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Logic-Based Benders Decomposition for Super Solutions: An Application to the Kidney Exchange Problem

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Principles and Practice of Constraint Programming (CP 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11802))

Abstract

When optimising under uncertainty, it is desirable that solutions are robust to unexpected disruptions and changes. A possible formalisation of robustness is given by super solutions. An assignment to a set of decision variables is an (a, b, c) super solution if any change involving at most a variables can be repaired by changing at most b other variables; the repair solution should have a cost of at most c units worse than a non-robust optimum. We propose a method exploiting Logic Based Benders Decomposition to find super solutions to an optimisation problem for generic disruptions. The master deals with the original problem, while subproblems try to find repair solutions for each possible disruption. As a case study, we consider the Kidney Exchange Problem, for which our method scales dramatically better on realistic instances than a reformulation-based approach from the literature.

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Notes

  1. 1.

    http://www.enckep-cost.eu/page/introduction.

  2. 2.

    https://pypi.org/project/docplex/.

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Acknowledgements

The Insight Centre for Data Analytics is supported by Science Foundation Ireland under Grant Number SFI/12/RC/2289, which is co-funded under the European Regional Development Fund.

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Authors and Affiliations

  1. Insight Centre for Data Analytics, University College Cork, Cork, Ireland

    Danuta Sorina Chisca & Barry O’Sullivan

  2. DISI, University of Bologna, Bologna, Italy

    Michele Lombardi & Michela Milano

Authors
  1. Danuta Sorina Chisca
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  2. Michele Lombardi
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  3. Michela Milano
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  4. Barry O’Sullivan
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Corresponding authors

Correspondence to Danuta Sorina Chisca , Michele Lombardi , Michela Milano or Barry O’Sullivan .

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Editors and Affiliations

  1. INRA, Castanet Tolosan, France

    Thomas Schiex

  2. INRA, Castanet Tolosan, France

    Simon de Givry

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Chisca, D.S., Lombardi, M., Milano, M., O’Sullivan, B. (2019). Logic-Based Benders Decomposition for Super Solutions: An Application to the Kidney Exchange Problem. In: Schiex, T., de Givry, S. (eds) Principles and Practice of Constraint Programming. CP 2019. Lecture Notes in Computer Science(), vol 11802. Springer, Cham. https://doi.org/10.1007/978-3-030-30048-7_7

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  • DOI: https://doi.org/10.1007/978-3-030-30048-7_7

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