A Hierarchical Grouping Algorithm for the Multi-Vehicle Dial-a-Ride Problem

TL;DR

This paper introduces HRA, a novel hierarchical grouping algorithm that provides the first non-trivial approximation for the Multi-Vehicle Dial-a-Ride Problem, improving route efficiency and rider experience in ride-sharing.

Contribution

The paper presents HRA, a new approximation algorithm that reduces the Multi-Vehicle DaRP to a capacitated partitioning problem, enabling more efficient routing solutions.

Findings

Routes have less total travel distance compared to baselines.

Routes exhibit small in-transit latency, reducing rider travel times.

HRA enhances rider experience and energy efficiency.

Abstract

Ride-sharing is an essential aspect of modern urban mobility. In this paper, we consider a classical problem in ride-sharing - the Multi-Vehicle Dial-a-Ride Problem (Multi-Vehicle DaRP). Given a fleet of vehicles with a fixed capacity stationed at various locations and a set of ride requests specified by origins and destinations, the goal is to serve all requests such that no vehicle is assigned more passengers than its capacity at any point along its trip. We propose an algorithm HRA, which is the first non-trivial approximation algorithm for the Multi-Vehicle DaRP. The main technical contribution is to reduce the Multi-Vehicle DaRP to a certain capacitated partitioning problem, which we solve using a novel hierarchical grouping algorithm. Experimental results show that the vehicle routes produced by our algorithm not only exhibit less total travel distance compared to state-of-the-art baselines, but also enjoy a small in-transit latency, which crucially relates to riders' traveling times. This suggests that HRA enhances rider experience while being energy-efficient.