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A scalable parallel implementation of the Cluster Benders Decomposition algorithm

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Abstract

Benders Decomposition (BD) is a method used to solve stochastic linear problems via scenario analysis. Cluster BD (CBD) is one of its smart improvements that speed up the execution time, taking advantage of tighter feasible cuts found by grouping scenarios into clusters. In this paper, we propose a new design for CBD, one which takes into account the role played by optimal cuts in the solution. Besides, we propose a new parallel scheme for CBD to deal with large-scale two-stage stochastic linear problems. Moreover, we characterise the problems for which our proposal performs best. The results obtained show computational gains from our proposal compared with the plain use of CPLEX, serial BD, parallel BD, serial CBD and parallel CBD.

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Acknowledgements

The Ministerio de Economía y Competitividad supported this work under contract TIN2017-84553-C2-2-R. Lluis M. Pla-Aragones wishes to acknowledge the financial support of the Spanish Research Program TRA2013-48180-C3-P. Some authors are members of the research group 2017-SGR363, funded by the Generalitat de Catalunya. Besides, this research is partly supported by the European Union FEDER (CAPAP-H6 network TIN2016-81840-REDT).

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Authors and Affiliations

  1. Department of Computer Science, University of Lleida, Jaume II 69, 25001, Lleida, Spain

    Jordi Mateo & Francesc Solsona

  2. Department of Mathematics, University of Lleida, Jaume II 71, 25001, Lleida, Spain

    Lluís M. Plà & Adela Pagès

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  1. Jordi Mateo
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  2. Lluís M. Plà
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  3. Francesc Solsona
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  4. Adela Pagès
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Correspondence to Francesc Solsona.

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Mateo, J., Plà, L.M., Solsona, F. et al. A scalable parallel implementation of the Cluster Benders Decomposition algorithm. Cluster Comput 22, 877–886 (2019). https://doi.org/10.1007/s10586-018-2878-4

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  • DOI: https://doi.org/10.1007/s10586-018-2878-4

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