第2卷第5期 智能系统学报 Vol.2№5 2007年10月 CAAI Transactions on Intelligent Systems 0ct.2007 动态多目标免疫优化算法及性能测试研究 钱淑渠2张著洪 (1.贵州大学理学院，贵州贵阳550025：2.贵州安顺学院数学系，贵州安顺561000) 摘要：基于生物免疫系统的自适应学习、免疫记忆抗体多样性及动态平衡维持等功能，提出一种动态多目标免疫 优化算法处理动态多目标优化问题.算法设计中，依据自适应飞邻域及抗体所处位置设计抗体的亲和力，基于P r心to控制的概念，利用分层选择确定参与进化的抗体，经由克隆扩张及自适应高斯变异，提高群体的平均亲和力，利 用免疫记忆动态维持和Average linkage聚类方法，设计环境识别规则和记忆池，借助3种不同类型的动态多目标 测试问题，通过与出众的动态环境优化算法比较，数值实验表明所提出算法解决复杂动态多目标优化问题具有较大 潜力. 关键词：动态多目标优化，时变Pareto面；环境跟踪；自适应（邻域；免疫算法 中图分类号：TP301.6文献标识码：A文章编号：16734785(2007)05006810 Dyna mic multiobjective immune optimization algorithm and performance test QIAN Shurqu'2,ZHAN G Zhuhong (1.College of Science,Guizhou University,Guizhou 550025,China;2.Department of Mathematics,Anshun College,Anshun 561000,China) Abstract:A dynamic multi-objective immune optimization algorithm suitable for dynamic multi-objective optimization problems is proposed based on the functions of adaptive learning,immune memory,antibody diversity and dynamic balance maintenance,etc.In the design of the algorithm,the scheme of antibody af- finity was designed based on the locations of adaptive-neighborhood and antibody;antibodies participating in evolution were selected by Pareto dominance.In order to enhance the average affinity of the population, clonal proliferation and adaptive Gaussian mutation were adopted to evolve excellent antibodies.Further- more,the average linkage method and several functions of immune memory and dynamic balance mainte- nance were used to design environmental recognition rules and the memory pool.The proposed algorithm was compared against several popular multi-objective algorithms by means of three different kinds of dy- namic multi-objective benchmark problems.Simulations show that the algorithm has great potential in sol- ving dynamic multi-objective optimization problems. Keywords:dynamic multi-objective optimization;time-varying Pareto front;environment tracking;adap- tive -neighborhood;immune algorithm 动态多目标优化(dynamic multi-objective opti- 等.尽管大量静态多目标进化算法已相继提出) mization,DMO)是指优化问题的目标函数、定义 其中较为典型的2种进化算法为SPEAII31和NS 域、约束条件中至少有一个随时间而变化的多目标 GAIT,但寻求解决DMO的算法研究甚少).文 优化问题.在工程应用领域，大量此类问题急需解 献[1-2,6-7]报道了有关动态多目标进化算法的 决山，如：交通信号灯控制、机器人控制、故障诊断 研究进展.特别是Marco等在文献[2]中设计了几 种动态多目标测试问题，相应地，提出了一种邻域搜 收稿日期：200612-05. 基金项目：因家自然科学基金资助项目(60565002) 索算法(directiombased method,DBM),从性能测 1994-2008 China Academic Journal Electronic Publishing House.All rights reserved.http://www.cnki.net第 2 卷第 5 期 智 能 系 统 学 报 Vol. 2 №. 5 2007 年 10 月 CAAI Transactions on Intelligent Systems Oct. 2007 动态多目标免疫优化算法及性能测试研究 钱淑渠1 ,2 ,张著洪1 (1. 贵州大学 理学院 ,贵州 贵阳 550025 ; 2. 贵州安顺学院 数学系 ,贵州 安顺 561000) 摘 要 :基于生物免疫系统的自适应学习、免疫记忆、抗体多样性及动态平衡维持等功能 , 提出一种动态多目标免疫 优化算法处理动态多目标优化问题. 算法设计中 , 依据自适应ζ邻域及抗体所处位置设计抗体的亲和力 , 基于 Pa2 reto 控制的概念 ,利用分层选择确定参与进化的抗体 , 经由克隆扩张及自适应高斯变异 ,提高群体的平均亲和力 ,利 用免疫记忆、动态维持和 Average linkage 聚类方法 , 设计环境识别规则和记忆池 , 借助 3 种不同类型的动态多目标 测试问题 ,通过与出众的动态环境优化算法比较 , 数值实验表明所提出算法解决复杂动态多目标优化问题具有较大 潜力. 关键词 :动态多目标优化 ; 时变 Pareto 面 ; 环境跟踪 ; 自适应ζ邻域 ; 免疫算法 中图分类号 : TP301. 6 文献标识码 :A 文章编号 :167324785 (2007) 0520068210 Dynamic multi2objective immune optimization algorithm and performance test QIAN Shu2qu 1 ,2 , ZHAN G Zhu2hong 1 (1. College of Science , Guizhou University , Guizhou 550025 , China ; 2. Department of Mathematics , Anshun College , Anshun 561000 , China) Abstract :A dynamic multi2objective immune optimization algorit hm suitable for dynamic multi2objective optimization problems is proposed based on the f unctions of adaptive learning , immune memory , antibody diversity and dynamic balance maintenance , etc. In t he design of t he algorithm , t he scheme of antibody af2 finity was designed based on t he locations of adaptive2neighborhood and antibody ; antibodies participating in evolution were selected by Pareto dominance. In order to enhance t he average affinity of t he pop ulation , clonal proliferation and adaptive Gaussian mutation were adopted to evolve excellent antibodies. Furt her2 more , t he average linkage method and several f unctions of immune memory and dynamic balance mainte2 nance were used to design environmental recognition rules and t he memory pool. The p roposed algorit hm was compared against several pop ular multi2objective algorit hms by means of three different kinds of dy2 namic multi2objective benchmark problems. Simulations show that t he algorit hm has great potential in sol2 ving dynamic multi2objective optimization problems. Keywords :dynamic multi2objective optimization ; time2varying Pareto front ; environment tracking ; adap2 tive 2neighborhood ; immune algorithm. 收稿日期 :2006212205. 基金项目 :国家自然科学基金资助项目(60565002) . 动态多目标优化(dynamic multi2objective opti2 mization ,DMO) 是指优化问题的目标函数、定义 域、约束条件中至少有一个随时间而变化的多目标 优化问题. 在工程应用领域 , 大量此类问题急需解 决[1 ] , 如 : 交通信号灯控制、机器人控制、故障诊断 等. 尽管大量静态多目标进化算法已相继提出[2 ] , 其中较为典型的 2 种进化算法为 SPEA II [ 3 ] 和 NS2 GAII [4 ] , 但寻求解决 DMO 的算法研究甚少[5 ] . 文 献[1 - 2 , 6 - 7 ]报道了有关动态多目标进化算法的 研究进展. 特别是 Marco 等在文献[ 2 ]中设计了几 种动态多目标测试问题 ,相应地 ,提出了一种邻域搜 索算法 ( direction2based method ,DBM) ,从性能测