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Improved mixed-integer programming models for the multiprocessor scheduling problem with communication delays

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Abstract

We revise existing and introduce new mixed-integer programming models for the Multiprocessor scheduling problem with communication delays. The basis for both is the identification of two major modeling strategies one of which can be considered ordering-based, and the other assignment-based. We first reveal redundancies in the encoding of feasible solutions found in present formulations and discuss how they can be avoided. For the assignment-based approach, we propose new inequalities that lead to provably stronger continuous relaxations and better performance in practice. Moreover, we derive a third, novel modeling strategy and show how to more compactly linearize assignment formulations with quadratic constraints. In a comprehensive experimental comparison of representative models that reflect the state-of-the-art in terms of strength and size, we evaluate not only running times but also the obtained lower and upper bounds on the makespan for the harder instances of a large scale benchmark set.

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  1. Institut für Informatik, Universität zu Köln, Albertus-Magnus-Platz, 50923, Cologne, Germany

    Sven Mallach

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Mallach, S. Improved mixed-integer programming models for the multiprocessor scheduling problem with communication delays. J Comb Optim 36, 871–895 (2018). https://doi.org/10.1007/s10878-017-0199-9

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