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ACS Searching for D 4t -Hadamard Matrices

  • Conference paper
Swarm Intelligence (ANTS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6234))

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Abstract

An Ant Colony System (ACS) looking for cocyclic Hadamard matrices over dihedral groups D 4t is described. The underlying weighted graph consists of the rooted trees described in [1], whose vertices are certain subsets of coboundaries. A branch of these trees defines a D 4t -Hadamard matrix if and only if two conditions hold: (i) I i  = i − 1 and, (ii) c i  = t, for every 2 ≤ i ≤ t, where I i and c i denote the number of i-paths and i-intersections (see [3] for details) related to the coboundaries defining the branch. The pheromone and heuristic values of our ACS are defined in such a way that condition (i) is always satisfied, and condition (ii) is closely to be satisfied.

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References

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Author information

Authors and Affiliations

  1. University of Sevilla, Sevilla, Spain

    Víctor Álvarez, José Andrés Armario, María Dolores Frau, Félix Gudiel, Belén Güemes, Elena Martín & Amparo Osuna

Authors
  1. Víctor Álvarez
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  2. José Andrés Armario
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  3. María Dolores Frau
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  4. Félix Gudiel
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  5. Belén Güemes
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  6. Elena Martín
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  7. Amparo Osuna
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Editor information

Editors and Affiliations

  1. IRIDIA, CoDE, Université Libre de Bruxelles, Brussels, Belgium

    Marco Dorigo

  2. IRIDIA, CoDE, Université Libre de Bruxelles, Av. F. Roosevelt 50, CP 194/6, 1050, Brussels, Belgium

    Mauro Birattari

  3. ’Dalla Molle’ Institute for Artificial Intelligence (IDSIA), Galleria 2, 6928, Manno-Lugano, Switzerland

    Gianni A. Di Caro

  4. Complex Systems Institute, Paris-Ile-de-France, CREA, Ecole Polytechnique & CNRS, 57-59, rue Lhomond, 75005, Paris, France

    René Doursat

  5. Department of Computer Science, University of Pretoria, 0002, P.O. Box, Pretoria, South Africa

    Andries P. Engelbrecht

  6. EPFL, Laboratory of Intelligent Systems, Lausanne, Switzerland

    Dario Floreano

  7. Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (IDSIA), Lugano, Switzerland

    Luca Maria Gambardella

  8. Department of Automatic Control and Systems Engineering, The University of Sheffield, Mappin Street, S1 3JD, Sheffield, UK

    Roderich Groß

  9. KOVAN Research Lab., Department of Computer Engineering, Middle East Technical University, Inonu Bulvari, 06531, Ankara, Turkey

    Erol Şahin

  10. Department of Bioengineering, Binghamton University, State University of New York, 13902-6000, Binghamton NY, USA

    Hiroki Sayama

  11. IRIDIA, CoDE, Université Libre de Bruxelles, Avenue F. Roosevelt 50, CP 194/6, 1050, Brussels, Belgium

    Thomas Stützle

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Álvarez, V. et al. (2010). ACS Searching for D 4t -Hadamard Matrices. In: Dorigo, M., et al. Swarm Intelligence. ANTS 2010. Lecture Notes in Computer Science, vol 6234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15461-4_33

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  • DOI: https://doi.org/10.1007/978-3-642-15461-4_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15460-7

  • Online ISBN: 978-3-642-15461-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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