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A new warmstarting strategy for the primal-dual column generation method

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Abstract

This paper presents a new warmstarting technique in the context of a primal-dual column generation method applied to solve a particular class of combinatorial optimization problems. The technique relies on calculating an initial point and on solving auxiliary linear optimization problems to determine the step direction needed to fully restore primal and dual feasibilities after new columns arrive. Conditions on the maximum size of the cuts and on a suitable initial point are discussed. Additionally, the strategy ensures that the duality gap of the warmstart is bounded by the old duality gap multiplied with a (small) constant, which depends on the relation between the old and modified problems. Computational experiments demonstrate the gains achieved when compared to a coldstart approach.

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Acknowledgments

We would like to thank the referees for their useful comments and suggestions which allowed us to improve the quality and presentation of this paper. Pablo González-Brevis would like to thank the support given by Facultad de Ingeniería, Universidad del Desarrollo and Beca Presidente de la República (CONICYT) from Chile. Jacek Gondzio was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) under grant EP/G060169/1.

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Authors and Affiliations

  1. School of Mathematics, Maxwell Institute, The University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ, UK

    Jacek Gondzio

  2. School of Engineering, Universidad del Desarrollo, Av. Sanhueza 1750, Pedro de Valdivia, Concepción, Chile

    Pablo González-Brevis

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  1. Jacek Gondzio
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  2. Pablo González-Brevis
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Correspondence to Pablo González-Brevis.

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Gondzio, J., González-Brevis, P. A new warmstarting strategy for the primal-dual column generation method. Math. Program. 152, 113–146 (2015). https://doi.org/10.1007/s10107-014-0779-8

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  • DOI: https://doi.org/10.1007/s10107-014-0779-8

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