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

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 single 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.