Enhancing Multiobjective Evolutionary Algorithms by Local Dominance and Local Recombination: Performance Verification in Multiobjective 0/1 Knapsack Problems

Abstract

This paper proposes a method to enhance single population multiobjective evolutionary algorithms (MOEAs) by searching based on local dominance and local recombination. In this method, first, all fitness vectors of individuals are transformed to polar coordinate vectors in objective function space. Then, the population is iteratively divided into several subpopulations by using declination angles. As a result, each sub-population covers a sub-region in the multiobjective space with its individuals located around the same search direction. Next, local dominance is calculated separately for each sub-population after alignment of its principle search direction by rotation. Selection, recombination, and mutation are applied to individuals within each sub-population. The proposed method can improve the performance of MOEAs that use dominance based selection, and can reduce the entire computational cost to calculate dominance among solutions as well. In this paper we verify the effectiveness of the proposed method obtaining Pareto optimal solutions in two representative MOEAs, i.e. NSGA-II and SPEA2, with Multiobjective 0/1 Knapsack Problems.