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Advances in the Parallelization of the Simplex Method

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Algorithms, Probability, Networks, and Games

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9295))

Abstract

The simplex method has been successfully used in solving linear programming problems for many years. Parallel approaches for the simplex method have been extensively studied in the literature due to the intensive computations required, especially for the solution of large linear problems (LPs). In this paper, first a detailed overview is given of the parallelization attempts concerning the standard and the revised simplex method made to date. Next, some of the most recent and significant relevant attempts are selected and presented in more detail along with experimental results. The latter include some impressive results obtained for the revised simplex method over a modern supercomputer, as well as the recent advances in GPU-based related attempts.

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Notes

  1. 1.

    Note also that the techniques applied in the proposed approaches, have been the basis for the integration of FICO Xpress parallel solver [42], which was the first commercial parallel simplex solver and has been regarded quite faster than the pre-existing ones in various kinds of large-scale LPs.

  2. 2.

    Note also that this paper has received recently the COAP (Computational Optimization and Applications) journal Best Paper Award for year 2013.

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Authors and Affiliations

  1. Department of Informatics, Technological Educational Institute of Athens, Athens, Greece

    Basilis Mamalis & Grammati Pantziou

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  1. Basilis Mamalis
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  2. Grammati Pantziou
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Correspondence to Basilis Mamalis .

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Editors and Affiliations

  1. University of Patras, Patras, Greece

    Christos Zaroliagis

  2. Technological Educational Institute of Athens, Athens, Greece

    Grammati Pantziou

  3. University of Ioannina, Ioannina, Greece

    Spyros Kontogiannis

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Mamalis, B., Pantziou, G. (2015). Advances in the Parallelization of the Simplex Method. In: Zaroliagis, C., Pantziou, G., Kontogiannis, S. (eds) Algorithms, Probability, Networks, and Games. Lecture Notes in Computer Science(), vol 9295. Springer, Cham. https://doi.org/10.1007/978-3-319-24024-4_17

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  • DOI: https://doi.org/10.1007/978-3-319-24024-4_17

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  • Online ISBN: 978-3-319-24024-4

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