Skip to main content
Log in

Genetic algorithms for the traveling salesman problem

  • Genetic Algorithms
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

This paper is a survey of genetic algorithms for the traveling salesman problem. Genetic algorithms are randomized search techniques that simulate some of the processes observed in natural evolution. In this paper, a simple genetic algorithm is introduced, and various extensions are presented to solve the traveling salesman problem. Computational results are also reported for both random and classical problems taken from the operations research literature.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E.H.L. Aarts, J.H.M. Korst and P.J.M. van Laarhoven, A quantitative analysis of the simulated annealing algorithm: A case study for the traveling salesman problem, J. Statist. Phys. 50(1988)189–206.

    Article  Google Scholar 

  2. J.D. Bagley, The behavior of adaptive systems which employ genetic and correlation algorithms, Doctoral Dissertation, University of Michigan, Dissertation Abstracts International 28(12), 5106B (1967).

  3. J. Bentley, Fast algorithms for geometric salesman problems, ORSA J. Comp. 4(1992)387–411.

    Google Scholar 

  4. J.L. Blanton and R.L. Wainwright, Multiple vehicle routing with time and capacity constraints using genetic algorithms, in:Proc. 5th Int. Conf. on Genetic Algorithms (ICGA '93), University of Illinois at Urbana-Champaign, Champaign, IL (1993) pp. 452–459.

    Google Scholar 

  5. L. Bodin, B.L. Golden, A. Assad and M. Ball, Routing and scheduling of vehicles and crews: The state of the art, Comp. Oper. Res. 10(1983)63–211.

    Article  Google Scholar 

  6. R.M. Brady, Optimization strategies gleaned from biological evolution, Nature 317(1985)804–806.

    Article  Google Scholar 

  7. H. Braun, On solving travelling salesman problems by genetic algorithms, in:Parallel Problem-Solving from Nature, ed. H.P. Schwefel and R. Manner, Lecture Notes in Computer Science 496 (Springer) pp. 129–133.

  8. V. Cerny, Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm, J. Optim. Theory Appl. 45(1985)41–55.

    Article  Google Scholar 

  9. L. Davis, Applying adaptive algorithms to epistactic domains, in:Proc. Int. Joint Conf. on Artificial Intelligence (IJCAI '85), Los Angeles, CA (1985) pp. 162–164.

  10. K.A. De Jong, An analysis of the behavior of a class of genetic adaptive systems, Doctoral Dissertation, University of Michigan, Dissertation Abstracts International 36(10), 5140B (1975).

  11. C.N. Fiechter, A parallel tabu search algorithm for large scale traveling salesman problems, Working paper 90/1, Department of Mathematics, Ecole Polytechnique Fédérale de Lausanne, Switzerland (1990).

    Google Scholar 

  12. L.J. Fogel, A.J. Owens and M.J. Walsh,Artificial Intelligence through Simulated Evolution (Wiley, 1966).

  13. B.R. Fox and M.B. McMahon, Genetic operators for sequencing problems, in:Foundations of Genetic Algorithms, ed. J.E. Rawlins (Morgan Kaufmann, 1991) pp. 284–300.

  14. P.S. Gabbert, D.E. Brown, C.L. Huntley, B.P. Markowitz and D.E. Sappington, A system for learning routes and schedules with genetic algorithms, in:Proc. 4th Int. Conf. on Genetic Algorithms (ICGA '91), University of California at San Diego, San Diego, CA (1991) pp. 430–436.

    Google Scholar 

  15. M. Gendreau, A. Hertz and G. Laporte, New insertion and post-optimization procedures for the traveling salesman problem, Oper. Res. 40(1992)1086–1094.

    Google Scholar 

  16. F. Glover, Tabu search, Part I, ORSA J. Comp. 1(1989)190–206.

    Google Scholar 

  17. F. Glover, Tabu Search, Part II, ORSA J. Comp. 2(1990)4–32.

    Google Scholar 

  18. D.E. Goldberg and R. Lingle, Alleles, loci and the traveling salesman problem, in:Proc. Ist Int. Conf. on Genetic Algorithms (ICGA '85), Carnegie-Mellon University, Pittsburg, PA (1985) pp. 154–159.

