Neural Combinatorial Optimization with Reinforcement Learning

TLDR

The authors propose a neural network–reinforcement learning framework for solving combinatorial optimization problems. They train a recurrent network on the traveling salesman problem, using negative tour length as a reward and policy‑gradient optimization, and compare training on a graph set versus individual test graphs. The method attains near‑optimal solutions on 2D Euclidean TSP instances up to 100 nodes and finds optimal solutions for knapsack instances with up to 200 items.

Abstract

This paper presents a framework to tackle combinatorial optimization problems using neural networks and reinforcement learning. We focus on the traveling salesman problem (TSP) and train a recurrent network that, given a set of city coordinates, predicts a distribution over different city permutations. Using negative tour length as the reward signal, we optimize the parameters of the recurrent network using a policy gradient method. We compare learning the network parameters on a set of training graphs against learning them on individual test graphs. Despite the computational expense, without much engineering and heuristic designing, Neural Combinatorial Optimization achieves close to optimal results on 2D Euclidean graphs with up to 100 nodes. Applied to the KnapSack, another NP-hard problem, the same method obtains optimal solutions for instances with up to 200 items.