Optimal Solutions for the Moving Target Vehicle Routing Problem via Branch-and-Price with Relaxed Continuity
This addresses a complex logistics problem for routing agents to intercept moving targets, with incremental improvements in computational efficiency.
The paper tackles the Moving Target Vehicle Routing Problem (MT-VRP) by introducing an exact algorithm called Branch-and-Price with Relaxed Continuity (BPRC), which finds optimal solutions more than an order of magnitude faster than a baseline on instances with up to 25 targets.
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.