Carbon-Aware Electric Vehicle Routing Problem with Decision-Focused Learning

Jaume Reixach; Wanru Chen; Jiaming Wu; Balázs Kulcsár

math.OCOct 29, 2026

Carbon-Aware Electric Vehicle Routing Problem with Decision-Focused Learning

Authors: Jaume Reixach, Wanru Chen, Jiaming Wu, Balázs Kulcsár

Organizations: Architecture and Civil Engineering, Chalmers University of Technology, Gothenburg, Sweden · Electrical Engineering, Chalmers University of Technology, Gothenburg, Sweden

Abstract

Electric vehicles produce no tailpipe emissions, but charging them produces emissions that depend on the time-varying generation mix of the electricity consumed. We study an Electric Vehicle Routing Problem with a carbon-aware objective that accounts for charging-related emissions alongside conventional routing costs. The problem determines routing, charging, and waiting decisions, allowing charging demand to be shifted toward periods with lower grid carbon intensity. Because these decisions depend on forecasts of future carbon intensity, we propose a decision-focused learning approach so that the training of the model employed for predicting the carbon intensity of the grid over time is solver-aware. In particular, we train a linear predictor using approximate SPO+ directions and employ a time-limited Large Neighborhood Search followed by exact postprocessing as the underlying solver. Experiments on realistic Germany-based instances show that explicitly considering charging-related emissions reduces realized emissions by 28.76% on average relative to carbon-blind optimization, although at the expense of higher non-carbon operating cost. Moreover, decision-focused training reduces realized total cost by 2.30% on average relative to conventional prediction-focused learning and performs better on 75.5% of the test instances, despite substantially lower pointwise predictive accuracy. Finally, we show that its average advantage remains positive across varied solver configurations and carbon-cost weights.

Figures & tables

Figure 2: Overview of the proposed methodology: (a) decision-focused training, validation, and model selection; (b) evaluation using the trained predictor.

Figure 3: Example problem instance used in the experimental evaluation.

Figure 4: Training dynamics over epochs. The figure on the left presents the evolution of the approximate SPO + loss, while the figure on the right presents the evolution of the validation regret percentage.

Model	MAE	RMSE
PFL	57.70	72.46
DFL	402.70	410.71
Naive 24-hour persistence	90.88	120.03

Table 1: Predictive performance on the 2025 evaluation data. Lower values indicate better pointwise predictive accuracy.

Figure 5: Observed carbon intensity and predictions produced by the PFL , DFL , and naive 24-hour persistence models over the 72-hour routing horizon beginning on 1 October 2025.

Figure 6: Sorted downstream improvement of the DFL -trained predictor over the PFL -trained predictor, the naive 24-hour persistence forecast, and the true-carbon-intensity benchmark.

Figure 7: Downstream solution improvement of the DFL -trained linear regression over the PFL -trained one, with the results organized by the month of the instances’ start date.

Customers	Mean stations	Optimality Proven	Mean gap (%)	Median gap (%)
3	5.6	10/10	1.46	0.77
4	7.5	5/10	2.48	1.43
5	9.3	0/10	–	–

Table 2: Small-scale comparison of the LNS with the exact MILP .

Figure 8: Downstream improvement of the DFL -trained predictor over the PFL -trained predictor under different LNS parameter configurations.

Figure 9: Downstream improvement of the DFL -trained predictor over the PFL -trained predictor for carbon-cost weights of 5, 10, and 20.

Figure 10: Effects of including charging-related emissions in the optimization objective.

Vehicle Routing

Vehicle routing studies how to assign and sequence trips for fleets while meeting capacity, time, energy, and service constraints.

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RL Control Multi-Objective Reinforcement Learning Electric Vehicle Charging Power Systems

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The rapid growth of Electric Vehicle (EV) adoption challenges power distribution networks through peak load spikes, voltage instability, and transformer overloads from uncoordinated charging. While Model Predictive Control (MPC) and standard Reinforcement Learning (RL) methods have addressed these issues, existing approaches rarely treat real-time carbon intensity or fluctuating renewable energy (RE) availability as primary scheduling objectives, leaving substantial decarbonisation potential unrealised. This paper proposes an emission-aware RL strategy based on the Soft Actor Critic (SAC) algorithm, with a multi-objective reward that penalises carbon emissions, curtailed on-site renewables, and unmet user demand. The agent is trained within a unified benchmarking framework on the EV2Gym platform, incorporating behind-the-meter solar and wind profiles, time-varying EirGrid carbon intensity data, and realistic workplace EV behaviour across 25 Electric Vehicle Supply Equipment (EVSE) units. Nine control strategies, including heuristics, emission-aware MPC variants, and the proposed RL agent, are compared under five renewable penetration scenarios (0%-50%) over ten independent runs each. The RL agent achieves a carbon intensity as low as 23.96 grams of carbon dioxide per kilowatt-hour under 50% wind penetration, representing up to 87% emission reduction versus the uncontrolled baseline, and outperforms the external graph-based Power Distribution Network (PDN) benchmark. Transformer overload remains below 7 kWh across scenarios, against up to 1093 kWh for the As Fast As Possible (AFAP) heuristic, and renewable self-consumption reaches 52% under combined wind and solar supply. Embedding carbon intensity forecasts into the RL state and reward aligns charging with low-emission periods while preserving grid compliance and user satisfaction.

Abstract

Vehicle Routing

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