Carbon footprint optimization (CFO) is important for sustainable heavy-duty e-truck transportation. We consider the CFO problem for timely transportation of e-trucks, where the truck travels from an origin to a destination across a national highway network subject to a deadline. The goal is to minimize the carbon footprint by orchestrating path planning, speed planning, and intermediary charging planning. We first show that it is NP-hard even just to find a feasible CFO solution. We then develop a $(1+\epsilon_F, 1+\epsilon_\beta)$ bi-criteria approximation algorithm that achieves a carbon footprint within a ratio of $(1+\epsilon_F)$ to the minimum with no deadline violation and at most a ratio of $(1+\epsilon_\beta)$ battery capacity violation (for any positive $\epsilon_F$ and $\epsilon_\beta$). Its time complexity is polynomial in the size of the highway network, $1/\epsilon_F$, and $1/\epsilon_\beta$. Such algorithmic results are among the best possible unless P=NP. Simulation results based on real-world traces show that our scheme reduces up to 11\% carbon footprint as compared to baseline alternatives considering only energy consumption but not carbon footprint.

翻译：碳足迹优化（CFO）对于可持续的重型电动卡车运输至关重要。我们研究了电动卡车准时运输中的CFO问题，其中卡车需在国家高速公路网络上从起点行驶至终点，并受截止时间约束。目标是通过协调路径规划、速度规划和中间充电规划来最小化碳足迹。我们首先证明，即使仅寻找一个可行的CFO解也是NP难的。随后，我们开发了一种$(1+\epsilon_F, 1+\epsilon_\beta)$双准则近似算法，该算法能在不违反截止时间的前提下，实现碳足迹不超过最小值的$(1+\epsilon_F)$倍，且电池容量违反率至多为$(1+\epsilon_\beta)$倍（对任意正数$\epsilon_F$和$\epsilon_\beta$）。其时间复杂度在高速公路网络规模、$1/\epsilon_F$和$1/\epsilon_\beta$上呈多项式级。除非P=NP，否则此类算法结果已属最优。基于真实轨迹的仿真结果表明，与仅考虑能耗而不关注碳足迹的基线方案相比，我们的方法最多可减少11%的碳足迹。