Unsupervised Learning for Solving the Travelling Salesman Problem

Yimeng Min, Yiwei Bai, Carla P Gomes

Keywords: Combinatorial Optimization, Graph Neural Network, Travelling Salesman Problem

TL;DR: use graph neural network, unsupervised learning and search to solve the Travelling Salesman Problem

Abstract:

We propose UTSP, an Unsupervised Learning (UL) framework for solving the Travelling Salesman Problem (TSP). We train a Graph Neural Network (GNN) using a surrogate loss. The GNN outputs a heat map representing the probability for each edge to be part of the optimal path. We then apply local search to generate our final prediction based on the heat map. Our loss function consists of two parts: one pushes the model to find the shortest path and the other serves as a surrogate for the constraint that the route should form a Hamiltonian Cycle.
Experimental results show that UTSP
outperforms the existing data-driven TSP heuristics.
Our approach is parameter efficient as well as data efficient: the model takes $\sim$ 10\% of the number of parameters and $\sim$ 0.2\% of training samples compared with Reinforcement Learning or Supervised Learning methods.

Submission Number: 8416