A Quantum Annealing Approach for Dynamic Multi-Depot Capacitated Vehicle Routing Problem

TL;DR

This paper introduces a quantum annealing method for solving the complex, real-world multi-depot capacitated vehicle routing problem and its dynamic variant, demonstrating potential quantum advantages in logistics optimization.

Contribution

It models MDCVRP and D-MDCVRP as QUBO problems suitable for quantum annealing, providing a novel approach to tackle these NP-hard routing challenges.

Findings

QUBO formulation enables quantum annealing solutions for MDCVRP

Dynamic rerouting in D-MDCVRP is effectively modeled for real-time applications

Quantum hardware can address complex routing problems with capacity constraints

Abstract

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.