Learning 2-opt Heuristics for the Traveling Salesman Problem via Deep Reinforcement Learning

TL;DR

This paper introduces a deep reinforcement learning approach to learn 2-opt local search heuristics for the Traveling Salesman Problem, improving solutions efficiently over initial guesses and surpassing previous deep learning methods.

Contribution

It presents a novel policy gradient method with a pointing attention mechanism to learn 2-opt heuristics, extending to more general k-opt moves.

Findings

Learned policies improve solutions over random initial solutions.

Approach approaches near-optimal solutions faster than prior deep learning methods.

Policy can be extended to more complex k-opt moves.

Abstract

Recent works using deep learning to solve the Traveling Salesman Problem (TSP) have focused on learning construction heuristics. Such approaches find TSP solutions of good quality but require additional procedures such as beam search and sampling to improve solutions and achieve state-of-the-art performance. However, few studies have focused on improvement heuristics, where a given solution is improved until reaching a near-optimal one. In this work, we propose to learn a local search heuristic based on 2-opt operators via deep reinforcement learning. We propose a policy gradient algorithm to learn a stochastic policy that selects 2-opt operations given a current solution. Moreover, we introduce a policy neural network that leverages a pointing attention mechanism, which unlike previous works, can be easily extended to more general k-opt moves. Our results show that the learned policies can improve even over random initial solutions and approach near-optimal solutions at a faster rate than previous state-of-the-art deep learning methods.