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.

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.