An adaptive penalty-based boundary intersection approach for multiobjective evolutionary algorithm based on decomposition

The multiobjective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multiobjective optimization problem into a number of single-objective problems and solves them collaboratively. Since its introduction, MOEA/D has gained increasing research interest and has become a benchmark for validating new designed algorithms. Despite that, some recent studies have revealed that MOEA/D faces some difficulties to solve problems with complicated characteristics. In this paper, we study the influence of the penalty-based boundary intersection (PBI) approach, one of the most popular decomposition approaches used in MOEA/D, on individuals' convergence and diversity, showing that the fixed same penalty value for all the subproblems is not very sensible. Based on this observation, we propose to use adaptive penalty values to enhance the balance between population convergence and diversity. Experimental studies show that the proposed adaptive PBI can generally improve the performance of the original PBI when solving the problems considered in this paper.