基于精英集选择与扩展策略的多目标智能算法研究
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摘要
最优化问题是科学研究和工程设计中的主要问题，现实当中这些优化问题大多具备多目标的特征，目标之间彼此冲突、相互制约，一个子目标性能提升的同时必然会导致其它至少一子目标性能的退化。与单目标优化问题不同，多目标优化问题(Multi-objectiveOptimization Problem，MOP）没有绝对的或者唯一的最优解，而是存在一个最优解集合，集合中的元素称为Pareto最优解，解集中的元素就所有目标而言是彼此不可比较的。智能优化算法是通过模拟某一自然现象或过程而提出的随机搜索算法，具有高度并行、自学习、自组织与自适应的特征，为求解复杂优化问题提供了一种新途径。智能优化算法中的遗传算法、差分算法、粒子群算法通过由潜在解组成种群不断进化的全局搜索方法非常适合求解多目标优化问题，受到国内、外专家和学者的广泛关注。本文旨在基于这三类智能优化算法对多目标优化问题的求解展开研究，如何将有关的智能优化算法、进化策略与多目标优化技巧进行有效地结合设计出较高搜索效率、较强鲁棒性的算法，进而提高求解问题解的质量，将是本文研究的重要问题。本文的主要内容和创新点可以概括如下：
（1）精英保留机制能够有效防止进化过程中由于随机因素所导致的最优个体丢失问题，保证算法的全局收敛；对精英保留机制的两种实现方法进行了改进和扩展，提出了基于区域的（μ+λ）选择法和具有自我更新机制的外部归档法，并将这两种方法应用于具体的算法设计中；
（2）针对经典多目标进化算法NSGA-II存在的模拟二进制交叉算子搜索性能较弱影响搜索效率以及精英保留机制不足影响种群的多样性问题，提出了一种基于渐变交叉分布指数和分层策略的多目标进化算法。算法通过分析模拟二进制交叉算子中包含的交叉分布指数的特征，利用与时间相关的逻辑斯蒂函数将其设计成随进化代数由小变大的渐变交叉分布指数。实验表明，这种渐变交叉分布指数能够改进算法的性能，提高收敛效率，保持种群多样性；针对NSGA-II算法精英保留机制存在的不足，应用基于区域的（μ+λ）选择法，提出了一种基于分层策略的精英保留机制，通过对目标空间分区间扫描的方式实现对精英个体的选择，有效地避免了在Pareto最优前沿的局部造成覆盖空白的局面，保持了种群多样性。数值仿真实验结果验证，对于ZDT系列的大部分测试函数，文中算法比NSGA-II算法具有更好的性能。
（3）有效地平衡收敛速度和多样性这一矛盾的统一体是多目标优化问题的永恒主题，文中引进差分进化算法提高多目标进化算法的优化速度，设计序值变异和基于拥挤距离最小淘汰选择有利于保持种群的多样性。算法根据进化过程中种群个体的非劣级别自适应地选择变异策略，改进了差分进化的变异操作；采用拥挤距离最小淘汰的精英保留机制实现下一代个体的选择，改进了差分进化的选择操作；将控制参数差分矢量缩放因子F和交叉概率CR设计成与进化代数相关的线性递减函数。对标准测试函数进行了数值仿真，并将结果与经典的多目标优化算法进行了比较，无论在解集的逼近性及均匀性方面均取得了良好的效果，而且具有良好的稳定性，是一种求解多目标优化问题的实用、有效的方法。
（4）利用粒子群算法对多目标优化问题的求解进行了研究，并将具有自我更新机制的外部归档法应用于精英保留机制的设计，提出了一种基于外部归档集自适应繁殖的多目标粒子群算法。该算法针对将粒子群算法用于解决多目标优化问题时出现的易陷入局部最优、收敛精度差、全局最优粒子难确定等问题，提出了相应的改进策略，具体表现在：①针对粒子群对初始解敏感，采用反向学习策略产生初始解，提高了初始种群解的质量；②使用自适应惯性权重和加速系数调整策略，增强算法初期的全局搜索能力，加大算法后期的局部精细化搜索能力；③根据外部归档集中非支配解的数量采用不同的繁殖策略改进外部归档集中非支配解的数量和质量；④与当前粒子具有较小的收敛距离且拥有较大的拥挤距离的非支配解将被选作全局最优粒子；⑤当连续几代个体最优粒子没有得到提升时，采用局部搜索的爬山算法更新个体最优粒子。数值仿真实验结果表明该算法相对于其它算法性能较好或相当。
Optimization problems are the main concern in scientific research and engineering design,most of which feature multiple objectives that are contradictory to and restrained by eachother. The performance improvement of one sub-objective will necessarily leads to theperformance degradation of at least another one sub-objective. Different fromSingle-objective Optimization Problem, Multi-objective Optimization Problem (MOP) has noabsolute or sole optimal solution but a optimal solution set, the elements in which are calledPareto optimal solutions. The elements of solution set are incomparable with each other interms of all objectives. Intelligent Optimization Algorithms is a random search algorithmcame up with through simulating certain natural phenomenon or process, featuringembarrassingly parallel, self-learning, self-organizing and self-adaptation, which provide anew method for solving complex optimization problems. Genetic Algorithm, DifferenceAlgorithm and Particle Swarm Optimization in Intelligent Optimization Algorithms, withconstantly-evolutionary overall searching method throng potential solutions constitutingpopulations, act very suitably as the solution for multi-objective optimization problems, andattract extensive attention from experts and scholars from home and abroad. This paper is tostudy the solutions of multi-objective optimization problem based on the aforesaid threeIntelligent Optimization Algorithms. An important issue in this paper is about how todesignate an algorithm with higher search efficiency and stronger robustness througheffective combination of relevant Intelligent Optimization Algorithms, evolutionary strategiesand Multi-objective optimization techniques so as to improve the quality of problem solutions.Main contents and innovative ideas in this paper are summarized as follows:
(1) Elite retention mechanism can effectively prevent optimal individual loss problemincurred by random factors during evolutionary process and ensure global convergence of thealgorithm. The two implementation methods of elite retention mechanism are improved andexpanded, and region-based (μ+λ) selection method as well as external archive set withself-update mechanism are put forward, which are adopted in specific algorithm design;
(2) A multi-objective evolutionary algorithm based on gradient cross distribution indexand layer strategy is put forward regarding the fact that the searching capability of thesimulated binary crossover operator in classical multi-objective evolutionary algorithmNSGA-II has relatively smaller impact on searching efficiency and that elite retentionmechanism is not robust enough to influence the population diversity. The algorithm, throughanalyzing the characteristics of cross distribution index contained in simulated binary crossover operators and using time-related logistic function, can designated it into gradientcross distribution index changing from small to large along with evolutionary generation.According to the experiment, this gradient cross distribution index can improve the algorithmperformance, enhance convergence efficiency and keep the population diversity; with regardto the deficiencies in elite retention mechanism of NSGA-II algorithm, an elite retentionmechanism based on layer strategy is proposed by adopting the region-based (μ+λ) selectionmethod, in which blank-coverage at part of Pareto optimal frontier is effectively avoided andthe population diversity is kept by selecting elitists with partition-based scanning to the targetspace. The result of numerical simulation experiment proves that, for most test functions ofZDT series, the algorithm in this paper demonstrates better performance than NSGA-IIalgorithm.
(3) To effectively balance convergence rate and diversity, which is a contradictory unity,maintains as the everlasting issue of multi-objective optimization problem. This paperintroduces Differential Evolution Algorithm to increase the optimization speed ofmulti-objective optimization algorithm. The designated rank mutation and crowding distancebased minimum excluded choices contribute to keeping the population diversity. According tothe non-inferiority grade of populations and individuals in evolutionary process, the algorithmselects mutation strategy self-adaptively, improving the mutation operation of differentialevolution; to realize the individual selection of the next generation by adopting elite retentionmechanism with minimum excluded choices improves the selecting operation of differentialevolution; zoom factor F of controlled variable difference vector and crossover probabilityCR are designed into linear decreasing function related to evolutionary generation. Numericalsimulation is carried out to standard test functions and the results are compared with classicalmulti-objective evolutionary algorithm, which shows good results in both approximation anduniformity of the solution sets with good stability. It's a practical and effective method forsolving multi-objective optimization problems.
(4) This paper studies the solutions of multi-objective optimization problem by usingparticle swarm optimization, and applies external archive set with self-update mechanism tothe design of elite retention mechanism, thus coming up with a Multiple Objective ParticleSwarm Optimization based on external archive collection and self-adaptive propagation. Thisalgorithm, regarding the easy tendency of local optimum, poor convergence precision anddifficult determination of global optimal particle etc. when applying particle swarmoptimization to solving multi-objective optimization problem, provides corresponding improvement strategies, specifically showing as:①using opposition based learning strategyto generate initial solution and improve the quality of initial population solution regardingparticle swarm's sensitivity to initial solution;②using adaptive inertia weight and speededadjustment strategy to increase early global searching ability of algorithm and to strengthenthe algorithm's late local fine search ability;③using different reproduction strategy toimprove the quantity and quality of non-dominated solutions in external archive set accordingto the quantity of non-dominated solutions in external archive set;④non-dominated solutionsthat has smaller convergence distance and larger crowding distance with current participleswill be selected as global optimal particles;⑤using hill climbing algorithm of local search toupdate individual optimal particles when the individual optimal particles of several successivegenerations are not promoted; the result of numerical simulation experiment shows that theperformance of this algorithm is better than or equal to the that of others.
