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The Asymmetric Traveling Salesman Problem: Algorithms, Instance Generators, and Tests

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Abstract

The purpose of this paper is to provide a preliminary report on the first broad-based experimental comparison of modern heuristics for the asymmetric traveling salesmen problem (ATSP). There are currently three general classes of such heuristics: classical tour construction heuristics such as Nearest Neighbor and the Greedy algorithm, local search algorithms based on re-arranging segments of the tour, as exemplified by the Kanellakis-Papadimitriou algorithm [KP80], and algorithms based on patching together the cycles in a minimum cycle cover, the best of which are variants on an algorithm proposed by Zhang [Zha93]. We test implementations of the main contenders from each class on a variety of instance types, introducing a variety of new random instance generators modeled on real-world applications of the ATSP. Among the many tentative conclusions we reach is that no single algorithm is dominant over all instance classes, although for each class the best tours are found either by Zhang’s algorithm or an iterated variant on Kanellakis-Papadimitriou.

Supported in part by NSF grants IRI-9619554 and IIS-0196057 and DARPA Cooperative Agreement F30602-00-2-0531.

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References

  1. D. Applegate, R. Bixby, V. Chvatal, and W. Cook. On the solution of traveling salesman problems. Doc. Mathemat-ica J. der Deutschen Mathematiker-Vereinigung, ICM III:645–656, 1998. The Concorde code is available from the website http://www.keck.caam.rice.edu/concorde.html

    MathSciNet  Google Scholar 

  2. D. Applegate, W. Cook, and A. Rohe. Chained Lin-Kernighan for large traveling salesman problems. To appear. A postscript draft is currently available from the website http://www.caam.rice.edu/~bico/

  3. G. Carpaneto, M. Dell’Amico, and P. Toth. Exact solution of large-scale, asymmetric traveling salesman problems. ACM Trans. Mathematical Software, 21(4):394–409, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  4. G. Carpaneto and P. Toth. Some new branching and bounding criteria for the asymmetric traveling salesman problem. Management Science, 26:736–743, 1980.

    MATH  MathSciNet  Google Scholar 

  5. A. M. Frieze, G. Galbiati, and F. Maffioli. On the worst-case performance of some algorithms for the asymmetric traveling salesman problem. Networks, 12:23–39, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  6. M. Fischetti and P. Toth. An additive bounding procedure for the asymmetric travelling salesman problem. Math. Programming A, 53:173–197, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  7. M. Fischetti and P. Toth. A polyhedral approach to the asymmetric traveling salesman problem. Management Sci., 43:1520–1536, 1997.

    MATH  Google Scholar 

  8. M. Fischetti, P. Toth, and D. Vigo. A branch and bound algorithm for the capacitated vehicle routing problem on directed graphs. Operations Res., 42:846–859, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  9. F. Glover, G. Gutin, A. Yeo, and A. Zverovich. Construction heuristics for the asymmetric TSP. European J. Operations Research. to appear.

    Google Scholar 

  10. R. Giancarlo. Personal communication, September 2000.

    Google Scholar 

  11. F. Glover. Finding a best traveling salesman 4-opt move in the same time as a best 2-opt move. J. Heuristics, 2(2):169–179, 1996.

    Article  MATH  Google Scholar 

  12. G. Gutin and A. Zverovich. Evaluation of the contract-or-patch heuristic for the asymmetric TSP. Manuscript, 2000.

    Google Scholar 

  13. M. Held and R. M. Karp. The traveling salesman problem and minimum spanning trees. Operations Res., 18:1138–1162, 1970.

    MATH  MathSciNet  Google Scholar 

  14. M. Held and R. M. Karp. The traveling salesman problem and minimum spanning trees: Part II. Math. Prog., 1:6–25, 1971.

    Article  MATH  MathSciNet  Google Scholar 

  15. D. S. Johnson, J. L. Bentley, L. A. McGeoch, and E. E. Rothberg. Near-Optimal Solutions to Very Large Traveling Salesman Problems. Monograph, to appear.

    Google Scholar 

  16. D. S. Johnson and L. A. McGeoch. The traveling salesman problem: A case study in local optimization. In E. H. L. Aarts and J. K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 215–310. John Wiley and Sons, Ltd., Chichester, 1997.

    Google Scholar 

  17. D. S. Johnson, L. A. McGeoch, and E. E. Rothberg. Asymptotic experimental analysis for the Held-Karp traveling salesman bound. In Proc. 7th Ann. ACM-SIAM Symp. on Discrete Algorithms, pages 341–350. Society for Industrial and Applied Mathematics, Philadelphia, 1996.

