  The Traveling Salesman Problem (TSP) is the most popular and most studied
combinatorial problem, starting with von Neumann in 1951. It has driven the
discovery of several optimization techniques such as cutting planes,
branch-and-bound, local search, Lagrangian relaxation, and simulated annealing.
The last five years have seen the emergence of promising techniques where
(graph) neural networks have been capable to learn new combinatorial
algorithms. The main question is whether deep learning can learn better
heuristics from data, i.e. replacing human-engineered heuristics? This is
appealing because developing algorithms to tackle efficiently NP-hard problems
may require years of research, and many industry problems are combinatorial by
nature. In this work, we propose to adapt the recent successful Transformer
architecture originally developed for natural language processing to the
combinatorial TSP. Training is done by reinforcement learning, hence without
TSP training solutions, and decoding uses beam search. We report improved
performances over recent learned heuristics with an optimal gap of 0.004% for
TSP50 and 0.39% for TSP100.
