Diversity improvement in Decomposition-Based Multi-Objective Evolutionary Algorithm for many-objective optimization problems

Decomposition-Based Multi-Objective Evolutionary Algorithms (DBMOEA), such as Multiple Single Objective Pareto Sampling (MSOPS) and Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D), have been successfully applied in finding Pareto-optimal fronts in Multiobjective Optimization Problems (MOPs), two or three-objective in general. DBMOEA decomposes one MOP into multiple Single-objective Optimization Problems (SOPs) where the convergence of approximated front is facilitated by finding the optimal solution of each SOP and its diversity is preserved by a group of well distributed SOPs. However, when solving problems with many objectives, one single solution can be the optimal solution of multiple SOPs which inadvertently leads to a severe loss of population diversity. In this paper, we propose a new diversity improvement method incorporated into a modified DBMOEA to directly handle this challenge. The design includes two steps. First, a few number of weight vectors guide the whole population towards a small number of solutions nearby the true Pareto front. Afterwards, initialize a subpopulation around each solution and diversify them toward well distribution. As a case study, a new algorithm based on this design is compared with three state-of-the-art DBMOEAs, MOEA/D, MSOPS, and MO-NSGA-II. Experimental results show that the proposed methods exhibit better performance in both convergence and diversity than the chosen competitors for solving many-objective optimization problems.