Combinatorial Optimization for Weighing Matrices with the Ordering Messy Genetic Algorithm

  • Christos Koukouvinos
  • Dimitris E. Simos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6630)


In this paper, we demonstrate that the search for weighing matrices constructed from two circulants can be viewed as a permutation problem. To solve it a set of two competent genetic algorithms (CGAs) are used to locate common integers in two sorted arrays. 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 a recent formalism on the support of two sequences with zero autocorrelation we use an adaptation of the ordering messy GA (OmeGA) where we combine the fast mGA with random keys to represent permutations of the two sequences under investigation. This transformation of the weighing matrices problem to an instance of a combinatorial optimization problem seems to be promising since we illustrate that our framework is capable to solve open cases for weighing matrices as these are listed in the second edition of the Handbook of Combinatorial Designs.


Weighing matrices messy genetic algorithm ordering messy genetic algorithm competent metaheuristics optimization 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Christos Koukouvinos
    • 1
  • Dimitris E. Simos
    • 1
  1. 1.Department of MathematicsNational Technical University of AthensAthensGreece

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