New Formulations and Discretization Insights for the Electric Autonomous Dial-a-Ride Problem

TL;DR

This paper explores discretization techniques for the Electric Autonomous Dial-a-Ride Problem, developing new formulations that improve computational efficiency, especially under coarse time discretization, with implications for routing electric autonomous vehicles.

Contribution

It introduces three novel formulations with different discretization levels, demonstrating how discretization impacts computational performance in E-ADARP.

Findings

Time discretization improves performance in many settings.

Explicit SoC discretization is only beneficial in restricted scenarios.

The improved event-based formulation outperforms previous models.

Abstract

The Electric Autonomous Dial-a-Ride Problem (E-ADARP) involves routing and scheduling electric autonomous vehicles under battery capacity and partial recharging constraints, aiming to minimize total travel cost and excess ride time. In practice, operational data for time and state-of-charge (SoC) are often available only at a coarse granularity. This raises a natural question: can discretization be exploited to improve computational performance by enabling alternative formulation structures? To investigate this question, we develop three formulations reflecting different levels of discretization. The first is an improved event-based formulation (IEBF) with arc-flow SoC variables for the continuous-parameter E-ADARP, serving as a strengthened baseline. The latter two are fragment-based formulations designed for discretized inputs. The second is a time-space fragment-based formulation with continuous SoC arc-flow variables (TSFFCS), which discretizes time while keeping SoC continuous. The third is a battery-time-space fragment-based formulation (BTSFF), which discretizes both time and SoC. Here, an event denotes a tuple consisting of a location and a set of onboard customers, while a fragment denotes a partial path. Computational results show that IEBF improves upon the existing event-based formulation for the original E-ADARP. Under discretized settings, TSFFCS tends to outperform IEBF, particularly when recharging is frequent and time discretization is relatively coarse, indicating that time discretization can improve computational performance across a wide range of settings. In contrast, BTSFF rarely outperforms TSFFCS unless the number of reachable SoC levels is limited, suggesting that explicit SoC discretization is beneficial only in relatively restricted settings.