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Phase Transitions in Swarm Optimization Algorithms

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Unconventional Computation and Natural Computation (UCNC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10867))

Abstract

Natural systems often exhibit chaotic behavior in their space-time evolution. Systems transiting between chaos and order manifest a potential to compute, as shown with cellular automata and artificial neural networks. We demonstrate that swarms optimisation algorithms also exhibit transitions from chaos, analogous to motion of gas molecules, when particles explore solution space disorderly, to order, when particles follow a leader, similar to molecules propagating along diffusion gradients in liquid solutions of reagents. We analyse these ‘phase-like’ transitions in swarm optimization algorithms using recurrence quantification analysis and Lempel-Ziv complexity estimation. We demonstrate that converging and non-converging iterations of the optimization algorithms are statistically different in a view of applied chaos, complexity and predictability estimating indicators.

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Acknowledgment

The following grants are acknowledged for the financial support provided for this research: Grant of SGS No. SGS 2018/177, VSB-Technical University of Ostrava and German Research Foundation (DFG projects no. MA 4759/9-1 and MA4759/8).

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Authors and Affiliations

  1. Department of Computer science, Technical University of Ostrava, Ostrava, Czech Republic

    Tomáš Vantuch & Ivan Zelinka

  2. Unconventional Computing Lab, UWE, Bristol, UK

    Andrew Adamatzky

  3. Transdisciplinary Concepts and Methods, Potsdam Institute for Climate Impact Research (PIK), Potsdam, Germany

    Norbert Marwan

Authors
  1. Tomáš Vantuch
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  2. Ivan Zelinka
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  3. Andrew Adamatzky
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  4. Norbert Marwan
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Corresponding author

Correspondence to Tomáš Vantuch .

Editor information

Editors and Affiliations

  1. University of York, Heslington, York, United Kingdom

    Susan Stepney

  2. Université Paris-Est Créteil, Créteil, France

    Sergey Verlan

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Vantuch, T., Zelinka, I., Adamatzky, A., Marwan, N. (2018). Phase Transitions in Swarm Optimization Algorithms. In: Stepney, S., Verlan, S. (eds) Unconventional Computation and Natural Computation. UCNC 2018. Lecture Notes in Computer Science(), vol 10867. Springer, Cham. https://doi.org/10.1007/978-3-319-92435-9_15

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  • DOI: https://doi.org/10.1007/978-3-319-92435-9_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-92434-2

  • Online ISBN: 978-3-319-92435-9

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