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

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.

arXiv comment23 pages, 10 figures

References in corpus (7)

• Ising formulations of many NP problems
• Physics-Inspired Optimization for Quadratic Unconstrained Problems Using a Digital Annealer
• A Tutorial on Formulating and Using QUBO Models
• Application of Quantum Annealing to Nurse Scheduling Problem
• Flight Gate Assignment with a Quantum Annealer
• Next-Generation Topology of D-Wave Quantum Processors
• QROSS: QUBO Relaxation Parameter Optimisation via Learning Solver Surrogates