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Stabilizer-based symmetry breaking constraints for mathematical programs

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  • Leo Liberti
  • James Ostrowski

Abstract

Mathematical programs whose formulation is symmetric often take a long time to solve using Branch-and-Bound type algorithms, because of the several symmetric optima. A simple technique used in these cases is to adjoin symmetry breaking constraints to the formulation before solving the problem. These constraints: (a) aim to guarantee that at least one optimum is feasible, whilst making some of the symmetric optima infeasible; and (b) are usually associated to the different orbits of the action of the formulation group on the set of variable indices. In general, one cannot adjoin symmetry breaking constraints from more than one orbit. In Liberti (Math Program A 131:273–304, doi: 10.1007/s10107-010-0351-0 , 2012 ), some (restrictive) sufficient conditions are presented which make it possible to adjoin such constraints from several orbits at the same time. In this paper we present a new, less restrictive method for the same task, and show it performs better computationally. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Leo Liberti & James Ostrowski, 2014. "Stabilizer-based symmetry breaking constraints for mathematical programs," Journal of Global Optimization, Springer, vol. 60(2), pages 183-194, October.
    • Handle: RePEc:spr:jglopt:v:60:y:2014:i:2:p:183-194
    DOI: 10.1007/s10898-013-0106-6
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    References listed on IDEAS

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    1. Matteo Fischetti & Michele Monaci & Domenico Salvagnin, 2012. "Three Ideas for the Quadratic Assignment Problem," Operations Research, INFORMS, vol. 60(4), pages 954-964, August.
    2. Hanif D. Sherali & J. Cole Smith, 2001. "Improving Discrete Model Representations via Symmetry Considerations," Management Science, INFORMS, vol. 47(10), pages 1396-1407, October.
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    Cited by:

    1. Jasper van Doornmalen & Christopher Hojny, 2024. "Efficient Propagation Techniques for Handling Cyclic Symmetries in Binary Programs," INFORMS Journal on Computing, INFORMS, vol. 36(3), pages 868-883, May.
    2. Shaoze Li & Zhibin Deng & Cheng Lu & Junhao Wu & Jinyu Dai & Qiao Wang, 2023. "An efficient global algorithm for indefinite separable quadratic knapsack problems with box constraints," Computational Optimization and Applications, Springer, vol. 86(1), pages 241-273, September.
    3. Gustavo Dias & Leo Liberti, 2021. "Exploiting symmetries in mathematical programming via orbital independence," Annals of Operations Research, Springer, vol. 298(1), pages 149-182, March.

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