Construction Heuristics and Domination Analysis for the Asymmetric TSP

  • Fred Glover
  • Gregory Gutin
  • Anders Yeo
  • Alexey Zverovich
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1668)


Non-Euclidean TSP construction heuristics, and especially asymmetric TSP construction heuristics, have been neglected in the literature by comparison with the extensive efforts devoted to studying Euclidean TSP construction heuristics. Motivation for remedying this gap in the study of construction approaches is increased by the fact that such methods are a great deal faster than other TSP heuristics, which can be important for real time problems requiring continuously updated response. The purpose of this paper is to describe two new construction heuristics for the asymmetric TSP and a third heuristic based on combining the other two. Extensive computational experiments are performed for several different families of TSP instances, disclosing that our combined heuristic clearly outperforms well-known TSP construction methods and proves significantly more robust in obtaining high quality solutions over a wide range of problems. We also provide a short overview of recent results in domination analysis of TSP construction heuristics.


Travel Salesman Problem Travel Salesman Problem Domination Number Combine Algorithm Construction Heuristic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    E. Balas and N. Simonetti, Linear time dynamic programming algorithms for some new classes of restricted TSP’s. Proc. IPCO V, LNCS 1084, Springer Verlag, 1996, 316–329.Google Scholar
  2. 2.
    J. Carlier and P. Villon, A new heuristic for the traveling salesman problem. RAIRO 24, 245–253 (1990).zbMATHMathSciNetGoogle Scholar
  3. 3.
    W.J. Cook, W.H. Cunninghan, W.R. Pulleyblank and A. Schrijver, Combinatorial Optimization, Wiley, New York, 1998.zbMATHGoogle Scholar
  4. 4.
    V. Deineko and G.J. Woeginger, A study of exponential neighbourhoods for the travelling salesman problem and for the quadratic assignment problem. TR Woe-05, TU of Graz, Graz, Austria, 1997.Google Scholar
  5. 5.
    F. Glover and A.P. Punnen, The travelling salesman problem: new solvable cases and linkages with the development of approximation algorithms, J. Oper. Res. Soc., 48 (1997) 502–510.zbMATHCrossRefGoogle Scholar
  6. 6.
    G. Gutin, Exponential neighbourhood local search for the traveling salesman problem. Computers & Operations Research 26 (1999) 313–320.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    G. Gutin and A. Yeo, Small diameter neighbourhood graphs for the traveling salesman problem: at most four moves from tour to tour. Computers & Operations Research 26 (1999) 321–327.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    G. Gutin and A. Yeo, TSP heuristics with large domination number. Manuscript, 1998.Google Scholar
  9. 9.
    G. Gutin and A. Yeo, Polynomial approximation algorithms for the TSP and the QAP with factorial domination number (submitted).Google Scholar
  10. 10.
    G. Gutin and A. Yeo, TSP tour domination and hamiltonian cycle decomposition of regular digraphs (submitted).Google Scholar
  11. 11.
    R. Häggkvist, Series of lectures on Hamilton decomposition, Seminar Orsey, France, 1986 and Hindsgavl’s Seminar, Denmark, 1994.Google Scholar
  12. 12.
    D.S. Johnson, private communication, 1998.Google Scholar
  13. 13.
    D.S. Johnson and L.A. McGeoch, The traveling salesman problem: a case study in local optimization. Local Search in Combinatorial Optimization, E.H.L. Aarts and J.K. Lenstra (eds.), Wiley, N.Y., 215–310 (1997).Google Scholar
  14. 14.
    R.M. Karp, A patching algorithm for the nonsymmetric Traveling Salesman Problem. SIAM J. Comput. 8 (1979) 561–73.zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    R.M. Karp and J.M. Steele, Probabilistic analysis of heuristics, in The Traveling Salesman Problem, E.L. Lawler, et al. (eds.), Wiley, N.Y., 1985, pp.181–205.Google Scholar
  16. 16.
    A.P. Punnen, The traveling salesman problem: new polynomial approximation algorithms and domination analysis. Manuscript, December (1996).Google Scholar
  17. 17.
    A.P. Punnan and S.N. Kabadi, Domination analysis of some heuristics for the asymmetric traveling salesman problem (submitted).Google Scholar
  18. 18.
    G. Reinelt, The traveling salesman problem: Computational Solutions for TSP Applications. Springer Lecture Notes in Computer Sci. 840, Springer-Verlag, Berlin (1994).Google Scholar
  19. 19.
    A. Yeo, Large exponential neighbourhoods for the TSP, preprint, Dept of Maths and CS, Odense University, Odense, Denmark, 1997.Google Scholar
  20. 20.
    R. Jonker and A. Volgenant, A shortest augmenting path algorithm for dense and sparse linear assignment problems, Computing 38 (1987) 325–340.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Fred Glover
    • 1
  • Gregory Gutin
    • 2
  • Anders Yeo
    • 3
  • Alexey Zverovich
    • 2
  1. 1.School of BusinessUniversity of ColoradoBoulderUSA
  2. 2.Department of Mathematics and StatisticsBrunel UniversityMiddlesexUK
  3. 3.Department of Mathematics and StatisticsUniversity of VictoriaVictoria B.C.Canada

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