基于反向学习的自适应差分进化算法
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摘要
为解决差分进化(DE)算法过早收敛与搜索能力低的问题,讨论对控制参数的动态调整,提出一种基于反向学习的自适应差分进化算法。该算法通过反向精英学习机制来增强种群的局部搜索能力,获取精确度更高的最优个体;同时,采用高斯分布随机性提高单个个体的开发能力,通过扩充种群的多样性,避免算法过早收敛,整体上平衡全局搜索与局部寻优的能力。采用CEC 2014中的6个测试函数进行仿真实验,并与其他差分进化算法进行对比,实验结果表明所提算法在收敛速度、收敛精度及可靠性上表现更优。
Concerning premature convergence and low searching capability of Differential Evolutionary( DE) algorithm,the dynamic adjustment of control parameters was dicussed, and a self-adaptive differential evolution algorithm based on opposition-based learning was proposed. In the proposed algorithm, opposition-based elite learning was used to enhance the local search ability of the population and obtain more accurate optimal individuals; meanwhile, Gaussian distribution was used to improve the exploitation ability of each individual and increase the diversity of the population, which avoids premature convergence of the algorithm and achieves the balance of the global exploitation and local exploitation. Comparison experiments with some other differential evolution algorithms were conducted on six test functions in CEC 2014. The experimental results show that the proposed algorithm outperforms the compared differential evolution algorithms in terms of convergence speed,solution accuracy and reliability.
Concerning premature convergence and low searching capability of Differential Evolutionary( DE) algorithm,the dynamic adjustment of control parameters was dicussed, and a self-adaptive differential evolution algorithm based on opposition-based learning was proposed. In the proposed algorithm, opposition-based elite learning was used to enhance the local search ability of the population and obtain more accurate optimal individuals; meanwhile, Gaussian distribution was used to improve the exploitation ability of each individual and increase the diversity of the population, which avoids premature convergence of the algorithm and achieves the balance of the global exploitation and local exploitation. Comparison experiments with some other differential evolution algorithms were conducted on six test functions in CEC 2014. The experimental results show that the proposed algorithm outperforms the compared differential evolution algorithms in terms of convergence speed,solution accuracy and reliability.
引文
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[2]LIAO T W.Two hybrid differential evolution algorithms for engineering design optimization[J].Applied Soft Computing,2010,10(4):1188-1199.
[3]PIOTROWSKI A P.Differential evolution algorithms applied to neural network training suffer from stagnation[J].Applied Soft Computing,2014,21:382-406.
[4]ZHOU Y-Z,YI W-C,GAO L,et al.Adaptive differential evolution with sorting crossover rate for continuous optimization problems[J].IEEE Transactions on Cybernetics,2017,47(9):2742-2753.
[5]FAN Q,YAN X.Self-adaptive differential evolution algorithm with zoning evolution of control parameters and adaptive mutation strategies[J].IEEE Transactions on Cybernetics,2016,46(1):219-232.
[6]薛羽,庄毅,顾晶晶,等.自适应离散差分进化算法策略的选择[J].软件学报,2014,25(5):984-996.(XUE Y,ZHUANG Y,GU J J,et al.Strategy selecting problem of self-adaptive discrete differential evolution algorithm[J].Journal of Software,2014,25(5):984-996)
[7]YANG M,LI C,CAI Z,et al.Differential evolution with auto-enhanced population diversity[J].IEEE Transactions on Cybernetics,2015,45(2):302-315.
[8]GUO J,LI Z,XIE W,et al.Dissipative differential evolution with self-adaptive control parameters[C]//CEC 2015:Proceedings of the 2015 IEEE Congress on Evolutionary Computation.Piscataway,NJ:IEEE,2015:3088-3095.
[9]QIN A K,SUGANTHAN P N.Self-adaptive differential evolution algorithm for numerical optimization[C]//CEC 2005:Proceedings of the 2005 IEEE Congress on Evolutionary Computation.Piscataway,NJ:IEEE,2005:1785-1791.
[10]BREST J,GREINER S,BOSKOVIC B,et al.Self-adapting control parameters in differential evolution:a comparative study on numerical benchmark problems[J].IEEE Transactions on Evolutionary Computation,2006,10(6):646-657.
[11]ZHANG J,SANDERSON A C.JADE:adaptive differential evolution with optional external archive[J].IEEE Transactions on Evolutionary Computation,2009,13(5):945-958.
[12]TANABE R,FUKUNAGA A.Success-history based parameter adaptation for differential evolution[C]//CEC 2013:Proceedings of the 2013 IEEE Congress on Evolutionary Computation.Piscataway,NJ:IEEE,2013:71-78.
[13]YI W,ZHOU Y,GAO L,et al.An improved adaptive differential evolution algorithm for continuous optimization[J].Expert Systems with Applications,2016,44:1-12.
[14]ZHANG J,ZHAN Z-H,LIN Y,et al.Evolutionary computation meets machine learning:a survey[J].IEEE Computational Intelligence Magazine,2011,6(4):68-75.
[15]TIZHOOSH H R.Opposition-based learning:a new scheme for machine intelligence[C]//CIMCA'05:Proceedings of the 2005International Conference on Computational Intelligence for Modelling,Control and Automation and International Conference on Intelligent Agents,Web Technologies and Internet Commerce(CIMCA-IAWTIC'06).Washington,DC:IEEE Computer Society,2005:695-701.
[16]WANG W,WANG H,SUN H,et al.Using opposition-based learning to enhance differential evolution:a comparative study[C]//CEC 2016:Proceedings of the 2016 IEEE Congress on Evolutionary Computation.Piscataway,NJ:IEEE,2016:71-77.
[17]WANG H,LI H,LIU Y,et al.Opposition-based particle swarm algorithm with Cauchy mutation[C]//CEC 2007:Proceedings of the 2007 IEEE Congress on Evolutionary Computation.Piscataway,NJ:IEEE,2007:4750-4756.
[18]EL-ABD M.Opposition-based artificial bee colony algorithm[C]//GECCO'11:Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation.New York:ACM,2011:109-116.
[19]RAHNAMAYAN S,TIZHOOSH H R,SALAMA M M A.Opposition-based differential evolution algorithms[C]//CEC 2006:Proceedings of the 2006 IEEE Congress on Evolutionary Computation.Piscataway,NJ:IEEE,2006:2010-2017.
[20]OMRAN M G H,SALMAN A.Constrained optimization using CODEQ[J].Chaos,Solitons&Fractals,2009,42(2):662-668.
[21]WANG H,RAHNAMAYAN S,WU Z.Parallel differential evolution with self-adapting control parameters and generalized opposition-based learning for solving high-dimensional optimization problems[J].Journal of Parallel and Distributed Computing,2013,73(1):62-73.
[22]RAHNAMAYAN S,TIZHOOSH H R,SALAMA M M A.Quasioppositional differential evolution[C]//CEC 2007:Proceedings of the 2007 IEEE Congress on Evolutionary Computation.Piscataway,NJ:IEEE,2007:2229-2236.
[23]WANG H,WU Z,RAHNAMAYAN S,et al.Enhancing particle swarm optimization using generalized opposition-based learning[J].Information Sciences,2011,181(20):4699-4714.
[24]SEIF Z,AHMADI M B.An opposition-based algorithm for function optimization[J].Engineering Applications of Artificial Intelligence,2015,37:293-306.
[25]GARCIA S,FERNANDEZ A,LUENGO J,et al.Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining:Experimental analysis of power[J].Information Sciences,2010,180(10):2044-2064.