NeuroLKH: Combining Deep Learning Model with Lin-Kernighan-Helsgaun Heuristic for Solving the Traveling Salesman Problem

TL;DR

NeuroLKH is a hybrid algorithm that integrates deep learning with the Lin-Kernighan-Helsgaun heuristic, significantly improving TSP solutions and generalizing across various routing problems and larger problem sizes.

Contribution

It introduces a novel combination of deep learning and traditional heuristics, enhancing TSP solving efficiency and adaptability to related routing problems.

Findings

NeuroLKH outperforms traditional LKH in TSP solutions.

The model generalizes well to larger problem instances.

Applicable to multiple routing problems beyond TSP.

Abstract

We present NeuroLKH, a novel algorithm that combines deep learning with the strong traditional heuristic Lin-Kernighan-Helsgaun (LKH) for solving Traveling Salesman Problem. Specifically, we train a Sparse Graph Network (SGN) with supervised learning for edge scores and unsupervised learning for node penalties, both of which are critical for improving the performance of LKH. Based on the output of SGN, NeuroLKH creates the edge candidate set and transforms edge distances to guide the searching process of LKH. Extensive experiments firmly demonstrate that, by training one model on a wide range of problem sizes, NeuroLKH significantly outperforms LKH and generalizes well to much larger sizes. Also, we show that NeuroLKH can be applied to other routing problems such as Capacitated Vehicle Routing Problem (CVRP), Pickup and Delivery Problem (PDP), and CVRP with Time Windows (CVRPTW).