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Competent genetic algorithms for weighing matrices

Author

Listed:
  • I. S. Kotsireas

    (Wilfrid Laurier University)

  • C. Koukouvinos

    (National Technical University of Athens)

  • P. M. Pardalos

    (University of Florida)

  • D. E. Simos

    (National Technical University of Athens)

Abstract

In this paper, we demonstrate that the search for weighing matrices constructed from two circulants can be viewed as a minimization problem together with two competent genetic algorithms to locate optima of an objective function. The motivation to deal with the messy genetic algorithm (mGA) is given from the pioneering results of Goldberg, regarding the ability of the mGA to put tight genes together in a solution which points directly to structural patterns in weighing matrices. In order to take into advantage certain properties of two ternary sequences with zero autocorrelation we use an adaptation of the fast messy GA (fmGA) where we combine mGA with advanced techniques, such as thresholding and tie-breaking. This transformation of the weighing matrices problem to an instance of a combinatorial optimization problem seems to be promising, since we resolved two open cases for weighing matrices as these are listed in the second edition of the Handbook of Combinatorial Designs.

Suggested Citation

  • I. S. Kotsireas & C. Koukouvinos & P. M. Pardalos & D. E. Simos, 2012. "Competent genetic algorithms for weighing matrices," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 508-525, November.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:4:d:10.1007_s10878-011-9404-4
    DOI: 10.1007/s10878-011-9404-4
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    References listed on IDEAS

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    1. I. S. Kotsireas & C. Koukouvinos & P. M. Pardalos & O. V. Shylo, 2010. "Periodic complementary binary sequences and Combinatorial Optimization algorithms," Journal of Combinatorial Optimization, Springer, vol. 20(1), pages 63-75, July.
    2. James C. Bean, 1994. "Genetic Algorithms and Random Keys for Sequencing and Optimization," INFORMS Journal on Computing, INFORMS, vol. 6(2), pages 154-160, May.
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    Cited by:

    1. L. A. C. Roque & D. B. M. M. Fontes & F. A. C. C. Fontes, 2014. "A hybrid biased random key genetic algorithm approach for the unit commitment problem," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 140-166, July.

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