Order of Nonlinearity as a Complexity Measure for Models Generated by Symbolic Regression via Pareto Genetic Programming

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@Article{Vladislavleva:2009:TEC,
  author =       "Ekaterina J. Vladislavleva and Guido F. Smits and 
                 Dick {den Hertog}",
  title =        "Order of Nonlinearity as a Complexity Measure for
                 Models Generated by Symbolic Regression via Pareto
                 Genetic Programming",
  journal =      "IEEE Transactions on Evolutionary Computation",
  year =         "2009",
  volume =       "13",
  number =       "2",
  pages =        "333--349",
  month =        apr,
  keywords =     "genetic algorithms, genetic programming, computational
                 complexity, regression analysis, Pareto genetic
                 programming, best-fit polynomial, data-driven
                 regression models, nonlinearity order, symbolic
                 regression, Complexity theory, Polynomials,
                 Computational modeling, Chebyshev approximation, Data
                 models, Approximation methods, Least squares
                 approximation, model selection, Complexity,
                 evolutionary multiobjective optimization,
                 extrapolation, GP, industrial data analysis",
  ISSN =         "1089-778X",
  DOI =          "doi:10.1109/TEVC.2008.926486",
  abstract =     "his paper presents a novel approach to generate
                 data-driven regression models that not only give
                 reliable prediction of the observed data but also have
                 smoother response surfaces and extra generalization
                 capabilities with respect to extrapolation. These
                 models are obtained as solutions of a genetic
                 programming (GP) process, where selection is guided by
                 a tradeoff between two competing objectives numerical
                 accuracy and the order of nonlinearity. The latter is a
                 novel complexity measure that adopts the notion of the
                 minimal degree of the best-fit polynomial,
                 approximating an analytical function with a certain
                 precision. Using nine regression problems, this paper
                 presents and illustrates two different strategies for
                 the use of the order of nonlinearity in symbolic
                 regression via GP. The combination of optimization of
                 the order of nonlinearity together with the numerical
                 accuracy strongly outperforms conventional optimisation
                 of a size-related expressional complexity and the
                 accuracy with respect to extrapolative capabilities of
                 solutions on all nine test problems. In addition to
                 exploiting the new complexity measure, this paper also
                 introduces a novel heuristic of alternating several
                 optimization objectives in a 2-D optimization
                 framework. Alternating the objectives at each
                 generation in such a way allows us to exploit the
                 effectiveness of 2-D optimization when more than two
                 objectives are of interest (in this paper, these are
                 accuracy, expressional complexity, and the order of
                 nonlinearity). Results of the experiments on all test
                 problems suggest that alternating the order of
                 nonlinearity of GP individuals with their structural
                 complexity produces solutions that are both compact and
                 have smoother response surfaces, and, hence,
                 contributes to better interpretability and
                 understanding.",
  notes =        "also known as \cite{4632147}",
}

Genetic Programming entries for Ekaterina (Katya) Vladislavleva Guido F Smits Dick den Hertog

Citations