模糊自适应排序变异多目标差分进化算法
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摘要
为提高多目标差分进化算法在求解问题时的收敛性和多样性,提出了一种模糊自适应排序变异多目标差分进化算法。首先,采用模糊系统自适应调节排序变异参数,均衡了算法的局部搜索能力和全局探索能力,在加快算法收敛速度的同时,减小了陷入局部最优的可能性;其次,采用均匀种群初始化方法,在算法开始阶段获得了一个分布均匀的初始种群,提高了算法的稳定性和多样性;最后,增加一个临时的种群以存储被丢弃的个体,用于每一代优化后的最终选择,提高了种群进化过程中的多样性。采用7个标准测试函数和3个具有偏好特征的测试函数进行仿真实验,并将所提算法与其他4种多目标进化算法进行对比。实验结果表明,所提算法在收敛性和多样性方面整体上优于其他几种对比算法,可以有效地逼近真实Pareto前沿。同时,实验也验证了所提算法中模糊自适应排序变异策略的有效性。
In order to improve the convergence and diversity of the multi-objective differential evolution algorithm in solving multi-objective optimization problems,this paper proposed a multi-objective differential evolution algorithm with fuzzy adaptive ranking-based mutation.Firstly,the global exploration and the local exploitation are balanced by using the fuzzy system which adaptively adjust the parameters of ranking-based mutation,so the convergence rate of the algorithm is accelerated and the possibility of the algorithm falling into a local optimum is reduced.Secondly,for the sake of improving the stability and diversity of the algorithm,an initial population with good diversity is obtained through the uniform population initialization method at the beginning of the algorithm.Finally,the discarded individuals is stored by adding them to a temporary population for the final selection in the end of each iteration,therefore,the population diversity during the evolution process is improved.Simulation experiments were conducted on the seven standard test functions and three test functions with bias features.The experimental results show that compared with other four algorithms,the proposed algorithm has better convergence and diversity,and it can effectively approach to the real Pareto frontier.The effectiveness of the fuzzy adaptive ranking-based mutation strategy in the proposed algorithm is also verified by experimental comparison method.
In order to improve the convergence and diversity of the multi-objective differential evolution algorithm in solving multi-objective optimization problems,this paper proposed a multi-objective differential evolution algorithm with fuzzy adaptive ranking-based mutation.Firstly,the global exploration and the local exploitation are balanced by using the fuzzy system which adaptively adjust the parameters of ranking-based mutation,so the convergence rate of the algorithm is accelerated and the possibility of the algorithm falling into a local optimum is reduced.Secondly,for the sake of improving the stability and diversity of the algorithm,an initial population with good diversity is obtained through the uniform population initialization method at the beginning of the algorithm.Finally,the discarded individuals is stored by adding them to a temporary population for the final selection in the end of each iteration,therefore,the population diversity during the evolution process is improved.Simulation experiments were conducted on the seven standard test functions and three test functions with bias features.The experimental results show that compared with other four algorithms,the proposed algorithm has better convergence and diversity,and it can effectively approach to the real Pareto frontier.The effectiveness of the fuzzy adaptive ranking-based mutation strategy in the proposed algorithm is also verified by experimental comparison method.
引文
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[18] TIAN Y,CHENG R,ZHANG X Y,et al.PlatEMO:a MATLAB platform for evolutionary multi-objective optimization [Educational Forum[J].IEEE Computational Intelligence Magazine,2017,12(4):73-87.
[19] TIAN Y,ZHANG X Y,CHENG R,et al.A multi-objective evolutionary algorithm based on an enhanced inverted generational distance metric[C]//Proceedings of the 2016 IEEE Congress on Evolutionary Computation.Vancouver,BC,Canada:IEEE Press,2016:5222-5229.
[20] COELLO C A C,PULIDO G T,LECHUGA M S.Handling multiple objectives with particle swarm optimization[J].IEEE Transactions on Evolutionary Computation,2004,8(3):256-279.
[2] SUN C F,ZHOU H Y,ZHANG Y H.Dynamic environment economic dispatch based on differential evolution algorithm[J].Computer Science,2012,39(11):208-211.(in Chinese)孙成富,周海岩,张亚红.基于差分进化算法的动态环境经济电力系统调度优化[J].计算机科学,2012,39(11):208-211.
