基于邻域竞赛的多目标优化算法

传统多目标优化算法（Multi-objective evolution algorithms，MOEAs）的基本框架大致分为两部分:首先是收敛性保持，采用Pareto支配方法将种群分成若干非支配层；其次是分布性保持，在临界层中，采用分布性保持机制维持种群的分布性.然而在处理高维优化问题（Many-objective optimization problems，MOPs）（目标维数大于3）时，随着目标维数的增加，种群的收敛性和分布性的冲突加剧，Pareto支配关系比较个体优劣的能力也迅速下降，此时传统的MOEA已不再适用于高维优化问题.鉴于此，本文提出了一种基于邻域竞赛的多目标优化算法（Evolutionary algorithm based on neighborhood competition for multi-objective optimization，NCEA）.NCEA首先将个体的各个目标之和作为个体的收敛性估计；然后，计算当前个体向量与收敛性最好的个体向量之间的夹角，并将其作为当前个体的邻域估计；最后，通过邻域竞赛方法将问题划分为若干个相互关联的子问题并逐步优化.为了验证NCEA的有效性，本文选取5个优秀的算法与NCEA进行对比实验.通过对比实验验证，NCEA具有较强的竞争力，能同时保持良好的收敛性和分布性.

An Evolutionary Algorithm Through Neighborhood Competition for Multi-objective Optimization

The basic framework of traditional multi-objective evolutionary algorithms (MOEAs) can be classified into two parts:one is the convergence holding of the population, for which the fast nondominated sort approach is used to sort the population into certain nondomination layers; the other is the distribution maintenance of the population, for which diversity maintenance mechanisms are adoopted to hold the distribution of the population. However, when dealing with many-objective optimization problems (MOPs) (The number of objective dimensions is greater than 3), with the incease of objective dimensions, the conflicts between convergence and distribution will intensifys, and the Pareto dominance's ability of comparing the individuals will decline. In this case, traditional MOEAs are no longer apt. In this paper, a evolutionary algorithm is proposed based on neighborhood competition for multi-objective optimization (denoted as NCEA). Firstly, the convergence of each individual in the population is estimated by summing its objective values; then the angles between current selected solutions and the best converged solution are calculated and taken as the estimates of the distribution of the selected solutions; lastly, an MOP is divided into a number of mutually correlated sub-problems through neghorhood competition and optimizing, respectively. From the comparative experiments with other five representative MOEAs, NCEA is found to be competitive and successful in finding well-converged and well-distributed solution set.