（1）精英保留机制能够有效防止进化过程中由于随机因素所导致的最优个体丢失问题，保证算法的全局收敛；对精英保留机制的两种实现方法进行了改进和扩展，提出了基于区域的（μ+λ）选择法和具有自我更新机制的外部归档法，并将这两种方法应用于具体的算法设计中；
（2）针对经典多目标进化算法NSGA-II存在的模拟二进制交叉算子搜索性能较弱影响搜索效率以及精英保留机制不足影响种群的多样性问题，提出了一种基于渐变交叉分布指数和分层策略的多目标进化算法。算法通过分析模拟二进制交叉算子中包含的交叉分布指数的特征，利用与时间相关的逻辑斯蒂函数将其设计成随进化代数由小变大的渐变交叉分布指数。实验表明，这种渐变交叉分布指数能够改进算法的性能，提高收敛效率，保持种群多样性；针对NSGA-II算法精英保留机制存在的不足，应用基于区域的（μ+λ）选择法，提出了一种基于分层策略的精英保留机制，通过对目标空间分区间扫描的方式实现对精英个体的选择，有效地避免了在Pareto最优前沿的局部造成覆盖空白的局面，保持了种群多样性。数值仿真实验结果验证，对于ZDT系列的大部分测试函数，文中算法比NSGA-II算法具有更好的性能。
（3）有效地平衡收敛速度和多样性这一矛盾的统一体是多目标优化问题的永恒主题，文中引进差分进化算法提高多目标进化算法的优化速度，设计序值变异和基于拥挤距离最小淘汰选择有利于保持种群的多样性。算法根据进化过程中种群个体的非劣级别自适应地选择变异策略，改进了差分进化的变异操作；采用拥挤距离最小淘汰的精英保留机制实现下一代个体的选择，改进了差分进化的选择操作；将控制参数差分矢量缩放因子F和交叉概率CR设计成与进化代数相关的线性递减函数。对标准测试函数进行了数值仿真，并将结果与经典的多目标优化算法进行了比较，无论在解集的逼近性及均匀性方面均取得了良好的效果，而且具有良好的稳定性，是一种求解多目标优化问题的实用、有效的方法。
（4）利用粒子群算法对多目标优化问题的求解进行了研究，并将具有自我更新机制的外部归档法应用于精英保留机制的设计，提出了一种基于外部归档集自适应繁殖的多目标粒子群算法。该算法针对将粒子群算法用于解决多目标优化问题时出现的易陷入局部最优、收敛精度差、全局最优粒子难确定等问题，提出了相应的改进策略，具体表现在：①针对粒子群对初始解敏感，采用反向学习策略产生初始解，提高了初始种群解的质量；②使用自适应惯性权重和加速系数调整策略，增强算法初期的全局搜索能力，加大算法后期的局部精细化搜索能力；③根据外部归档集中非支配解的数量采用不同的繁殖策略改进外部归档集中非支配解的数量和质量；④与当前粒子具有较小的收敛距离且拥有较大的拥挤距离的非支配解将被选作全局最优粒子；⑤当连续几代个体最优粒子没有得到提升时，采用局部搜索的爬山算法更新个体最优粒子。数值仿真实验结果表明该算法相对于其它算法性能较好或相当。
Optimization problems are the main concern in scientific research and engineering design,most of which feature multiple objectives that are contradictory to and restrained by eachother. The performance improvement of one sub-objective will necessarily leads to theperformance degradation of at least another one sub-objective. Different fromSingle-objective Optimization Problem, Multi-objective Optimization Problem (MOP) has noabsolute or sole optimal solution but a optimal solution set, the elements in which are calledPareto optimal solutions. The elements of solution set are incomparable with each other interms of all objectives. Intelligent Optimization Algorithms is a random search algorithmcame up with through simulating certain natural phenomenon or process, featuringembarrassingly parallel, self-learning, self-organizing and self-adaptation, which provide anew method for solving complex optimization problems. Genetic Algorithm, DifferenceAlgorithm and Particle Swarm Optimization in Intelligent Optimization Algorithms, withconstantly-evolutionary overall searching method throng potential solutions constitutingpopulations, act very suitably as the solution for multi-objective optimization problems, andattract extensive attention from experts and scholars from home and abroad. This paper is tostudy the solutions of multi-objective optimization problem based on the aforesaid threeIntelligent Optimization Algorithms. An important issue in this paper is about how todesignate an algorithm with higher search efficiency and stronger robustness througheffective combination of relevant Intelligent Optimization Algorithms, evolutionary strategiesand Multi-objective optimization techniques so as to improve the quality of problem solutions.Main contents and innovative ideas in this paper are summarized as follows:
(1) Elite retention mechanism can effectively prevent optimal individual loss problemincurred by random factors during evolutionary process and ensure global convergence of thealgorithm. The two implementation methods of elite retention mechanism are improved andexpanded, and region-based (μ+λ) selection method as well as external archive set withself-update mechanism are put forward, which are adopted in specific algorithm design;
(2) A multi-objective evolutionary algorithm based on gradient cross distribution indexand layer strategy is put forward regarding the fact that the searching capability of thesimulated binary crossover operator in classical multi-objective evolutionary algorithmNSGA-II has relatively smaller impact on searching efficiency and that elite retentionmechanism is not robust enough to influence the population diversity. The algorithm, throughanalyzing the characteristics of cross distribution index contained in simulated binary crossover operators and using time-related logistic function, can designated it into gradientcross distribution index changing from small to large along with evolutionary generation.According to the experiment, this gradient cross distribution index can improve the algorithmperformance, enhance convergence efficiency and keep the population diversity; with regardto the deficiencies in elite retention mechanism of NSGA-II algorithm, an elite retentionmechanism based on layer strategy is proposed by adopting the region-based (μ+λ) selectionmethod, in which blank-coverage at part of Pareto optimal frontier is effectively avoided andthe population diversity is kept by selecting elitists with partition-based scanning to the targetspace. The result of numerical simulation experiment proves that, for most test functions ofZDT series, the algorithm in this paper demonstrates better performance than NSGA-IIalgorithm.
(3) To effectively balance convergence rate and diversity, which is a contradictory unity,maintains as the everlasting issue of multi-objective optimization problem. This paperintroduces Differential Evolution Algorithm to increase the optimization speed ofmulti-objective optimization algorithm. The designated rank mutation and crowding distancebased minimum excluded choices contribute to keeping the population diversity. According tothe non-inferiority grade of populations and individuals in evolutionary process, the algorithmselects mutation strategy self-adaptively, improving the mutation operation of differentialevolution; to realize the individual selection of the next generation by adopting elite retentionmechanism with minimum excluded choices improves the selecting operation of differentialevolution; zoom factor F of controlled variable difference vector and crossover probabilityCR are designed into linear decreasing function related to evolutionary generation. Numericalsimulation is carried out to standard test functions and the results are compared with classicalmulti-objective evolutionary algorithm, which shows good results in both approximation anduniformity of the solution sets with good stability. It's a practical and effective method forsolving multi-objective optimization problems.
(4) This paper studies the solutions of multi-objective optimization problem by usingparticle swarm optimization, and applies external archive set with self-update mechanism tothe design of elite retention mechanism, thus coming up with a Multiple Objective ParticleSwarm Optimization based on external archive collection and self-adaptive propagation. Thisalgorithm, regarding the easy tendency of local optimum, poor convergence precision anddifficult determination of global optimal particle etc. when applying particle swarmoptimization to solving multi-objective optimization problem, provides corresponding improvement strategies, specifically showing as:①using opposition based learning strategyto generate initial solution and improve the quality of initial population solution regardingparticle swarm's sensitivity to initial solution;②using adaptive inertia weight and speededadjustment strategy to increase early global searching ability of algorithm and to strengthenthe algorithm's late local fine search ability;③using different reproduction strategy toimprove the quantity and quality of non-dominated solutions in external archive set accordingto the quantity of non-dominated solutions in external archive set;④non-dominated solutionsthat has smaller convergence distance and larger crowding distance with current participleswill be selected as global optimal particles;⑤using hill climbing algorithm of local search toupdate individual optimal particles when the individual optimal particles of several successivegenerations are not promoted; the result of numerical simulation experiment shows that theperformance of this algorithm is better than or equal to the that of others.
