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Permutation-Based Genetic, Tabu, And Variable Neighborhood Search Heuristics For Multiprocessor Scheduling With Communication Delays

Author

Listed:
  • TATJANA DAVIDOVIĆ

    (Mathematical Institute, Serbian Academy of Science and Arts, Kneza Mihaila 35, 11000 Belgrade, Serbia and Montenegro)

  • PIERRE HANSEN

    (GERAD and École des Hautes Études Commerciales, 3000 chemin de la Côte-Sainte-Catherine, Montréal H3T 2A7, Canada)

  • NENAD MLADENOVIĆ

    (Mathematical Institute, Serbian Academy of Science and Arts, Kneza Mihaila 35, 11000 Belgrade, Serbia and Montenegro;
    GERAD and École des Hautes Études Commerciales, 3000 chemin de la Côte-Sainte-Catherine, Montréal H3T 2A7, Canada)

Abstract

The multiprocessor scheduling problem with communication delays that we consider in this paper consists of finding a static schedule of an arbitrary task graph onto a homogeneous multiprocessor system, such that the total execution time (i.e. the time when all tasks are completed) is minimum. The task graph contains precedence relations as well as communication delays (or data transferring time) between tasks if they are executed on different processors. The multiprocessor architecture is assumed to contain identical processors connected in an arbitrary way, which is defined by a symmetric matrix containing minimum distances between every two processors. The solution is represented by a feasible permutation of tasks. In order to obtain the objective function value (i.e. schedule length, makespan), the feasible permutation has to be transformed into the actual schedule by the use of some heuristic method. For solving this NP-hard problem, we develop basic tabu search and variable neighborhood search heuristics, where various types of reduced Or-opt-like neighborhood structures are used for local search. A genetic search approach based on the same solution space is also developed. Comparative computational results on random graphs with up to 500 tasks and 8 processors are reported. On average, it appears that variable neighborhood search outperforms the other metaheuristics. In addition, a detailed performance analysis of both the proposed solution representation and heuristic methods is presented.

Suggested Citation

  • Tatjana Davidović & Pierre Hansen & Nenad Mladenović, 2005. "Permutation-Based Genetic, Tabu, And Variable Neighborhood Search Heuristics For Multiprocessor Scheduling With Communication Delays," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 297-326.
    • Handle: RePEc:wsi:apjorx:v:22:y:2005:i:03:n:s021759590500056x
    DOI: 10.1142/S021759590500056X
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    Cited by:

    1. Abdessamad Ait El Cadi & Omar Souissi & Rabie Ben Atitallah & Nicolas Belanger & Abdelhakim Artiba, 2018. "Mathematical programming models for scheduling in a CPU/FPGA architecture with heterogeneous communication delays," Journal of Intelligent Manufacturing, Springer, vol. 29(3), pages 629-640, March.
    2. Mladenović, Nenad & Kratica, Jozef & Kovačević-Vujčić, Vera & Čangalović, Mirjana, 2012. "Variable neighborhood search for metric dimension and minimal doubly resolving set problems," European Journal of Operational Research, Elsevier, vol. 220(2), pages 328-337.
    3. Pierre Hansen & Nenad Mladenović & José Moreno Pérez, 2010. "Variable neighbourhood search: methods and applications," Annals of Operations Research, Springer, vol. 175(1), pages 367-407, March.

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