  The recently presented idea to learn heuristics for combinatorial
optimization problems is promising as it can save costly development. However,
to push this idea towards practical implementation, we need better models and
better ways of training. We contribute in both directions: we propose a model
based on attention layers with benefits over the Pointer Network and we show
how to train this model using REINFORCE with a simple baseline based on a
deterministic greedy rollout, which we find is more efficient than using a
value function. We significantly improve over recent learned heuristics for the
Travelling Salesman Problem (TSP), getting close to optimal results for
problems up to 100 nodes. With the same hyperparameters, we learn strong
heuristics for two variants of the Vehicle Routing Problem (VRP), the
Orienteering Problem (OP) and (a stochastic variant of) the Prize Collecting
TSP (PCTSP), outperforming a wide range of baselines and getting results close
to highly optimized and specialized algorithms.