    Google Scholar 

  18. R. M. Karp. A patching algorithm for the nonsymmetric traveling-salesman problem. SI AM J. Comput., 8(4):561–573, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  19. D. E. Knuth. The Art of Computer Programming, Volume 2: Seminumer-ical Algorithms (2nd Edition). Addison-Wesley, Reading, MA, 1981. See pages 171–172.

    Google Scholar 

  20. P. C. Kanellakis and C. H. Papadimitriou. Local search for the asymmetric traveling salesman problem. Oper. Res., 28(5):1066–1099, 1980.

    MathSciNet  Google Scholar 

  21. R. M. Karp and J. M. Steele. Probabilistic analysis of heuristics. In E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan, and D. B Shmoys, editors, The Traveling Salesman Problem, pages 181–205. John Wiley and Sons, Chichester, 1985.

    Google Scholar 

  22. S. Lin and B. W. Kernighan. An effective heuristic algorithm for the traveling salesman problem. Operations Res., 21:498–516, 1973.

    MATH  MathSciNet  Google Scholar 

  23. O. Martin, S. W. Otto, and E. W. Felten. Large-step Markov chains for the TSP incorporating local search heuristics. Operations Res. Lett., 11:219–224, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  24. D. L. Miller and J. F. Pekny. Exact solution of large asymmetric traveling salesman problems. Science, 251:754–761, 15 September 1996.

    Google Scholar 

  25. G. Reinelt. TSPLIB-A traveling salesman problem library. ORSA J. Comput., 3(4):376–384, 1991. The TSPLIB website is http://www.iwr.uni-heidelberg.de/iwr/comopt/software/TSPLIB95/.

    MATH  Google Scholar 

  26. G. Reinelt. The Traveling Salesman: Computational Solutions of TSP Applications. LNCS 840. Springer-Verlag, Berlin, 1994.

    Google Scholar 

  27. B. W. Repetto. Upper and Lower Bounding Procedures for the Asymmetric Traveling Salesman Problem. PhD thesis, Graduate School of Industrial Administration, Carnegie-Mellon University, 1994.

    Google Scholar 

  28. N. Simonetti and E. Balas. Implementation of a linear time algorithm for certain generalized traveling salesman problems. In Integer Programming and Combinatorial Optimization: Proc. 5th Int. IPCO Conference, LNCS 840, pages 316–329, Berlin, 1996. Springer-Verlag.

    Google Scholar 

  29. D. Williamson. Analysis of the Held-Karp lower bound for the asymmetric TSP. Operations Res. Lett., 12:83–88, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  30. Young, D. S. Johnson, D. R. Karger, and M. D. Smith. Near-optimal intraprocedural branch alignment. In Proceedings 1997 Symp. on Programming Languages, Design, and Implementation, pages 183–193. ACM, 1997.

    Google Scholar 

  31. W. Zhang. Truncated branch-and-bound: A case study on the asymmetric TSP. In Proc. of AAAI 1993 Spring Symposium on AI and NP-Hard Problems, pages 160–166, Stanford, CA, 1993.

    Google Scholar 

  32. W. Zhang. Depth-first branch-and-bound versus local search: A case study. In Proc. 17th National Conf. on Artificial Intelligence (AAAI-2000), pages 930–935, Austin, TX, 2000.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Boston Architectural Center Library, 320 Newbury Street, Boston, MA, 02115

    Jill Cirasella

  2. AT&T Labs - Research, Room C239, Florham Park, NJ, 07932-0971, USA

    David S. Johnson

  3. Department of Mathematics and Computer Science, Amherst College, Amherst, MA, 01002

    Lyle A. McGeoch

  4. Department of Computer Science, Washington University, Box 1045, One Brookings Drive, St. Louis, MO, 63130

    Weixiong Zhang

Authors
  1. Jill Cirasella
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  2. David S. Johnson
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  3. Lyle A. McGeoch
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  4. Weixiong Zhang
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Editor information

Editors and Affiliations

  1. AT&T Labs Research, 180 Park Ave., P.O. Box 971, Florham Park, NJ, 07932-0000, USA

    Adam L. Buchsbaum

  2. Department of Computer Science, The University of North Carolina at Chapel Hill, CB 3175, Sitterson Hall, Chapel Hill, NC, 27599-3175, USA

    Jack Snoeyink

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© 2001 Springer-Verlag Berlin Heidelberg

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Cirasella, J., Johnson, D.S., McGeoch, L.A., Zhang, W. (2001). The Asymmetric Traveling Salesman Problem: Algorithms, Instance Generators, and Tests. In: Buchsbaum, A.L., Snoeyink, J. (eds) Algorithm Engineering and Experimentation. ALENEX 2001. Lecture Notes in Computer Science, vol 2153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44808-X_3

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  • DOI: https://doi.org/10.1007/3-540-44808-X_3

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  • Print ISBN: 978-3-540-42560-1

  • Online ISBN: 978-3-540-44808-2

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