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

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  title =        "Multiobjective Evolutionary Search of Difference
                 Equations-based Models for Understanding Chaotic
  author =       "Luciano Sanchez and Jose R. Villar",
  booktitle =    "Foundations of Generic Optimization Volume 2:
                 Applications of Fuzzy Control, Genetic Algorithms and
                 Neural Networks",
  publisher =    "Springer",
  year =         "2008",
  editor =       "R. Lowen and A. Verschoren",
  volume =       "24",
  series =       "Mathematical Modelling: Theory and Applications",
  pages =        "181--201",
  keywords =     "genetic algorithms, genetic programming, Nonlinear
                 approximation, Chaotic signals, Simulated annealing",
  isbn13 =       "978-1-4020-6667-2",
  ISSN =         "1386-2960",
  URL =          "",
  URL =          "",
  DOI =          "doi:10.1007/978-1-4020-6668-9_4",
  bibsource =    "OAI-PMH server at",
  contributor =  "CiteSeerX",
  language =     "en",
  oai =          "oai:CiteSeerXPSU:",
  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.",

Genetic Programming entries for Luciano Sanchez Jose R Villar