A K-means Inspired Solution Framework for Large-Scale Multi-Traveling Salesman Problems

TL;DR

The paper tackles large-scale MTSP for multi-agent task allocation, where conventional optimization methods become intractable as task and agent counts grow. It introduces a K-means-inspired framework that partitions the task space into spatially coherent clusters, then solves local routing within clusters using precomputed distance matrices and a 2-opt heuristic, with a lexicographic neighborhood migration to balance load. The key contributions are a cluster-then-route decomposition, a distance-matrix–based local routing, and a lightweight, lexicographic migration strategy that guarantees monotonic improvement. Empirical results demonstrate scalability to 1000 agents and 5000 tasks, with substantial speedups over a GA baseline and stable performance where GA struggles or times out.

Abstract

The Multi-Traveling Salesman Problem (MTSP) is a commonly used mathematical model for multi-agent task allocation. However, as the number of agents and task targets increases, existing optimization-based methods often incur prohibitive computational costs, posing significant challenges to large-scale coordination in unmanned systems. To address this issue, this paper proposes a K-means-inspired task allocation framework that reformulates the MTSP as a spatially constrained classification process. By leveraging spatial coherence, the proposed method enables fast estimation of path costs and efficient task grouping, thereby fundamentally reducing overall computational complexity. Extensive simulation results demonstrate that the framework can maintain high solution quality even in extremely large-scale scenarios-for instance, in tasks involving 1000 agents and 5000 targets. The findings indicate that this "cluster-then-route" decomposition strategy offers an efficient and reliable solution for large-scale multi-agent task allocation.