    Google Scholar 

  19. B.L. Golden and W.R. Stewart, Empirical analysis of heuristics, in:The Traveling Salesman Problem. A Guided Tour of Combinatorial Optimization, ed. E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys (Wiley, 1985).

  20. D.E. Goldberg,Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989).

  21. M. Gorges-Schleuter, ASPARAGOS: An asynchronous parallel genetic optimization strategy, in:Proc. 3rd Int. Conf. on Genetic Algorithms (ICGA '89), George Mason University, Fairfax, VA (1989) pp. 422–427.

    Google Scholar 

  22. J. Grefenstette, R. Gopal, B.J. Rosmaita and D.V. Gucht, Genetic algorithms for the traveling salesman problem, in:Proc. 1st. Int. Conf. on Genetic Algorithms (ICGA '85), Carnegie-Mellon University, Pittsburgh, PA (1985) pp. 160–168.

    Google Scholar 

  23. J. Grefenstette, Incorporating problem specific knowledge into genetic algorithms, in:Genetic Algorithms and Simulated Annealing, ed. L. Davis (Morgan Kaufmann, 1987) pp. 42–60.

  24. M. Grötschel and O. Holland, Solution of large-scale symmetric traveling salesman problems, Report 73, Institut für Mathematik, Universität Augsburg (1988).

  25. M. Held and R.M. Karp, The traveling salesman problem and minimum spanning trees, Oper. Res. 18(1970)1138–1162.

    Google Scholar 

  26. J.H. Holland,Adaptation in Natural and Artificial Systems (The University of Michigan Press, Ann Arbor, 1975); reprinted by MIT Press, 1992.

    Google Scholar 

  27. A. Homaifar, S. Guan and G. Liepins, A new approach to the traveling salesman problem by genetic algorithms, in:Proc. 5th Int. Conf. on Genetic Algorithms (ICGA '93), University of Illinois at Urbana-Champaign, Champaign, IL (1993) pp. 460–466.

    Google Scholar 

  28. J.J. Hopfield and D.W. Tank, Neural computation of decisions in optimization problems, Biol. Cybern. 52(1985)141–152.

    PubMed  Google Scholar 

  29. P. Jog, J.Y. Suh and D.V. Gucht, The effects of population size, heuristic crossover and local improvement on a genetic algorithm for the traveling salesman problem, in:Proc. 3rd Int. Conf. on Genetic Algorithms (ICGA '89), George Mason University, Fairfax, VA (1989) pp. 110–115.

    Google Scholar 

  30. D.S. Johnson, Local optimization and the traveling salesman problem, in:Automata, Languages and Programming, ed. G. Goos and J. Hartmanis, Lecture Notes in Computer Science 443 (Springer, 1990) pp. 446–461.

  31. R.L. Karg and G.L. Thompson, A heuristic approach to solving traveling salesman problems, Manag. Sci. 10(1964)225–248.

    Google Scholar 

  32. S. Kirkpatrick, C.D. Gelatt and M.P. Vecchi, Optimization by simulated annealing, Science 220(1983)671–680.

    Google Scholar 

  33. P.D. Krolak, W. Felts and G. Marble, A man-machine approach toward solving the traveling salesman problem, Commun. ACM 14(1971)327–334.

    Article  Google Scholar 

  34. G. Laporte, The traveling salesman problem: An overview of exact and approximate algorithms, Euro. J. Oper. Res. 59(1992)231–247.

    Article  Google Scholar 

  35. E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan and D.B. Shmoys,The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization (Wiley, 1985).

  36. G.E. Liepins, M.R. Hilliard, M. Palmer and M. Morrow, Greedy genetics, in:Proc. 2nd Int. Conf. on Genetic Algorithms (ICGA '87), Massachusetts Institute of Technology, Cambridge, MA (1987) pp. 90–99.

