Unsupervised Learning for Solving the Travelling Salesman Problem
This work addresses the TSP, a classic combinatorial optimization problem, with an incremental improvement in efficiency for data-driven approaches.
The authors tackled the Travelling Salesman Problem (TSP) by proposing UTSP, an unsupervised learning framework using a Graph Neural Network with a surrogate loss, which outperforms existing data-driven TSP heuristics and is parameter and data efficient, using ~10% of parameters and ~0.2% of training samples compared to other methods.
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.