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Journal of Combinatorial Optimization

, Volume 24, Issue 4, pp 508–525 | Cite as

Competent genetic algorithms for weighing matrices

  • I. S. Kotsireas
  • C. Koukouvinos
  • P. M. Pardalos
  • D. E. Simos
Article

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.

Keywords

Weighing matrices Messy genetic algorithm Fast messy genetic algorithm Competent metaheuristics Optimization 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • I. S. Kotsireas
    • 1
  • C. Koukouvinos
    • 2
  • P. M. Pardalos
    • 3
  • D. E. Simos
    • 2
  1. 1.Department of Physics and Computer ScienceWilfrid Laurier UniversityWaterlooCanada
  2. 2.Department of MathematicsNational Technical University of AthensAthensGreece
  3. 3.Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA

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