Defeating symmetry in combinatorial optimization via objective perturbations and hierarchical constraints

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.