Defeating symmetry in combinatorial optimization via objective perturbations and hierarchical constraints

Ahmed Ghoniem and Hanif Sherali

IISE Transactions, 2011, vol. 43, issue 8, 575-588

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.

Date: 2011
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DOI: 10.1080/0740817X.2010.541899

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