Combining Reinforcement Learning with Lin-Kernighan-Helsgaun Algorithm for the Traveling Salesman Problem

TL;DR

This paper introduces VSR-LKH, a novel approach that integrates reinforcement learning techniques with the Lin-Kernighan-Helsgaun algorithm to improve solutions for the NP-hard Traveling Salesman Problem, demonstrating superior performance on large benchmarks.

Contribution

The paper presents a new hybrid method combining reinforcement learning with LKH, allowing adaptive decision-making during TSP search processes, which enhances solution quality and flexibility.

Findings

Outperforms traditional LKH on 111 TSPLIB benchmarks

Successfully scales to problems with up to 85,900 cities

Demonstrates significant improvement in solution quality

Abstract

We address the Traveling Salesman Problem (TSP), a famous NP-hard combinatorial optimization problem. And we propose a variable strategy reinforced approach, denoted as VSR-LKH, which combines three reinforcement learning methods (Q-learning, Sarsa and Monte Carlo) with the well-known TSP algorithm, called Lin-Kernighan-Helsgaun (LKH). VSR-LKH replaces the inflexible traversal operation in LKH, and lets the program learn to make choice at each search step by reinforcement learning. Experimental results on 111 TSP benchmarks from the TSPLIB with up to 85,900 cities demonstrate the excellent performance of the proposed method.