An Advanced Hybrid Quantum Tabu Search Approach to Vehicle Routing Problems

TL;DR

This paper introduces a hybrid quantum-classical tabu search algorithm for vehicle routing problems, demonstrating improved solution quality and runtime by integrating quantum computing into classical optimization frameworks.

Contribution

It presents a novel hybrid quantum-classical tabu search (HQTS) algorithm that leverages quantum computing for routing, enhancing classical methods for solving large-scale vehicle routing problems.

Findings

HQTS achieved optimal or near-optimal solutions for several CVRP instances.

More frequent quantum routing improved solution quality and runtime.

HQTS outperformed other hybrid algorithms in reducing the optimality gap.

Abstract

Quantum computing (QC) is expected to solve incredibly difficult problems, including finding optimal solutions to combinatorial optimization problems. However, to date, QC alone is still far to demonstrate this capability except on small-sized problems. Hybrid approaches where QC and classical computing work together have shown the most potential for solving real-world scale problems. This work aims to show that we can enhance a classical optimization algorithm with QC so that it can overcome this limitation. We present a new hybrid quantum-classical tabu search (HQTS) algorithm to solve the capacitated vehicle routing problem (CVRP). Based on our prior work, HQTS leverages QC for routing within a classical tabu search framework. The quantum component formulates the traveling salesman problem (TSP) for each route as a QUBO, solved using D-Wave's Advantage system. Experiments investigate the impact of quantum routing frequency and starting solution methods. While different starting solution methods, including quantum-based and classical heuristics methods, it shows minimal overall impact. HQTS achieved optimal or near-optimal solutions for several CVRP problems, outperforming other hybrid CVRP algorithms and significantly reducing the optimality gap compared to preliminary research. The experimental results demonstrate that more frequent quantum routing improves solution quality and runtime. The findings highlight the potential of integrating QC within meta-heuristic frameworks for complex optimization in vehicle routing problems.