A Bi-objective Hybrid Constrained Optimization (HyCon) Method Using a Multi-Objective and Penalty Function Approach

Abstract

Single objective evolutionary constrained optimization has been widely researched by plethora of researchers in the last two decades whereas 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 on hybrid constraint handling methodology (HyCon) to deal with constraints in bi-objective optimization problems. HyCon is a combination of an Evolutionary Multi-objective Optimization (EMO) coupled with classical weighted sum approach and is an extended version of our previously developed constraint handling method for single objective optimization. A constrained bi-objective problem is converted into a triobjective problem where the additional objective is formed using summation of constrained violation. The performance of HyCon is tested on four constrained bi-objective problems. The non-dominated solutions are compared with a standard evolutionary multi-objective optimization algorithm (NSGAII) with respect to hypervolume and attainment surface. The simulation results illustrates the effectiveness of the HyCon method. The HyCon either outperformed or produced similar performance as compared to NSGA-II.