Solving The Vehicle Routing Problem via Quantum Support Vector Machines

TL;DR

This paper explores hybrid quantum machine learning methods, specifically quantum support vector machines, to solve small-scale vehicle routing problems, demonstrating potential quantum advantages in combinatorial optimization.

Contribution

It introduces a novel approach combining QSVMs with variational quantum eigensolvers for VRP, testing different encoding strategies and optimizers on small problem instances.

Findings

Quantum methods can effectively model small VRPs.

Different encoding strategies impact solution quality.

Quantum algorithms show promise for combinatorial optimization.

Abstract

The Vehicle Routing Problem (VRP) is an example of a combinatorial optimization problem that has attracted academic attention due to its potential use in various contexts. VRP aims to arrange vehicle deliveries to several sites in the most efficient and economical manner possible. Quantum machine learning offers a new way to obtain solutions by harnessing the natural speedups of quantum effects, although many solutions and methodologies are modified using classical tools to provide excellent approximations of the VRP. In this paper, we implement and test hybrid quantum machine learning methods for solving VRP of 3 and 4-city scenarios, which use 6 and 12 qubit circuits, respectively. The proposed method is based on quantum support vector machines (QSVMs) with a variational quantum eigensolver on a fixed or variable ansatz. Different encoding strategies are used in the experiment to transform the VRP formulation into a QSVM and solve it. Multiple optimizers from the IBM Qiskit framework are also evaluated and compared.