引文
[1] Deb K.. Multi-Objective Optimization Using Evolutionary Algorithms[M]. Chichester:John Wiley&Sons,2001
[2] Steuer R. E.. Multiple Criteria Optimization: Theory, Computation, and Application[M].New York: Wilev,1986
[3]崔逊学.多目标进化算法及其应用[M].北京:国防工业出版社,2006
[4] Holland J. H.. Adaptation in natural and artificial systems[M]. Ann Arbor: The Universityof Michigan Press, MI,1975
[5] Rechenberg I.. Evolutions strategie: Optimierung technischer System nach Prinzipien derbiologischen Evolution[M]. Stuttgart: Frommann-Holzboog,1973
[6] Schwefel H. P.. Numerische optimierung von computer-modellen mittels der evolutionsstrategie[J]. Interdisciplinary Systems Research, Basel: Birkhuser,1977(26):5-8
[7] Fogel L. J., Owens A. J., Walsh M. J.. Artificial intelligence through simulated evolution[M]. New York：Wiley,1966
[8] Koza J. R.. Genetic Programming: A paradigm for genetically breeding populations ofcomputer programs to solve problems[M]. Stanford University, Department of ComputerScience,1990
[9]徐宗本,张讲社,郑亚林.计算智能中的仿生学:理论与算法[M].科学出版社:北京:2003:4-11
[10]焦李成,尚荣华,马文萍,等.多目标优化免疫算法、理论和应用[M].科学出版社:北京:2010
[11] Fonseca C. M., Fleming P. J.. An overview of evolutionary algorithms in multi-objectiveoptimization[J]. Evolutionary Computation,1995,3(1):1-16
[12] Rendon V., Charre U.. A non-generational genetic algorithm for multi-objectiveoptimization[A]. In Proceedings of the Seventh International Conference on GeneticAlgorithms[C]. Back T(Ed.), San Francisco, California, Morgan Kaufmann,1997:658-665
[13] Wolpert D.H., Macready W. G.. No free lunch theorems for optimization[J]. IEEETransactions in Evolutionary Computation,1997,1(1):67-82
[14] Coello Coello CA.. Evolutionan multiobjective optimization: past, present and future[C].In Workshops and Tutorials of the Seventh International Conference Oil ParallelProblem Solvimg from Nature, Granada, Spain, September,2002
[15] Rosenberg R. S.. Simulation of genetic populations with biochemical properties[D].Ph.D.dissertation, University of Michigan, Ann Harbor, Michigan,1967
[16] Schaffer J. D.. Multiple objective optimization with vector evaluated geneticalgorithms[A]. Proceedings of1st International Conference on Genetic Algorithms andTheir Application[C]. Hillsdale: Lawrence Erlbaum Associates, Inc.,1985:93-100
[17] Fourtman M. P.. Compaction of symbolic layout using genetic algorithms[A].Proceedings of the1st International Conference on Genetic Algorithms[C]. L. ErlbaumAssociates Inc.,1985:141-153
[18] Kursawe F.. A Variant of Evolution Strategies for Vector Optimization[A]. In H. P.Schwefel and R. Manner (Eds.), Parallel Problem Solving from Nature-Proceedings ofthe first workshop PPSN[C]. Berlin, Springer,1991:193-197
[19] Andersson J.. A Survey of Multiobjective Optimization in Engineering Design[R].Technical Report No. LiTH-IKP-R-1097, Department of Mechanical Engineering,Linkoping University, Sweden,2000
[20] Goldberg D. E.. Genetic Algorithms for Search, Optimization and Machine Learning[M].Boston: Addison-Wesley Longman Publishing Co., Inc.,1989
[21] Fonscea C. M., Fleming P. J.. Genetic Algorithm for multi-objective optimization:Formulation, discussion and generation[A]. In Proceedings of the5th InternationalConference on Genetic Algorithms[C]. San Mateo, California,1993:416-423
[22] Coello Coello CA.. An updated survey of evolutionary multiobjective optimizationtechniques:State of the art and future trends[A].Proceedings of the IEEE Congress onEvolutionary Computation[C]. Piscataway: IEEE Service Center,1999:3-13
[23] Coello Coello CA.. Evolutionary multi-objective optimization: Current and futurechallenges [C]. Advances in Soft Computing-Engineering, Design and Manufacturing.Berlin: Springer,2003:243-256
[24] Coello Coello CA.. Recent trends in evolutionary multi-objective optimization[C].Evolutionary Multi-objective Optimization:Theoretical Advances and Applications.Berlin: Springer,2005:7-32
[25] Coello Coello CA..Evolutionary multi-objective optimization: A historical view of thefield[J]. IEEE Computational Intelligence Magazine,2006,1(1):28-36
[26] Srinivas N., Deb K.. Multi-objective optimization using non-dominated sorting in geneticalgorithms[J]. Evolutionary Computation,1994,2(4):221-248
[27] Horn J., Nafpliotis N.,Goldberg D. E.. A niched Pareto genetic algorithm formultiobjective optimization[A]. Proceedings of1st IEEE Congress on EvolutionaryComputation[C]. Piscataway: IEEE Press,1994:82-87
[28] Zitzler E., Thiele L.. Multi-objective evolutionary algorithms: A comparative case studyand the strength Pareto approach[J].IEEE transactions on Evolutionary Computation,1999,3(4):257-271
[29] Zitzler E., Laumanns M., Thiele L.. SPEA2: Improving the ctrength pareto evolutionaryalgorithm[A]. In Proceedings of the Conference on Evolutionary Methods for Design,Optimization and Control With Applications to Industrial Problems[C].2001
[30] Knowles, J. D., Corne D. W.. Approximating the non-dominated front using the Paretoarchived evolution strategy[J]. Evolutionary Computation,2000,8(2):149-172
[31] Corne D. W., Knowles J. D., Oates M. J.. The Pareto envelope based selection algorithmfor Multiobjective Optimization[A]. Proceedings of6th International Conference onParallel Problem Solving from Nature [C]. Berlin: Springer,2000:869-878
[32] Corne D. W., Jerram N. R., J. D., Knowles J. D.,et al. PESA-II: Region-based selectionin evolutionary multi-objective optimization[A]. Proceedings of the Genetic andEvolutionary Computation Conference[C]. San Francisco:Morgan Kaufmann Publishers,2001:283-290
[33] Erickson M., Maryer A., Horn J.. The niched Pareto genetic algorithm2Applied to thedesign of groundwater remediation system[A]. Proceedings of1st InternationalConference on Evolutionary Multi-Criterion Optimization[C]. Berlin: Springer,2001:681-695
[34] Coello Coello CA., Pulido G. T.. A micro-genetic algorithm for multiobjectiveoptimization[A]. Proceedings of the Genetic and Evolutionary ComputationConference[C]. San Francisco: Morgan Kaufmann Publishers,2001:274-282
[35] Deb K., Pratab A., Agrawal S., et al. A fast and elitist multi-objective genetic algorithm:NSGA-II[J]. IEEE transactions on Evolutionary Computation,2002,6(2):182-197
[36] Storn R., Price K.. Differential evolution---A simple and Efficient heuristic for globaloptimization over continuous spaces[J]. Journal of Global Optimization,1997,11(4):341-359.
[37] Kennedy J., Eberhart R., C.. Particle swarm optimization[A]. Proceedings of IEEEInternational Conference on Neural Networks[C]. Piscataway: IEEE Service Center,1995, IV:1942-1948
[38] Tarakanov A.O., Dasgupta D.. A formal model of an artifical immune system[J].Biosystems,2000,55:151-158
[39]Parsopoulos K. E.,Vrahatis M. N.. Particle Swarm Optimization Method in MultiobjectiveProblems[A]. Proceedings of2002ACM Symposium on Applied Computing [C]. NewYork: ACM Press,2002:603-607
[40] Hu X., Eberhart R.. Multiobjective optimization using dynamic neighborhood particleswarm optimization[A]. Proceedings of the IEEE Congress on EvolutionaryComputation[C]. Piscataway: IEEE Service Center,2002,2:1677-1682
[41] Fieldsend J. E. and Singh S.. A multi-objective algorithm based upon particle swarmoptimization, an efficient data structure and turbulence[A].Proceedings of2002U.K.Workshop on Computational Intelligence [C]. Birmingham,2002:37-44
[42] Mostaghim S., Teich J.. Strategies for finding good local guides in multiobjective particleswarm optimization(MOPSO)[A]. Proceedings of2003IEEE Swarm IntelligenceSymposium [C]. Indianapolis,2003:26-33
[43] Coello Coello CA., Pulido GT., Lechuga MS.. Handing multiple objectives with particleswarm optimization[J].IEEE transactions on Evolutionary Computations,2004,8(3):256-279
[44] Parsopoulos K. E., Vrahatis M. N.. On the computation of all global minimizers throughparticle swarm optimization[J]. IEEE transactions on Evolutionary Computations,2004,8(3):211-224
[45] Ratnaweera A., Halgamuge S. K., Waston H. C.. Self-organizing hierarchical particalswarm optimizer with time-varying acceleration coefficients[J]. IEEE transactions onEvolutionary Computations,2004,8(3):240-255
[46] Sierra M. R., Coello Coello CA.. Improving PSO-based multiobjective optimizationusing crowing, mutation and ε-dominance[C]. Evolutionary Multi-Criterion Optimization.Berlin: Springer-Verlag,2005:505-519
[47] Liu B., Wang L., Jin Y. H., et al. Improved particle swarm optimization combined withchaos[J]. Chaos, Solitons&Fractals,2005,25(5):1261-1271
[48] Raquel C. R., Naval P. C. Jr.. An effective use of crowding distance in multiobjectiveparticle swarm optimization[A].Proceedings of the Conference on Genetic andEvolutionary Computation[C]. NY: ACM Press,2005:257-264