[3] SONG X Y,ZHU J Y,SUN H L.Hybrid differential evolution algorithm for vehicle routing problem with time windows[J].Computer Science,2014,41(12):220-225.(in Chinese)宋晓宇,朱加园,孙焕良.一种求解带时间窗车辆路径问题的混合差分进化算法[J].计算机科学,2014,41(12):220-225.
[4] SUN Z,WU J,YANG J,et al.Path planning for GEO-UAV bistatic SAR using constrained adaptive multiobjective differential evolution[J].IEEE Transactions on Geoscience & Remote Sensing,2016,54(11):6444-6457.
[5] ZHANG Q F,LI H.MOEA/D:A multiobjective evolutionary algorithm based on decomposition[J].IEEE Transactions on Evolutionary Computation,2007,11(6):712-731.
[6] LI H,ZHANG Q F.Multiobjective optimization problems with complicated Pareto sets,MOEA/D and NSGA-II[J].IEEE Transactions on Evolutionary Computation,2009,13(2):284-302.
[7] SONG T,ZHUANG Y.A kind of multi-objective optimization algorithm based on differential evolution with multi-population mechanism[J].Computer Science,2012,39(8):205-209.(in Chinese)宋通,庄毅.基于多种群差分进化的多目标优化算法[J].计算机科学,2012,39(8):205-209.
[8] XIE C W,LI K,LIAO G Y.Improved NSGA2 algorithm with differential evolution local search[J].Computer Science,2013,40(10):235-238.(in Chinese)谢承旺,李凯,廖国勇.一种带差分局部搜索的改进型NSGA2算法[J].计算机科学,2013,40(10):235-238.
[9] JARIYATANTIWAIT C,YEN G G.Fuzzy multiobjective dif- ferential evolution using performance metrics feedback[C]//IEEE Congress on Evolutionary Computation.Beijing,China:IEEE Press,2014:1959-1966.
[10] WANG X,TANG L.An adaptive multi-population differential evolution algorithm for continuous multi-objective optimization[J].Information Sciences,2016,348(2):124-141.
[11] ALI M,SIARRY P,PANT M.An efficient differential evolution based algorithm for solving multi-objective optimization problems[J].European Journal of Operational Research,2011,217(2):404-416.
[12] GONG W Y,CAI Z H.Differential evolution with ranking-based mutation operators[J].IEEE Transactions on Cybernetics,2013,43(6):2066-2081.
[13] CHEN X,DU W L,QIAN F.Multi-objective differential evolution with ranking-based mutation operator and its application in chemical process optimization[J].Chemometrics & Intelligent Laboratory Systems,2014,136(16):85-96.
[14] ROBIC T,FILIPIC B.DEMO:differential evolution for multiobjective optimization[C]//International Conference on Evolutionary Multi-Criterion Optimization.Berlin Heidelberg:Springer-Verlag Press,2005:520-533.
[15] DEB K,PRATAP A,AGARWAL S,et al.A fast and elitist multiobjective genetic algorithm:NSGA-II[J].IEEE Transactions on Evolutionary Computation,2002,6(2):182-197.
[16] TIAN Y,CHENG R,ZHANG X Y,et al.An indicator based multiobjective evolutionary algorithm with reference point adaptation for better versatility[J].IEEE Transactions on Evolutionary Computation,2018,4(22):609-622.
[17] LI H,ZHANG Q F,DENG J.Biased multiobjective optimization and decomposition algorithm[J].IEEE Transactions on Cybernetics,2016,47(1):52-66.
[18] TIAN Y,CHENG R,ZHANG X Y,et al.PlatEMO:a MATLAB platform for evolutionary multi-objective optimization [Educational Forum[J].IEEE Computational Intelligence Magazine,2017,12(4):73-87.
[19] TIAN Y,ZHANG X Y,CHENG R,et al.A multi-objective evolutionary algorithm based on an enhanced inverted generational distance metric[C]//Proceedings of the 2016 IEEE Congress on Evolutionary Computation.Vancouver,BC,Canada:IEEE Press,2016:5222-5229.
[20] COELLO C A C,PULIDO G T,LECHUGA M S.Handling multiple objectives with particle swarm optimization[J].IEEE Transactions on Evolutionary Computation,2004,8(3):256-279.