)換成單一目標(biāo)。 （2006），Talei等。2011）因此，土地利用配置可以被視為一個(gè)優(yōu)化問(wèn)題。這類問(wèn)題需要考慮多且被認(rèn)為是同時(shí)相互沖突的目標(biāo)（如生態(tài)和經(jīng)濟(jì)目標(biāo)）（chandramouli等人。此外，同時(shí)它考慮不同的土地用途并試圖優(yōu)化多個(gè)目標(biāo)關(guān)鍵詞：安排。用戶可以選擇最合適的解決方案根據(jù)他/她的重點(diǎn)。本研究的主要目的是同時(shí)考慮多個(gè)目標(biāo)限制，利用多目標(biāo)粒子群優(yōu)化算法來(lái)找到最佳用于城市土地安排地塊的水平。多目標(biāo)粒子群優(yōu)化算法在配置城市土地使用上的應(yīng)用Considering the everincreasing urban population, it appears that land management is of major importance. Land uses must be properly arranged so that they do not interfere with one another and can meet each other’s needs as much as possible。地理空間信息系統(tǒng)是在開(kāi)發(fā)模型時(shí)，用來(lái)準(zhǔn)備數(shù)據(jù)和研究不同空間場(chǎng)景。該方法使用區(qū)域7德黑蘭1的數(shù)據(jù)進(jìn)行了測(cè)試。城市，土地利用，地理信息系統(tǒng)。2009，小李等人。在土地利用多目標(biāo)優(yōu)化（陌路）模型時(shí)，考慮了不同的組合目標(biāo)。 （2007年），江平與群（2009），哈克和麻美（2011），以及庫(kù)門(mén)等。在一個(gè)單一的目標(biāo)模式搜索解空間，一些研究人員采用經(jīng)典的優(yōu)化方法如線性規(guī)劃（LP）。 （ 2011）采用粒子群優(yōu)化算法（PSO）優(yōu)化劃撥土地使用，考慮最大土地適宜性和最小改變土地形狀的成本。此外，決策者希望探索一套替代解決方案，權(quán)衡不同的目標(biāo)并做出相應(yīng)的決策。 instead, it was applied step by step for any of the objective functions, and the best results were then taken for optimization of the next function. LigmannZielinska et al. (2008) focused on the efficient utilization of urban space through infill development,patibility of adjacent land uses, and defensible redevelopment. Cao et al. (2011) used NonDominated Sorting Genetic Algorithm (NSGAII) to propose optimal landuse scenarios with three objective functions: minimizing conversion costs, maximizing accessibility, and maximizing patibilities between land uses.在其他一些研究中，目標(biāo)是專注于Pareto前沿在多目標(biāo)模式下同時(shí)優(yōu)化。帕累托解的集合是德布等的描述。土地利用優(yōu)化的許多研究都使用了Pareto前沿。在這一倡議算法，優(yōu)化過(guò)程中不同時(shí)進(jìn)行；相反，它是一步一步的任何目標(biāo)函數(shù)，得到最好的結(jié)果用于隨后采取的下一個(gè)函數(shù)的優(yōu)化。 （ 2011 ）使用的非支配排序遺傳算法（ NSGAII ）提出了優(yōu)化土地利用三目標(biāo)函數(shù)最小化的情景：轉(zhuǎn)換成本，最大化可達(dá)性，最大限度地土地使用兼容性。這表明許多目標(biāo)必須同時(shí)考慮，具有廣闊的搜索空間（多土地用途可能的安排） 。最好39。該模型提出了一些基于決策者指定的參數(shù)土地整理決策。 in other words,fk (xi) ≥ fk（xj）for all k ∈ {1, 2, . . . ,m} (1)? The answer to xi is better than xj, in at least one objective, that is,fk (xi) fk(xj)for at least one k ∈ {1, 2, . . . ,m} (2)In multiobjective optimization, when the objective functions are plex and/or the search space is extensive, AIbased methods are often used. Using these methods, the entire search space is not investigated. Therefore, there is no guarantee that the definitely optimum solution can be found. Instead, there is a promise that some solutions near enough to the optimum can be found in reasonable time, regardless of the numerous feasible solutions(Coello Coello and Lamont 2004). 多目標(biāo)優(yōu)化多目標(biāo)優(yōu)化問(wèn)題的目的是同時(shí)優(yōu)化幾個(gè)目標(biāo)函數(shù)（希利爾和利伯曼1995；該和拉蒙特1999）。..FM是一個(gè)問(wèn)題的目標(biāo)函數(shù)，然后xi 可以是一個(gè)非支配的答案，如果滿足以下條件，（科埃略科埃略和2004年Lomont，Sivanandam和2008年和Deepa）：?答案xi不應(yīng)該比所有的目標(biāo)的xj更糟，換句話說(shuō)，fk (xi) ≥ fk(xj) for all k ∈ {1, 2, . . . ,m} (1)對(duì)于所有的k∈{1，2。 。取而代之的是一個(gè)承諾，在眾多可行的解決方案中的一些能在合理時(shí)間內(nèi)被發(fā)現(xiàn)近優(yōu)解，（科埃略科埃略和2004年拉蒙特）。 and c1 and c2 are weighting factors, also called the cognitive and social parameters, respectively (Shi and Eberhart 1998, Poli et al. 2007). The weight coefficients c1 and c2 control the relative effect of the Pbest and Gbest locations on the velocity of a particle. Although lower values for c1 and c2 allow each particle to explore locations far away from already uncovered good points, higher values of these parameters encourage more intensive search of regions close to previous points (Clerc 2006). 粒子群優(yōu)化算法PSO算法是由甘乃迪和Eberhart開(kāi)發(fā)的（1995），作為一種基于人工智能的優(yōu)化方法。所有的粒子移動(dòng)時(shí)下一次迭代發(fā)生。這些說(shuō)明中，粒子的方程的在d的任何一個(gè)維度上移動(dòng)是（此向量的第d部分會(huì)與D指數(shù)一起顯示）為（Parsopoulos和Vrahatis2010）：其中和為在第d維度上之前的速度和粒子的位置，和是在同樣維度上的新的粒子速度和粒子的位置，此外，w為慣性重量（通常為2），r1和r2是在[0,1]范圍內(nèi)均勻地產(chǎn)生的隨機(jī)數(shù)，并且提供群的隨機(jī)性飛行；C1和C2是加權(quán)因子，也分別稱為認(rèn)知參數(shù)和社會(huì)參數(shù)（Shi和埃伯哈特1998年，波利等人，2007）。 Fan et ). In this article, a method proposed by Coello Coello and Lamont (2004) was used because it has less putational plexity and a quicker convergence (ReyesSierra and Coello Coello 2006). The following is a brief explanation of the method.First, an initial population is created, the values of the objective functions are calculated, and nondominant answers are preserved in an external archive. In the archive of nondominant answers, some hypercubes (with the same dimension as objective functions) are created. In Figure 1, an example of a twodimensional search space and its division into hypercubes is shown. In the twodimensional search space, the hypercubes are squares. Then, the following process is employed until the n