一种基于参考点约束支配的NSGA-Ⅲ算法
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摘要
针对带约束的高维多目标优化问题,设计一种基于参考点的约束支配关系(RPCDP),将可行解与不可行解作为一个整体看待,进而综合考虑它们的收敛性、多样性和可行性,并基于此提出用于解决约束高维多目标优化问题的NSGA-Ⅲ算法.将所提出算法与著名的3种约束高维多目标进化算法进行对比,实验结果表明在标准测试函数集CDTLZ上,相对于其他算法,所提出算法的解集具有更好的收敛性和分布性.
For constrained many-objective optimization problems, a reference point-based constrained dominance principle(RPCDP) is designed, regareding the feasible solutions and infeasible solutions as a whole and considering the convergence, the diversity and the feasibility simultaneously. Then on this basis, an improved NSGA-Ⅲ algorithm is proposed. The experimental results on CDTLZ test suite show that compared with three state-of-the-art constrained many-objective evolutionary algorithms, the proposed algorithm has better performance on convergence and distribution.
For constrained many-objective optimization problems, a reference point-based constrained dominance principle(RPCDP) is designed, regareding the feasible solutions and infeasible solutions as a whole and considering the convergence, the diversity and the feasibility simultaneously. Then on this basis, an improved NSGA-Ⅲ algorithm is proposed. The experimental results on CDTLZ test suite show that compared with three state-of-the-art constrained many-objective evolutionary algorithms, the proposed algorithm has better performance on convergence and distribution.
引文
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[3]von Lücken C,Barán B,Brizuela C.A survey on multi-objective evolutionary algorithms for many-objective problems[J].Computational optimization and Applications,2014,58(3):707-756.
[4]Garcia J,Berlanga A,López J M M.Effective evolutionary algorithms for many-specifications attainment:Application to air traffic control tracking filters[J].IEEE Trans on Evolutionary Computation,2009,13(1):151-168.
[5]Jain H,Deb K.An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach,Part I:Handling constraints and extending to an adaptive approach[J].IEEE Trans on Evolutionary Computation,2014,18(4):602-622.
[6]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 Trans on Evolutionary Computation,2014,18(4):577-601.
[7]Li K,Deb Q,Zhang Q,et al.An evolutionary many-objective optimization algorithm based on dominance and decomposition[J].IEEE Trans on Evolutionary Computation,2015,19(5):694-716.
[8]Cheng R,Jin Y,Olhofer M,et al.A reference vector guided evolutionary algorithm for many-objective optimization[J].IEEE Trans on Evolutionary Computation,2016,20(5):773-791.
[9]Deb K,Pratap A,Agarwal S,et al.A fast and elitis multiobjective genetic algorithm:Nsga-Ii[J].IEEE Trans on Evolutionary Computation,2002,6(2):182-197.
[10]龙文,梁昔明,徐松金,等.聚类佳点集交叉的约束优化混合进化算法[J].计算机研究与发展,2012,49(8)1753-1761.(Long W,Liang X M,Xu S J,et al.A hybrid evolutionary algorithm based on clustering good-point set crossover for constrained optimization[J].J of Computer Research&Development,2012,49(8):1753-1761.)
[11]孙浩,杨景明,刘醒,等.基于环境Pareto支配选择策略的有约束多目标差分进化算法[J].控制与决策,201631(1):45-51.(Sun H,Yang J M,Liu X,et al.Differential evolution algorithm based on environment Pareto dominated selection strategy in constrained multi-objective optimization problem[J].Control&Decision,201631(1):45-51.)
[12]王勇,蔡自兴,周育人,等.约束优化进化算法[J].软件学报,2009,20(1):11-29.(Wang Y,Cai Z X,Zhou Y R,et al.Constrained optimization evolutionary algorithms[J].J of Software,2009,20(1):11-29.)
[13]Fan Z,Li W,Cai X,et al.Angle-based constrained dominance principle in moea/D for constrained multi-objective optimization problems[C].2016 IEEECongress on Evolutionary Computation(CEC).Vancouver,2016:460-467.
[14]Das I,Dennis J E.Normal-boundary intersection:A new method for generating the pareto surface in nonlinear multicriteria optimization problems[J].SIAMJ on Optimization,1998,8(3):631-657.
[15]Tian Y,Cheng R,Zhang X,et al.Platemo:A matlab platform for evolutionary multi-objective optimization[J].IEEE Computational Intelligence Magazine,2017,12(4):73-87.
[16]Deb K,Thiele L,Laumanns M,et al.Scalable test problems for evolutionary multiobjective optimization[C].Evolutionary Multiobjective Optimization-A.London:Springer,2005:105-145.
[17]Zitzler E,Thiele L,Laumanns M,et al.Performance assessment of multiobjective optimizers:An analysis and review[J].IEEE Trans on Evolutionary Computation,2003,7(2):117-132.