Solving Constrained Multi-objective Optimization Problems with Evolutionary Algorithms

Abstract

Most optimization problems in real-life have multiple constraints. Constrained optimization problems with more than one objective, with at least two objectives in conflict with one another, are referred to as constrained multi-objective optimization problems (CMOPs). Two main approaches to solve constrained problems are to add a penalty to each objective function and then optimizing the new adapted objective function, or to adapt the Pareto-dominance principle that are used to compare two solutions in such a way that constraint violations are taken into consideration. This paper investigates how these two approaches affect the performance of the steady-state non-dominated sorting genetic algorithm II (SNSGAII), the Pareto-archived evolution strategy (PAES), the multi-objective evolutionary algorithm based on decomposition (MOEA/D) and a cultural algorithm (CA) when solving CMOPs. The results indicate that there is no statistical significant difference in performance between these two approaches. However, depending on the multi-objective evolutionary algorithm (MOEA) one approach does provide slightly better solutions than the other approach.