Attention, Learn to Solve Routing Problems!

Wouter Kool, Herke van Hoof, Max Welling

Abstract: 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.

Keywords: learning, routing problems, heuristics, attention, reinforce, travelling salesman problem, vehicle routing problem, orienteering problem, prize collecting travelling salesman problem

TL;DR: Attention based model trained with REINFORCE with greedy rollout baseline to learn heuristics with competitive results on TSP and other routing problems

Code: [ wouterkool/attention-tsp](https://github.com/wouterkool/attention-tsp) + [ 13 community implementations](https://paperswithcode.com/paper/?openreview=ByxBFsRqYm)