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,
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author = "Ekaterina J. Vladislavleva and Guido F. Smits and
Dick {den Hertog}",
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title = "Order of Nonlinearity as a Complexity Measure for
Models Generated by Symbolic Regression via Pareto
Genetic Programming",
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journal = "IEEE Transactions on Evolutionary Computation",
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year = "2009",
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volume = "13",
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number = "2",
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pages = "333--349",
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month = apr,
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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",
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ISSN = "1089-778X",
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DOI = "doi:10.1109/TEVC.2008.926486",
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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.",
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notes = "also known as \cite{4632147}",
- }
Genetic Programming entries for
Ekaterina (Katya) Vladislavleva
Guido F Smits
Dick den Hertog
Citations