DAN: Decentralized Attention-based Neural Network for the MinMax Multiple Traveling Salesman Problem

TL;DR

This paper introduces DAN, a decentralized attention-based neural network using Transformer architecture and multi-agent reinforcement learning to efficiently solve large-scale MinMax mTSP instances, outperforming existing methods in solution quality and speed.

Contribution

DAN is a novel decentralized neural approach that scales to large mTSP instances, leveraging Transformer architecture and multi-agent RL for improved collaboration and efficiency.

Findings

DAN matches or outperforms state-of-the-art solvers on large-scale mTSP instances.

DAN maintains low planning times while solving instances with up to 1000 cities.

DAN exhibits enhanced agent collaboration compared to baseline methods.

Abstract

The multiple traveling salesman problem (mTSP) is a well-known NP-hard problem with numerous real-world applications. In particular, this work addresses MinMax mTSP, where the objective is to minimize the max tour length among all agents. Many robotic deployments require recomputing potentially large mTSP instances frequently, making the natural trade-off between computing time and solution quality of great importance. However, exact and heuristic algorithms become inefficient as the number of cities increases, due to their computational complexity. Encouraged by the recent developments in deep reinforcement learning (dRL), this work approaches the mTSP as a cooperative task and introduces DAN, a decentralized attention-based neural method that aims at tackling this key trade-off. In DAN, agents learn fully decentralized policies to collaboratively construct a tour, by predicting each other's future decisions. Our model relies on the Transformer architecture and is trained using multi-agent RL with parameter sharing, providing natural scalability to the numbers of agents and cities. Our experimental results on small- to large-scale mTSP instances ($50$ to $1000$ cities and $5$ to $20$ agents) show that DAN is able to match or outperform state-of-the-art solvers while keeping planning times low. In particular, given the same computation time budget, DAN outperforms all conventional and dRL-based baselines on larger-scale instances (more than 100 cities, more than 5 agents), and exhibits enhanced agent collaboration. A video explaining our approach and presenting our results is available at \url{https://youtu.be/xi3cLsDsLvs}.