[49]雷德明,吴智铭. Pareto档案多目标粒子群优化[J].模式识别与人工智能,2006,19(4):475-480
[50] Liang J. J., Qin A. K., Suganthan P. N., et al. Evaluation of comprehensive learningparticle swarm optimizer[C]. Neural Information Processing. Springer Berlin Heidelberg,2004:230-235
[51] Huang V. L., Suganthan P. N., Liang J. J.. Comprehensive learning particle swarmoptimizer for solving multiobjective optimization problems[J]. International Journal ofIntelligent Systems,2006,21(2):209-226
[52] Abido M. A.. Two level of nondominated solutions approach to multiobjective particleswarm optimization[A]. Proceedings of the Genetic and Evolutionary ComputationConference [C]. New York: ACM Press,2007:726-733
[53] Santana R. A., Pontes M. R., Bastos-Filho C. J. A.. A multiple objective particle swarmoptimization approach using crowding distance and roulette wheel[C].Intelligent SystemsDesign and Applications,2009:237-242
[54] Tsai S. J., Sun T. Y., Liu C. C., et al. An improved multi-objective particle swarmoptimizer for multi-objective problems[J]. Expert Systems with Applications,2010,37(8):5872-5886
[55] Sha Z., Liu Y., Dong S.. Multi-objective PSO based on evolutionary programming[M].Advanced Intelligent Computing Theories and Applications. Springer Berlin Heidelberg,2010:602-610
[56] Daneshyari M., Yen G. G..Cultural-based multiobjective particle swarm optimization[J].Systems,Man,and Cybernetics, Part B: Cybernetics, IEEE Transactions on,2011,41(2):553-567
[57] Liang J. J., Qu B.Y., Suganthan P. N., et al. Dynamic multi-swarm particle swarmoptimization for multi-objective optimization problems[C]. Evolutionary Computation(CEC),2012:1-8
[58] Liang J. J., Suganthan P. N.. Dynamic multi-swarm particle swarm optimizer[C]. SwarmIntelligence Symposium,2005:124-129
[59] Peng H., Huang W., Deng C. S.. Multi-objective particle swarm optimization algorithmof multi-swarm co-evolution[J]. Journal of Computer Applications,2012,32(2):456-460
[60] Price K.. Differential evolution vs. the functions of the2ndICEO [A]. Proc of the1997IEEE International Conference on Evolutionary Computation[C]. Indianapolis,1997:153-157
[61] Abbass H. A., Sarker R., Newton C.. PDE: A Pareto-Frontier differential evolutionapproach for Multi-objective optimization problems[A]. In Proc of the Congress onEvolutionary Computation[C]. Piscataway,2001:971-978
[62] Abbass H. A.. The self-adaptive Pareto differential evolution algorithm[A]. In: Proc ofthe Congress on EvolutionaryComputation(CEC’2002)[C]. Piscataway: IEEE ServiceCenter,2002:831-836
[63] Madavan N. K.. Multiobjective Optimization using A Pareto differential evolutionapproach[A]. In: Proc of the congress on Evolutionary Computation(CEC’2002)[C].Piscataway: IEEE Service Center,2002:1145-1150
[64] Xue F., Sanderson A. C., Graves R. J.. Pareto-based Multi-objective differential evolution
[A]. In: Proc of the2003Congress on Evolutionary Computation (CEC’2003)[C].Piscataway, NJ: IEEE Press,2003:862-869
[65] Robic T., Filipic B.. DEMO: Differential Evolution for Multiobjective Optimization[A].In:Proceedings of the Third International Conference on Evolutionary Multi-CriterionOptimization(EMO2005)[C]. Guanajuato: Springer,2005:520-533
[66]张利彪,周春光,马铭,孙彩堂.基于极大极小距离密度的多目标微分进化算法[J].计算机研究与发展,2007,44(1):177-184
[67]孟红云,张小华,刘三阳.用于约束多目标优化问题的双群体差分进化算法[J].计算机学报,2008,31(2):228-235
[68] Qin A. K., Suganthan P. N.. Self-adaptive differential evolution algorithm for numericaloptimization[C]. IEEE Congress on Evolutionary Computation,2005:1785-1791
[69] Huang V. L., Qin A. K., Suganthan P. N.,et al. Multi-objective optimization based onself-adaptive differential evolution algorithm[C]. IEEE Congress on EvolutionaryComputation,2007:3601-3608
[70] Huang V.L., Zhao S.Z., Mallipeddi R., et al. Multi-objective optimization usingself-adaptive differential evolution algorithm.[C]. IEEE Congress on EvolutionaryComputation,2009:190-194
[71]龚文引,蔡之华.基于ε占优的正交多目标差分演化算法研究[J].计算机研究与发展,2009,46(4):656-666
[72] Monta o A. A., Coello Coello CA., Mezura-Montes E.. MODE-LD+SS: A NovelDifferential Evolution Algorithm Incorporating Local Dominance and Scalar SelectionMechanisms for Multi-Objective Optimization[A]. In:Proceedings of the congressConference on Evolutionary Computation (CEC’2010)[C].2010:1-8
[73] Santana-Quintero L.V., Hernandez-Diaz A. G., Molina J., et al. DEMORS: A hybridmulti-objective optimization algorithm using differential evolution and rough set theoryfor constrained problems[J]. Computers&Operations Research,2010,37(3):470-480
[74] Sindhya K., Ruuska S., Haanpaa T., et al. A new hybrid mutation operator formultiobjective optimization with differential evolution[J]. Soft Computing,2011,158(10):2041-2055
[75] Leung S W, Zhang X, Yuen S Y. Multiobjective differential evolution algorithm withopposition-based parameter control[C].Evolutionary Computation (CEC’2012),2012:1-8
[76] Wu Z, Xia X, Zhang J. MMODE: A Memetic Multiobjective Differential EvolutionAlgorithm[M].Advances in Swarm Intelligence. Springer Berlin Heidelberg,2013:422-430
[77]肖人彬,王磊.人工免疫系统原理、模型、分析及展望[J].计算机学报,2002,25(12):1280-1293
[78] Coello Coello CA., Cruz Cortés N.. An approach to solve multiobjective optimizationproblems based on an artificial immune system[A]. Proceedings of1st InternationalConference on Artificial Immune Systems[C]. Canterbury,2002:212-221
[79] Cruz Cortés N.,Coello Coello C. A.. Multiobjective optimization using ideas from theclonal selection principle[A]. Proceedings the Genetic and Evolutionary ComputationConference[C]. Berlin: Springer,2003:158-170
[80] Coello Coello C., Cruz Cortés N.. Solving multiobjective optimization problems usingan artificial immune system[J]. Genetic Programming and Evolvable Machines,2005,6(2):163-190
[81] Jiao L. C., Gong M.G., Shang R. H., et al. Clonal selection with immune dominance andanergy based multiobjective optimization[A]. Proceedings of3rd International Conferenceon Evolutionary Multi-criterion Optimization[C]. Berlin: Springer,2005:474-489
[82] Lu B., Jiao L. C., Du H., et al. IFMOA: Immune forgetting multiobjective optimizationalgorithm[A]. Proceedings of1rd International Conference on Advances in NaturalComputation[C]. Changsha,2005:399-408
[83] Gong M.G., Jiao L. C., Du H. F., et al. Multiobjective immune algorithm withnondominated neighbor-based selection[J]. Evolutionary Computation,2008,16(2):225-255
[84] Lu H.M., Yen G.. Rank-density-based multiobjective genetic algorithm and benchmarktest function study[J]. IEEE Transactions on Evolutionary Computation,2003,7(4):325-343
[85] Yen G., Lu H.M.. Dynamic multiobjective evolutionary algorithm: Adaptive cell-basedrank and density estimation[J]. IEEE Transactions on Evolutionary Computation,2003,7(3):253-274
[86]郑金华,史忠植,谢勇.基于聚类的快速多目标遗传算法[J].计算机研究与发展,2004,41(7):1081-1087
[87] Zeng Sanyou, Lishan S. K., Lixing X. D.. An Orthogonal Multi-Objective Evolutionaryalgorithm for Multi-Objective Optimization Problems with Constraints[J]. EvolutionaryComputation,2004,12(1):77-98
[88]雷德明,吴智铭.基于个体密集距离的多目标进化算法[J].计算机学报,2005,28(8):1320-1326
[89] Tan K. C., Yang Y. J., Goh C. K.. A Distributed Cooperative Coevolutionary Algorithmfor Multiobjective Optimization[J]. IEEE Transactions on Evolutionary Computation,2006,10(5):527-547
[90]雷德明,严新平,吴智铭,等.多目标混沌进化算法[J].电子学报,2006,34(6):1142-1145
[91]郑金华,蒋浩,邝达,等.用擂台赛法则构造多目标Pareto最优解集的方法[J].软件学报,2007,18(6):1287-1297
[92]石川,李清勇,史忠植.一种快速的基于占优树的多目标进化算法[J].软件学报,2007,18(3):505-516
[93] Zhang Q., Li H.. MOEA/D: A Multiobjective Evolutionary Algorithm based onDecomposition[J]. IEEE Transactions on Evolutionary Computation,2007,11(6):712-731
[94] Liu H.L., Li X.Q., Chen Y.Q.. Multi-objective evolutionary algorithm based ondynamical crossover and mutation[A]. In Proceedings of the International Conference onComputational Intelligence and Security [C].2008,(1):150-155
[95] Larranaga P., Lozano J. A.. Estimation of distribution algorithms: A new tool forevolutionary computation [M]. Boston, MA: Kluver,2002:57-100
[96] Pelikan M.. Hierarchical Bayesian Optimization Algorithm [A]. Studies in Fuzziness andSoft Computing [C]. New York: Springer-Verlag,2005,(17):105-129
[97] Zhang Q., Zhou A., Jin Y.. RM-MEDA: A regularity model-based multiobjectiveestimation of distribution algorithm [J]. IEEE Transactions on Evolutionary Computation,2008,12(1):41-63
[98] Zhou A., Zhang Q., Jin Y.. Approximating the set of Pareto-optimal solutions in both thedecision and objective spaces by anestimation of distribution algorithm[J]. IEEETransactions on Evolutionary Computation,2009,13(5):1167-1189
[99] Liu H.L., Wang Y.P.. A novel multiobjective evolutionary algorithm based on min-maxstrategy[A]. Intelligent data engineering and automated learning, Lecture Notes inComputer Science [C].2003:361-368
