摘要： 反向微分进化(ODE)算法基于反向优化对种群进行初始化更新以保持种群多样性。但该算法中反向个体容易偏离全局最优个体,不能很快达到全局最优,在函数优化过程中收敛速度慢且容易陷入局部最优。为此,提出一种基于M-H 采样的快速反向微分进化算法。M-H 采样用于ODE 算法的变异操作,满足马尔可夫链可逆条件。马尔可夫链的一步转移概率根据个体等级分配的选择概率进行计算,既能选择最优个体,又能寻找优化方向 并保持种群多样性。仿真结果表明,M-H 采样得到的个体具有马尔可夫链平稳分布特性,该算法在单峰函数和多峰函数优化中都能快速收敛,全局和局部搜索性能达到平衡,具有较高的搜索精度及较好的鲁棒性。

关键词: 微分进化算法, 反向微分进化算法, 转移概率, 平稳分布, 马尔可夫链蒙特卡洛, 反向学习

Abstract: In Differential Evolution ( DE ) algorithm, the population initialization is updated by using opposition optimization rule,so as to maintain the population diversity. However,the reverse individuals are easy to deviate from the global optimal solution,has slow convergence speed and easy to fall into local optimum in function optimization. This paper proposes a fast Opposition Differential Evolution(ODE) algorithm based on M-H(Metropolis-Hastings) sampling method. M-H sampling is used in the mutation operation of ODE. M-H sampling satisfies Markov Chain reversible conditions. One step transition probability of Markov Chain is calculated according to the selecting probability of individual ranking-assignment,not only chooses the best individual,but also searches for the optimal direction and keeps the population diversity. Simulation results show these individuals from M-H sampling have Markov stationary distribution property. The algorithm can accelerate the speed of convergence in unimodal functions and multimodal functions,balance the performance of global searching and local searching,and has higher precision and better robustness.

Key words: Differential Evolution ( DE) algorithm, Opposition Differential Evolution ( ODE ) algorithm, transition probability, stationary distribution, Markov Chain Monte Carlo(MCMC), Opposition-based Learning(OBL)

中图分类号: 

• TP301. 6