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 opti-
mization 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 dis-
tribution 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

Multiobjective optimization, Metaheuristics, Pareto optimality