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Integral Simplex Using Decomposition with Primal Cuts

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Experimental Algorithms (SEA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8504))

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Abstract

The integral simplex using decomposition (ISUD) algorithm [22] is a dynamic constraint reduction method that aims to solve the popular set partitioning problem (SPP). It is a special case of primal algorithms, i.e. algorithms that furnish an improving sequence of feasible solutions based on the resolution, at each iteration, of an augmentation problem that either determines an improving direction, or asserts that the current solution is optimal. To show how ISUD is related to primal algorithms, we introduce a new augmentation problem, MRA. We show that MRA canonically induces a decomposition of the augmentation problem and deepens the understanding of ISUD. We characterize cuts that adapt to this decomposition and relate them to primal cuts. These cuts yield a major improvement over ISUD, making the mean optimality gap drop from 33.92% to 0.21% on some aircrew scheduling problems.

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Authors and Affiliations

  1. GERAD, 2920 ch. de la Tour, H3T1J4, Montréal, Canada

    Samuel Rosat, Issmail Elhallaoui & François Soumis

  2. Polytechnique Montréal, 2900 bd. Édouard Montpetit, H3T1J4, Montréal, Canada

    Samuel Rosat, Issmail Elhallaoui & François Soumis

  3. DEIS, Università di Bologna, viale Risorgimento 2, 40136, Bologna, Italy

    Andrea Lodi

Authors
  1. Samuel Rosat
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  2. Issmail Elhallaoui
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  3. François Soumis
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  4. Andrea Lodi
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Editor information

Editors and Affiliations

  1. School of IT, University of Sydney, Building J12, 2006, Sydney, NSW, Australia

    Joachim Gudmundsson

  2. Department of Computer Science, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen East, Denmark

    Jyrki Katajainen

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Rosat, S., Elhallaoui, I., Soumis, F., Lodi, A. (2014). Integral Simplex Using Decomposition with Primal Cuts. In: Gudmundsson, J., Katajainen, J. (eds) Experimental Algorithms. SEA 2014. Lecture Notes in Computer Science, vol 8504. Springer, Cham. https://doi.org/10.1007/978-3-319-07959-2_3

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  • DOI: https://doi.org/10.1007/978-3-319-07959-2_3

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07958-5

  • Online ISBN: 978-3-319-07959-2

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