采用放松支配关系的高维多目标微分进化算法
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摘要
为了提高进化算法在求解高维多目标优化问题时的收敛性和多样性,提出了采用放松支配关系的高维多目标微分进化算法。该算法采用放松的Pareto支配关系,以增加个体的选择压力;采用群体和外部存储器协同进化的方案,并通过混合微分变异算子,生成子代群体;采用基于指标的方法计算个体的适应度并对群体进行更新;采用基于Lp范数(0 In order to improve the convergence and diversity of many-objective evolutionary algorithms, a many-objective differential evolution algorithm using a relaxed dominance relation is proposed. In the proposed algorithm, a relaxed domination relation is designed and incorporated to increase the selection pressure of individuals. Population is coevolved with an external archive, and the child population is generated by the mixed differential mutation operators. The fitness of each individual is evaluated based on an indicator method, and the population is updated. The archive is updated according to the Lp norm(0
引文
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[11]Qin Xin,Xu Jianxin,Xu Yinghao.A new differential evolution algorithm for minimax optimization in robust design[J].IEEE Trans on Evolutionary Cybernetics,2017:1-14.
[12]Wang X,Zhao S G.Differential evolution algorithm with self-adaptive population resizing mechanis[J].Mathematics Problems in Engineering,2013(2):237-245.
[13]Lauanns M,Thiele L,Deb K,et al.Combining convergence and diversity in evolutionary multi-objective optimization[J].Evolutionary Computation,2002,10(3):263-282.
[14]Wang Handing,Jiao Licheng,Yao Xin.Two_Arch2:an improved two-archive algorithm for many-objective optimization[J].IEEE Transactions on Evolutionary Computation,2015,19(4):524-541.
[15]Aggarwal C C,Hinneburg A,Keim D A.On the surprising behavior of distance metrics in high dimensional space[M].New York,USA:Springer,2001.
[16]Deb K,Thiele L.Scalable test problems for evolutionary multiobjective optimization[M].London:Springer,2005:105-145.
[17]Praditwong K,Yao X.A new multi-objective evolutionary optimization algorithm:the two-archive algorithm[C]//Proceedings of International Conference on Computational Intellgence&Security,2006:286-291.
[18]Deb K,Jain H.An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach,part I:solving problems with box constraints[J].IEEE Transactions on Evolutionary Computation,2014,18(4):577-601.
[19]Edgar M L,Carlos A,Coello C A C.IGD+-EMOA:A multi-objective evolutionary algorithm based on IGD+[C]//IEEE Conference Publications,2016:999-1006.
[20]Sallem A,Benhela B,Kotti M,et al.Simulation-based multi-objective optimization of current conveyors:performance evaluations[C]//International Conference on Design&Technology of Integrated Systems in Nanoscale Era,2012:1-5.
[21]Li M,Yang S,Liu X.Shift-based density estimation for pareto-based algorithms in many-objective optimization[J].IEEE Transactions on Evolutionary Computation,2014,18(3):348-365.
[2]韩红艳.基于Pareto支配的高维多目标进化算法研究[D].大连:大连理工大学,2016.
[3]Fleming P J,Purshouse R C,Lygoe R J.Many-objective optimization:an engineering design perspective[C]//Evolutionary Multi-Criterion Optimization.Berlin:Springer-Verlag,2005,19(4):14-32.
[4]Deb K,Saxena D K.On finding pareto-optimal solutions through dimensionality reduction for certain large-dimensional multi-objective problems[R].Kanpur:Indian Institute of Technology,2005.
[5]Deb K,Amrit P,Sameer A,et al.A fast and elitist multiobjective genetic algorithm:NSGA-II[J].IEEE Trans on Evolutionary Computation,2002,6(2):182-197.
[6]Yuan Jiawei,Liu Hailin.A new dominance relation based on simplex for many objective optimization problems[C]//IEEE Conference Publications,2016:175-178.
[7]Drechsler N,Drechsler R,Becker B.Multi-objective optimization based on relation favour[C]//Evolutionary MultiCriterion Optimization,2001:154-166.
[8]Dai C,Wang Y,Hu L.An improvedα-dominance strategy for many-objective optimization problems[J].Soft Computing,2015,15(3):1-7.
[9]Zhang Q,Li H.MOEA/D:a multi-objective evolutionary algorithm based on decomposition[J].IEEE Trans on Evolutionary Computation,2007,11(6):712-731.
[10]Zitzler E,Kunzli S.Indicator-based selection in multiobjective search[C]//Parallel Problem Solving from Nature(PPSN VIII).Berlin,Germany:Springer,2004:832-842.
[11]Qin Xin,Xu Jianxin,Xu Yinghao.A new differential evolution algorithm for minimax optimization in robust design[J].IEEE Trans on Evolutionary Cybernetics,2017:1-14.
[12]Wang X,Zhao S G.Differential evolution algorithm with self-adaptive population resizing mechanis[J].Mathematics Problems in Engineering,2013(2):237-245.
[13]Lauanns M,Thiele L,Deb K,et al.Combining convergence and diversity in evolutionary multi-objective optimization[J].Evolutionary Computation,2002,10(3):263-282.
[14]Wang Handing,Jiao Licheng,Yao Xin.Two_Arch2:an improved two-archive algorithm for many-objective optimization[J].IEEE Transactions on Evolutionary Computation,2015,19(4):524-541.
[15]Aggarwal C C,Hinneburg A,Keim D A.On the surprising behavior of distance metrics in high dimensional space[M].New York,USA:Springer,2001.
[16]Deb K,Thiele L.Scalable test problems for evolutionary multiobjective optimization[M].London:Springer,2005:105-145.
[17]Praditwong K,Yao X.A new multi-objective evolutionary optimization algorithm:the two-archive algorithm[C]//Proceedings of International Conference on Computational Intellgence&Security,2006:286-291.
[18]Deb K,Jain H.An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach,part I:solving problems with box constraints[J].IEEE Transactions on Evolutionary Computation,2014,18(4):577-601.
[19]Edgar M L,Carlos A,Coello C A C.IGD+-EMOA:A multi-objective evolutionary algorithm based on IGD+[C]//IEEE Conference Publications,2016:999-1006.
[20]Sallem A,Benhela B,Kotti M,et al.Simulation-based multi-objective optimization of current conveyors:performance evaluations[C]//International Conference on Design&Technology of Integrated Systems in Nanoscale Era,2012:1-5.
[21]Li M,Yang S,Liu X.Shift-based density estimation for pareto-based algorithms in many-objective optimization[J].IEEE Transactions on Evolutionary Computation,2014,18(3):348-365.