Two-Phase Bilevel Search for the Moving-Target Traveling Salesman Problem with Moving Obstacles

2026-06-17

AI Summary

This study addresses the Traveling Salesman Problem with moving targets and mobile obstacles (TSPMO), wherein an agent must compute a minimum-cost trajectory that departs from a fixed depot, visits multiple moving targets within prescribed time windows, and returns to the depot, all while avoiding dynamically moving obstacles. The work introduces mobile obstacles into this problem formulation for the first time and proposes two solution approaches: an exact mixed-integer conic programming (MICP) model and a highly efficient, scalable two-phase bi-level search (TPBS) algorithm. Experimental results demonstrate that, in scenarios involving up to 40 moving targets and 40 mobile obstacles, both proposed methods significantly outperform existing baselines in terms of success rate, solution quality, and computational efficiency.

Abstract

The Moving-Target Traveling Salesman Problem (MT-TSP) seeks a minimum cost trajectory for an agent that departs from a static depot, visits a set of moving targets, each within one of their assigned time windows, and returns to the depot. In this article, we study the Moving-Target Traveling Salesman Problem with Moving Obstacles (MT-TSP-MO), a generalization of the MT-TSP where the agent trajectory must avoid moving obstacles. We present a Mixed-Integer Conic Programming (MICP) formulation that can be solved using off-the-shelf solvers, as well as a fast and scalable Two-Phase Bilevel Search (TPBS) algorithm that computes high-quality feasible solutions for the problem. We evaluate our approaches against an existing baseline algorithm on a broad range of problem instances with up to 40 targets and 40 obstacles. The results demonstrate that both the proposed methods significantly outperform the baseline with respect to success rates, solution costs, and computation time.

Problem

• Moving-Target Traveling Salesman Problem
• Moving Obstacles
• Trajectory Planning
• Time Windows
• Collision Avoidance

Innovation

• Moving-Target TSP
• Moving Obstacles
• Mixed-Integer Conic Programming
• Two-Phase Bilevel Search
• Trajectory Planning