Journal of Intelligent Manufacturing

, Volume 23, Issue 4, pp 1179–1194 | Cite as

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

  • Xiaohui Li
  • Farouk Yalaoui
  • Lionel Amodeo
  • Hicham Chehade


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 NP-hard 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.


Scheduling problem Parallel machines Metaheuristics NSGA-II Fuzzy logic Two phase method 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Xiaohui Li
    • 1
  • Farouk Yalaoui
    • 1
  • Lionel Amodeo
    • 1
  • Hicham Chehade
    • 1
  1. 1.Institut Charles Delaunay, LOSIUniversity of Technology of Troyes, UMR-STMR 6279Troyes CedexFrance

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