Metaheuristics and exact methods to solve a multiobjective parallel machines scheduling problem

Abstract

This paper deals with a multiobjective parallel machines scheduling problem. It consists in scheduling n independent jobs on m identical parallel machines. The job data such as processing times, release dates, due dates and sequence dependent setup times are considered. The goal is to optimize two different objectives: the makespan and the total tardiness. A mixed integer linear program is proposed to model the studied problem. As this problem is NPhard in the strong sense, a metaheuristic method which is the second version of the non dominated sorting genetic algorithm (NSGA-II) is proposed to solve this problem. Since the parameters setting of a genetic algorithm is difficult, a fuzzy logic controller coupled with the NSGA-II (FLC-NSGA-II) is therefore proposed. The role of the fuzzy logic is to better set the crossover and the mutation probabilities in order to update the search ability. After that, an exact method based on the two phase method is also developed. We have used four measuring criteria to compare these methods. The experimental results show the advantages and the efficiency of FLC-NSGA-II.

Multiobjective Hybrid Genetic Algorithms for Manufacturing Scheduling: Part I Models and Algorithms

“…Li et al [20] proposed metaheuristics and exact methods to solve a multiobjective parallel machines scheduling (MoPMS) problem, Pm|s i j , r j |C max , T j in which consists in scheduling n independent jobs on m identical parallel proposed machines and the job data such as processing times, release dates, due dates and sequence dependent setup times are considered where s i j and r j are the sequence dependent setup times if job j is the immediate successor of the job i on the same machine and the release of job j, respectively and C max , T j are the makespan and the tardiness of job j. They formulated a mixed integer linear program (MILP) model for the MoPMS problem for solving it by CPLEX solver and proposed the nondominated sorting genetic algorithm (FLC-NSGA-II) coupled with a fuzzy logic controller (FLC) to solve the problem.…”

“…The role of the fuzzy logic is to better set the crossover and the mutation probabilities in order to update the search ability as demonstrated in hybrid genetic algorithm (HGA) by Yun and Gen [16] as introducing in Subsection 3.2 Fuzzy Logic Controller for Tuning Parameters and also auto-tuning strategy for balancing between exploration and exploitation by Lin and Gen [21]. The experimental results for the MoPMS problem shown the advantages and the efficiency of the FLC-NSGA-II [20].…”

A new method coupling simulation and a hybrid metaheuristic to solve a multiobjective hybrid flowshop scheduling problem

“…The output of the controller is the variation of the two probabilities ∆p c and ∆p m . In the works of [28], [29], [30], [31] and [32], the authors have proposed a combination of the fuzzy logic and different genetic algorithms to solve different optimization problems.…”

“…Two fuzzy logic controllers are proposed in this study to enhance the crossover probability and the mutation probability respectively. The details of the three parts are presented in our previous work [31], such as the settings of the membership functions, the linguistic terms and the decision tables.…”

“…Yalaoui et al [30] have developed the FLC-GA and FLC-NSGA-II for the reentrant scheduling problem. In our previous works [31][32], we have developed FLC-NSGA-II and FLC-SPEA-II algorithms to solve a multiobjective parallel machines scheduling problem.…”