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Multi-objective scheduling on two dedicated processors

Author

Listed:
  • Adel Kacem

    (University of Sfax)

  • Abdelaziz Dammak

    (University of Sfax)

Abstract

We study a multi-objective scheduling problem on two dedicated processors. The aim is to minimize simultaneously the makespan, the total tardiness and the total completion time. This NP-hard problem requires the use of well-adapted methods. For this, we adapted genetic algorithms to multi-objective case. Four methods are presented to solve this problem. The first is an aggregative genetic algorithm (GA), the second is a Pareto GA, the third is a non-dominated sorting GA (NSGA-II) and the fourth is a constructive algorithm based on lower bounds (CABLB). We proposed some adapted lower bounds for each criterion to evaluate the quality of the found results on a large set of instances. Indeed, these bounds also make it possible to determine the dominance of one algorithm over another based on the different results found by each of them. We used two metrics to measure the quality of the Pareto front: the hypervolume indicator (HV) and the number of solutions in the Pareto front (ND). The obtained results show the effectiveness of the proposed algorithms.

Suggested Citation

  • Adel Kacem & Abdelaziz Dammak, 2021. "Multi-objective scheduling on two dedicated processors," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 694-721, October.
    • Handle: RePEc:spr:topjnl:v:29:y:2021:i:3:d:10.1007_s11750-020-00588-5
    DOI: 10.1007/s11750-020-00588-5
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    References listed on IDEAS

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