一种基于局部Lipschitz下界估计支撑面的差分进化算法  

Differential Evolution Algorithm Based on Local Lipschitz Underestimate Supporting Hyperplanes

作　　者：周晓根 张贵军[1] 郝小虎[1] 俞立[1] 

机构地区：[1]浙江工业大学信息工程学院,杭州310023

出　　处：《计算机学报》2016年第12期2631-2651,共21页Chinese Journal of Computers

基　　金：国家自然科学基金(61075062;61573317);浙江省自然科学基金(LY13F030008);浙江省科技厅公益项目(2014C33088);浙江省重中之重学科开放基金资助项目(20151008;20151015)资助~~

摘　　要：为了减少智能优化算法求解复杂问题时所需的目标函数评价次数,降低算法计算代价,在差分进化算法框架下,结合Lipschitz估计理论,提出一种基于局部Lipschitz下界估计支撑面的差分进化算法.首先,对新个体的N邻近个体构建Lipschitz下界估计支撑面,进而通过支撑面获取新个体的下界估计值;然后,根据下界估计值设计Lipschitz估计选择策略来指导种群更新;其次,利用下界估计区域的极值信息排除部分无效区域,逐步缩小搜索区域;最后,根据N邻近个体下降方向和主导支撑面下降方向设计广义下降方向做局部增强.数值实验结果表明,所提算法与文中给出的主流算法相比,能够以较少的目标函数评价次数获得高质量的最优解.To reduce the number of function evaluations required to find optimal solutions of computationally expensive problems for intelligent optimization algorithms, a new algorithm which introduces the Lipschitz underestimate theory into basic differential evolution algorithm is proposed, referred to as differential evolution algorithm based on local Lipschitz underestimate supporting hyperplanes. Firstly, the Lipschitz underestimate supporting hyperplanes are constructed for the N neighboring individuals of the trial individual to obtain the underestimate value of the trial individual. Secondly, the Lipschitz underestimate selection strategy that designed according to the underestimate value of the trial individual is used to guide the population updating process. Thirdly, by excluding the invalid regions where the global optimum solution cannot be found according to the extremum information of the underestimate region, the search domain narrows gradually. Finally, the generalized descent direction based on the descent directions of the N neighboring individuals and the dominant supporting hyperplane is designed for local enhancement. Experiments results show that the proposed algorithm can obtain better quality optimal solutions with less number of function evaluations compare with the main-stream algorithms given in this paper.

关 键 词：差分进化 智能优化算法 Lipschitz下界估计 全局优化 支撑面 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]