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  On a genetic algorithm for the selection of optimally generalizing neural network topologies (1996) [7 citations — 4 self]

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by Dr. -ing Stephan Rudolph
Proceedings of the 2nd International Conference on Adaptive Computing in Engineering Design and Control'96, I.C.Parmee (ed.), University of Plymouth, March 26th-28th, Plymouth, United Kingdom
http://www.isd.uni-stuttgart.de/~rudolph/papers/genetic03.96-paper.ps
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Abstract:

Abstract. A genetic algorithm is used for the topology design of feed-forward neural networks. The generated neural network topology populations are then trained to approximate non-linear relationships of multiple variables. A specifically designed fitness function using the epistemological principle of dimensional homogeneity is used for the evaluation of the individual neural network generations and for the selection of the best generalizing neural networks topologies. A general theory for the topology design and the explanation of the correct generalization capability of non-linear feed-forward neural networks is developed, mathematically proved and explained using simulation results. 1

Citations

800 Multilayer feedforward networks are universal approximators – Hornik, Stinchcombe, et al. - 1989
530 Approximation by superposition of a sigmoidal function – Cybenko - 1989
257 Universal approximation bounds for superposition of a sigmoid function – Barron - 1993
27 Dimensional analysis – Bridgman - 1922
25 Genetic Programming of Minimal Neural Nets Using Occam's Razor – Zhang, Muehlenbein - 1993
23 Genetische Algorithmen und Evolutionsstrategien – Schoneburg, Heinzmann, et al. - 1994
21 Eine Methodik zur systematischen Bewertung von Konstruktionen – Rudolph - 1995
6 A Methodology for the Systematic Evaluation of Engineering Design Objects, Ph.D. dissertation, translation of the original german PhD thesis [28] into english language. A copy of this translated Ph.D. thesis is available on request by email from: rudolph@ – Rudolph - 1995
2 Neural network and genetic algorithm for economic forecasting – Wong, Tan - 1992
1 Funktionsapproximation mit Neuronalen Netzen. Thesis, Institut fur Statik und Dynamik der Luft- und Raumfahrtkonstruktionen – Emrich - 1993
1 Optimierung r uckkopplungsfreier Neuronaler Netze mittels Genetischer Algorithmen. Thesis, Institut fur Statik und Dynamik der Luft- und Raumfahrtkonstruktionen – Gruninger - 1995
1 Ahnlichkeitsmechanik - Potentiale einer interdisziplin aren Forschungsmethodik, in: Dinkler, D. und Hanle, U. (Hrsg.): Numerische und experimentelle Methoden in der Statik und Dynamik – Rudolph - 1994