A Hybrid Framework Using a QUBO Solver For Permutation-Based Combinatorial Optimization

TL;DR

This paper presents a hybrid framework leveraging a QUBO solver for large permutation-based combinatorial problems, incorporating techniques like parameter tuning, landscape smoothing, and divide-and-conquer to improve solution quality and scalability.

Contribution

The paper introduces a novel hybrid approach combining QUBO solvers with problem-specific techniques for large-scale permutation problems, including a machine learning-based parameter tuning and a divide-and-conquer strategy.

Findings

Achieved less than 10% optimality gap on Euclidean TSP instances.

Attained less than 11% optimality gap on Flow Shop Problems.

Demonstrated effectiveness on provably hard combinatorial problems.

Abstract

In this paper, we propose a hybrid framework to solve large-scale permutation-based combinatorial problems effectively using a high-performance quadratic unconstrained binary optimization (QUBO) solver. To do so, transformations are required to change a constrained optimization model to an unconstrained model that involves parameter tuning. We propose techniques to overcome the challenges in using a QUBO solver that typically comes with limited numbers of bits. First, to smooth the energy landscape, we reduce the magnitudes of the input without compromising optimality. We propose a machine learning approach to tune the parameters for good performance effectively. To handle possible infeasibility, we introduce a polynomial-time projection algorithm. Finally, to solve large-scale problems, we introduce a divide-and-conquer approach that calls the QUBO solver repeatedly on small sub-problems. We tested our approach on provably hard Euclidean Traveling Salesman (E-TSP) instances and Flow Shop Problem (FSP). Optimality gap that is less than $10\%$ and $11\%$ are obtained respectively compared to the best-known approach.