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Genetic Algorithm with Optimal Recombination for the Asymmetric Travelling Salesman Problem

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Large-Scale Scientific Computing (LSSC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10665))

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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.

Y. V. Kovalenko—This research is supported by the Russian Science Foundation grant 15-11-10009.

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References

  1. Brown, B.W., Hollander, M.: Statistics: A Biomedical Introduction. Wiley Inc., New York (1977)

    Book  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  3. Cook, W., Seymour, P.: Tour merging via branch-decomposition. INFORMS J. Comput. 15(2), 233–248 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  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. Eppstein, D.: The traveling salesman problem for cubic graphs. J. Graph Algorithms Appl. 11(1), 61–81 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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

    Chapter  Google Scholar 

  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)

    MATH  Google Scholar 

  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. 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. Kanellakis, P.C., Papadimitriou, C.H.: Local search for the asymmetric traveling salesman problem. Oper. Res. 28, 1086–1099 (1980)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  13. Radcliffe, N.J.: The algebra of genetic algorithms. Ann. Math. Artif. Intell. 10(4), 339–384 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  14. Reeves, C.R.: Genetic algorithms for the operations researcher. INFORMS J. Comput. 9(3), 231–250 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  15. Reinelt, G.: TSPLIB - a traveling salesman problem library. ORSA J. Comput. 3(4), 376–384 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. Yagiura, M., Ibaraki, T.: The use of dynamic programming in genetic algorithms for permutation problems. Eur. J. Oper. Res. 92, 387–401 (1996)

    Article  MATH  Google Scholar 

  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 

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, 4, Akad. Koptyug avenue, 630090, Novosibirsk, Russia

    Anton V. Eremeev & Yulia V. Kovalenko

Authors
  1. Anton V. Eremeev
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  2. Yulia V. Kovalenko
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Correspondence to Yulia V. Kovalenko .

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Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar Margenov

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Eremeev, A.V., Kovalenko, Y.V. (2018). Genetic Algorithm with Optimal Recombination for the Asymmetric Travelling Salesman Problem. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2017. Lecture Notes in Computer Science(), vol 10665. Springer, Cham. https://doi.org/10.1007/978-3-319-73441-5_36

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  • DOI: https://doi.org/10.1007/978-3-319-73441-5_36

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  • Print ISBN: 978-3-319-73440-8

  • Online ISBN: 978-3-319-73441-5

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