Larger Sparse Quadratic Assignment Problem Optimization Using Quantum Annealing and a Bit-Flip Heuristic Algorithm

TL;DR

This paper introduces a novel approach combining quantum annealing with a bit-flip heuristic to solve larger sparse quadratic assignment problems, successfully handling problems of size 19 on D-Wave Advantage.

Contribution

The paper presents a new method that enhances quantum annealing for larger QAPs by integrating a bit-flip heuristic, overcoming previous size limitations.

Findings

Successfully solved a size 19 sparse QAP using D-Wave Advantage.

The bit-flip heuristic effectively converts infeasible solutions into feasible ones.

The method demonstrates high accuracy and computational efficiency.

Abstract

Quantum annealing and D-Wave quantum annealer attracted considerable attention for their ability to solve combinatorial optimization problems. In order to solve other type of optimization problems, it is necessary to apply certain kinds of mathematical transformations. However, linear constraints reduce the size of problems that can be represented in quantum annealers, owing to the sparseness of connections between qubits. For example, the quadratic assignment problem (QAP) with linear equality constraints can be solved only up to size 12 in the quantum annealer D-Wave Advantage, which has 5640 qubits. To overcome this obstacle, Ohzeki developed a method for relaxing the linear equality constraints and numerically verified the effectiveness of this method with some target problems, but others remain unsolvable. In particular, it is difficult to obtain feasible solutions to problems with hard constraints, such as the QAP. We therefore propose a method for solving the QAP with quantum annealing by applying a post-processing bit-flip heuristic algorithm to solutions obtained by the Ohzeki method. In a numerical experiment, we solved a sparse QAP by the proposed method. This sparse QAP has been used in areas such as item listing on an E-commerce website. We successfully solved a QAP of size 19 with high accuracy for the first time using D-Wave Advantage. We also confirmed that the bit-flip heuristic algorithm moves infeasible solutions to nearby feasible solutions in terms of Hamming distance with good computational efficiency.