Skip to main content
SpringerLink
Log in

Local optimization and the Traveling Salesman Problem

  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 443))

Included in the following conference series:

Abstract

The Traveling Salesman Problem (TSP) is often cited as the prototypical “hard” combinatorial optimization problem. As such, it would seem to be an ideal candidate for nonstandard algorithmic approaches, such as simulated annealing, and, more recently, genetic algorithms. Both of these approaches can be viewed as variants on the traditional technique called local optimization. This paper surveys the state of the art with respect to the TSP, with emphasis on the performance of traditional local optimization algorithms and their new competitors, and on what insights complexity theory does, or does not, provide.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. L. Bentley, “Experiments on traveling salesman heuristics,” in Proc. 1st Ann. ACM-SIAM Symp. on Discrete Algorithms, SIAM, Philadelphia, PA, 1990, 91–99.

    Google Scholar 

  2. J. L. Bentley, “Fast algorithms for geometric traveling salesman problems,” in preparation.

    Google Scholar 

  3. J. L. Bentley, D. S. Johnson, L. A. McGeoch, and E. E. Rothberg, “Near-optimal solutions to very large traveling salesman problems,” in preparation.

    Google Scholar 

  4. R. G. Bland and D. F. Shallcross, “Large traveling salesman problems arising from experiments in X-ray crystallography: A preliminary report on computation,” Operations Res. Lett.8 (1989), 125–128.

    Google Scholar 

  5. R. M. Brady, “Optimization strategies gleaned from biological evolution,” Nature317 (October 31, 1985), 804–806.

    Google Scholar 

  6. N. E. Collins, R. W. Eglese, and B. L. Golden, “Simulated Annealing: An Annotated Bibliography,” Amer. J. Math. & Mgmt. Sci.8 (1988), 205–307.

    Google Scholar 

  7. V. Cerny, “A Thermodynamical Approach to the Travelling Salesman Problem: An Efficient Simulation Algorithm,” J. Optimization Theory and Appl.45 (1985), 41–51.

    Google Scholar 

  8. N. Christofides, “Worst-case analysis of a new heuristic for the travelling salesman problem,” Report No. 388, GSIA, Carnegie-Mellon University, Pittsburgh, PA, 1976.

    Google Scholar 

  9. G. Dueck, “Threshold Accepting: A general purpose optimization algorithm appearing superior to simulated annealing,” TR88.10.011, Heidelberg Scientific Center, IBM Germany, 1988.

    Google Scholar 

  10. R. Durbin and D. Willshaw, “An analogue approach to the travelling salesman problem using an elastic net method,” Nature326 (April 16, 1987), 689–691.

    Google Scholar 

  11. M. R. Garey, and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman, San Francisco, 1979.

    Google Scholar 

  12. F. Glover, “Tabu search — Part I,” ORSA J. Comput.1 (1989), 190–206.

    Google Scholar 

  13. M. Grötschel and O. Holland, “Solution of large-scale symmetric travelling salesman problems,” Report No. 73, Institut für Mathematik, Universität Augsburg, 1988.

    Google Scholar 

  14. M. Held and R. M. Karp, “The traveling-salesman problem and minimum spanning trees,” Operations Res.18 (1970), 1138–1162.

    Google Scholar 

  15. M. Held and R. M. Karp, “The traveling-salesman problem and minimum spanning trees: Part II,” Math. Programming1 (1971), 6–25.

    Google Scholar 

  16. J. J. Hopfield and D. W. Tank, “'Neural’ computation of decisions in optimization problems,” Biol. Cybern52 (1985), 141–152.

    Google Scholar 

  17. D. S. Johnson, “More approaches to the travelling salesman guide,” Nature330 (December 10, 1987), 525.

    Google Scholar 

  18. D. S. Johnson, C. R. Aragon, L. A. McGeoch, and C. Schevon, “Optimization by Simulated Annealing: An Experimental Evaluation, Part I (Graph Partitioning),” Operations Res.37 (1989), 865–892.

    Google Scholar 

  19. D. S. Johnson, C. R. Aragon, L. A. McGeoch, and C. Schevon, “Optimization by Simulated Annealing: An Experimental Evaluation, Part III (The Traveling Salesman Problem),” in preparation.

    Google Scholar 

  20. D. S. Johnson, L. A. McGeoch, and G. Ostheimer, “Data structures for traveling salesmen,” in preparation.

    Google Scholar 

  21. D. S. Johnson, C. H. Papadimitriou, and M. Yannakakis, “How easy is local search?,” J. Comput. System Sci.37 (1988), 79–100.

    Google Scholar 

  22. D. S. Johnson and E. E. Rothberg, “Asymptotic experimental analysis of the Held-Karp lower bound for the traveling salesman problem,” in preparation.

    Google Scholar 

  23. R. M. Karp, “Probabilistic analysis of partitioning algorithms for the traveling-salesman in the plane,” Math. Oper. Res.2 (1977), 209–224.

