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Genetic Algorithm with Optimal Recombination for the Asymmetric Travelling Salesman Problem

  • Anton V. Eremeev
  • Yulia V. Kovalenko
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10665)

Abstract

We propose a new genetic algorithm with optimal recombination for the asymmetric instances of travelling salesman problem. The algorithm incorporates several new features that contribute to its effectiveness: 1. Optimal recombination problem is solved within crossover operator. 2. A new mutation operator performs a random jump within 3-opt or 4-opt neighborhood. 3. Greedy constructive heuristic of Zhang and 3-opt local search heuristic are used to generate the initial population. A computational experiment on TSPLIB instances shows that the proposed algorithm yields competitive results to other well-known memetic algorithms for asymmetric travelling salesman problem.

Keywords

Genetic algorithm Optimal recombination Local search 

References

  1. 1.
    Brown, B.W., Hollander, M.: Statistics: A Biomedical Introduction. Wiley Inc., New York (1977)CrossRefzbMATHGoogle Scholar
  2. 2.
    Buriol, L.S., Franca, P.M., Moscato, P.: A new memetic algorithm for the asymmetric traveling salesman problem. J. Heuristics 10, 483–506 (2004)CrossRefzbMATHGoogle Scholar
  3. 3.
    Cook, W., Seymour, P.: Tour merging via branch-decomposition. INFORMS J. Comput. 15(2), 233–248 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Dongarra, J.J.: Performance of various computers using standard linear equations software. Technical Report CS-89-85, 110 p. University of Manchester (2014)Google Scholar
  5. 5.
    Eppstein, D.: The traveling salesman problem for cubic graphs. J. Graph Algorithms Appl. 11(1), 61–81 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Eremeev, A.V., Kovalenko, J.V.: Optimal recombination in genetic algorithms for combinatorial optimization problems: Part II. Yugoslav J. Oper. Res. 24(2), 165–186 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Eremeev, A.V., Kovalenko, J.V.: Experimental evaluation of two approaches to optimal recombination for permutation problems. In: Chicano, F., Hu, B., García-Sánchez, P. (eds.) EvoCOP 2016. LNCS, vol. 9595, pp. 138–153. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-30698-8_10 CrossRefGoogle Scholar
  8. 8.
    Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of NP-completeness. W. H. Freeman and Company, San Francisco (1979)zbMATHGoogle Scholar
  9. 9.
    Goldberg, D., Thierens, D.: Elitist recombination: An integrated selection recombination GA. In: First IEEE World Congress on Computational Intelligence, vol. 1, pp. 508–512. IEEE Service Center, Piscataway, New Jersey (1994)Google Scholar
  10. 10.
    Johnson, D.S., McGeorch, L.A.: The traveling salesman problem: a case study. In: Aarts, E., Lenstra, J.K. (eds.) Local Search in Combinatorial Optimization, pp. 215–336. Wiley Ltd. (1997)Google Scholar
  11. 11.
    Kanellakis, P.C., Papadimitriou, C.H.: Local search for the asymmetric traveling salesman problem. Oper. Res. 28, 1086–1099 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Karp, R.M.: A patching algorithm for the nonsymmetric traveling-salesman problem. SIAM J. Comput. 8, 561–573 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Radcliffe, N.J.: The algebra of genetic algorithms. Ann. Math. Artif. Intell. 10(4), 339–384 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Reeves, C.R.: Genetic algorithms for the operations researcher. INFORMS J. Comput. 9(3), 231–250 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Reinelt, G.: TSPLIB - a traveling salesman problem library. ORSA J. Comput. 3(4), 376–384 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Tinós, R., Whitley, D., Ochoa, G.: Generalized asymmetric partition crossover (GAPX) for the asymmetric TSP. In: The 2014 Annual Conference on Genetic and Evolutionary Computation, pp. 501–508. ACM, New York (2014)Google Scholar
  17. 17.
    Whitley, D., Starkweather, T., Shaner, D.: The traveling salesman and sequence scheduling: Quality solutions using genetic edge recombination. In: Davis, L. (ed.) Handbook of Genetic Algorithms, pp. 350–372. Van Nostrand Reinhold (1991)Google Scholar
  18. 18.
    Yagiura, M., Ibaraki, T.: The use of dynamic programming in genetic algorithms for permutation problems. Eur. J. Oper. Res. 92, 387–401 (1996)CrossRefzbMATHGoogle Scholar
  19. 19.
    Zhang, W.: Depth-first branch-and-bound versus local search: A case study. In: 17th National Conference on Artificial Intelligence, Austin, pp. 930–935 (2000)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

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