Quantum walk-based vehicle routing optimisation

TL;DR

This paper applies a quantum walk-based algorithm to vehicle routing problems, showing it can efficiently find near-optimal solutions and outperform classical random sampling in simulations.

Contribution

It introduces a quantum walk-based optimization method tailored for the Capacitated Vehicle Routing Problem, including algorithms for solution space indexing and phase unitaries.

Findings

QWOA converges to near-optimal solutions for 8-location CVRP

Quantum solutions outperform classical random sampling

High-quality solutions achieved through amplified quantum states

Abstract

This paper demonstrates the applicability of the Quantum Walk-based Optimisation Algorithm(QWOA) to the Capacitated Vehicle Routing Problem (CVRP). Efficient algorithms are developedfor the indexing and unindexing of the solution space and for implementing the required alternatingphase-walk unitaries, which are the core components of QWOA. Results of numerical simulationdemonstrate that the QWOA is capable of producing convergence to near-optimal solutions for arandomly generated 8 location CVRP. Preparation of the amplified quantum state in this exampleproblem is demonstrated to produce high-quality solutions, which are more optimal than expectedfrom classical random sampling of equivalent computational effort.