几乎所有多目标进化算法(multi-objective optimization evolutionary algorithm,MOEA)都是针对Pareto最优面为均匀分布问题而言.然而现实中很多问题Pareto最优面是非均匀分布的,决策者希望得到一个与Pareto最优面分布类似的解集.现存算法并不能有效解决该问题.对此,提出一种针对于非均匀分布多目标优化问题的维护方法(non-u-niformly diversity maintenance method,NUDMM).该方法定义一个反映个体分布"规则"程度的指标-杂乱度,并设计一种降低种群杂乱度的方法,在未知Pareto最优面分布规律情况下有效剔除造成种群混乱的个体.通过与NSGA-Ⅱ和SPEA2在不同维数下8个非均匀函数上对比实验,表明NUDMM在有效保持问题真实分布的同时,具有良好的收敛性.%Almost all of the multi-objective optimization evolutionary algorithms(MOEAs) are designed for the Pareto optimal front which is distributed uniformly. But in real world opfimizations, the Pareto optimal front usually has a non-uniform distribution. A similar solution set distribution with Pareto optimal front is expected to obtain by decision makers. However, the existing algorithms cannot solve such problems effectively. In this paper, a diversity maintenance method for non-uniformly distributed multiobjective optimization problem(NUDMM) is proposed. In the algorithm, an indicator reflecting 'regular' degree of distributionMessy is defined. And a method to decrease Messy of population is designed, which eliminates disordered individual on the condition that the distribution of the Pareto optimal front is unknown. From an extensive comparative study with NSGA-Ⅱ and SPEA2 on eight non-uniform distribution test problems, it is observed that the proposed method has a good performance in maintaining the real distribution and convergence.
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