[100] Liu H.L., Wang Y.P., Cheung Y.M.. A multiobjective evolutionary algorithm usingmin-max strategy and sphere coordinate transformation[J]. Intelligent Automation andSoft Computing,2009,15(3):361-384
[101] Wang Y. P., Dang C.Y., Li H.C., et al. A clustering multi-objective evolutionaryalgorithm based on orthogonal and uniform design[A]. In Proceedings of the IEEEInternational Conference on Evolutionary Computation[C]. Piscataway: IEEE Press,2009:2927-2933
[102] Qu B.Y., Suganthan P.N.. Multiobjective Evolutionary Programming withoutNon-domination Sorting is up to Twenty Times Faster[A]. In Proceedings of the IEEEInternational Conference on Evolutionary Computation[C]. Piscataway: IEEE Press,2009:2934-2939
[103] Venkatesh P., Lee K.Y.. Multi-objective evolutionary programming for economicemission dispatch problem[A]. In Proceedings of the IEEE Power and Energy SocietyGeneral Meeting: Conversion and Delivery of Electrical Energy in the21st Century [C].2008:1-8
[104] Adra S., Dodd T., Griffin I., et al. Convergence acceleration operator for multiobjectiveoptimization[J]. IEEE Transactions on Evolutionary Computation,2009,13(4):825-847
[105] Ishibuchi H., Tsukamoto N., Nojima Y.. Diversity improvement by non-geometricbinary crossover in evolutionary multiobjective optimization[J]. IEEE Transactions onEvolutionary Computation,2010,14(6):985-998
[106] Liang J, You J, Han G, et al. Double space based multiobjective evolutionaryalgorithm[C]. ICMLC,2012:1406-1411
[107] Zhou A., Zhang Q, Zhang G.. A multiobjective evolutionary algorithm based ondecomposition and probability model[C].Evolutionary Computation (CEC’2012),2012:1-8
[108]马清亮,胡昌华.多目标进化算法及其在控制领域中的应用综述[J].控制与决策,2006,21(5):481-486
[109] Meza J. L. C., Yildirim M. B., Masud A. S. M.. A multiobjective evolutionaryprogramming algorithm and its applications to power generation expansion planning[J].Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on,2009,39(5):1086-1096
[110] Gen M., Lin L.. Multiobjective evolutionary algorithm for manufacturing schedulingproblems: state-of-the-art survey[J]. Journal of Intelligent Manufacturing,2013:1-18
[111] Metaxiotis K., Liagkouras K.. Multiobjective evolutionary algorithms for portfoliomanagement: a comprehensive literature review[J]. Expert Systems with Applications,2012,39(14):11685-11698
[112] Beatriz I., Reynolds A., Rayward-Smith V. J.. Development on a Multi-objectiveMetaheuristic(MOMH) Algorithm for Finding Interesting Sets of ClassificationRules[C]. Evolutionary Multi-criterion Optimization, Third International Conference,Guanajuato: Springer,2005:826-840
[113] Mukhopadhyay A., Mandal M.. A Hybrid Multiobjective Particle Swarm OptimizationApproach for Non-redundant Gene Marker Selection[A]. Proceedings of SeventhInternational Conference on Bio-Inspired Computing: Theories and Applications(BIC-TA2012)[C]. Springer India,2013:205-216
[114] Rudolph, G.. On a multi-objective evolutionary algorithm and its convergence to thePareto set[A]. Proceedings of the fifth IEEE Conference on Evolutionary Computation
[C]. Piscataway, New Jersey,1998:511-516
[115] Cui Xunxue, MiaoLi and Tingjian Fang. Study of Population Diversity ofMultiobjective Evolutionary Algorithm Based on Immune and EntropyPrinciples[A].Proceedings of the Congress on Evolutionary Computation[C].IEEEService Center, Piscataway, New Jersey,2001,2:1316-1321
[116] Rudolph, G.. Evolutionary Search under Partially Ordered Fitness Sets[A]. InProceedings of the International NAISO Congress on Information ScienceInnovations[C]. ICSC Academic Press: Millet, Sliedrecht,2001:818-822
[117] Joshua K., Corne D.. Properties of an Adaptive Archiving Algorithm for StoringNondominated Vectors[J]. IEEE Transactions on Evolutionary Computation,2003,7(2):100-116
[118]周育人,闵华清,许孝元,等.多目标演化算法的收敛性研究[J].计算机学报,2004,27(10):1415-1421
[119] Whitley D., Mathias K., Rana S., Dzubera J.. Evaluating Evolutionary Algorithms[J].Artificial Intelligence.1996,85:245-276
[120] Deb K., Thiele L., Laumanns M., et al. Scalable test problems for evolutionarymultiobjective optimization[M]. Springer London,2005
[121] Huband S., Hingston P., Barone L., et al.. A review of multiobjective test problems anda scalable test problem toolkit[J]. IEEE Transactions on Evolutionary Computation,2006,10(5):477-506
[122] Zitzler E., Deb K., Thiele L.. Comparison of multiobjective evolutionary algorithms:Empirical results[J]. Evolutionary Computation,2000,8(2):173-195
[123] Zitzler E., Thiele L., Laumanns M., et al. Performance assessment of multiobjectiveoptimizers: An analysis and review[J].IEEE transactions on Evolutionary Computation,2003,7(2):117-132
[124]郑金华.多目标进化算法及其应用[M].北京:科学出版社,2007
[125] Cavicchio D. J.. Reproductive Adaptive Plans[A]. Proceedings of the ACM1972Annual Conference[C].1972:1-11
[126] Goldberg D. E., Richardson J.. Genetic Algorithms with Sharing for MultimodalFunction Optimization[A]. Genetic Algorithms and Their Applications: Proceedings ofthe Second International Conference on Genetic Algorithms[C].1987:41-49
[127] De Jong K. A.. An analysis of the behavior of a class of generic adaptive system[D].University of Michigan,1975
[128] Fogel David B.. Evolutionary computation: Toward a new philosophy of machineintelligence[M].2nd Edition. Wiley IEEE Press,1999
[129] Holland J. H.. Building blocks, cohort genetic algorithms, and hyperplane-definedfunctions [J]. IEEE transactions on Evolutionary Computation,2000,8(4):373-391
[130] Deb, K.. Multi-objective Genetic Algorithms: Problem Difficulties and Construction ofTest Problems[J]. IEEE transactions on Evolutionary Computation,1999,7(3):205-230
[131] Veldhuizen D. A.V., Lamont G. B..Multiobjective Evolutionary Algorithm TestSuites[A]. Proceedings of the1999ACM Symposium on Applied Computing[C].SanAntonio, Texas: ACM,1999
[132] Runarsson T. P., X.,Yao.. Stochastic ranking for constrained evolutionaryoptimization[J]. IEEE transactions on Evolutionary Computation,2000,4:284-294
[133] Deb K., Thiele L., Laumanns M., et al. Scalable multi-objective optimization testproblems[A]. Proceedings of the2002Congress on Evolutionary Computation[C].2002:825-830
[134] Deb K., Thiele L., Laumanns M., et al. Scalable Test Problems for EvolutionaryMultiobjective Optimization[C]. Evolutionary multiobjective Optimization: TheoreticalAdvances and Applications, Springer,2005:105-145
[135] Zitzler E., Kunzil S.. Indicator-based selection in multiobjective search[A]. InConference on Parallel Problem Solving from Nature[C]. Birmingham, UK,2004:832-842
[136] Deb K., Jain S.. Running performance metrics for evolutionary multiobjectiveoptimization[R]. KanGAL Report2002004, Kanpur: Indian Institute of Technology,Kanpur,2002
[137] Zhou A., Qu B-Y., Li H., et al. Multiobjective evolutionary algorithms: A survey of thestate-of-the-art [J].Swarm and Evolutionary Computation,2011,1(1):32-49
[138]公茂果,焦李成,杨咚咚,等.进化多目标优化算法研究[J].软件学报,2009,20(2):271-289
[139] Kollat J.B., Reed P. M.. The value of online adaptive search: A performance comparisonof NSGAII,-NSGAII and MOEA[A]. In Proceedings of the third InternationalConference on Evolutionary Multi-Criterion Optimization [C].Lecture Notes in ComputerScience,2005:386-398
[140] Chen X., Hou Z., Guo L., et al. Improved multi-objective genetic algorithm basedon NSGA-II [J]. Journal of Computer Applications,2006,10:060
[141] Francesco P., Khu S., Savic D.. An investigation on preference order ranking scheme formultiobjective evolutionary optimization[J]. IEEE Transactions on EvolutionaryComputation,2007,11(1):17-45
[142] Sindhya K., Sinha A., Deb K., et al. Local search based evolutionary multiobjectiveoptimization algorithm for constrained and unconstrained problems[A]. In Proceedings ofthe IEEE International Conference on Evolutionary Computation [C]. Piscataway: IEEEPress,2009:2919-2926
[143] Deb K., Agrawal R. B.. Simulated binary crossover for continuous search space[J].Complex Systems,1995,9(2):115-148
[144]李学强,郝志峰,黄翰.基于分方向选择搜索的多目标进算法[J].华南理工大学学报:自然科学版,2011,39(2):134-139
[145] Lalwani S., Singhal S., Kumar R., et al. A comprehensive survey: Applications ofmulti-objective particle swarm optimization (MOPSO) algorithm[J]. Transactions onCombinatorics,2013,2(1):39-101
[146] Tizhoosh H. R.. Opposition-based learning: a new scheme for machine intelligence[C].Computational intelligence for modelling, control and automation and internationalconference on intelligent agents, web technologies and internet commerce, internationalconference on.2005,1:695-701
[147] Shi Y., Eberhart R.. A modified particle swarm optimizer[C].Evolutionary ComputationProceedings,1998:69-73.
