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Genetic algorithms (GAs) and genetic programming (GP)
Published in A. W. Jayawardena, Environmental and Hydrological Systems Modelling, 2013
The problem of finding a function in symbolic form that fits a given set of data is called symbolic regression. Genetic symbolic regression is a special application of GP in the field of symbolic regression. The aim of symbolic regression is to determine a functional relationship between input and output data sets. Symbolic regression is error-driven evolution and it may be linear, quadratic, or higher-order polynomial. Details of GP can be found in Liong et al. (2002). The function set may contain operators such as +, −, ×, /, *, power(x, y), exp(x), etc. The ends of a parse tree are called ‘Terminals’, which are actually the input variables. The nodes are functions taken from the ‘Function Set’.
20 years of intelligent rock mechanics
Published in Xia-Ting Feng, Rock Mechanics and Engineering, 2017
In each modeling process, the model structure defines the essential behavior and has to be determined before the estimation of model parameters. These kinds of methods view the constitutive model as a nonlinear combination of a set of input variables, such as the stress, strain, stress history, strain history, et al., or a set of constitutive units, such as the elastic unit, viscous unit and plastic unit. Feng & Yang (2004) proposed using genetic programming (GP) method to evolve the best model structure through so-called symbolic regression. And an extra parameter estimation procedure is used to determine the model parameters.
A learning automated 3D architecture synthesis model: demonstrating a computer governed design of minimal apartment units based on human perceptual and physical needs
Published in Architectural Science Review, 2019
Dafna Fisher-Gewirtzman, Nir Polak
The non-linear classifier (the formula that distinguishes between units with reasonable and functional layouts, and units with unreasonable layouts) is deduced through ‘Symbolic Regression’, which forms links between sets of data and also determines the structure of the correlation formula. Symbolic regression applies the genetic algorithm (see Section 3.3) to optimize the structure of the formula with regards to its symbols (addition, multiplication, trigonometric functions, etc.) and factors, with the objective of maximizing the correlations between the given sets. Thus, the model will refrain from making prior assumptions based on the relationship between the sets (Quade et al. 2016). The data analysing software ‘Eureqa’ (by Nutonian) runs the algorithm to find a binary classifier defining the quality of the interior layout, a metric based on the geometric parameters of the apartment unit.
Modelling, analysis and improvement of an integrated chance-constrained model for level of repair analysis and spare parts supply control
Published in International Journal of Production Research, 2020
Weimiao Liu, Kanglin Liu, Tianhu Deng
Recognising the limited availability of spare parts, three joint models of LORA and spare parts stocks have been studied since the 1990s. Alfredsson (1997) presents a multi-echelon repairable item system and focuses on the minimisation of expected total number of backorders of spare parts, instead of the maximisation of the spare parts availability. Basten, Van der Heijden, and Schutten (2012) and Basten et al. (2015) extend the model of Alfredsson (1997), which allows more practically realistic component-resource relations, and multi-indenture product structure, respectively. Ghaddar, Sakr, and Asiedu (2016) use genetic programming-based symbolic regression to evolve simpler mathematical expressions.
Supervised learning-based approximation method for single-server open queueing networks with correlated interarrival and service times
Published in International Journal of Production Research, 2022
The functional form resulting from Gaussian Process Regression method cannot be interpreted. Our experiments with Symbolic Regression yielded interpretable functions but their overall predictive performance was lower. Similarly, our experiments with neural networks also gave prediction performance comparable to the Gaussian Process Regression. GPR was chosen since it is more accurate compared to other methods and the uncertainty measurements on the predictions are available when GPR is used.