A bi-objective hybrid constrained optimization (HyCon) method using a multi-objective and penalty function approach

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 tri-objective 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 (NSGA-II) 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.