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IEEE International Conference on Quantum Computing and Engineering (QCE)

A Flexible Hybrid Quantum Algorithm for Vehicle Routing

Arun Vellat Sadashivan, Robin Ajmera, Shantom Kumar Borah, Akansha Kumar, Shailesh Kumar

Published Sep 15, 2024• 1 citation
Publisher

Abstract

The capacitated vehicle routing problem (CVRP) is an important problem for logistics optimization in supply chain. We propose a novel hybrid classical quantum algorithm that works by splitting the problem into a quantum travelling salesman problem (TSP) phase and a partitioning phase. In order to validate our methods, we run tests using D-Wave's Leap framework on random test cases, as well as a real-world data set from the retail domain. We run a comparison study against existing state of the art hybrid quantum-classical approaches for the CVRP, in addition to classical heuristic methods. Our method is shown to have the additional flexibility to handle fleet extension, and the solution quality is at least as good as the considered state of the art quantum hybrid algorithms. Further, we show that the algorithm can easily be modified for tackling other realistic vehicle routing variants.

DOI
10.1109/qce60285.2024.00078

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The capacitated vehicle routing problem (CVRP) is an important problem for logistics optimization in supply chain. We propose a novel hybrid classical quantum algorithm that works by splitting the problem into a quantum travelling salesman problem (TSP) phase and a partitioning phase. In order to validate our methods, we run tests using D-Wave's Leap framework on random test cases, as well as a real-world data set from the retail domain. We run a comparison study against existing state of the art hybrid quantum-classical approaches for the CVRP, in addition to classical heuristic methods. Our method is shown to have the additional flexibility to handle fleet extension, and the solution quality is at least as good as the considered state of the art quantum hybrid algorithms. Further, we show that the algorithm can easily be modified for tackling other realistic vehicle routing variants.
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Quantum computing (QC) is expected to solve incredibly difficult problems, including finding optimal solutions to combinatorial optimization problems. However, to date, QC alone has still been unable to demonstrate this capability except for 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 Quadratic Unconstrained Binary Optimization (QUBO) and solves it using D-Wave’s Advantage system. Experiments investigate the impact of quantum routing frequency and starting solution methods. Across different starting solution methods, including quantum-based and classical heuristics, 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 relative 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.
There has never been a more exciting time for the future of quantum computing than now. Real-world 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 issues. 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 meta-heuristic 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.
The Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem (NPO) that has been of great interest for decades for both, science and industry. The CVRP is a variant of the vehicle routing problem characterized by capacity constrained vehicles. The aim is to plan tours for vehicles to supply a given number of customers as efficiently as possible. The problem is the combinatorial explosion of possible solutions, which increases superexponentially with the number of customers. Classical solutions provide good approximations to the globally optimal solution. D-Wave's quantum annealer is a machine designed to solve optimization problems. This machine uses quantum effects to speed up computation time compared to classic computers. The problem on solving the CVRP on the quantum annealer is the particular formulation of the optimization problem. For this, it has to be mapped onto a quadratic unconstrained binary optimization (QUBO) problem. Complex optimization problems such as the CVRP can be translated to smaller subproblems and thus enable a sequential solution of the partitioned problem. This work presents a quantum-classic hybrid solution method for the CVRP. It clarifies whether the implemenation of such a method pays off in comparison to existing classical solution methods regarding computation time and solution quality. Several approaches to solving the CVRP are elaborated, the arising problems are discussed, and the results are evaluated in terms of solution quality and computation time.
Many relevant problems in industrial settings result in NP-hard optimization problems, such as the Capacitated Vehicle Routing Problem (CVRP) or its reduced variant, the Travelling Salesperson Problem (TSP). Even with today's most powerful classical algorithms, the CVRP is challenging to solve classically. Quantum computing may offer a way to improve the time to solution, although the question remains open as to whether Noisy Intermediate-Scale Quantum (NISQ) devices can achieve a practical advantage compared to classical heuristics. The most prominent algorithms proposed to solve combinatorial optimization problems in the NISQ era are the Quantum Approximate Optimization Algorithm (QAOA) and the more general Variational Quantum Eigensolver (VQE). However, implementing them in a way that reliably provides high-quality solutions is challenging, even for toy examples. In this work, we discuss decomposition and formulation aspects of the CVRP and propose an application-driven way to measure solution quality. Considering current hardware constraints, we reduce the CVRP to a clustering phase and a set of TSPs. For the TSP, we extensively test both QAOA and VQE and investigate the influence of various hyperparameters, such as the classical optimizer choice and strength of constraint penalization. Results of QAOA are generally of limited quality because the algorithm does not reach the energy threshold for feasible TSP solutions, even when considering various extensions such as recursive and constraint-preserving mixer QAOA. On the other hand, the VQE reaches the energy threshold and shows a better performance. Our work outlines the obstacles to quantum-assisted solutions for real-world optimization problems and proposes perspectives on how to overcome them.
This study introduces a hybrid quantum-classical approach to solving the Capacitated Vehicle Routing Problems (CVRP), combining the Column Generation method and the Quantum Alternating Operator Ansatz (QAOAnsatz). The column generation method divides the problem into a master problem and subproblems to effectively solve the problem. We solved the subproblem by using QAOAnsatz to enhance the optimal solution search. Moreover, we generated the problem Hamiltonian using an Augmented Lagrangian-inspired Method to reduce the number of required qubits to handle the inequality. As a result, our experiments obtained an optimal solution for a CVRP problem with 6 customers. This study demonstrates a practical quantum application in logistics and sets a new technique for hybrid quantum-classical optimization frameworks.