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Combining Metaheuristics and Exact Methods for Solving Exactly Multi-objective Problems on the Grid

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Journal of Mathematical Modelling and Algorithms

Abstract

This paper presents a parallel hybrid exact multi-objective approach which combines two metaheuristics – a genetic algorithm (GA) and a memetic algorithm (MA), with an exact method – a branch and bound (B&B) algorithm. Such approach profits from both the exploration power of the GA, the intensification capability of the MA and the ability of the B&B to provide optimal solutions with proof of optimality. To fully exploit the resources of a computational grid, the hybrid method is parallelized according to three well-known parallel models – the island model for the GA, the multi-start model for the MA and the parallel tree exploration model for the B&B. The obtained method has been experimented and validated on a bi-objective flow-shop scheduling problem. The approach allowed to solve exactly for the first time an instance of the problem – 50 jobs on 5 machines. More than 400 processors belonging to 4 different administrative domains have contributed to the resolution process during more than 6 days.

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Authors and Affiliations

  1. Laboratoire d’Informatique Fondamentale de Lille, Université des Sciences et Technologies de Lille, 59655, Villeneuve d’Ascq Cedex, France

    Mohand Mezmaz, Nouredine Melab & El-Ghazali Talbi

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  1. Mohand Mezmaz
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  2. Nouredine Melab
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  3. El-Ghazali Talbi
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Correspondence to Mohand Mezmaz.

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Mezmaz, M., Melab, N. & Talbi, EG. Combining Metaheuristics and Exact Methods for Solving Exactly Multi-objective Problems on the Grid. J Math Model Algor 6, 393–409 (2007). https://doi.org/10.1007/s10852-007-9063-8

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  • DOI: https://doi.org/10.1007/s10852-007-9063-8

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