Grey wolves attack process for the Pareto optimal front construction in the multiobjective optimization

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 epsilon-constraint approach, which is an aggregation technique. The epsilon-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 epsilon-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.