Quantum annealing (QA) is a quantum computing algorithm that works on the principle of Adiabatic Quantum Computation (AQC), and it has shown significant computational advantages in solving combinatorial optimization problems such as vehicle routing problems (VRP) when compared to classical algorithms. This paper presents a QA approach for solving a variant VRP known as multi-depot capacitated vehicle routing problem (MDCVRP). This is an NP-hard optimization problem with real-world applications in the fields of transportation, logistics, and supply chain management. We consider heterogeneous depots and vehicles with different capacities. Given a set of heterogeneous depots, the number of vehicles in each depot, heterogeneous depot/vehicle capacities, and a set of spatially distributed customer locations, the MDCVRP attempts to identify routes of various vehicles satisfying the capacity constraints such as that all the customers are served. We model MDCVRP as a quadratic unconstrained binary optimization (QUBO) problem, which minimizes the overall distance traveled by all the vehicles across all depots given the capacity constraints. Furthermore, we formulate a QUBO model for dynamic version of MDCVRP known as D-MDCVRP, which involves dynamic rerouting of vehicles to real-time customer requests. We discuss the problem complexity and a solution approach to solving MDCVRP and D-MDCVRP on quantum annealing hardware from D-Wave.

中文翻译：

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一种解决动态多站点容量车辆路由问题的量子退火方法

量子退火（QA）是一种基于绝热量子计算（AQC）原理的量子计算算法，与经典算法相比，它在解决车辆路径问题（VRP）等组合优化问题方面表现出显着的计算优势。本文提出了一种 QA 方法，用于解决称为多站点容量车辆路由问题 (MDCVRP) 的变体 VRP。这是一个 NP 难优化问题，在运输、物流和供应链管理领域具有实际应用。我们考虑具有不同容量的异构仓库和车辆。给定一组异构车场、每个车场的车辆数量、异构车场/车辆容量以及一组空间分布的客户位置，MDCVRP 尝试识别满足容量限制的各种车辆的路线，例如为所有客户提供服务。我们将 MDCVRP 建模为二次无约束二元优化 (QUBO) 问题，在给定容量限制的情况下，该问题将所有车辆在所有仓库中行驶的总距离最小化。此外，我们为 MDCVRP 的动态版本制定了一个 QUBO 模型，称为 D-MDCVRP，它涉及车辆根据实时客户请求动态重新路由。我们讨论了在 D-Wave 的量子退火硬件上解决 MDCVRP 和 D-MDCVRP 的问题复杂性和解决方案。考虑到容量限制，这最大限度地减少了所有车辆在所有仓库中行驶的总距离。此外，我们为 MDCVRP 的动态版本制定了一个 QUBO 模型，称为 D-MDCVRP，它涉及车辆根据实时客户请求动态重新路由。我们讨论了在 D-Wave 的量子退火硬件上解决 MDCVRP 和 D-MDCVRP 的问题复杂性和解决方案。考虑到容量限制，这最大限度地减少了所有车辆在所有仓库中行驶的总距离。此外，我们为 MDCVRP 的动态版本制定了一个 QUBO 模型，称为 D-MDCVRP，它涉及车辆根据实时客户请求动态重新路由。我们讨论了在 D-Wave 的量子退火硬件上解决 MDCVRP 和 D-MDCVRP 的问题复杂性和解决方案。