用于約束多目標(biāo)優(yōu)化問題的雙群體差分進(jìn)化算法-閱讀頁
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【正文】 ．最后利用新生成的群體更新最優(yōu)個體集合和，群體的更新方法和SPEA算法中外部群體的更新方法相同，而的更新方法如下：如果新生成的可行解Pareto優(yōu)于對應(yīng)的局部最優(yōu)解，則用替換，否則不予替換．綜上所述，基于雙群體的差分進(jìn)化算法的約束處理技術(shù)的流程可表示如下：step1. 隨機(jī)生成個個體，判斷每一個體的可行性，然后根據(jù)個體可行性將其插入到對應(yīng)的群體或中；并初始化和及參數(shù)和．step2. 判斷搜索是否結(jié)束，如果結(jié)束，轉(zhuǎn)向step5，否則轉(zhuǎn)向step3.step3. 生成隨機(jī)數(shù)，如果，根據(jù)方法1，生成新的個體；否則，根據(jù)方法2生成新的個體，如果是可行解，將插入到中；否則插入到中，反復(fù)執(zhí)行直到生成個可行解．step4. 根據(jù)新生成的群體更新最優(yōu)個體集和，轉(zhuǎn)向step2．step5. 輸出最優(yōu)解集．3 算法分析 算法的性能衡量約束優(yōu)化問題的算法性能的衡量可分為兩部分，一部分為最終獲得的最優(yōu)解的性能的衡量，如通過GD[15]來度量最優(yōu)群體的逼近性，SP[16]來衡量最優(yōu)解的分布均勻性，或通過計算目標(biāo)函數(shù)的次數(shù)衡量算法的復(fù)雜度和算法的收斂速度．另一部分是針對約束優(yōu)化問題來衡量群體的多樣性，Koziel amp。接下來我們的研究將致力于如何降低算法的時間復(fù)雜度及本文算法的實(shí)際應(yīng)用。 Engineering Design. John Wiley amp。[3]. David , Genetic in search, optimization and machine learning. AddisonWesley Publishing Co.,Reading,Massachusetts,1989.[4]. Wang Yuexuan, Liu Lianchen, etc,. Constrained Multiobjective Optimization Evolutionary Algorithm. Journal of Tsinghua Univ(Sci amp。nez and Jos233。rgen Zimmermann, editor, 7th European Congress on Intelligent Techniques and Soft Computing (EUFIT39。2002, volume Constrained Optimization Problem。BackgroundConstrained optimization, both for nonlinear programming and multiobjective optimization, is a very important problem and has a variety of applications in engineering, management, mathematics and other fields. A mon way to constrained optimization problem is to deal with constraints by penalty function, with the disadvantage and difficulty in choosing the penalty factors. In this paper, the authors propose a differential evolution based on double populations for constrained multiobjective optimization problem. By using the definitions and the mechanism in the paper, an effective evolutionary algorithm for constrained multiobjective optimization problem is given and the time plexity is discussed and pared with the state of the art—NSGAⅡand SPEA, which shows the time plexity of the proposed algorithm is as the same magnitude as SPEA and is higher than that of NSGAⅡ, while simulations illustrate that the proposed algorithm is superior to NSGAⅡin the measure of GD and SP. However, it is worthy to note that the time plexity of our algorithm will decrease greatly if a strategy like NSGAⅡis taken for updating optimal population.孟紅云，女， 1975年生，博士，副教授，主要研究領(lǐng)域?yàn)閮?yōu)化理論與方法、自然計算、圖像處理. Email: mhyxdmath. 張小華，男，1974年生，博士，副教授，主要研究領(lǐng)域?yàn)樽匀挥嬎?、智能信息處理、?shù)據(jù)挖掘和數(shù)字水印. 劉三陽，男，1959年生，博士，教授，博士生導(dǎo)師，主要研究領(lǐng)域?yàn)閮?yōu)化理論與方法.MENG Hongyun, born in 1975, Ph. D. , associate professor. Her research interests include Optimization theory and algorithm, natural putation, image processing.ZHANG Xiaohua, born in 1974, Ph. D. , associate professor. His research interests include natural putation, intelligent information processing, data mining, and digital watermark. LIU Sanyang, born in 1959, ., professor, . supervisor. His research interests include Optimization theory and methods.第一作者照片 作者孟紅云的聯(lián)系方式： Email: mhyxdmath手機(jī)：013636804033 12 / 12
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