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Multiobjective Evolutionary Search of Difference Equations-based Models for Understanding Chaotic Systems

  • Chapter
Foundations of Generic Optimization

Part of the book series: Mathematical Modelling: Theory and Applications ((MMTA,volume 24))

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Abstract

In control engineering, it is well known that many physical processes exhibit a chaotic component. In point of fact, it is also assumed that conventional modeling procedures disregard it, as stochastic noise, beside nonlinear universal approximators (like neural networks, fuzzy rule-based or genetic programming-based models,) can capture the chaotic nature of the process. In this chapter we will show that this is not always true. Despite the nonlinear capabilities of the universal approximators, these methods optimize the one step prediction of the model. This is not the most adequate objective function for a chaotic model, because there may exist many different nonchaotic processes that have near zero prediction error for such an horizon. The learning process will surely converge to one of them. Unless we include in the objective function some terms that depend on the properties on the reconstructed attractor, we may end up with a non chaotic model. Therefore, we propose to follow a multiobjective approach to model chaotic processes, and we also detail how to apply either genetic algorithms or simulated annealing to obtain a difference equations-based model.

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Authors and Affiliations

  1. Computer Science Department, Universidad de Oviedo, Campus de Viesques, 33213, Gijon, Spain

    Luciano Sánchez & José R. Villar

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  1. Luciano Sánchez
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  2. José R. Villar
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Editors and Affiliations

  1. University of Antwerp, Antwerp, Belgium

    Robert Lowen  & Alain Verschoren  & 

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Sánchez, L., Villar, J.R. (2008). Multiobjective Evolutionary Search of Difference Equations-based Models for Understanding Chaotic Systems. In: Lowen, R., Verschoren, A. (eds) Foundations of Generic Optimization. Mathematical Modelling: Theory and Applications, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6668-9_4

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