On neighborhood exploration and subproblem exploitation in decomposition based multiobjective evolutionary algorithms

The decomposition based multiobjective evolutionary algorithm, denoted as MOEA/D, is an open framework for multiobjective optimization. This paper addresses the reproduction operation in MOEA/D. Generally, the solutions from a neighborhood of a subproblem are chosen as the mating pool for offspring reproduction. Since the Pareto set of an MOP shows some kind of structure in the decision space, the newly generated solutions based on the mating pool are arguable more likely to distribute along the population structure, which is called neighborhood exploration, and less likely to push a solution forward along the subproblem, which is called subproblem exploitation. To balance neighborhood exploration and subproblem exploitation, we propose to utilize both history and neighbor solutions for offspring reproduction. This idea is implemented through two operators based on the multivariate Gaussian distribution model, one is based on neighbor solutions and the other is based on previously visited solutions. When generating a new trial solution for a subproblem, one of the two operators is chosen with a probability. The proposed reproduction strategy is embedded in the MOEA/D framework and applied to a test suite. The comparison study has demonstrated that the new reproduction strategy is promising.