Balancing convergence and diversity in resource allocation strategy for decomposition-based multi-objective evolutionary algorithm

Abstract Decomposition-based multi-objective evolutionary algorithm decomposes a multi-objective optimization problem into a set of scalar subproblems and then optimizes them simultaneously. However, it does not take into account that subproblems of different difficulties need unequal computing resources. The resource allocation (RA) strategy based on MOEA/D was proposed to solve this problem. But most RA strategies generate a large number of solutions around some easy optimization subproblems, which cause the deterioration of the distribution. And the way they measure the subproblem difficulty ignores that subproblems may lose their evolvability in an evolutionary period. This paper aims to balance the convergence and diversity in RA strategy. Firstly, we introduce the accumulated escape probability (AEP) to calculate the historical improvement probability of each subproblem and then measure the subproblem evolvability, which can detect whether the subproblem has lost its evolvability in an evolutionary period. Secondly, we propose a density penalty-based individual screening mechanism (ISM) to enhance diversity. It gives priority to update the subproblem surrounded with more solutions and greater relative improvement on aggregated function. Finally, the above two methods are cooperated in MOEA/D and named it MOEA/D-BRA. Then the effectiveness of these two methods and the comprehensive performance of MOEA/D-BRA are tested. Furthermore, the BRA strategy is applied to more cases to balance convergence and diversity. Several experimental results indicate that the BRA strategy performers well on tackling a set of complicated optimization problems.