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Combinatorial Optimization for Weighing Matrices with the Ordering Messy Genetic Algorithm

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Experimental Algorithms (SEA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6630))

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Zografou, 15773, Athens, Greece

    Christos Koukouvinos & Dimitris E. Simos

Authors
  1. Christos Koukouvinos
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  2. Dimitris E. Simos
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Editor information

Editors and Affiliations

  1. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

  2. Division of Economics and Business, Colorado School of Mines, Engineering Hall 310, 816 15th Street, 80401, Golden, CO, USA

    Steffen Rebennack

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Koukouvinos, C., Simos, D.E. (2011). Combinatorial Optimization for Weighing Matrices with the Ordering Messy Genetic Algorithm. In: Pardalos, P.M., Rebennack, S. (eds) Experimental Algorithms. SEA 2011. Lecture Notes in Computer Science, vol 6630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20662-7_13

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  • DOI: https://doi.org/10.1007/978-3-642-20662-7_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20661-0

  • Online ISBN: 978-3-642-20662-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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