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Proximity Benders: a decomposition heuristic for stochastic programs

  • Published: 07 December 2015

Proximity Benders: a decomposition heuristic for stochastic programs

Journal of Heuristics

volume 22pages 181–198 (2016)

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Abstract

In this paper we present a heuristic approach to two-stage mixed-integer linear stochastic programming models with continuous second stage variables. A common solution approach for these models is Benders decomposition, in which a sequence of (possibly infeasible) solutions is generated, until an optimal solution is eventually found and the method terminates. As convergence may require a large amount of computing time for hard instances, the method may be unsatisfactory from a heuristic point of view. Proximity search is a recently-proposed heuristic paradigm in which the problem at hand is modified and iteratively solved with the aim of producing a sequence of improving feasible solutions. As such, proximity search and Benders decomposition naturally complement each other, in particular when the emphasis is on seeking high-quality, but not necessarily optimal, solutions. In this paper, we investigate the use of proximity search as a tactical tool to drive Benders decomposition, and computationally evaluate its performance as a heuristic on instances of different stochastic programming problems.

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Acknowledgments

This research of Fischetti and Monaci was supported by the University of Padova (Progetto di Ateneo “Exploiting randomness in Mixed Integer Linear Programming”), and by MiUR, Italy (PRIN project “Mixed-Integer Nonlinear Optimization: Approaches and Applications”). We thank Merve Bodur and Mike Hewitt for their support and for providing the data used in the computational analysis. Thanks are also due to three anonymous referees for their helpful comments leading to an improved presentation.

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Boland, N., Fischetti, M., Monaci, M. et al. Proximity Benders: a decomposition heuristic for stochastic programs. J Heuristics 22, 181–198 (2016). https://doi.org/10.1007/s10732-015-9306-1

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  • Received: 09 April 2015

  • Revised: 23 November 2015

  • Accepted: 24 November 2015

  • Published: 07 December 2015

  • Issue Date: April 2016

  • DOI:

    https://doi.org/10.1007/s10732-015-9306-1

Keywords

  • Integer programming
  • Benders decomposition
  • Stochastic programming
  • Heuristics

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