Modeling asphalt pavement overlay transverse cracks using the genetic operation tree and Levenberg–Marquardt Method

The Artificial Neural Network (ANN) and the nonlinear regression method are commonly used to build models from experimental data. However, the ANN has been criticized for incapable of providing clear relationships and physical meanings, and is usually regarded as a black box. The nonlinear regression method needs predefined and correct formula structures to process parameter search in terms of the minimal sum of square errors. Unfortunately, the formula structures of these models are often unclear and cannot be defined in advance. To overcome these challenges, this study proposes 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. Meanwhile, the LM takes advantage of its merit for solving nonlinear continuous optimization problems, and determines the coefficients in the GOTs that best fit the experimental data. This paper uses the LMGOT to investigate the data sets of pavement cracks from a 15-year experiment conducted by the Texas Departments of Transportation. Results show a concise formula for predicting the length of pavement transverse cracking, and indicate that the LMGOT is an efficient approach to building an accurate crack model.