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Strengthening of Feasibility Cuts in Logic-Based Benders Decomposition

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12735))

Abstract

As for any decomposition method, the computational performance of a logic-based Benders decomposition (LBBD) scheme relies on the quality of the feedback information. Therefore, an important acceleration technique in LBBD is to strengthen feasibility cuts by reducing their sizes. This is typically done by solving additional subproblems to evaluate potential cuts. In this paper, we study three cut-strengthening algorithms that differ in the computational efforts made to find stronger cuts and in the guarantees with respect to the strengths of the cuts. We give a unified description of these algorithms and present a computational evaluation of their impact on the efficiency of a LBBD scheme. This evaluation is made for three different problem formulations, using over 2000 instances from five different applications. Our results show that it is usually beneficial to invest the time needed to obtain irreducible cuts. In particular, the use of the depth-first binary search cut-strengthening algorithm gives a good performance. Another observation is that when the subproblem can be separated into small independent problems, the impact of cut strengthening is dominated by that of the separation, which has an automatic strengthening effect.

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Notes

  1. 1.

    https://gitlab.liu.se/eliro15/lbbd_instances.

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Acknowledgement

Emil Karlsson is funded by the Research School in Interdisciplinary Mathematics at Linköping University. The work is also partly funded by the Center for Industrial Information Technology (CENIIT), Project-ID 16.05. Computational experiments were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at National Supercomputer Centre (NSC).

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Authors and Affiliations

  1. Department of Mathematics, Linköping University, 581 83, Linköping, Sweden

    Emil Karlsson & Elina Rönnberg

  2. Saab AB, 581 88, Linköping, Sweden

    Emil Karlsson

Authors
  1. Emil Karlsson
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  2. Elina Rönnberg
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Correspondence to Elina Rönnberg .

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Editors and Affiliations

  1. Monash University, Melbourne, VIC, Australia

    Peter J. Stuckey

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Karlsson, E., Rönnberg, E. (2021). Strengthening of Feasibility Cuts in Logic-Based Benders Decomposition. In: Stuckey, P.J. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2021. Lecture Notes in Computer Science(), vol 12735. Springer, Cham. https://doi.org/10.1007/978-3-030-78230-6_3

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  • DOI: https://doi.org/10.1007/978-3-030-78230-6_3

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