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A two-phase hybrid evolutionary algorithm for solving the bi-objective scheduling multiprocessor tasks on two dedicated processors

Author

Listed:
  • Fatma-Zohra Baatout

    (USTHB)

  • Mhand Hifi

    (USTHB
    UPJV)

Abstract

In this paper, we solve the bi-objective scheduling problem on two dedicated processors, an NP-Hard combinatorial optimization problem with a hybrid scatter search-based method. The goal of the problem is to schedule all tasks on their related processors such that the makespan and the total tardiness are minimized. The proposed method starts with an initial reference set, namely Pareto front set, provided by applying an adaptation of the knapsack type procedure. It then solves the problem by making a cooperation between two stages: (i) the first stage focuses on improving the reference set by optimizing the objective related to makespan and, (ii) the second stage tries to highlight the final reference set by favoring the optimization of the total tardiness. Further, at each stage, the $$\varepsilon $$ ε -constraint strategy is employed as a learning strategy, where its aim is to enlarge the search process around reference solutions for covering some unvisited subspaces and so, to avoid a premature convergence. In order to link both stages of the method, the path-relinking is injected whenever a new/modified reference set is reached. Finally, the performance of the designed algorithm is evaluated on instances extracted from the literature. Its results are compared to the results obtained by more recent methods of the literature. Encouraging results have been obtained.

Suggested Citation

  • Fatma-Zohra Baatout & Mhand Hifi, 2023. "A two-phase hybrid evolutionary algorithm for solving the bi-objective scheduling multiprocessor tasks on two dedicated processors," Journal of Heuristics, Springer, vol. 29(2), pages 229-267, June.
    • Handle: RePEc:spr:joheur:v:29:y:2023:i:2:d:10.1007_s10732-023-09511-0
    DOI: 10.1007/s10732-023-09511-0
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    References listed on IDEAS

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    1. M Hifi & M Michrafy, 2006. "A reactive local search-based algorithm for the disjunctively constrained knapsack problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(6), pages 718-726, June.
    2. Manuel Laguna & Rafael Marti, 1999. "GRASP and Path Relinking for 2-Layer Straight Line Crossing Minimization," INFORMS Journal on Computing, INFORMS, vol. 11(1), pages 44-52, February.
    3. Drozdowski, Maciej, 1996. "Scheduling multiprocessor tasks -- An overview," European Journal of Operational Research, Elsevier, vol. 94(2), pages 215-230, October.
    4. Adel Kacem & Abdelaziz Dammak, 2019. "Bi-objective scheduling on two dedicated processors," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 13(5), pages 681-700.
    5. L. Bianco & J. Blazewicz & P. Dell'Olmo & M. Drozdowski, 1997. "Preemptive multiprocessor task scheduling with release times and time windows," Annals of Operations Research, Springer, vol. 70(0), pages 43-55, April.
    6. Adel Manaa & Chengbin Chu, 2010. "Scheduling multiprocessor tasks to minimise the makespan on two dedicated processors," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 4(3), pages 265-279.
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