MOEA/ICD:一种基于适应度指标ICD的高维多目标进化算法

MOEA/ICD:A Many-objective Evolutionary Algorithm Based on Fitness Index ICD

关键词:  高维多目标优化问题|进化算法|收敛性|多样性|适应度指标

Key words:  Many-Objective|Optimization|Problems  evolutionary|algorithm  convergence  diversity  fitness|index

摘要:

已有的基于参考点(参考向量)或标量化效用函数的多目标进化算法(Multi-Objective Evolutionary Algorithm，MOEA)在求解高维多目标优化问题(Many-objective Optimization Problems，MaOPs)时存在不足。基于此，本文提出一种动态度量解个体收敛性与多样性综合性能的适应度指标(Fitness indicator considering convergence and diversity of individual adaptively， I_CD)，该指标随进化过程的推进而自适应地调整种群个体的收敛性和多样性所占比例，即初期I_CD强调收敛性而后期侧重多样性，以平衡高维多目标种群的收敛性和多样性，并获得高质量的解集。进一步地，将I_CD嵌入NSGA-Ⅱ算法框架，设计一种基于I_CD的高维多目标进化算法(Many-Objective Evolutionary Algorithm Based on I_CD， MOEA/I_CD)。最后，将新算法与5种代表性算法一同在DTLZ和MaF系列测试问题上进行反转世代距离(Inverted Generational Distance，IGD)性能测试。实验结果表明：相比5种对比算法，MOEA/I_CD具有显著较优的收敛性和多样性。因此，MOEA/I_CD是一种颇具前景的高维多目标进化算法(Many-Objective Evolutionary Algorithm,MaDEA)。

Abstract:

The existing Many-Objective Evolutionary Algorithms based on reference points (reference vectors) or scalar utility functions have shortcomings in solving Many-objective Optimization Problems.Based on this,a novel fitness index I_CD that dynamically measured the comprehensive performance of individual convergence and diversity was proposed in this article.This index adaptively adjusted the proportion of convergence and diversity of population individuals as the evolutionary process progressed,that was,I_CD emphasized the convergence in the early stage,and in the later stage,it focused on the diversity to balance the convergence and diversity of high-dimensional multi-objective populations and obtained high-quality solution sets.Furthermore,the I_CD was embedded into the NSGA-Ⅱ algorithm framework to design a Many-Objective Evolutionary Algorithm based on I_CD,which was MOEA/I_CD.Finally,Inverted Generational Distance (IGD) performance tests were carried out on DTLZ and MaF series test problems with the new algorithm and five representative algorithms.The experimental results show that compared with the five comparison algorithms,MOEA/I_CD has significantly better convergence and diversity.Therefore,MOEA/I_CD is a promising Many-Objective Evolutionary Algorithm (MaOEA).