Algorithm Based on the Grey Wolves Attack Technique Method for Generating Pareto Optimal Front

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Résumé

This paper proposes an algorithm for solving
multiobjective optimization problems using the attack technique
of the Grey Wolf. It is a metaheuristic method called a
Multiobjective Optimizer based on Grey Wolf Attack Technique
(MOGWAT). In fact, it is inspired by the modified Hybrid Grey
Wolf Optimizer and Genetic Algorithm (HmGWOGA), which is
a single objective optimization algorithm specially designed for
positive objective functions. The MOGWAT method combines
the multiple objective functions of the initial problem into a sin-
gle objective function, and then penalizes constraint functions
to get an unconstrained single-objective optimization. The use
of an effective single-objective optimizer allows reaching the
optimal solutions. These solutions are also the Pareto optimal
solutions of the initial problem according to some parameters.
Through some theorems, we have established the theoretical
foundation and performance of our method. Furthermore, in
order to highlight the numerical performance of the method, we
have tackled three groups of problems: 16 test problems from
the Zitzler-Deb-Thiele benchmarks, 2 instances from the CEC
2009 benchmarks, and 2 real-world problems from literature.
Our numerical results have been compared to the ones obtained
with the NSGA-II method. This comparison was made using
some computed performance parameters. The outcomes of
the comparison have enabled us to prove the effectiveness
and efficiency of our new approach in terms of speed and
convergence.

Mots-clés

Multiobjective optimization; Metaheuristic methods; Pareto Optimality; Grey Wolf optimizer