Learning to Dial-a-Ride: A Deep Graph Reinforcement Learning Approach to the Electric Dial-a-Ride Problem

TL;DR

This paper introduces a deep reinforcement learning method using graph neural networks to efficiently solve the electric dial-a-ride problem, optimizing routing and charging in urban electric mobility systems.

Contribution

It presents a novel edge-centric graph neural network approach that captures complex routing costs and jointly optimizes routing, charging, and service quality for electric ride-sharing.

Findings

Achieves solutions within 0.4% of best-known results on benchmarks.

Reduces computation time by orders of magnitude compared to traditional methods.

Outperforms ALNS in large-scale instances with 9.5% better solution quality.

Abstract

Urban mobility systems are transitioning toward electric, on-demand services, creating operational challenges for fleet management under energy and service-quality constraints. The Electric Dial-a-Ride Problem (E-DARP) extends the classical dial-a-ride problem by incorporating limited battery capacity and nonlinear charging dynamics, increasing computational complexity and limiting the scalability of exact methods for real-time use. This paper proposes a deep reinforcement learning approach based on an edge-centric graph neural network encoder and an attention-driven route construction policy. By operating directly on edge attributes such as travel time and energy consumption, the method captures non-Euclidean, asymmetric, and energy-dependent routing costs in real road networks. The learned policy jointly optimizes routing, charging, and service quality without relying on Euclidean assumptions or handcrafted heuristics. The approach is evaluated on two case studies using ride-sharing data from San Francisco. On benchmark instances, the method achieves solutions within 0.4% of best-known results while reducing computation times by orders of magnitude. A second case study considers large-scale instances with up to 250 request pairs, realistic energy models, and nonlinear charging. On these instances, the learned policy outperforms Adaptive Large Neighborhood Search (ALNS) by 9.5% in solution quality while achieving 100% service completion, with inference times under 10 seconds compared to hours for the metaheuristic. Finally, sensitivity analyses quantify the impact of battery capacity, fleet size, ride-sharing capacity, and reward weights, while robustness experiments show that deterministically trained policies generalize effectively under stochastic conditions.