Parallel, Asymptotically Optimal Algorithms for Moving Target Traveling Salesman Problems

2025-09-10

AI Summary

This paper addresses the Mobile Target Traveling Salesman Problem (MT-TSP) involving nonlinearly moving targets and agent dynamics constraints—such as Dubins vehicles and redundant manipulators. To tackle this, we propose the Iterative Randomized Generalized (IRG) framework, which alternates between random sampling and generalized TSP solving to achieve asymptotically optimal interception trajectory planning. Furthermore, we design two parallel algorithms—IRG-PGLNS and PCG—that integrate the Parallel Guided Local Neighborhood Search (PGLNS) solver with multi-point synchronous communication, significantly accelerating convergence and improving computational efficiency. Experiments across three MT-TSP variants demonstrate that our approach converges faster than baseline methods while balancing real-time performance and solution optimality. Notably, this work is the first to systematically guarantee asymptotically optimal solution generation for MT-TSP under nontrivial kinodynamic constraints.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search
• Multiagent Systems: Multiagent Planning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Assisted, interactive, and conversational search

Abstract

The Moving Target Traveling Salesman Problem (MT-TSP) seeks an agent trajectory that intercepts several moving targets, within a particular time window for each target. In the presence of generic nonlinear target trajectories or kinematic constraints on the agent, no prior algorithm guarantees convergence to an optimal MT-TSP solution. Therefore, we introduce the Iterated Random Generalized (IRG) TSP framework. The key idea behind IRG is to alternate between randomly sampling a set of agent configuration-time points, corresponding to interceptions of targets, and finding a sequence of interception points by solving a generalized TSP (GTSP). This alternation enables asymptotic convergence to the optimum. We introduce two parallel algorithms within the IRG framework. The first algorithm, IRG-PGLNS, solves GTSPs using PGLNS, our parallelized extension of the state-of-the-art solver GLNS. The second algorithm, Parallel Communicating GTSPs (PCG), solves GTSPs corresponding to several sets of points simultaneously. We present numerical results for three variants of the MT-TSP: one where intercepting a target only requires coming within a particular distance, another where the agent is a variable-speed Dubins car, and a third where the agent is a redundant robot arm. We show that IRG-PGLNS and PCG both converge faster than a baseline based on prior work.

Problem

• Intercepting multiple moving targets within time windows
• Handling nonlinear target trajectories and agent constraints
• Ensuring asymptotic convergence to optimal solutions

Innovation

• Iterated Random Generalized TSP framework
• Parallelized PGLNS algorithm for GTSP
• Parallel Communicating GTSPs simultaneous solution