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

arXiv: https://arxiv.org/abs/2601.22052 · HTML: https://mlsanity.com/paper/2601.22052/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for energy, networks and operations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 13 of its 49 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Placed in

- Deep reinforcement learning methods / [RL for energy, networks and operations](https://mlsanity.com/deeprl/rl-for-energy-networks-and-operations/)

## Builds on (most cited first, 13 of 13)

- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018)
- [Explainable Reinforcement Learning: A Survey](https://mlsanity.com/paper/2005.06247/) (2020)
- [A Survey on Interpretable Reinforcement Learning](https://mlsanity.com/paper/2112.13112/) (2021)
- [Heterogeneous Attentions for Solving Pickup and Delivery Problem via Deep Reinforcement Learning](https://mlsanity.com/paper/2110.02634/) (2021)
- [Control of Robotic Mobility-On-Demand Systems: a Queueing-Theoretical Perspective](https://mlsanity.com/paper/1404.4391/) (2014)
- [A Branch-and-Price Algorithm for the Electric Autonomous Dial-A-Ride Problem](https://mlsanity.com/paper/2206.13496/) (2022)
- [Mechanistic Interpretability for Neural TSP Solvers](https://mlsanity.com/paper/2510.21693/) (2025)

## Abstract (arXiv)

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.