# Learning the Multiple Traveling Salesmen Problem with Permutation Invariant Pooling Networks

## TL;DR

This paper introduces a neural network approach for the Multiple Traveling Salesmen Problem that effectively handles varying set sizes and outperforms traditional meta-heuristics.

## Contribution

It presents a novel neural network architecture with permutation-invariant pooling, specialized output layers, and a search method for solving the MTSP.

## Key findings

- Outperforms existing meta-heuristics in solution quality
- Handles varying numbers of salesmen, cities, and depots
- Demonstrates strong generalization to different problem sizes

## Abstract

While there are optimal TSP solvers, as well as recent learning-based approaches, the generalization of the TSP to the Multiple Traveling Salesmen Problem is much less studied. Here, we design a neural network solution that treats the salesmen, cities and depot as three different sets of varying cardinalities. We apply a novel technique that combines elements from recent architectures that were developed for sets, as well as elements from graph networks. Coupled with new constraint enforcing output layers, a dedicated loss, and a search method, our solution is shown to outperform all the meta-heuristics of the leading solver in the field.