带截止期的两车排队优化
Optimizing Two-Truck Platooning with Deadlines
摘要：
我们研究的运输问题，两辆重型卡车穿越国道从不同的起点到目的地，受到个人的最后期限的限制。我们的目标是通过联合优化路径规划、速度规划和队列配置来最大限度地减少它们的总油耗。这样的两卡车排队问题在实践中是普遍存在的，但具有挑战性的解决，由于硬期限约束和巨大的排队配置考虑。我们首先利用一个独特的问题结构，显着简化排队优化，并提出了一种新的配方。我们证明了两卡车排队问题是弱NP-困难的，并承认一个完全多项式时间近似计划（FPTAS）。FPTAS可以实现在$(1+ε)$与最优（对于任何$ε>0$）的比率内的燃料消耗，其中时间复杂度多项式为运输网络和$1/ε$的大小。这些结果与一般的多卡车排队问题形成鲜明对比，该问题被认为是APX困难的，并且排斥任何FPTAS。由于FPTAS在大规模的情况下仍然会产生过多的运行时间，我们设计了一个有效的双次梯度算法来解决大规模/国家规模的情况。这是一个迭代算法，总是收敛。我们证明，每次迭代只会产生多项式时间的复杂性，虽然它需要解决一个整数线性规划问题的最佳。我们描述了一个条件下，该算法产生一个最优解，并推导出后验性能界时，条件不满足。基于真实世界轨迹的大量模拟表明，与基准替代方案相比，我们的路径规划、速度规划和队列行驶的联合解决方案节省了高达$24\%$的燃料。
英文摘要：
We study a transportation problem where two heavy-duty trucks travel across the national highway from separate origins to destinations, subject to individual deadline constraints. Our objective is to minimize their total fuel consumption by jointly optimizing path planning, speed planning, and platooning configuration. Such a two-truck platooning problem is pervasive in practice yet challenging to solve due to hard deadline constraints and enormous platooning configurations to consider. We first leverage a unique problem structure to significantly simplify platooning optimization and present a novel formulation. We prove that the two-truck platooning problem is weakly NP-hard and admits a Fully Polynomial Time Approximation Scheme (FPTAS). The FPTAS can achieve a fuel consumption within a ratio of $(1+ε)$ to the optimal (for any $ε>0$) with a time complexity polynomial in the size of the transportation network and $1/ε$. These results are in sharp contrast to the general multi-truck platooning problem, which is known to be APX-hard and repels any FPTAS. As the FPTAS still incurs excessive running time for large-scale cases, we design an efficient dual-subgradient algorithm for solving large-/national- scale instances. It is an iterative algorithm that always converges. We prove that each iteration only incurs polynomial-time complexity, albeit it requires solving an integer linear programming problem optimally. We characterize a condition under which the algorithm generates an optimal solution and derive a posterior performance bound when the condition is not met. Extensive simulations based on real-world traces show that our joint solution of path planning, speed planning, and platooning saves up to $24\%$ fuel as compared to baseline alternatives.
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