基于多目标进化算法的MOEA/D权重向量产生方法

Multi-objective Evolutionary Algorithm Based Weight Vectors Generation Method of MOEA/D

在进化多目标优化研究领域,多目标优化是指对含有2个及以上目标的多目标问题的同时优化,其在近些年来受到越来越多的关注。随着MOEA/D的提出,基于聚合的多目标进化算法得到越来越多的研究,对MOEA/D算法的改进已有较多成果,但是很少有成果研究MOEA/D中权重的产生方法。提出一种使用多目标进化算法产生任意多个均匀分布的权重向量的方法,将其应用到MOEA/D,MSOPS和NSGA-III中,对这3个经典的基于聚合的多目标进化算法进行系统的比较研究。通过该类算法在DTLZ测试集、多目标旅行商问题MOTSP上的优化结果来分别研究该类算法在连续性问题、组合优化问题上的优化能力,以及使用矩形测试问题使得多目标进化算法的优化结果在决策空间可视化。实验结果表明,没有一个算法能适用于所有特性的问题。然而,MOEA/D采用不同聚合函数的两个算法MOEA/D_Tchebycheff和MOEA/D_PBI在多数情况下的性能比MSOPS和NSGA-III更好。

In the evolutionary multi-objective optimization(EMO)community,multi-objective optimization refers to simultaneous optimization of multi-objective problems with more than one objective,which has gained more and more attention in recent years.After the raise of MOEA/D,the aggregation-based multi-objective evolutionary algorithms have obtained more and more research,and there have been many achievements with regard to the improvement of MOEA/D.While,there has been little research about the generation method of weight vectors for MOEA/D.This paper proposed a method to generate any number of well-distributed weight vectors using MOEAs.And the generated weight vectors are applied to MOEA/D,MSOPS and NSGA-III.Then,the three aggregation-based multi-objective evolutionary algorithms are comprehensively compared through testing on DTLZ test suit,multi-objective TSP and rectangle test problem in order to study their optimization abilities on continuous and combinatorial problems and a visual observation in the decision space,respectively.The experimental results show that,none of the algorithms is able to solve problems with all different properties.While,the performance of MOEA/D_Tchebycheff and MOEA/D_PBI is better than MSOPS and NSGA-III in most cases.