Efficient Propagation Techniques for Handling Cyclic Symmetries in Binary Programs

TL;DR

This paper introduces efficient algorithms for variable fixing to eliminate cyclic symmetries in binary programs, significantly improving branch-and-bound solver performance by reducing symmetric solutions.

Contribution

The paper presents guaranteed algorithms for symmetry-based variable fixing in binary programs, applicable to any cyclic symmetry group, enhancing symmetry handling efficiency.

Findings

Algorithms find all symmetry-based variable fixings.

Numerical experiments show improved efficiency over existing methods.

Applicable to any binary program with cyclic symmetries.

Abstract

The presence of symmetries of binary programs typically degrade the performance of branch-and-bound solvers. In this article, we derive efficient variable fixing algorithms to discard symmetric solutions from the search space based on propagation techniques for cyclic groups. Our algorithms come with the guarantee to find all possible variable fixings that can be derived from symmetry arguments, i.e., one cannot find more variable fixings than those found by our algorithms. Since every permutation symmetry group of a binary program has cyclic subgroups, the derived algorithms can be used to handle symmetries in any symmetric binary program. In experiments we also provide numerical evidence that our algorithms handle symmetries more efficiently than other variable fixing algorithms for cyclic symmetries.