变邻域分解多目标自适应差分进化算法

Decomposition with ensemble neighborhood size multi-objective adaptive differential evolutionary algorithm

中文关键词  分解  邻域种群集  概率匹配方法  差分进化  多目标优化  复杂度分析

英文关键词  decomposition  ensemble neighborhood size  probability matching method  differential evolution  multiobjective optimization  complexity analysis

中文摘要

      分解方法是处理复杂问题常用的一种手段, 而差分进化算法被广泛地应用于多目标优化问题(multi-objective optimization problems, MOP), 为了克服经典差分进化算法和分解方法的缺陷, 本文提出了一种自适应差分进化算法和变邻域分解方法相结合的新颖算法---ADEMO/D-ENS, 该算法采用Tchebycheff方法将多目标优化问题分解成多维标量优化子问题, 并利用邻域子问题的信息进行优化, 基于邻域种群集依概率自适应选择邻域种群规模; 同时采用概率匹配(probability match, PM)自适应方法从差分策略池中选择差分进化策略; 同时分析了算法的复杂度; 最后, 通过和经典的非支配排序遗传算法(non-dominated sorting genetic algorithms II, NSGA--II)和多目标差分进化算法(multi-objective differential evolution algorithm, MODE)仿真对比, 说明ADEMO/D-ENS方法可以更有效的处理多目标优化问题.

英文摘要

      Decomposition is a conventional optimization method, and the differential evolutionary algorithm is widely applied in the multi-objective optimization problems (MOP). A novel algorithm—ADEMO/D-ENS which combines the two algorithms, the adaptive differential evolutionary algorithm and the decomposition with variable neighborhood size, is proposed to overcome the drawbacks of the classical differential evolution algorithm and the decomposition method. The approach makes use of the Tchebycheff method to decompose the multi-objective optimization problems into scalar optimization sub-problems. And the sub-problems are optimized by neighborhood relations among them. The adaptive selection approach based on ensemble of neighborhood size is used to determine the neighborhood size. Meanwhile, the probability match adaptive method is used to select differential strategy from the differential strategy pool. Moreover, the complexity of the algorithm is analyzed. Finally, compared with the classical non-dominated sorting genetic algorithms II (NSGA–II) algorithm and the multi-objective differential evolution algorithm (MODE), simulation results verified that the ADEMO/D-ENS approach can deal with the multi-objective optimization problems more effectively.