Grey Wolves Attack Process for the Pareto Optimal Front Construction in the Multiobjective Optimization

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Résumé

We propose a new metaheuristic, HmGWOGA-MO, for solving multiobjective optimization problems operating with a population of solutions. The method is a hybridization of the HmGWOGA method, which is a single objective optimization method, and the ϵ-constraint approach, which is an aggregation technique. The ϵ-constraint technique is one of the best ways to transform a problem with many objective functions into a single objective problem because it works even if the problem has any kind of Pareto optimal front. Previously, the HmGWOGA method was designed to optimize a positive single-objective function without constraints. The obtained solutions are good. That is why, in this current work, we combined have it with the ϵ-constraint approach for the resolution of multiobjective optimization problems. Our new method proceeds by transforming a given multiobjective optimization problem with constraints into an unconstrained optimization of a single objective function. With the HmGWOGA method, five different test problems with varying Pareto fronts have been successfully solved, and the results are compared with those of NSGA-II regarding convergence towards the Pareto front and the distribution of solutions on the Pareto front. This numerical study indicates that HmGWOGA-MO is the best choice for solving a multiobjective optimization problem when convergence is the most important performance parameter.

Mots-clés

Mathematical optimization, Multi-objective optimization, Mathematics, Constraint (computer-aided design), Convergence (economics), Pareto principle, Optimization problem, Metaheuristic