Mathematical Programming Computation

, Volume 1, Issue 2, pp 119–163

General k-opt submoves for the Lin–Kernighan TSP heuristic

Full Length Paper

DOI: 10.1007/s12532-009-0004-6

Cite this article as:
Helsgaun, K. Math. Prog. Comp. (2009) 1: 119. doi:10.1007/s12532-009-0004-6


Local search with k-exchange neighborhoods, k-opt, is the most widely used heuristic method for the traveling salesman problem (TSP). This paper presents an effective implementation of k-opt in LKH-2, a variant of the Lin–Kernighan TSP heuristic. The effectiveness of the implementation is demonstrated with experiments on Euclidean instances ranging from 10,000 to 10,000,000 cities. The runtime of the method increases almost linearly with the problem size. LKH-2 is free of charge for academic and non-commercial use and can be downloaded in source code.


Traveling salesman problem TSP Lin–Kernighan k-opt 

Mathematics Subject Classification (2000)

90C27 90C35 90C59 

Copyright information

© Springer and Mathematical Programming Society 2009

Authors and Affiliations

  1. 1.Department of Communication, Business and Information TechnologiesRoskilde UniversityRoskildeDenmark

Personalised recommendations