[148] Ratnaweera A., Halgamuge S. K., Watson H. C.. Self-organizing hierarchical particleswarm optimizer with time-varying acceleration coefficients[J]. EvolutionaryComputation, IEEE Transactions on,2004,8(3):240-255
[2] Steuer R. E.. Multiple Criteria Optimization: Theory, Computation, and Application[M].New York: Wilev,1986
[3]崔逊学.多目标进化算法及其应用[M].北京:国防工业出版社,2006
[4] Holland J. H.. Adaptation in natural and artificial systems[M]. Ann Arbor: The Universityof Michigan Press, MI,1975
[5] Rechenberg I.. Evolutions strategie: Optimierung technischer System nach Prinzipien derbiologischen Evolution[M]. Stuttgart: Frommann-Holzboog,1973
[6] Schwefel H. P.. Numerische optimierung von computer-modellen mittels der evolutionsstrategie[J]. Interdisciplinary Systems Research, Basel: Birkhuser,1977(26):5-8
[7] Fogel L. J., Owens A. J., Walsh M. J.. Artificial intelligence through simulated evolution[M]. New York：Wiley,1966
[8] Koza J. R.. Genetic Programming: A paradigm for genetically breeding populations ofcomputer programs to solve problems[M]. Stanford University, Department of ComputerScience,1990
[9]徐宗本,张讲社,郑亚林.计算智能中的仿生学:理论与算法[M].科学出版社:北京:2003:4-11
[10]焦李成,尚荣华,马文萍,等.多目标优化免疫算法、理论和应用[M].科学出版社:北京:2010
[11] Fonseca C. M., Fleming P. J.. An overview of evolutionary algorithms in multi-objectiveoptimization[J]. Evolutionary Computation,1995,3(1):1-16
[12] Rendon V., Charre U.. A non-generational genetic algorithm for multi-objectiveoptimization[A]. In Proceedings of the Seventh International Conference on GeneticAlgorithms[C]. Back T(Ed.), San Francisco, California, Morgan Kaufmann,1997:658-665
[13] Wolpert D.H., Macready W. G.. No free lunch theorems for optimization[J]. IEEETransactions in Evolutionary Computation,1997,1(1):67-82
[14] Coello Coello CA.. Evolutionan multiobjective optimization: past, present and future[C].In Workshops and Tutorials of the Seventh International Conference Oil ParallelProblem Solvimg from Nature, Granada, Spain, September,2002
[15] Rosenberg R. S.. Simulation of genetic populations with biochemical properties[D].Ph.D.dissertation, University of Michigan, Ann Harbor, Michigan,1967
[16] Schaffer J. D.. Multiple objective optimization with vector evaluated geneticalgorithms[A]. Proceedings of1st International Conference on Genetic Algorithms andTheir Application[C]. Hillsdale: Lawrence Erlbaum Associates, Inc.,1985:93-100
[17] Fourtman M. P.. Compaction of symbolic layout using genetic algorithms[A].Proceedings of the1st International Conference on Genetic Algorithms[C]. L. ErlbaumAssociates Inc.,1985:141-153
[18] Kursawe F.. A Variant of Evolution Strategies for Vector Optimization[A]. In H. P.Schwefel and R. Manner (Eds.), Parallel Problem Solving from Nature-Proceedings ofthe first workshop PPSN[C]. Berlin, Springer,1991:193-197
[19] Andersson J.. A Survey of Multiobjective Optimization in Engineering Design[R].Technical Report No. LiTH-IKP-R-1097, Department of Mechanical Engineering,Linkoping University, Sweden,2000
[20] Goldberg D. E.. Genetic Algorithms for Search, Optimization and Machine Learning[M].Boston: Addison-Wesley Longman Publishing Co., Inc.,1989
[21] Fonscea C. M., Fleming P. J.. Genetic Algorithm for multi-objective optimization:Formulation, discussion and generation[A]. In Proceedings of the5th InternationalConference on Genetic Algorithms[C]. San Mateo, California,1993:416-423
[22] Coello Coello CA.. An updated survey of evolutionary multiobjective optimizationtechniques:State of the art and future trends[A].Proceedings of the IEEE Congress onEvolutionary Computation[C]. Piscataway: IEEE Service Center,1999:3-13
[23] Coello Coello CA.. Evolutionary multi-objective optimization: Current and futurechallenges [C]. Advances in Soft Computing-Engineering, Design and Manufacturing.Berlin: Springer,2003:243-256
[24] Coello Coello CA.. Recent trends in evolutionary multi-objective optimization[C].Evolutionary Multi-objective Optimization:Theoretical Advances and Applications.Berlin: Springer,2005:7-32
[25] Coello Coello CA..Evolutionary multi-objective optimization: A historical view of thefield[J]. IEEE Computational Intelligence Magazine,2006,1(1):28-36
[26] Srinivas N., Deb K.. Multi-objective optimization using non-dominated sorting in geneticalgorithms[J]. Evolutionary Computation,1994,2(4):221-248
[27] Horn J., Nafpliotis N.,Goldberg D. E.. A niched Pareto genetic algorithm formultiobjective optimization[A]. Proceedings of1st IEEE Congress on EvolutionaryComputation[C]. Piscataway: IEEE Press,1994:82-87
[28] Zitzler E., Thiele L.. Multi-objective evolutionary algorithms: A comparative case studyand the strength Pareto approach[J].IEEE transactions on Evolutionary Computation,1999,3(4):257-271
[29] Zitzler E., Laumanns M., Thiele L.. SPEA2: Improving the ctrength pareto evolutionaryalgorithm[A]. In Proceedings of the Conference on Evolutionary Methods for Design,Optimization and Control With Applications to Industrial Problems[C].2001
[30] Knowles, J. D., Corne D. W.. Approximating the non-dominated front using the Paretoarchived evolution strategy[J]. Evolutionary Computation,2000,8(2):149-172
[31] Corne D. W., Knowles J. D., Oates M. J.. The Pareto envelope based selection algorithmfor Multiobjective Optimization[A]. Proceedings of6th International Conference onParallel Problem Solving from Nature [C]. Berlin: Springer,2000:869-878
[32] Corne D. W., Jerram N. R., J. D., Knowles J. D.,et al. PESA-II: Region-based selectionin evolutionary multi-objective optimization[A]. Proceedings of the Genetic andEvolutionary Computation Conference[C]. San Francisco:Morgan Kaufmann Publishers,2001:283-290
[33] Erickson M., Maryer A., Horn J.. The niched Pareto genetic algorithm2Applied to thedesign of groundwater remediation system[A]. Proceedings of1st InternationalConference on Evolutionary Multi-Criterion Optimization[C]. Berlin: Springer,2001:681-695
[34] Coello Coello CA., Pulido G. T.. A micro-genetic algorithm for multiobjectiveoptimization[A]. Proceedings of the Genetic and Evolutionary ComputationConference[C]. San Francisco: Morgan Kaufmann Publishers,2001:274-282
[35] Deb K., Pratab A., Agrawal S., et al. A fast and elitist multi-objective genetic algorithm:NSGA-II[J]. IEEE transactions on Evolutionary Computation,2002,6(2):182-197
[36] Storn R., Price K.. Differential evolution---A simple and Efficient heuristic for globaloptimization over continuous spaces[J]. Journal of Global Optimization,1997,11(4):341-359.
[37] Kennedy J., Eberhart R., C.. Particle swarm optimization[A]. Proceedings of IEEEInternational Conference on Neural Networks[C]. Piscataway: IEEE Service Center,1995, IV:1942-1948
[38] Tarakanov A.O., Dasgupta D.. A formal model of an artifical immune system[J].Biosystems,2000,55:151-158
[39]Parsopoulos K. E.,Vrahatis M. N.. Particle Swarm Optimization Method in MultiobjectiveProblems[A]. Proceedings of2002ACM Symposium on Applied Computing [C]. NewYork: ACM Press,2002:603-607
[40] Hu X., Eberhart R.. Multiobjective optimization using dynamic neighborhood particleswarm optimization[A]. Proceedings of the IEEE Congress on EvolutionaryComputation[C]. Piscataway: IEEE Service Center,2002,2:1677-1682
[41] Fieldsend J. E. and Singh S.. A multi-objective algorithm based upon particle swarmoptimization, an efficient data structure and turbulence[A].Proceedings of2002U.K.Workshop on Computational Intelligence [C]. Birmingham,2002:37-44
[42] Mostaghim S., Teich J.. Strategies for finding good local guides in multiobjective particleswarm optimization(MOPSO)[A]. Proceedings of2003IEEE Swarm IntelligenceSymposium [C]. Indianapolis,2003:26-33
[43] Coello Coello CA., Pulido GT., Lechuga MS.. Handing multiple objectives with particleswarm optimization[J].IEEE transactions on Evolutionary Computations,2004,8(3):256-279
[44] Parsopoulos K. E., Vrahatis M. N.. On the computation of all global minimizers throughparticle swarm optimization[J]. IEEE transactions on Evolutionary Computations,2004,8(3):211-224
[45] Ratnaweera A., Halgamuge S. K., Waston H. C.. Self-organizing hierarchical particalswarm optimizer with time-varying acceleration coefficients[J]. IEEE transactions onEvolutionary Computations,2004,8(3):240-255
[46] Sierra M. R., Coello Coello CA.. Improving PSO-based multiobjective optimizationusing crowing, mutation and ε-dominance[C]. Evolutionary Multi-Criterion Optimization.Berlin: Springer-Verlag,2005:505-519
[47] Liu B., Wang L., Jin Y. H., et al. Improved particle swarm optimization combined withchaos[J]. Chaos, Solitons&Fractals,2005,25(5):1261-1271
[48] Raquel C. R., Naval P. C. Jr.. An effective use of crowding distance in multiobjectiveparticle swarm optimization[A].Proceedings of the Conference on Genetic andEvolutionary Computation[C]. NY: ACM Press,2005:257-264
