Comparison of constraint handling approaches in multi-objective optimization

Abstract

When considering real-world optimization problems the possibility of encountering problems having constraints is quite high. Constraint handling approaches such as the penalty function and others have been researched and developed to incorporate an optimization problem’s constraints into the optimization process. With regards to multi-objective optimization, in this paper the two main approaches of incorporating constraints are explored, namely: Penalty functions and dominance based selection operators. This paper aims to measure the effectiveness of these two approaches by comparing the empirical results produced by each approach. Each approach is tested using a set of ten benchmark problems, where each problem has certain constraints. The analysis of the results in this paper showed no overall statistical difference between the effectiveness of penalty functions and dominance based selection operators. However, significant statistical differences between the constraint handling approaches were found with regards to specific performance indicators.