Rollout-Based Charging Strategy for Electric Trucks with Hours-of-Service Regulations (Extended Version)

TL;DR

This work addresses optimal charging for electric trucks along a pre-planned route while strictly obeying HoS regulations and delivery deadlines. It formulates the problem as a bilinear mixed-integer program that captures battery dynamics, rest/driving constraints, and timing, then proposes a rollout-based approximation that scales linearly with the number of stations. The rollout approach, using greedy and relaxed base solutions, yields near-optimal results with substantial computational speedups, validated by simulations on a realistic Swedish road network. The method enables real-time decision-making under travel-time uncertainties and provides a foundation for handling limited charging resources at stations in future work.

Abstract

Freight drivers of electric trucks need to design charging strategies for where and how long to recharge the truck in order to complete delivery missions on time. Moreover, the charging strategies should be aligned with drivers' driving and rest time regulations, known as hours-of-service (HoS) regulations. This letter studies the optimal charging problems of electric trucks with delivery deadlines under HoS constraints. We assume that a collection of charging and rest stations is given along a pre-planned route with known detours and that the problem data are deterministic. The goal is to minimize the total cost associated with the charging and rest decisions during the entire trip. This problem is formulated as a mixed integer program with bilinear constraints, resulting in a high computational load when applying exact solution approaches. To obtain real-time solutions, we develop a rollout-based approximate scheme, which scales linearly with the number of stations while offering solid performance guarantees. We perform simulation studies over the Swedish road network based on realistic truck data. The results show that our rollout-based approach provides near-optimal solutions to the problem in various conditions while cutting the computational time drastically.

Figures (11)

• Figure 1: A simplified route model of electric trucks, where each charging and rest station, denoted by $S_k$, provides both charging and rest services. Each ramp in the route leading to $S_k$ with the shortest detour is denoted by $r_k$ and shown by a grey node, where $k\!=\!0,\dots, N\!-\!1$.
• Figure 2: The consecutive driving time when first arriving at $r_{k+1}$.
• Figure 3: (a) Swedish road network with $105$ road terminals, from which the OD pair of each delivery mission is selected. (b) The potential charging and rest stations considered are shown by the green nodes. (c) The transport route model of one truck, where $5$ charging and rest stations are available, and ramps leading to the shortest detours to stations are shown by the yellow nodes.
• Figure 4: Comparison results of scenario 1 ($N\!=\!5$).
• Figure 5: Comparison results of scenario 2 ($N\!=\!6$).

Theorems & Definitions (6)

• Proposition IV.1
• proof
• Remark IV.1
• Remark IV.2
• Proposition 1.1
• proof : Proof of Prop. \ref{['prop:rollout_mixed_int']}