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Competitive genetic algorithms for the open-shop scheduling problem

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  • Christian Prins

Abstract

For more than two machines, and when preemption is forbidden, the computation of minimum makespan schedules for the open-shop problem is NP-hard. Compared to the flow-shop and the job-shop, the open-shop has free job routes which lead to a much larger solution space, to smaller gaps between the optimal makespan and the lower bounds, and to disappointing results for the algorithms based on the disjunctive graph model. For instance, the best existing branch and bound method cannot solve some 7 ×7 hard instances to optimality, and all published metaheuristics (working by reversing some disjunctions already fixed) do not better than some greedy or steepest-descent heuristics which need a much smaller computational effort. In this context, the intrinsic parallelism of genetic algorithms (GAs) seems well adapted, for detecting global optima disseminated among many quasi-optimal schedules. This paper presents several GAs for the open-shop problem. It is shown that even simple and fast versions can compete with the best known heuristics and metaheuristics, thanks to two key-features: a population in which each individual has a distinct makespan, and a special procedure which reorders every new chromosome. Using problem-specific heuristics, it is possible to design more powerful GAs which give excellent results, even on the hardest benchmarks of the literature: for instance, all hard open instances from Taillard are broken, except one for which the best known solution is improved. Copyright Springer-Verlag Berlin Heidelberg 2000

Suggested Citation

  • Christian Prins, 2000. "Competitive genetic algorithms for the open-shop scheduling problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(3), pages 389-411, December.
    • Handle: RePEc:spr:mathme:v:52:y:2000:i:3:p:389-411
    DOI: 10.1007/s001860000090
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    Citations

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    Cited by:

    1. Martin, Clarence H, 2009. "A hybrid genetic algorithm/mathematical programming approach to the multi-family flowshop scheduling problem with lot streaming," Omega, Elsevier, vol. 37(1), pages 126-137, February.
    2. Mejía, Gonzalo & Yuraszeck, Francisco, 2020. "A self-tuning variable neighborhood search algorithm and an effective decoding scheme for open shop scheduling problems with travel/setup times," European Journal of Operational Research, Elsevier, vol. 285(2), pages 484-496.
    3. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.
    4. Shahaboddin Shamshirband & Mohammad Shojafar & A. Hosseinabadi & Maryam Kardgar & M. Nasir & Rodina Ahmad, 2015. "OSGA: genetic-based open-shop scheduling with consideration of machine maintenance in small and medium enterprises," Annals of Operations Research, Springer, vol. 229(1), pages 743-758, June.
    5. Lizhong Zhao & Chen-Fu Chien & Mitsuo Gen, 2018. "A bi-objective genetic algorithm for intelligent rehabilitation scheduling considering therapy precedence constraints," Journal of Intelligent Manufacturing, Springer, vol. 29(5), pages 973-988, June.
    6. Selcuk Colak & Anurag Agarwal, 2005. "Non‐greedy heuristics and augmented neural networks for the open‐shop scheduling problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(7), pages 631-644, October.
    7. Ansis Ozolins, 2021. "Dynamic programming approach for solving the open shop problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(1), pages 291-306, March.
    8. Arnaud Malapert & Hadrien Cambazard & Christelle Guéret & Narendra Jussien & André Langevin & Louis-Martin Rousseau, 2012. "An Optimal Constraint Programming Approach to the Open-Shop Problem," INFORMS Journal on Computing, INFORMS, vol. 24(2), pages 228-244, May.
    9. Tamer Abdelmaguid & Mohamed Shalaby & Mohamed Awwad, 2014. "A tabu search approach for proportionate multiprocessor open shop scheduling," Computational Optimization and Applications, Springer, vol. 58(1), pages 187-203, May.
    10. Guillermo Campos Ciro & Frédéric Dugardin & Farouk Yalaoui & Russell Kelly, 2016. "Open shop scheduling problem with a multi-skills resource constraint: a genetic algorithm and an ant colony optimisation approach," International Journal of Production Research, Taylor & Francis Journals, vol. 54(16), pages 4854-4881, August.

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