基于聚集密度的自适应选择多目标进化算法

Adaptive Selection Multi-Objective Evolutionary Algorithm Based on Crowding-Density

分析了线性选择方法的两个缺陷,提出了一种基于聚集密度的非线性自适应选择方法。算法基本思想是:首先将每代种群划分成Pareto劣解集和Pareto非劣解集,然后依照个体的聚集密度分别在劣解集和非劣解集中构造一种偏序集,分别按照不同的等概率在这两个偏序集中选择个体,其中劣解偏序集的个体选择概率远小于非劣解偏序集的个体选择概率,根据两个偏序集中的容量自动计算出两个选择概率。这种非线性选择方法既体现了劣解集和非劣解集中个体的绝对平等性及非劣解集对劣解集的相对优先选择权,又充分考虑到了Pareto最优解的分布性。理论分析和数值计算表明,这种新的选择机制不仅能改善排序选择法的收敛性,而且能得到分布性良好的Pareto最优解。

Abstract：An adaptive nonlinear selection method based on the crowding-density is put forward for overcoming the defects of linear selection method. The basic idea of new method is that every population is divided into sets of dominated solutions and non-dominated solutions, and two partial order sets of dominated solutions and non-dominated solutions are set up ac- cording to the crowding-density. The individuals of every partial order set are selected in equal probability and the selection probability of dominated solutions set is much bigger than the selection probability of non-dominated solutions set. Two selection probabilities may be automatically computed according to the number of individuals. The new method not only embodies fully the preferential selection privilege of dominated solutions set and the equality in individuals of every set, but also considers the distribution of Pareto optimal solution. Theoretical analysis and simulation results indicate that the new selection method can not only improve the convergence of select sort method, but also get Pareto optimal solution with a good distribution.