A Unified Framework for Symmetry Handling

TL;DR

This paper introduces a comprehensive framework for symmetry handling in optimization that unifies existing methods, enables their combination, and extends applicability beyond binary variables, leading to improved solver performance.

Contribution

The paper presents a unified, flexible framework that combines and generalizes symmetry handling methods, surpassing existing approaches in efficiency and scope.

Findings

Framework outperforms existing methods in SCIP

Applicable to general variable types

Numerical experiments confirm superior performance

Abstract

Handling symmetries in optimization problems is essential for devising efficient solution methods. In this article, we present a general framework that captures many of the already existing symmetry handling methods. While these methods are mostly discussed independently from each other, our framework allows to apply different methods simultaneously and thus outperforming their individual effect. Moreover, most existing symmetry handling methods only apply to binary variables. Our framework allows to easily generalize these methods to general variable types. Numerical experiments confirm that our novel framework is superior to the state-of-the-art symmetry handling methods as implemented in the solver SCIP on a broad set of instances.