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Defeating symmetry in combinatorial optimization via objective perturbations and hierarchical constraints

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  • Ahmed Ghoniem
  • Hanif Sherali

Abstract

This article introduces the concept of defeating symmetry in combinatorial optimization via objective perturbations based on, and combined with, symmetry-defeating constraints. Under this novel reformulation, the original objective function is suitably perturbed using a weighted sum of expressions derived from hierarchical symmetry-defeating constraints in a manner that preserves optimality and judiciously guides and curtails the branch-and-bound enumeration process. Computational results are presented for a noise dosage problem, a doubles tennis scheduling problem, and a wagon load-balancing problem to demonstrate the efficacy of using this strategy in concert with traditional hierarchical symmetry-defeating constraints. The proposed methodology is shown to significantly outperform the use of hierarchical constraints or objective perturbations in isolation, as well as the automatic symmetry-defeating feature that is enabled by CPLEX, version 11.2.

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  • Ahmed Ghoniem & Hanif Sherali, 2011. "Defeating symmetry in combinatorial optimization via objective perturbations and hierarchical constraints," IISE Transactions, Taylor & Francis Journals, vol. 43(8), pages 575-588.
    • Handle: RePEc:taf:uiiexx:v:43:y:2011:i:8:p:575-588
    DOI: 10.1080/0740817X.2010.541899
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    Cited by:

    1. Andrew Romich & Guanghui Lan & J. Cole Smith, 2015. "A robust sensor covering and communication problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(7), pages 582-594, October.
    2. Hanif D. Sherali & Ki-Hwan Bae & Mohamed Haouari, 2013. "An Integrated Approach for Airline Flight Selection and Timing, Fleet Assignment, and Aircraft Routing," Transportation Science, INFORMS, vol. 47(4), pages 455-476, November.
    3. Brian Lunday & Hanif Sherali & Kevin Lunday, 2012. "The coastal seaspace patrol sector design and allocation problem," Computational Management Science, Springer, vol. 9(4), pages 483-514, November.
    4. Caballero, William N. & Lunday, Brian J. & Meissner, Finn, 2024. "Regulating the rebound effect in the traveling purchaser problem," European Journal of Operational Research, Elsevier, vol. 317(3), pages 660-677.
    5. Azrah Anparasan & Miguel Lejeune, 2019. "Resource deployment and donation allocation for epidemic outbreaks," Annals of Operations Research, Springer, vol. 283(1), pages 9-32, December.

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