    Google Scholar 

  37. G.E. Liepins, M.R. Hilliard, J. Richardson and M. Palmer, Genetic algorithm applications to set covering and traveling salesman problems, in:Operations Research and Artificial Intelligence: The Integration of Problem Solving Strategies, ed. Brown and White (Kluwer Academic, 1990) pp. 29–57.

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

    Google Scholar 

  39. S. Lin and B. Kernighan, An effective heuristic algorithm for the traveling salesman problem, Oper. Res. 21(1973)498–516.

    Google Scholar 

  40. M. Malek, M. Guruswamy, M. Pandya and H. Owens, Serial and parallel simulated annealing and tabu search algorithms for the traveling salesman problem, Ann. Oper. Res. 21(1989)59–84.

    Article  Google Scholar 

  41. Z. Michalewicz and C.Z. Janikow, Handling constraints in genetic algorithms, in:Proc. 4th Int. Conf. on Genetic Algorithms (ICGA '91), University of California at San Diego, San Diego, CA (1991) pp. 151–157.

    Google Scholar 

  42. Z. Michalewicz, G.A. Vigaux and M. Hobbs, A nonstandard genetic algorithm for the nonlinear transportation problem, ORSA J. Comp. 3(1991)307–316.

    Google Scholar 

  43. H. Mulhenbein, M. Gorges-Schleuter and O. Kramer, New solutions to the mapping problem of parallel systems — the evolution approach, Parallel Comp. 4(1987)269–279.

    Article  Google Scholar 

  44. H. Mulhenbein, M. Gorges-Schleuter and O. Kramer, Evolution algorithms in combinatorial optimization, Parallel Comp. 7(1988)65–85.

    Article  Google Scholar 

  45. H. Mulhenbein, Evolution in time and space — the parallel genetic algorithm, in:Foundations of genetic algorithms, ed. G.J.E. Rawlins (Morgan Kaufmann, 1991) pp. 316–337.

  46. K.E. Nygard and C.H. Yang, Genetic algorithms for the traveling salesman problem with time windows, in:Computer Science and Operations research: New Developments in their Interfaces, ed. O. Balci, R. Sharda and S.A. Zenios (Pergamon, 1992) pp. 411–423.

  47. I.M. Oliver, D.J. Smith and J.R.C. Holland, A study of permutation crossover operators on the traveling salesman problem, in:Proc. 2nd Int. Conf. on Genetic Algorithms (ICGA '87), Massachusetts Institute of Technology, Cambridge, MA (1987) pp. 224–230.

    Google Scholar 

  48. I. Or, Traveling salesman-type combinatorial optimization problems and their relation to the logistics of regional blood banking, Ph.D. Dissertation, Northwestern University, Evanston, IL (1976).

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  50. M. Padberg and G. Rinaldi, A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems, Technical Report R-247, Instituto di Analisi dei Sistemi ed Informatica. Consiglio Nazionale delle Ricerche, Roma (1988).

    Google Scholar 

  51. M. Padberg and G. Rinaldi, Facet identification for the symmetric traveling salesman problem, Math. Progr. 47(1990)219–257.

    Article  Google Scholar 

  52. J.T. Richardson, M. Palmer, G.E. Liepins and M. Hilliard, Some guidelines for genetic algorithms with penalty functions, in:Proc. 3rd Int. Conf. on Genetic Algorithms (ICGA '89), George Mason University, Fairfax, VA (1989) pp. 191–197.

    Google Scholar 

  53. D. Rosenkrantz, R. Sterns and P. Lewis, An analysis of several heuristics for the traveling salesman problem, SIAM J. Comp. 6(1977)563–581.

    Article  Google Scholar 

  54. W. Siedlecki and J. Sklansky, Constrained genetic optimization via dynamic reward-penalty balancing and its use in pattern recognition, in:Proc. 3rd Int. Conf. on Genetic Algorithms (ICGA '89), George Mason University, Fairfax, VA (1989) pp. 141–150.

