aiqbench analysis
This paper presents Lazy Branch-and-Price with Relaxed Continuity (Lazy BPRC), an exact algorithm designed to optimize trajectories for agents intercepting moving targets while navigating static obstacles. By utilizing cheap lower bounds and lazily updating them to true costs via shortest-path searches on graphs of convex sets, the method achieves up to an order-of-magnitude speedup over previous approaches. This advancement directly addresses computational bottlenecks in complex robotic coordination and dynamic routing scenarios.
Optimal Solutions for the Moving Target Vehicle Routing Problem with Obstacles via Lazy Branch-and-Price
arXiv:2603.21880v5 Announce Type: replace Abstract: The Moving Target Vehicle Routing Problem with Obstacles (MT-VRP-O) seeks trajectories for several agents that collectively intercept a set of moving targets. Each target has one or more time windows where it can be visited, and the agents must avoid static obstacles and satisfy speed and capacity constraints. Previously studied VRPs are often addressed using a framework called branch-and-price. This framework requires computing the cost for a single agent to visit a given sequence of target-time window pairings, for several candidate sequences. These sequences are called tours. Computing tour costs is more expensive in the MT-VRP-O than in previously studied VRPs due to the presence of both moving targets and static obstacles. Thus, we introduce a new exact algorithm, Lazy Branch-and-Price with Relaxed Continuity (Lazy BPRC), for the MT-VRP-O. The key idea in Lazy BPRC is to use cheap-to-compute lower bounds on tour costs where costs are traditionally used, and lazily update lower bounds to true costs. When computing a tour's true cost is needed, we do so by searching for a shortest path on a graph of convex sets, and we introduce a new heuristic to accelerate the search. We demonstrate that Lazy BPRC runs up to an order of magnitude faster than two ablations.
Abstract:The Moving Target Vehicle Routing Problem with Obstacles (MT-VRP-O) seeks trajectories for several agents that collectively intercept a set of moving targets. Each target has one or more time windows where it can be visited, and the agents must avoid static obstacles and satisfy speed and capacity constraints. Previously studied VRPs are often addressed using a framework called branch-and-price. This framework requires computing the cost for a single agent to visit a given sequence of target-time window pairings, for several candidate sequences. These sequences are called tours. Computing tour costs is more expensive in the MT-VRP-O than in previously studied VRPs due to the presence of both moving targets and static obstacles. Thus, we introduce a new exact algorithm, Lazy Branch-and-Price with Relaxed Continuity (Lazy BPRC), for the MT-VRP-O. The key idea in Lazy BPRC is to use cheap-to-compute lower bounds on tour costs where costs are traditionally used, and lazily update lower bounds to true costs. When computing a tour's true cost is needed, we do so by searching for a shortest path on a graph of convex sets, and we introduce a new heuristic to accelerate the search. We demonstrate that Lazy BPRC runs up to an order of magnitude faster than two ablations.
Robotics (cs.RO)
arXiv:2603.21880 [cs.RO]
(or arXiv:2603.21880v5 [cs.RO] for this version)
https://doi.org/10.48550/arXiv.2603.21880 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 297 words
