Function approximations by superimposing genetic programming trees: with applications to engineering problems

Yeun, Yun Seog; Suh, Junghun; Yang, YoungSoon

doi:10.1016/s0020-0255(99)00121-8

Cited by 16 publications

(6 citation statements)

References 8 publications

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“…The reason for choosing the representation is that the tree can be created and evolved using the existing or modified tree-structure-based approaches, i.e., genetic programming (GP) [41], probabilistic incremental program evolution (PIPE) [12], ant programming (AP) etc.…”

Section: Encoding and Evaluationmentioning

confidence: 99%

Time-series forecasting using flexible neural tree model

Chen

Yang

Dong

et al. 2005

Information Sciences

261

146

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Section: Encoding and Evaluationmentioning

confidence: 99%

Time-series forecasting using flexible neural tree model

Chen

Yang

Dong

et al. 2005

Information Sciences

261

146

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“…In the last few years, GP has been extensively used both in Industry and Academia (Arcuri & Yao, 2010;Chan, Kwong, & Fogarty, 2010;Choi & Choi, 2012;dos Santos, Ferreira, Torres, Gonçalves, & Lamparelli, 2011;Koza, Streeter, & Keane, 2008;Moreno-Torres, Llorá, Goldberg, & Bhargava, 2013;Ravisankar, Ravi, & Bose, 2010;Trujillo, Legrand, Olague, & Lévy-Véhel, 2012;Yeun, Suh, & Yang, 2000;Wongseree, Chaiyaratana, Vichittumaros, Winichagoon, & Fucharoen, 2007) and it has produced a wide set of results that have been defined human-competitive (Koza, 2010). While these results have demonstrated the appropriateness of GP in tackling real-life problems, research has recently focused on developing new variants of GP in order to further improve its performance.…”

Section: Geometric Semantic Operatorsmentioning

confidence: 99%

Prediction of the Unified Parkinson’s Disease Rating Scale assessment using a genetic programming system with geometric semantic genetic operators

Castelli

Vanneschi

Silva

2014

Expert Systems with Applications

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“…(6). The matrix A transforms the linear observed samples to non-linear problems by mapping the data into a higher dimensional feature space.…”

Section: A Training Phasementioning

confidence: 99%

“…For example, the hybrid model of ANN with PSO has been proposed by [4][5] for function approximation. Genetic programming [6][7], evolutionary algorithms [8], and fuzzy systems [9][10] are other well-known techniques that can be found in the literature. However, most existing approximation algorithms perform well given sufficiently large samples.…”

Section: Introductionmentioning

confidence: 99%

Enhanced Nadaraya-Watson Kernel Regression: Surface Approximation for Extremely Small Samples

Shapiai

Ibrahim

Khalid

et al. 2011

2011 Fifth Asia Modelling Symposium

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The function approximation problem is to find the appropriate relationship between a dependent and independent variable(s). Function approximation algorithms generally require sufficient samples to approximate a function. Insufficient samples may cause any approximation algorithm to result in unsatisfactory predictions. To solve this problem, a function approximation algorithm called Weighted Kernel Regression (WKR), which is based on Nadaraya-Watson kernel regression, is proposed. In the proposed framework, the original NadarayaWatson kernel regression algorithm is enhanced by expressing the observed samples in a square kernel matrix. The WKR is trained to estimate the weight for the testing phase. The weight is estimated iteratively and is governed by the error function to find a good approximation model. Two experiments are conducted to show the capability of the WKR. The results show that the proposed WKR model is effective in cases where the target surface function is non-linear and the given training sample is small. The performance of the WKR is also compared with other existing function approximation algorithms, such as artificial neural networks (ANN).

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Function approximations by superimposing genetic programming trees: with applications to engineering problems

Cited by 16 publications

References 8 publications

Time-series forecasting using flexible neural tree model

Time-series forecasting using flexible neural tree model

Prediction of the Unified Parkinson’s Disease Rating Scale assessment using a genetic programming system with geometric semantic genetic operators

Enhanced Nadaraya-Watson Kernel Regression: Surface Approximation for Extremely Small Samples

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