### Fuzzy Logic Controller Based Multiobjective Metaheuristics to Solve a Parallel Machines Scheduling Problem

Abstract

This paper considers a multiobjective optimization problem which focus on a parallel machines scheduling problem. It consists of scheduling n independent jobs on m identical parallel machines. Release dates, due dates and sequence dependent setup times are considered as constraints. The aim is to optimize two different objectives at the same time: the makespan and the total tardiness. First, the solutions encoding and a mathematical formulation for this problem are presented. Then, our main contribution is to propose two metaheuristics (FLC-NSGA-II and FLC-SPEA-II) since this problem is NP-hard. These two methods are based on the traditional NSGA-II and SPEA-II and use a fuzzy logic controller to improve the parameters settings such as the crossover probability and the mutation probability. Experimental results show the advantage of the proposed algorithm FLC-NSGA-II compared to NSGA-II and FLC-SPEA-II.