An Advanced Hybrid Quantum Tabu Search Approach to Vehicle Routing Problems
James B. Holliday, Eneko Osaba, Khoa Luu
TL;DR
This work tackles the Capacitated Vehicle Routing Problem (CVRP) by embedding a quantum routing step into a classical tabu-search framework, forming Hybrid Quantum-Classic Tabu Search (HQTS). Each route’s TSP subproblem is cast as a QUBO and solved on a D-Wave annealer, with the quantum component used to intensify the search while the classical TS handles route allocation and neighbor exploration. Experiments on the CVRP-CMT dataset show HQTS achieving optimal or near-optimal solutions across multiple problems, with stronger performance when quantum routing is invoked more frequently; CW-based starting solutions often yield robust results. The study demonstrates the potential of integrating quantum optimization within meta-heuristics to tackle large, real-world VRPs, while highlighting resource constraints and the need for improved neighborhood operators for further gains.
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.