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

2026-02-28

AI Summary

This work addresses the trajectory planning problem for multi-agent interception of moving targets under simultaneous constraints on velocity, time windows, and agent capacity. The authors propose BPRC, an exact algorithm built upon a branch-and-price framework, whose key innovation lies in a tailored pricing subproblem solver designed specifically for moving targets. This solver incorporates a novel label-setting algorithm and customized dominance rules to efficiently handle time-varying travel costs. Experimental results demonstrate that BPRC achieves more than an order-of-magnitude speedup over baseline methods on instances with up to 25 targets, with particularly pronounced advantages in scenarios where agent capacity is limited.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Multiagent Systems: Multiagent Planning
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Agentic search
• Security and Privacy: Large-scale security measurements

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.

Problem

• Moving Target Vehicle Routing Problem
• vehicle routing
• moving targets
• time windows
• capacity constraints

Innovation

• Moving Target Vehicle Routing Problem
• Branch-and-Price
• Relaxed Continuity
• Labeling Algorithm
• Dominance Criterion