Modeling routing problems in QUBO with application to ride-hailing

TL;DR

This paper formulates the Ride Pooling Problem (RPP) as a QUBO model, enabling the use of quantum and classical metaheuristics for efficient routing solutions in resource-sharing services.

Contribution

It introduces a novel QUBO formulation for RPP and develops efficient methods to solve it using quantum and classical metaheuristics.

Findings

QUBO formulation effectively models RPP.

Metaheuristics can solve the QUBO for RPP.

Potential for quantum algorithms to optimize ride pooling.

Abstract

Many emerging commercial services are based on the sharing or pooling of resources for common use with the aim of reducing costs. Businesses such as delivery-, mobility-, or transport-as-a-service have become standard in many parts of the world, fulfilling on-demand requests for customers in live settings. However, it is known that many of these problems are NP-hard, and therefore both modeling and solving them accurately is a challenge. Here we focus on one such routing problem, the Ride Pooling Problem (RPP), where multiple customers can request on-demand pickups and drop-offs from shared vehicles within a fleet. The combinatorial optimization task is to optimally pool customer requests using the limited set of vehicles, akin to a small-scale flexible bus route. In this work, we propose a quadratic unconstrained binary optimization (QUBO) program and introduce efficient formulation methods for the RPP to be solved using metaheuristics, and specifically emerging quantum optimization algorithms.