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Evolution of mathematical models of chaotic systems based on multiobjective genetic programming

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Abstract

This work is concerned with the identification of models for nonlinear dynamical systems using multiobjective evolutionary algorithms. Systems modelling involves the processes of structure selection, parameter estimation, model performance and model validation and involves a complex solution space. Evolutionary Algorithms (EAs) are search and optimisation tools founded on the principles of natural evolution and genetics, which are suitable for a wide range of application areas. Due to the versatility of these tools and motivated by the versatility of genetic programming (GP), this evolutionary paradigm is proposed for this modelling problem. GP is then combined with a multiobjective function definition scheme. Multiobjective genetic programming (MOGP) is applied to multiple, conflicting objectives and yields a set of candidate parsimonious and valid models, which reproduce the original system behaviour. The MOGP approach is then demonstrated as being applicable for system modelling with chaotic dynamics. The circuit introduced by Chua, being one of the most popular benchmarks for studying nonlinear oscillations, and the Duffing–Holmes oscillator are the systems to test the evolutionary-based modelling approach introduced in this paper.

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Authors and Affiliations

  1. IIMAS-UNAM, Circuito Escolar, Ciudad Universitaria, 04510, Coyoacán, México City, Mexico

    Katya Rodríguez-Vázquez

  2. Automatic Control and Systems, Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD, United Kingdom

    Peter J. Fleming

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  1. Katya Rodríguez-Vázquez
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  2. Peter J. Fleming
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Correspondence to Katya Rodríguez-Vázquez.

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Rodríguez-Vázquez, K., Fleming, P. Evolution of mathematical models of chaotic systems based on multiobjective genetic programming. Knowl Inf Syst 8, 235–256 (2005). https://doi.org/10.1007/s10115-004-0184-3

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  • DOI: https://doi.org/10.1007/s10115-004-0184-3

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