2012
DOI: 10.1016/j.eswa.2011.10.005
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Modeling asphalt pavement overlay transverse cracks using the genetic operation tree and Levenberg–Marquardt Method

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Cited by 9 publications
(3 citation statements)
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“…Levenberg–Marquardt (Levenberg 1944; Marquardt 1963) algorithm is a blend of gradient descent and Gauss–Newton iterations, aimed to solve nonlinear least square problems. The method works as a steepest descent method when the parameters are far away from their optimal values and acts like a Gauss–Newton method when the parameters are closer to their optimal values (Hsie et al 2012). The parameter set is updated iteratively by adding negative of the scaled gradient at each step, with the error between measurements written as: fip1,p2,pn=hnormalobshnormalsim, where, f i is the error estimated based on observed ( h obs ) and simulated ( h sim ) measurements.…”
Section: Materials and Methodologymentioning
confidence: 99%
“…Levenberg–Marquardt (Levenberg 1944; Marquardt 1963) algorithm is a blend of gradient descent and Gauss–Newton iterations, aimed to solve nonlinear least square problems. The method works as a steepest descent method when the parameters are far away from their optimal values and acts like a Gauss–Newton method when the parameters are closer to their optimal values (Hsie et al 2012). The parameter set is updated iteratively by adding negative of the scaled gradient at each step, with the error between measurements written as: fip1,p2,pn=hnormalobshnormalsim, where, f i is the error estimated based on observed ( h obs ) and simulated ( h sim ) measurements.…”
Section: Materials and Methodologymentioning
confidence: 99%
“…Aminian et al 18 presented a new empirical model to estimate the base shear of plane steel structures subjected to earthquake load using a hybrid method integrating genetic programming GP and simulated annealing SA , called GP/SA. Hsie et al 19 proposed a novel approach, called "LMGOT," that integrates two optimization techniques: the Levenberg Marquardt LM Method and the genetic operation tree GOT . The GOT borrows the concept from the genetic algorithm, a famous algorithm for solving discrete optimization problems, to generate operation trees OTs , which represent the structures of the formulas.…”
Section: Genetic Programmingmentioning
confidence: 99%
“…Artificial neural network models are considered by many researchers as "black-boxes" (Attoh-Okine et al 2009;Hsie et al 2012;Benítez et al 1997;Prechelt 1998). With a complex network structure, it is difficult to explicitly describe the learned relationship between the input and the output variables.…”
Section: Forward Calculationsmentioning
confidence: 99%