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Solving a Problem With a Continuous Variables and One Binary

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Abstract

We discuss a class of tightly feasible MILP for which branch-and-bound is ineffective. We consider its hardness, evaluate the probability that randomly generated instances are feasible, and introduce a heuristic solution method based on the old idea of reformulating binary variables to continuous while introducing a linear complementarity constraint. We show the extent of the computational advantage, under a time limit, of our heuristic with respect to a state-of-the-art branch-and-bound implementation.

Keywords

  • Reformulation
  • Infeasible
  • Market split
  • Market share
  • Hard instances

This work was partially supported by: the PGMO grant "Projet 2016-1751H"; a Siebel Energy Institute Seed Grant; the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement n. 764759 ETN "MINOA".

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Authors and Affiliations

  1. LIX CNRS, École Polytechnique, Institut Polytechnique de Paris, 91128, Palaiseau, France

    Leo Liberti

Corresponding author

Correspondence to Leo Liberti .

Editor information

Editors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, Russia

    Prof. Dr. Alexander Strekalovsky

  2. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

    Prof. Yury Kochetov

  3. Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, Russia

    Prof. Tatiana Gruzdeva

  4. Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, Russia

    Prof. Andrei Orlov

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Liberti, L. (2021). Continuous Reformulation of Binary Variables, Revisited. In: Strekalovsky, A., Kochetov, Y., Gruzdeva, T., Orlov, A. (eds) Mathematical Optimization Theory and Operations Research: Recent Trends. MOTOR 2021. Communications in Computer and Information Science, vol 1476. Springer, Cham. https://doi.org/10.1007/978-3-030-86433-0_14

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  • DOI : https://doi.org/10.1007/978-3-030-86433-0_14

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