MOEA/D with Constraint Objectivization and Adaptive Weight Adjustment for Constrained Optimization

Abstract

In this paper, MOEA/D is extended to constrained optimization by making the constraints an objective function. An adaptive adjustment method is proposed to introduce a parameter for varying weights. The parameter for varying the weights is given in such a way that the bias of the search towards the feasible and infeasible regions can be adjusted. The parameter is tuned based on two guidelines to properly utilize infeasible solutions. The first is actively utilizing infeasible solutions with large constraint violations and encouraging global search including the infeasible regions. The second is actively utilizing infeasible solutions with small constraint violations and encouraging a search on the boundary of the feasible regions. This is expected to improve the global optimization performance to the feasible regions, which is a non-convex set, and the convergence performance to feasible solutions. We verify the usefulness of the proposed method for problems where the feasible regions are a convex set and a nonconvex set.