Attention, Learn to Solve Routing Problems!

TL;DR

This paper advances learning heuristics for routing problems by introducing an attention-based model trained with REINFORCE, achieving near-optimal solutions for TSP, VRP, OP, and PCTSP, outperforming existing methods.

Contribution

It proposes a novel attention-based model for routing problems and demonstrates an efficient training method using REINFORCE with a simple baseline, improving heuristic quality.

Findings

Achieves near-optimal solutions for TSP up to 100 nodes.

Outperforms recent learned heuristics on VRP, OP, and PCTSP.

Uses a more efficient training approach with REINFORCE and a greedy baseline.

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.