The Conflict-Free Electric Vehicle Routing Problem (CF-EVRP) is an extension of the Vehicle Routing Problem (VRP), a combinatorial optimization problem of designing routes for vehicles to visit customers such that a cost function, typically the number of vehicles or the total travelled distance, is minimized. The problem finds many logistics applications, particularly for highly automated logistic systems for material handling. The CF-EVRP involves constraints such as time windows on the delivery to the customers, limited operating range of the vehicles, and limited capacity on the number of vehicles that a road segment can accommodate at the same time. In this paper, the compositional algorithm ComSat for solving the CF-EVRP is presented. The algorithm iterates through the sub-problems until a globally feasible solution is found. The proposed algorithm is implemented using an optimizing SMT-solver and is evaluated against an implementation of a previously presented monolithic model. The soundness and completeness of the algorithm are proven, and it is benchmarked on a set of generated problems and found to be able to solve problems of industrial size. Note to Practitioners—The need to define and solve the CF-EVRP relates to an industrial application where a fleet of autonomous robots navigates in a heterogeneous environment, shared with humans and other vehicles and obstacles. To allow for a low-level trajectory controller to handle dynamic obstacles, like humans and fork-lifts, the CF-EVRP includes capacity constraints on the road segments. This increases the problem complexity, and thus requires to trade off optimality for feasability; this so to get solutions in reasonable time with respect to how long ahead the jobs to schedule are known. The overall problem is to find feasible solutions that satisfy all constraints while avoiding travelling unnecessarily long routes, and at the same time meet the stipulated time-windows to deliver material just-in-time. The compositional algorithm (ComSat) presented in this work is based on the idea to break down the overall scheduling problem into sub-problems that are easier to solve, and then to build a schedule based on the solutions of the sub-problems. ComSat is designed to work well for industrial scenarios where there are good reasons to believe that feasible solutions do exist. This seems a reasonable assumption as in an industrial setting a sufficient number of mobile robots can typically be assumed to be available.

中文翻译：

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无冲突电动汽车路径问题的组合算法


无冲突电动汽车路线问题 (CF-EVRP) 是车辆路线问题 (VRP) 的扩展，这是一个组合优化问题，设计车辆拜访客户的路线，使得成本函数（通常是车辆数量或总行驶距离最小化。这个问题存在于许多物流应用中，特别是用于物料搬运的高度自动化物流系统。 CF-EVRP 涉及诸如向客户交付的时间窗口、车辆的有限运行范围以及路段可同时容纳的车辆数量的限制等限制。本文提出了求解CF-EVRP的组合算法ComSat。该算法迭代子问题，直到找到全局可行的解决方案。所提出的算法是使用优化 SMT 求解器来实现的，并根据先前提出的整体模型的实现进行评估。该算法的可靠性和完整性得到了证明，并且以一组生成的问题为基准，发现能够解决工业规模的问题。从业者须知——定义和解决 CF-EVRP 的需求与工业应用相关，其中一组自主机器人在异构环境中导航，与人类和其他车辆和障碍物共享。为了让低级轨迹控制器能够处理动态障碍物，例如人类和叉车，CF-EVRP 包括路段的容量限制。这增加了问题的复杂性，因此需要权衡最优性和可行性；这样做是为了在合理的时间内获得关于已知的工作安排时间的解决方案。 总体问题是找到满足所有约束条件的可行解决方案，同时避免不必要的长途旅行，同时满足规定的时间窗口以准时交付材料。本文提出的组合算法（ComSat）的思想是将整个调度问题分解为更容易解决的子问题，然后根据子问题的解决方案构建调度。 ComSat 的设计非常适合工业场景，有充分的理由相信确实存在可行的解决方案。这似乎是一个合理的假设，因为在工业环境中，通常可以假设有足够数量的移动机器人可用。