Symmetries of Symmetry Breaking Constraints

TL;DR

This paper explores how symmetries of symmetry breaking constraints can be utilized to improve constraint programming, demonstrating their effectiveness through model restarts on benchmark problems.

Contribution

It introduces the idea that symmetries of symmetry breaking constraints can be used to enhance search strategies in constraint programming.

Findings

Effective in reducing conflicts between symmetry breaking and heuristics

Improves search efficiency on benchmark problems

Demonstrates practical benefits of symmetry-based techniques

Abstract

Symmetry is an important feature of many constraint programs. We show that any problem symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each symmetry class. This simple but powerful idea can be used in a number of different ways. We describe one application within model restarts, a search technique designed to reduce the conflict between symmetry breaking and the branching heuristic. In model restarts, we restart search periodically with a random symmetry of the symmetry breaking constraints. Experimental results show that this symmetry breaking technique is effective in practice on some standard benchmark problems.