    Google Scholar 

  55. T. Starkweather, S. McDaniel, K. Mathias, D. Whitley and C. Whitley, A comparison of genetic sequencing operators, in:Proc. 4th Int. Conf. on Genetic Algorithms (ICGA '91), University of California at San Diego, San Diego, CA (1991) pp. 69–76.

    Google Scholar 

  56. J.Y. Suh and D.V. Gucht, Incorporating heuristic information into genetic search, in:Proc. 2nd Int. Conf. on Genetic Algorithms (ICGA '87), Massachusetts Institute of Technology, Cambridge, MA (1987) pp. 100–107.

    Google Scholar 

  57. G. Syswerda, Uniform crossover in genetic algorithms, in:Proc. 3rd Int. Conf. on Genetic Algorithms (ICGA '89), George Mason University, Fairfax, VA (1989) pp. 2–9.

    Google Scholar 

  58. G. Syswerda, Schedule optimization using genetic algorithms, in:Handbook of Genetic Algorithms, ed. L. Davis (Van Nostrand Reinhold, 1990) pp. 332–349.

  59. S.R. Thangiah, K.E. Nygard and P. Juell, GIDEON: A genetic algorithm system for vehicle routing problems with time windows, in:Proc. 7th IEEE Conf. on Applications of Artificial Intelligence, Miami, FL (1991) pp. 322–328.

  60. S.R. Thangiah and K.E. Nygard, School bus routing using genetic algorithms, in:Proc. Applications of Artificial Intelligence X: Knowledge Based Systems, Orlando, FL (1992) pp. 387–397.

  61. S.R. Thangiah and A.V. Gubbi, Effect of genetic sectoring on vehicle routing problems with time windows, in:Proc. IEEE Int. Conf. on Developing and Managing Intelligent System Projects, Washington, DC (1993) pp. 146–153.

  62. S.R. Thangiah and K.E. Nygard, Dynamic trajectory routing using an adaptive search strategy, in:Proc. ACM Symp. on Applied Computing, Indianapolis, IN (1993) pp. 131–138.

  63. S.R. Thangiah, R. Vinayagamoorty and A.V. Gubbi, Vehicle routing and time deadlines using genetic and local algorithms, in:Proc. 5th Int. Conf. on Genetic Algorithms (ICGA '93), University of Illinois at Urbana-Champaign, Champaign, IL (1993) pp. 506–515.

    Google Scholar 

  64. N.L.J. Ulder, E.H.L. Aarts, H.J. Bandelt, P.J.M. van Laarhoven and E. Pesch, Genetic local search algorithms for the traveling salesman problem, in:Parallel Problem-Solving from Nature, ed. H.P. Schwefel and R. Manner, Lecture Notes in Computer Science 496 (Springer, 1991) pp. 109–116.

  65. G.A Vigaux and Z. Michalewicz, A genetic algorithm for the linear transportation problem, IEEE Trans. Syst., Man, Cybern. 21(1991)445–452.

    Google Scholar 

  66. D. Whitley, The genitor algorithm and selection pressure: Why rankbased allocation of reproductive trials is best, in:Proc. 3rd Int. Conf. on Genetic Algorithms (ICGA '89), George Mason University, Fairfax, VA (1989) pp. 116–121.

    Google Scholar 

  67. D. Whitley, T. Starkweather and D. Fuquay, Scheduling problems and traveling salesmen: The genetic edge recombination operator, in:Proc. 3rd Int. Conf. on Genetic Algorithms (ICGA '89), George Mason University, Fairfax, VA (1989) pp. 133–140.

    Google Scholar 

  68. D. Whitley, T. Starkweather and D. Shaner, Traveling saleman and sequence scheduling: Quality solutions using genetic edge recombination, in:Handbook of Genetic Algorithms, ed. L. Davis (Van Nostrand Reinhold, 1990) pp. 350–372.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Potvin, JY. Genetic algorithms for the traveling salesman problem. Ann Oper Res 63, 337–370 (1996). https://doi.org/10.1007/BF02125403

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02125403

Keywords

Navigation