A Mixed-Integer Conic Program for the Moving-Target Traveling Salesman Problem based on a Graph of Convex Sets

• Published in: Proceedings of the ... IEEE/RSJ International Conference on Intelligent Robots and Systems pp. 8847 - 8853
• Main Authors: Philip, Allen George, Ren, Zhongqiang, Rathinam, Sivakumar, Choset, Howie
• Format: Conference Proceeding
• Language: English
• Published: IEEE 14.10.2024
• Subjects: Costs; Intelligent robots; Runtime; Trajectory; Traveling salesman problems
• ISSN: 2153-0866
• DOI: 10.1109/IROS58592.2024.10802374

This paper introduces a new formulation that finds the optimum for the Moving-Target Traveling Salesman Problem (MT-TSP), which seeks to find a shortest path for an agent, that starts at a depot, visits a set of moving targets exactly once within their assigned time-windows, and returns to the depot. The formulation relies on the key idea that when the targets move along lines, their trajectories become convex sets within the space-time coordinate system. The problem then reduces to finding the shortest path within a graph of convex sets, subject to some speed constraints. We compare our formulation with the current state-of-the-art Mixed Integer Conic Program (MICP) formulation for the MT-TSP. The experimental results show that our formulation outperforms the MICP for instances with up to 20 targets, with up to two orders of magnitude reduction in runtime, and up to a 60% tighter optimality gap. We also show that the solution cost from the convex relaxation of our formulation provides significantly tighter lower-bounds for the MT-TSP than the ones from the MICP.