QUBO Formulations for MIP Symmetry Detection

TL;DR

This paper investigates using QUBO models to detect symmetry in mixed-integer programming, aiming to leverage quantum computing despite current hardware limitations, and proposes various formulations to improve input size handling.

Contribution

It introduces new QUBO formulations for MIP symmetry detection, including full, reduced, decomposed, and QUBO-Plus models, to address input size constraints for quantum algorithms.

Findings

QUBO formulations can represent MIP symmetry detection problems.

Computational experiments estimate quantum resources needed for practical instances.

Proposed models improve scalability for quantum symmetry detection.

Abstract

Formulation symmetry in mixed-integer programming (MIP) can hinder solver performance by inducing redundant search, but detecting such symmetries is also a significant computational challenge. This paper explores the potential for quantum computing to handle symmetry detection. Quantum is a promising alternative to classical compute, but this emerging technology has limited hardware capacity in terms of input problem size. This paper explores the use of Quadratic Unconstrained Binary Optimization (QUBO) models for symmetry detection, as QUBO is the canonical format for quantum optimization platforms. To help address the input size bottleneck, we develop full, reduced, and decomposed QUBO as well as QUBO-Plus formulations for MIP symmetry detection. Computational experiments on the MIPLIB 2017 benchmark are used to estimate the quantum computing resources needed for practical problems.