A Bi-objective Constrained Optimization Methodology Using a Hybrid Multi-Objective and Penalty Function Approach

Single objective evolutionary constrained optimization has been widely searched and researched by plethora of researchers in last two decades. On the other hand, multi-objective constraint handling using evolutionary algorithms has not been actively proposed. However, real-world multi-objective optimization problems consist of one or many non-linear and non-convex constraints. In the present work, we develop an evolutionary algorithm based constraint handling methodology, to deal with constraints in multi-objective optimization problems. The method is a combination of an evolutionary multi-objective optimization coupled with classical weighted sum approach based local search method and is an extended version of our previously developed constraint handling method for single objective optimization [4]. A constrained bi-objective problem is converted into a tri-objective problem where the additional objective is formed using summation of constrained violation. The proposed method is applied to four constrained multi-objective problem. The non-dominated solutions are compared with a standard evolutionary multiobjective optimization algorithm (NSGA-II) with respect to hypervolume and attainment surface. The simulation results illustrates the effectiveness of the proposed approach.