Hybrid Quantum Tabu Search for Solving the Vehicle Routing Problem

TL;DR

This work addresses solving the CVRP by introducing Hybrid Quantum Tabu Search (HQTS), a hybrid quantum-classical metaheuristic that couples a classical Tabu Search with quantum-assisted route re-sequencing via a QUBO solved on a quantum annealer. The method leverages adiabatic quantum computing concepts and QUBO formulations to perform selective, sparse re-sequencing of routes within an otherwise classical search, aiming to overcome limitations of near-term quantum hardware. Empirically, HQTS and its variant with strategic oscillation show competitive performance against established hybrid CVRP solvers on classic benchmarks, and in some cases reach the best-known solutions. The study demonstrates the potential of integrating quantum optimization steps into established metaheuristics to achieve higher-quality CVRP solutions under realistic hardware constraints, with future work targeting simulated QA and robustness on more constrained VRP variants.

Abstract

There has never been a more exciting time for the future of quantum computing than now. Near-term quantum computing usage is now the next XPRIZE. With that challenge in mind we have explored a new approach as a hybrid quantum-classical algorithm for solving NP-Hard optimization problems. We have focused on the classic problem of the Capacitated Vehicle Routing Problem (CVRP) because of its real-world industry applications. Heuristics are often employed to solve this problem because it is difficult. In addition, meta-heuristic algorithms have proven to be capable of finding reasonable solutions to optimization problems like the CVRP. Recent research has shown that quantum-only and hybrid quantum/classical approaches to solving the CVRP are possible. Where quantum approaches are usually limited to minimal optimization problems, hybrid approaches have been able to solve more significant problems. Still, the hybrid approaches often need help finding solutions as good as their classical counterparts. In our proposed approach, we created a hybrid quantum/classical metaheuristic algorithm capable of finding the best-known solution to a classic CVRP problem. Our experimental results show that our proposed algorithm often outperforms other hybrid approaches.

Figures (8)

• Figure 1: Our Proposed Approach. Step 1. An initial solution is provided to the classical TS algorithm. Step 2. TS is performed. Step 3. At different times during TS an individual route from a solution is selected to be optimized. Step 4: Route re-sequencing (TSP) is performed via QUBO formulation on a QA. Step 5. The re-sequenced route is returned to TS. Step 6. When TS reaches its stopping criteria, the best solution found is returned.
• Figure 2: Flowchart of Tabu search w/o strategic oscillation
• Figure 3: Visualization of CMT 1
• Figure 4: Visualization of CMT 11
• Figure 5: CMT 1 Result using DBSS