Lin-Kernighan heuristic adaptations for the generalized traveling salesman problem
by Daniel Karapetyan, Gregory Gutin
Abstract:
The Lin-Kernighan heuristic is known to be one of the most successful heuristics for the Traveling Salesman Problem (TSP). It has also proven its efficiency in application to some other problems. In this paper, we discuss possible adaptations of TSP heuristics for the generalized traveling salesman problem (GTSP) and focus on the case of the Lin-Kernighan algorithm. At first, we provide an easy-to-understand description of the original Lin-Kernighan heuristic. Then we propose several adaptations, both trivial and complicated. Finally, we conduct a fair competition between all the variations of the Lin-Kernighan adaptation and some other GTSP heuristics. It appears that our adaptation of the Lin-Kernighan algorithm for the GTSP reproduces the success of the original heuristic. Different variations of our adaptation outperform all other heuristics in a wide range of trade-offs between solution quality and running time, making Lin-Kernighan the state-of-the-art GTSP local search. ?? 2010 Published by Elsevier B.V. All rights reserved.
Reference:
Lin-Kernighan heuristic adaptations for the generalized traveling salesman problem (Daniel Karapetyan, Gregory Gutin), European Journal of Operational Research 208, 221–232, 2011.
Bibtex Entry:
@Article{Karapetyan2011,
  Title                    = {{L}in-{K}ernighan heuristic adaptations for the generalized traveling salesman problem},
  Author                   = {Karapetyan, Daniel and Gutin, Gregory},
  Journal                  = {European Journal of Operational Research},
  Year                     = {2011},
  Pages                    = {221--232},
  Volume                   = {208},
  Abstract                 = {The Lin-Kernighan heuristic is known to be one of the most successful heuristics for the Traveling Salesman Problem (TSP). It has also proven its efficiency in application to some other problems. In this paper, we discuss possible adaptations of TSP heuristics for the generalized traveling salesman problem (GTSP) and focus on the case of the Lin-Kernighan algorithm. At first, we provide an easy-to-understand description of the original Lin-Kernighan heuristic. Then we propose several adaptations, both trivial and complicated. Finally, we conduct a fair competition between all the variations of the Lin-Kernighan adaptation and some other GTSP heuristics. It appears that our adaptation of the Lin-Kernighan algorithm for the GTSP reproduces the success of the original heuristic. Different variations of our adaptation outperform all other heuristics in a wide range of trade-offs between solution quality and running time, making Lin-Kernighan the state-of-the-art GTSP local search. ?? 2010 Published by Elsevier B.V. All rights reserved.},
  Archiveprefix            = {arXiv},
  Arxivid                  = {1003.5330},
  DOI                      = {10.1016/j.ejor.2010.08.011},
  Eprint                   = {1003.5330},
  ISBN                     = {0377-2217},
  ISSN                     = {03772217},
  Keywords                 = {Combinatorial optimization,Generalized traveling salesman problem,Heuristics,Lin-Kernighan}
}