1. Introduction :
Among the solutions to the Traveling Salesman Problem (TSP), the LKH (Lin-Kernighan-Helsgaun) solver has attracted much attention due to its excellent performance. As a heuristic method, LKH combines the strategy of k-opt movement and successfully provides an efficient solution to the TSP problem. This article will introduce you to the basic principles of LKH in detail and how to use it to solve actual TSP problems.
2. Introduction to Traveling Salesman Problem (TSP) :
The traveling salesman problem, also known as the TSP problem, is a classic problem in combinatorial optimization. Simply put, it is described like this: given a set of cities and the distance between each pair of cities, find the shortest possible route that allows the traveler to visit each city once and return to the departure city.
As a simple example, assume there are 4 cities and the distances between the cities are as follows:
A-B: 10
A-C: 15
A-D: 20
B-C: 35
B-D: 25
C-D: 30
The goal of the TSP problem is to find a path that starts from one city, passes through all cities once, and returns to the starting city in the shortest total distance.
3. Origin of LKH solver :
The LKH solver is an improved implementation based on the Lin-Kernighan heuristic. It was further optimized by Keld Helsgaun, which is where the "H" in its name comes from. Lin and Kernighan first proposed the k-opt technique, which is a heuristic method for efficient search in the TSP solution space. Helsgaun made some improvements to the original Lin-Kernighan algorithm to make it perform even better.