[49]雷德明,吴智铭. Pareto档案多目标粒子群优化[J].模式识别与人工智能,2006,19(4):475-480
[50] Liang J. J., Qin A. K., Suganthan P. N., et al. Evaluation of comprehensive learningparticle swarm optimizer[C]. Neural Information Processing. Springer Berlin Heidelberg,2004:230-235
[51] Huang V. L., Suganthan P. N., Liang J. J.. Comprehensive learning particle swarmoptimizer for solving multiobjective optimization problems[J]. International Journal ofIntelligent Systems,2006,21(2):209-226
[52] Abido M. A.. Two level of nondominated solutions approach to multiobjective particleswarm optimization[A]. Proceedings of the Genetic and Evolutionary ComputationConference [C]. New York: ACM Press,2007:726-733
[53] Santana R. A., Pontes M. R., Bastos-Filho C. J. A.. A multiple objective particle swarmoptimization approach using crowding distance and roulette wheel[C].Intelligent SystemsDesign and Applications,2009:237-242
[54] Tsai S. J., Sun T. Y., Liu C. C., et al. An improved multi-objective particle swarmoptimizer for multi-objective problems[J]. Expert Systems with Applications,2010,37(8):5872-5886
[55] Sha Z., Liu Y., Dong S.. Multi-objective PSO based on evolutionary programming[M].Advanced Intelligent Computing Theories and Applications. Springer Berlin Heidelberg,2010:602-610
[56] Daneshyari M., Yen G. G..Cultural-based multiobjective particle swarm optimization[J].Systems,Man,and Cybernetics, Part B: Cybernetics, IEEE Transactions on,2011,41(2):553-567
[57] Liang J. J., Qu B.Y., Suganthan P. N., et al. Dynamic multi-swarm particle swarmoptimization for multi-objective optimization problems[C]. Evolutionary Computation(CEC),2012:1-8
[58] Liang J. J., Suganthan P. N.. Dynamic multi-swarm particle swarm optimizer[C]. SwarmIntelligence Symposium,2005:124-129
[59] Peng H., Huang W., Deng C. S.. Multi-objective particle swarm optimization algorithmof multi-swarm co-evolution[J]. Journal of Computer Applications,2012,32(2):456-460
[60] Price K.. Differential evolution vs. the functions of the2ndICEO [A]. Proc of the1997IEEE International Conference on Evolutionary Computation[C]. Indianapolis,1997:153-157
[61] Abbass H. A., Sarker R., Newton C.. PDE: A Pareto-Frontier differential evolutionapproach for Multi-objective optimization problems[A]. In Proc of the Congress onEvolutionary Computation[C]. Piscataway,2001:971-978
[62] Abbass H. A.. The self-adaptive Pareto differential evolution algorithm[A]. In: Proc ofthe Congress on EvolutionaryComputation(CEC’2002)[C]. Piscataway: IEEE ServiceCenter,2002:831-836
[63] Madavan N. K.. Multiobjective Optimization using A Pareto differential evolutionapproach[A]. In: Proc of the congress on Evolutionary Computation(CEC’2002)[C].Piscataway: IEEE Service Center,2002:1145-1150
[64] Xue F., Sanderson A. C., Graves R. J.. Pareto-based Multi-objective differential evolution
[A]. In: Proc of the2003Congress on Evolutionary Computation (CEC’2003)[C].Piscataway, NJ: IEEE Press,2003:862-869
[65] Robic T., Filipic B.. DEMO: Differential Evolution for Multiobjective Optimization[A].In:Proceedings of the Third International Conference on Evolutionary Multi-CriterionOptimization(EMO2005)[C]. Guanajuato: Springer,2005:520-533
[66]张利彪,周春光,马铭,孙彩堂.基于极大极小距离密度的多目标微分进化算法[J].计算机研究与发展,2007,44(1):177-184
[67]孟红云,张小华,刘三阳.用于约束多目标优化问题的双群体差分进化算法[J].计算机学报,2008,31(2):228-235
[68] Qin A. K., Suganthan P. N.. Self-adaptive differential evolution algorithm for numericaloptimization[C]. IEEE Congress on Evolutionary Computation,2005:1785-1791
[69] Huang V. L., Qin A. K., Suganthan P. N.,et al. Multi-objective optimization based onself-adaptive differential evolution algorithm[C]. IEEE Congress on EvolutionaryComputation,2007:3601-3608
[70] Huang V.L., Zhao S.Z., Mallipeddi R., et al. Multi-objective optimization usingself-adaptive differential evolution algorithm.[C]. IEEE Congress on EvolutionaryComputation,2009:190-194
[71]龚文引,蔡之华.基于ε占优的正交多目标差分演化算法研究[J].计算机研究与发展,2009,46(4):656-666
[72] Monta o A. A., Coello Coello CA., Mezura-Montes E.. MODE-LD+SS: A NovelDifferential Evolution Algorithm Incorporating Local Dominance and Scalar SelectionMechanisms for Multi-Objective Optimization[A]. In:Proceedings of the congressConference on Evolutionary Computation (CEC’2010)[C].2010:1-8
[73] Santana-Quintero L.V., Hernandez-Diaz A. G., Molina J., et al. DEMORS: A hybridmulti-objective optimization algorithm using differential evolution and rough set theoryfor constrained problems[J]. Computers&Operations Research,2010,37(3):470-480
[74] Sindhya K., Ruuska S., Haanpaa T., et al. A new hybrid mutation operator formultiobjective optimization with differential evolution[J]. Soft Computing,2011,158(10):2041-2055
[75] Leung S W, Zhang X, Yuen S Y. Multiobjective differential evolution algorithm withopposition-based parameter control[C].Evolutionary Computation (CEC’2012),2012:1-8
[76] Wu Z, Xia X, Zhang J. MMODE: A Memetic Multiobjective Differential EvolutionAlgorithm[M].Advances in Swarm Intelligence. Springer Berlin Heidelberg,2013:422-430
[77]肖人彬,王磊.人工免疫系统原理、模型、分析及展望[J].计算机学报,2002,25(12):1280-1293
[78] Coello Coello CA., Cruz Cortés N.. An approach to solve multiobjective optimizationproblems based on an artificial immune system[A]. Proceedings of1st InternationalConference on Artificial Immune Systems[C]. Canterbury,2002:212-221
[79] Cruz Cortés N.,Coello Coello C. A.. Multiobjective optimization using ideas from theclonal selection principle[A]. Proceedings the Genetic and Evolutionary ComputationConference[C]. Berlin: Springer,2003:158-170
[80] Coello Coello C., Cruz Cortés N.. Solving multiobjective optimization problems usingan artificial immune system[J]. Genetic Programming and Evolvable Machines,2005,6(2):163-190
[81] Jiao L. C., Gong M.G., Shang R. H., et al. Clonal selection with immune dominance andanergy based multiobjective optimization[A]. Proceedings of3rd International Conferenceon Evolutionary Multi-criterion Optimization[C]. Berlin: Springer,2005:474-489
[82] Lu B., Jiao L. C., Du H., et al. IFMOA: Immune forgetting multiobjective optimizationalgorithm[A]. Proceedings of1rd International Conference on Advances in NaturalComputation[C]. Changsha,2005:399-408
[83] Gong M.G., Jiao L. C., Du H. F., et al. Multiobjective immune algorithm withnondominated neighbor-based selection[J]. Evolutionary Computation,2008,16(2):225-255
[84] Lu H.M., Yen G.. Rank-density-based multiobjective genetic algorithm and benchmarktest function study[J]. IEEE Transactions on Evolutionary Computation,2003,7(4):325-343
[85] Yen G., Lu H.M.. Dynamic multiobjective evolutionary algorithm: Adaptive cell-basedrank and density estimation[J]. IEEE Transactions on Evolutionary Computation,2003,7(3):253-274
[86]郑金华,史忠植,谢勇.基于聚类的快速多目标遗传算法[J].计算机研究与发展,2004,41(7):1081-1087
[87] Zeng Sanyou, Lishan S. K., Lixing X. D.. An Orthogonal Multi-Objective Evolutionaryalgorithm for Multi-Objective Optimization Problems with Constraints[J]. EvolutionaryComputation,2004,12(1):77-98
[88]雷德明,吴智铭.基于个体密集距离的多目标进化算法[J].计算机学报,2005,28(8):1320-1326
[89] Tan K. C., Yang Y. J., Goh C. K.. A Distributed Cooperative Coevolutionary Algorithmfor Multiobjective Optimization[J]. IEEE Transactions on Evolutionary Computation,2006,10(5):527-547
[90]雷德明,严新平,吴智铭,等.多目标混沌进化算法[J].电子学报,2006,34(6):1142-1145
[91]郑金华,蒋浩,邝达,等.用擂台赛法则构造多目标Pareto最优解集的方法[J].软件学报,2007,18(6):1287-1297
[92]石川,李清勇,史忠植.一种快速的基于占优树的多目标进化算法[J].软件学报,2007,18(3):505-516
[93] Zhang Q., Li H.. MOEA/D: A Multiobjective Evolutionary Algorithm based onDecomposition[J]. IEEE Transactions on Evolutionary Computation,2007,11(6):712-731
[94] Liu H.L., Li X.Q., Chen Y.Q.. Multi-objective evolutionary algorithm based ondynamical crossover and mutation[A]. In Proceedings of the International Conference onComputational Intelligence and Security [C].2008,(1):150-155
[95] Larranaga P., Lozano J. A.. Estimation of distribution algorithms: A new tool forevolutionary computation [M]. Boston, MA: Kluver,2002:57-100
[96] Pelikan M.. Hierarchical Bayesian Optimization Algorithm [A]. Studies in Fuzziness andSoft Computing [C]. New York: Springer-Verlag,2005,(17):105-129
[97] Zhang Q., Zhou A., Jin Y.. RM-MEDA: A regularity model-based multiobjectiveestimation of distribution algorithm [J]. IEEE Transactions on Evolutionary Computation,2008,12(1):41-63
[98] Zhou A., Zhang Q., Jin Y.. Approximating the set of Pareto-optimal solutions in both thedecision and objective spaces by anestimation of distribution algorithm[J]. IEEETransactions on Evolutionary Computation,2009,13(5):1167-1189
[99] Liu H.L., Wang Y.P.. A novel multiobjective evolutionary algorithm based on min-maxstrategy[A]. Intelligent data engineering and automated learning, Lecture Notes inComputer Science [C].2003:361-368
