🤖 AI Summary
This work addresses the computational inefficiency caused by symmetry in integer programming, which leads to redundant search. The authors propose an algebraic approach that leverages arbitrary basis polynomials and problem-specific permutation groups to automatically generate random polynomial inequalities for symmetry breaking. This method constitutes the first general-purpose framework for generating symmetry-breaking constraints grounded in algebraic structure, applicable to any permutation group and seamlessly integrable into mainstream symbolic computation platforms. Experimental results on nearly half-capacity 0–1 bin packing instances demonstrate that incorporating only a small number of quadratic symmetry-breaking constraints significantly reduces solution time, with the most consistent performance gains observed when combining limited variables and permutations.
📝 Abstract
Symmetry in integer programming causes redundant search and is often handled with symmetry breaking constraints that remove as many equivalent solutions as possible. We propose an algebraic method which allows to generate a random family of polynomial inequalities which can be used as symmetry breakers. The method requires as input an arbitrary base polynomial and a group of permutations which is specific to the integer program. The computations can be easily carried out in any major symbolic computation software. In order to test our approach, we describe a case study on near half-capacity 0-1 bin packing instances which exhibit substantial symmetries. We statically generate random quadratic breakers and add them to a baseline integer programming problem which we then solve with Gurobi. It turns out that simple symmetry breakers, especially combining few variables and permutations, most consistently reduce work time.