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

TL;DR

This work tackles the Electric Dial-a-Ride Problem (E-DARP) by introducing an edge-centric graph neural network framework, GREAT, combined with deep reinforcement learning to jointly optimize routing and charging under energy and service quality constraints. The method learns unsupervised routing policies that operate directly on edge attributes, enabling natural handling of asymmetric, non-Euclidean costs and nonlinear charging dynamics. Through two case studies, it achieves near-optimal solutions on benchmarks with substantial speedups and scales to 250-request instances via curriculum learning, outperforming ALNS in solution quality while guaranteeing 100% service completion and sub-second inference. The results demonstrate the practical potential of edge-based DRL for real-time, energy-aware fleet management in urban electric mobility, with thorough sensitivity analyses guiding fleet design and policy robustness under uncertainty.

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 a 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 sub-second inference times 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.

Figures (5)

• Figure 1: Example E-DARP solution with seven vehicles serving pickup--delivery requests and visiting charging stations in San Francisco.
• Figure 2: Example E-DARP solution with three vehicle routes and time windows. The depot (node 0) is shown as a filled black circle. Each request $i$ consists of a pickup node $i \in P$ (triangle) and delivery node $n+i \in D$ (square) in matching colors. Black horizontal bars represent the planning horizon for each node, while the overlaid red bars indicate the feasible service time windows $[a_i, \ell_i]$ during which the vehicle must arrive. Green diamonds represent charging stations $f \in F$ that are available throughout the planning horizon. Routes $\rho^1$ and $\rho^3$ include charging stops to maintain battery feasibility throughout their journeys. Each vehicle can carry up to $Q$ passengers simultaneously while respecting both time window constraints and passenger ride time limits.
• Figure 3: Validation profit over training epochs for all hyperparameter configurations. Most configurations converge to similar performance levels ($\sim$36000) by epoch 50, with $d=128$ (blue) and $d=64$ (purple) configurations showing comparable convergence rates. The $d=192$, $h=8$, $L=5$ configuration (green dashed) diverged early and failed to recover.
• Figure 4: Reward weight sensitivity analysis.
• Figure 5: Validation profit convergence trajectories for all twelve configurations. Each subplot shows three ride-sharing capacity settings (1, 2, and 3 passengers per vehicle) for a given battery and fleet size combination.