Mathematical Programming Computation

, Volume 7, Issue 3, pp 269–287 | Cite as

Solving the equality generalized traveling salesman problem using the Lin–Kernighan–Helsgaun Algorithm

  • Keld HelsgaunEmail author
Full Length Paper


The equality generalized traveling salesman problem (E-GTSP) is an extension of the traveling salesman problem (TSP) where the set of cities is partitioned into clusters, and the salesman has to visit every cluster exactly once. It is well known that any instance of E-GTSP can be transformed into a standard asymmetric instance of the TSP, and therefore solved with a TSP solver. This paper evaluates the performance of the state-of-the art TSP solver Lin–Kernighan–Helsgaun (LKH) on transformed E-GTSP instances. Although LKH is used without any modifications, the computational evaluation shows that all instances in a well-known library of benchmark instances, GTSPLIB, could be solved to optimality in a reasonable time. In addition, it was possible to solve a series of new very-large-scale instances with up to 17,180 clusters and 85,900 vertices. Optima for these instances are not known but it is conjectured that LKH has been able to find solutions of a very high quality. The program’s performance has also been evaluated on a large number of instances generated by transforming arc routing problem instances into E-GTSP instances. The program is free of charge for academic and non-commercial use and can be downloaded in source code.


Equality generalized traveling salesman problem E-GTSP Traveling salesman problem TSP Lin–Kernighan  Heuristics Arc routing problems 

Mathematics Subject Classification

90C27 90C35 90C59 


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Copyright information

© Springer-Verlag Berlin Heidelberg and The Mathematical Programming Society 2015

Authors and Affiliations

  1. 1.Computer ScienceRoskilde UniversityRoskildeDenmark

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