    Google Scholar 

  24. W. Kern, “A probabilistic analysis of the switching algorithm for the Euclidean TSP,” Math. Programming44 (1989), 213–219.

    Google Scholar 

  25. S. Kirkpatrick, “Optimization by simulated annealing: Quantitative studies,” J. Stat. Physics34 (1984), 976–986.

    Google Scholar 

  26. S. Kirkpatrick, C. D. Gelatt, Jr, and M. P. Vecchi, “Optimization by Simulated Annealing,” Science220 (13 May 1983), 671–680.

    Google Scholar 

  27. S. Kirkpatrick and G. Toulouse, “Configuration space and the travelling salesman problem,” J. Physique46 (1985), 1277–1292.

    Google Scholar 

  28. B. Korte, “Applications of combinatorial optimization,” talk at the 13th International Mathematical Programming Symposium, Tokyo, 1988.

    Google Scholar 

  29. W. Krauth and M. Mézard, “The cavity method and the travelling-salesman problem,” Europhys. Lett.8 (1989), 213–218.

    Google Scholar 

  30. J. Lam and J.-M. Delosme, “An efficient simulated annealing schedule: implementation and evaluation,” manuscript (1988).

    Google Scholar 

  31. E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan, and D. B. Shmoys, The Traveling Salesman Problem, John Wiley & Sons, Chichester, 1985.

    Google Scholar 

  32. S. Lin, “Computer solutions of the traveling salesman problem,” Bell Syst. Tech. J.44 (1965), 2245–2269.

    Google Scholar 

  33. S. Lin and B. W. Kernighan, “An Effective Heuristic Algorithm for the Traveling-Salesman Problem,” Operations Res.21 (1973), 498–516.

    Google Scholar 

  34. J. D. Litke, “An improved solution to the traveling salesman problem with thousands of nodes,” Comm. ACM27 (1984), 1227–1236.

    Google Scholar 

  35. G. Lueker, manuscript, Princeton University, 1976.

    Google Scholar 

  36. O. Martin, S. W. Otto, and E. W. Felten, “Large-step Markov chains for the traveling salesman problem,” manuscript (1989).

    Google Scholar 

  37. D. Mitra, F. Romeo, and A. Sangiovanni-Vincentelli, “Convergence and finite-time behavior of simulated annealing,” J. Advan. Appl. Prob.18 (1986), 747–771.

    Google Scholar 

  38. H. Mühlenbein, “The dynamics of evolution and learning — Towards genetic neural networks,” manuscript (1989).

    Google Scholar 

  39. H. Mühlenbein, M. Gorges-Schleuter, and O. Krämer, “Evolution algorithms in combinatorial optimization,” Parallel Comput.7 (1988), 65–85.

    Google Scholar 

  40. M. Padberg and G. Rinaldi, “Optimization of a 532-city symmetric traveling salesman problem by branch and cut,” Operations Res. Lett.6 (1987), 1–7.

    Google Scholar 

  41. M. Padberg and G. Rinaldi, “A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems,” Report R. 247, Istituto di Analisi dei Sistimi ed Informatica del CNR, Rome, 1988.

    Google Scholar 

  42. C. H. Papadimitriou, “The complexity of the Lin-Kernighan heuristic for the traveling salesman problem,” manuscript (1990).

    Google Scholar 

  43. C. H. Papadimitriou and K. Steiglitz, “On the complexity of local search for the traveling salesman problem,” SIAM J. Comput.6 (1977), 76–83.

    Google Scholar 

  44. C. H. Papadimitriou and K. Steiglitz, “Some examples of difficult traveling salesman problems,” Operations Res.26 (1978), 434–443.

    Google Scholar 

  45. L. K. Platzman and J. J. Bartholdi, III, “Spacefilling curves and the planar travelling salesman problem,” J. Assoc. Comput. Mach.36 (1989), 719–737.

    Google Scholar 

  46. D. J. Rosenkrantz, R. E. Stearns, and P. M. Lewis, II, “An analysis of several heuristics for the traveling salesman problem,” SIAM J. Comput.6 (1977), 563–581.

    Google Scholar 

  47. S. Sahni and T. Gonzalez, “P-complete approximation problems,” J. Assoc. Comput. Mach.23 (1976), 555–565.

    Google Scholar 

  48. G. H. Sasaki and B. Hajek, “The time complexity of maximum matching by simulated annealing,” J. Assoc. Comput. Mach.35 (1988), 387–403.

    Google Scholar 

  49. H. S. Stone, private communication (1989).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. AT&T Bell Laboratories, Room 2D-150, 07974, Murray Hill, NJ, USA

    David S. Johnson

Authors
  1. David S. Johnson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Michael S. Paterson

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Johnson, D.S. (1990). Local optimization and the Traveling Salesman Problem. In: Paterson, M.S. (eds) Automata, Languages and Programming. ICALP 1990. Lecture Notes in Computer Science, vol 443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032050

Download citation

  • DOI: https://doi.org/10.1007/BFb0032050

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52826-5

  • Online ISBN: 978-3-540-47159-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation