Optimal Solutions for the Moving Target Vehicle Routing Problem via Branch-and-Price with Relaxed Continuity

TL;DR

This paper presents an exact branch-and-price algorithm with a novel labeling technique for efficiently solving the Moving Target Vehicle Routing Problem, outperforming previous methods especially in capacity-limited scenarios.

Contribution

The paper introduces a new labeling algorithm and dominance criterion tailored for MT-VRP, significantly improving solution speed over existing approaches.

Findings

The algorithm finds optimal solutions over ten times faster than previous methods.

It performs well on instances with up to 25 targets.

Particularly effective in scenarios with limited agent capacities.

Abstract

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.