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A Hybrid Genetic Algorithm for the Traveling Salesman Problem Using Generalized Partition Crossover

  • Darrell Whitley
  • Doug Hains
  • Adele Howe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6238)

Abstract

We present a hybrid genetic algorithm that incorporates the Generalized Partition Crossover (GPX) operator to produce an algorithm that is competitive with the state of the art for the Traveling Salesman Problem (TSP). GPX is respectful, transmits alleles and is capable of tunneling directly to new local optima. Our results show that the hybrid genetic algorithm quickly finds optimal and near optimal solution on problems ranging from 500 to 1817 cities using a population size of 10. It is also superior to Chained-LK given similar computational effort. Additional analysis shows that all the edges found in the globally optimal solution are present in a population after only a few generations in almost every run. Furthermore the number of unique edges in the population is also less than twice the problem size.

Keywords

Traveling Salesman Problem Generalized Partition Crossover Hybrid Genetic Algorithm Chained-LK 

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References

  1. 1.
    Applegate, D., Cook, W., Rohe, A.: Chained Lin-Kernighan for large traveling salesman problems. INFORMS Journal on Computing 15(1), 82–92 (2003)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Whitley, D., Hains, D., Howe, A.: Tunneling between optima: partition crossover for the traveling salesman problem. In: Proceedings of the 11th Annual conference on Genetic and evolutionary computation, pp. 915–922. ACM, New York (2009)CrossRefGoogle Scholar
  3. 3.
    Radcliffe, N., Surry, P.: Fitness variance of formae and performance predictions. In: Whitley, D., Vose, M. (eds.) FOGA - 3, pp. 51–72. Morgan Kaufmann, San Francisco (1995)Google Scholar
  4. 4.
    Croes, G.: A method for solving traveling-salesman problems. Operations Research, 791–812 (1958)Google Scholar
  5. 5.
    Lin, S., Kernighan, B.: An effective heuristic algorithm for the traveling-salesman problem. Operations Research, 498–516 (1973)Google Scholar
  6. 6.
    Boese, K.D., Kahng, A.B., Muddu, S.: A new adaptive multi-start technique for combinatorial global optimizations. Operations Research Letters 16, 101–113 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Johnson, D.S., McGeoch, L.A.: The traveling salesman problem: A case study in local optimization. In: Aarts, E.H.L., Lenstra, J. (eds.) Local Search in Combinatorial Optimization, pp. 215–310. John Wiley and Sons Ltd., Chichester (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Darrell Whitley
    • 1
  • Doug Hains
    • 1
  • Adele Howe
    • 1
  1. 1.Colorado State UniversityFort Collins

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