[100] Liu H.L., Wang Y.P., Cheung Y.M.. A multiobjective evolutionary algorithm usingmin-max strategy and sphere coordinate transformation[J]. Intelligent Automation andSoft Computing,2009,15(3):361-384
[101] Wang Y. P., Dang C.Y., Li H.C., et al. A clustering multi-objective evolutionaryalgorithm based on orthogonal and uniform design[A]. In Proceedings of the IEEEInternational Conference on Evolutionary Computation[C]. Piscataway: IEEE Press,2009:2927-2933
[102] Qu B.Y., Suganthan P.N.. Multiobjective Evolutionary Programming withoutNon-domination Sorting is up to Twenty Times Faster[A]. In Proceedings of the IEEEInternational Conference on Evolutionary Computation[C]. Piscataway: IEEE Press,2009:2934-2939
[103] Venkatesh P., Lee K.Y.. Multi-objective evolutionary programming for economicemission dispatch problem[A]. In Proceedings of the IEEE Power and Energy SocietyGeneral Meeting: Conversion and Delivery of Electrical Energy in the21st Century [C].2008:1-8
[104] Adra S., Dodd T., Griffin I., et al. Convergence acceleration operator for multiobjectiveoptimization[J]. IEEE Transactions on Evolutionary Computation,2009,13(4):825-847
[105] Ishibuchi H., Tsukamoto N., Nojima Y.. Diversity improvement by non-geometricbinary crossover in evolutionary multiobjective optimization[J]. IEEE Transactions onEvolutionary Computation,2010,14(6):985-998
[106] Liang J, You J, Han G, et al. Double space based multiobjective evolutionaryalgorithm[C]. ICMLC,2012:1406-1411
[107] Zhou A., Zhang Q, Zhang G.. A multiobjective evolutionary algorithm based ondecomposition and probability model[C].Evolutionary Computation (CEC’2012),2012:1-8
[108]马清亮,胡昌华.多目标进化算法及其在控制领域中的应用综述[J].控制与决策,2006,21(5):481-486
[109] Meza J. L. C., Yildirim M. B., Masud A. S. M.. A multiobjective evolutionaryprogramming algorithm and its applications to power generation expansion planning[J].Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on,2009,39(5):1086-1096
[110] Gen M., Lin L.. Multiobjective evolutionary algorithm for manufacturing schedulingproblems: state-of-the-art survey[J]. Journal of Intelligent Manufacturing,2013:1-18
[111] Metaxiotis K., Liagkouras K.. Multiobjective evolutionary algorithms for portfoliomanagement: a comprehensive literature review[J]. Expert Systems with Applications,2012,39(14):11685-11698
[112] Beatriz I., Reynolds A., Rayward-Smith V. J.. Development on a Multi-objectiveMetaheuristic(MOMH) Algorithm for Finding Interesting Sets of ClassificationRules[C]. Evolutionary Multi-criterion Optimization, Third International Conference,Guanajuato: Springer,2005:826-840
[113] Mukhopadhyay A., Mandal M.. A Hybrid Multiobjective Particle Swarm OptimizationApproach for Non-redundant Gene Marker Selection[A]. Proceedings of SeventhInternational Conference on Bio-Inspired Computing: Theories and Applications(BIC-TA2012)[C]. Springer India,2013:205-216
[114] Rudolph, G.. On a multi-objective evolutionary algorithm and its convergence to thePareto set[A]. Proceedings of the fifth IEEE Conference on Evolutionary Computation
[C]. Piscataway, New Jersey,1998:511-516
[115] Cui Xunxue, MiaoLi and Tingjian Fang. Study of Population Diversity ofMultiobjective Evolutionary Algorithm Based on Immune and EntropyPrinciples[A].Proceedings of the Congress on Evolutionary Computation[C].IEEEService Center, Piscataway, New Jersey,2001,2:1316-1321
[116] Rudolph, G.. Evolutionary Search under Partially Ordered Fitness Sets[A]. InProceedings of the International NAISO Congress on Information ScienceInnovations[C]. ICSC Academic Press: Millet, Sliedrecht,2001:818-822
[117] Joshua K., Corne D.. Properties of an Adaptive Archiving Algorithm for StoringNondominated Vectors[J]. IEEE Transactions on Evolutionary Computation,2003,7(2):100-116
[118]周育人,闵华清,许孝元,等.多目标演化算法的收敛性研究[J].计算机学报,2004,27(10):1415-1421
[119] Whitley D., Mathias K., Rana S., Dzubera J.. Evaluating Evolutionary Algorithms[J].Artificial Intelligence.1996,85:245-276
[120] Deb K., Thiele L., Laumanns M., et al. Scalable test problems for evolutionarymultiobjective optimization[M]. Springer London,2005
[121] Huband S., Hingston P., Barone L., et al.. A review of multiobjective test problems anda scalable test problem toolkit[J]. IEEE Transactions on Evolutionary Computation,2006,10(5):477-506
[122] Zitzler E., Deb K., Thiele L.. Comparison of multiobjective evolutionary algorithms:Empirical results[J]. Evolutionary Computation,2000,8(2):173-195
[123] Zitzler E., Thiele L., Laumanns M., et al. Performance assessment of multiobjectiveoptimizers: An analysis and review[J].IEEE transactions on Evolutionary Computation,2003,7(2):117-132
[124]郑金华.多目标进化算法及其应用[M].北京:科学出版社,2007
[125] Cavicchio D. J.. Reproductive Adaptive Plans[A]. Proceedings of the ACM1972Annual Conference[C].1972:1-11
[126] Goldberg D. E., Richardson J.. Genetic Algorithms with Sharing for MultimodalFunction Optimization[A]. Genetic Algorithms and Their Applications: Proceedings ofthe Second International Conference on Genetic Algorithms[C].1987:41-49
[127] De Jong K. A.. An analysis of the behavior of a class of generic adaptive system[D].University of Michigan,1975
[128] Fogel David B.. Evolutionary computation: Toward a new philosophy of machineintelligence[M].2nd Edition. Wiley IEEE Press,1999
[129] Holland J. H.. Building blocks, cohort genetic algorithms, and hyperplane-definedfunctions [J]. IEEE transactions on Evolutionary Computation,2000,8(4):373-391
[130] Deb, K.. Multi-objective Genetic Algorithms: Problem Difficulties and Construction ofTest Problems[J]. IEEE transactions on Evolutionary Computation,1999,7(3):205-230
[131] Veldhuizen D. A.V., Lamont G. B..Multiobjective Evolutionary Algorithm TestSuites[A]. Proceedings of the1999ACM Symposium on Applied Computing[C].SanAntonio, Texas: ACM,1999
[132] Runarsson T. P., X.,Yao.. Stochastic ranking for constrained evolutionaryoptimization[J]. IEEE transactions on Evolutionary Computation,2000,4:284-294
[133] Deb K., Thiele L., Laumanns M., et al. Scalable multi-objective optimization testproblems[A]. Proceedings of the2002Congress on Evolutionary Computation[C].2002:825-830
[134] Deb K., Thiele L., Laumanns M., et al. Scalable Test Problems for EvolutionaryMultiobjective Optimization[C]. Evolutionary multiobjective Optimization: TheoreticalAdvances and Applications, Springer,2005:105-145
[135] Zitzler E., Kunzil S.. Indicator-based selection in multiobjective search[A]. InConference on Parallel Problem Solving from Nature[C]. Birmingham, UK,2004:832-842
[136] Deb K., Jain S.. Running performance metrics for evolutionary multiobjectiveoptimization[R]. KanGAL Report2002004, Kanpur: Indian Institute of Technology,Kanpur,2002
[137] Zhou A., Qu B-Y., Li H., et al. Multiobjective evolutionary algorithms: A survey of thestate-of-the-art [J].Swarm and Evolutionary Computation,2011,1(1):32-49
[138]公茂果,焦李成,杨咚咚,等.进化多目标优化算法研究[J].软件学报,2009,20(2):271-289
[139] Kollat J.B., Reed P. M.. The value of online adaptive search: A performance comparisonof NSGAII,-NSGAII and MOEA[A]. In Proceedings of the third InternationalConference on Evolutionary Multi-Criterion Optimization [C].Lecture Notes in ComputerScience,2005:386-398
[140] Chen X., Hou Z., Guo L., et al. Improved multi-objective genetic algorithm basedon NSGA-II [J]. Journal of Computer Applications,2006,10:060
[141] Francesco P., Khu S., Savic D.. An investigation on preference order ranking scheme formultiobjective evolutionary optimization[J]. IEEE Transactions on EvolutionaryComputation,2007,11(1):17-45
[142] Sindhya K., Sinha A., Deb K., et al. Local search based evolutionary multiobjectiveoptimization algorithm for constrained and unconstrained problems[A]. In Proceedings ofthe IEEE International Conference on Evolutionary Computation [C]. Piscataway: IEEEPress,2009:2919-2926
[143] Deb K., Agrawal R. B.. Simulated binary crossover for continuous search space[J].Complex Systems,1995,9(2):115-148
[144]李学强,郝志峰,黄翰.基于分方向选择搜索的多目标进算法[J].华南理工大学学报:自然科学版,2011,39(2):134-139
[145] Lalwani S., Singhal S., Kumar R., et al. A comprehensive survey: Applications ofmulti-objective particle swarm optimization (MOPSO) algorithm[J]. Transactions onCombinatorics,2013,2(1):39-101
[146] Tizhoosh H. R.. Opposition-based learning: a new scheme for machine intelligence[C].Computational intelligence for modelling, control and automation and internationalconference on intelligent agents, web technologies and internet commerce, internationalconference on.2005,1:695-701
[147] Shi Y., Eberhart R.. A modified particle swarm optimizer[C].Evolutionary ComputationProceedings,1998:69-73.
[148] Ratnaweera A., Halgamuge S. K., Watson H. C.. Self-organizing hierarchical particleswarm optimizer with time-varying acceleration coefficients[J]. EvolutionaryComputation, IEEE Transactions on,2004,8(3):240-255