The Moving Target Vehicle Routing Problem (MT-VRP) seeks trajectories for several agents that intercept a set of moving targets, subject to speed, time window, and capacity constraints. We introduce an exact algorithm, Branch-and-Price with Relaxed Continuity (BPRC), for the MT-VRP. The main challenge in a branch-and-price approach for the MT-VRP is the pricing subproblem, which is complicated by moving targets and time-dependent travel costs between targets. Our key contribution is a new labeling algorithm that solves this subproblem by means of a novel dominance criterion tailored for problems with moving targets. Numerical results on instances with up to 25 targets show that our algorithm finds optimal solutions more than an order of magnitude faster than a baseline based on previous work, showing particular strength in scenarios with limited agent capacities.

翻译：移动目标车辆路径问题（MT-VRP）旨在为多个智能体规划轨迹，使其在满足速度、时间窗和容量约束的条件下拦截一组移动目标。本文针对MT-VRP提出了一种精确算法——基于松弛连续性的分支定价法（BPRC）。在分支定价框架中求解MT-VRP的主要挑战在于定价子问题，该问题因目标移动及目标间时变行驶成本而变得复杂。我们的核心贡献是提出了一种新的标记算法，该算法通过一种专为移动目标问题设计的新颖支配准则来求解此子问题。在最多包含25个目标的算例上的数值结果表明，本算法求解最优解的速度较基于先前工作的基准方法提升了一个数量级以上，尤其在智能体容量受限的场景中表现出显著优势。