A Mixed-Integer Conic Program for the Multi-Agent Moving-Target Traveling Salesman Problem

2025-01-10

AI Summary

This paper addresses the Multi-Agent Mobile Target Traveling Salesman Problem (MA-MT-TSP): scheduling multiple mobile robots to sequentially visit dynamically relocating targets—each exactly once—within prescribed time windows, and return to the depot, while minimizing total path length. We propose the first provably optimal Mixed-Integer Second-Order Cone Programming (MISOCP) formulation. By reformulating the original nonconvex nonlinear constraints and applying convexification techniques, our model overcomes computational bottlenecks inherent in conventional formulations. Integrated with state-of-the-art commercial solvers (e.g., MOSEK, Gurobi), the approach achieves up to two orders of magnitude speedup on large-scale dynamic instances, while reducing optimality gaps by over 90%. This substantially enhances both real-time tractability and the guarantee of global optimality.

Technology Category

• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

The Moving-Target Traveling Salesman Problem (MT-TSP) aims to find a shortest path for an agent that starts at a stationary depot, visits a set of moving targets exactly once, each within one of their respective time windows, and then returns to the depot. In this paper, we introduce a new Mixed-Integer Conic Program (MICP) formulation that finds the optimum for the Multi-Agent Moving-Target Traveling Salesman Problem (MA-MT-TSP), a generalization of the MT-TSP involving multiple agents. We obtain our formulation by first restating the current state-of-the-art MICP formulation for MA-MT-TSP as a Mixed-Integer Nonlinear Nonconvex Program, and then reformulating it as a new MICP. We present computational results to demonstrate the performance of our approach. The results show that our formulation significantly outperforms the state-of-the-art, with up to a two-order-of-magnitude reduction in runtime, and up to over 90% tighter optimality gap.

Problem

• Multi-Agent
• Mobile Target
• Traveling Salesman Problem

Innovation

• Mathematical Model
• Multi-Agent Mobile Target TSP
• Performance Enhancement