Solving the vehicle routing problem via quantum support vector machines

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 employ 6 and 12 qubit circuits, respectively, to build and evaluate a hybrid quantum machine learning approach for solving VRP of 3- and 4-city scenarios. The approach employs quantum support vector machines (QSVMs) trained using a variational quantum eigensolver on a static or dynamic 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