Shape-constrained multi-objective genetic programming for symbolic regression

Haider, Christian; França, Fabrício Olivetti de; Burlacu, Bogdan; Kronberger, Gabriel

doi:10.1016/j.asoc.2022.109855

Cited by 14 publications

(5 citation statements)

References 25 publications

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“…These issues, as well as a concise review of the advantages and challenges of symbolic regression, are presented by Smits and Kotanchek (2005). Recently, Haider et al (2023) continued improving symbolic regression algorithms, in particular by focusing on issues with the shape the regression functions and including prior knowledge about it.…”

Section: Forecasting Methods Challengesmentioning

confidence: 99%

Forecasting Selected Commodities’ Prices with the Bayesian Symbolic Regression

Drachal,

Pawłowski

2024

IJFS

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This study firstly applied a Bayesian symbolic regression (BSR) to the forecasting of numerous commodities’ prices (spot-based ones). Moreover, some features and an initial specification of the parameters of the BSR were analysed. The conventional approach to symbolic regression, based on genetic programming, was also used as a benchmark tool. Secondly, various other econometric methods dealing with variable uncertainty were estimated including Bayesian Model Averaging, Dynamic Model Averaging, LASSO, ridge, elastic net, and least-angle regressions, etc. Therefore, this study reports a concise and uniform comparison of an application of several popular econometric models to forecasting the prices of numerous commodities. Robustness checks and statistical tests were performed to strengthen the obtained conclusions. Monthly data beginning from January 1988 and ending in August 2021 were analysed.

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Section: Forecasting Methods Challengesmentioning

confidence: 99%

Forecasting Selected Commodities’ Prices with the Bayesian Symbolic Regression

Drachal,

Pawłowski

2024

IJFS

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“…A number of other approaches exist in the literature that narrow down the equation search space of SR for analyzing scientific data. One is the shape-constrained SR [14,15], which incorporates constraints on function shape (such as partial derivatives and monotonicity) using an efficient application of integer arithmetic. Additionally, other variations of SR direct the search for unit correctness [16][17][18], conserve physical properties [17,[19][20][21], and guide using predefined forms derived from the dataset [19,[22][23][24].…”

Section: Incorporating Background Knowledge Into Srmentioning

confidence: 99%

“…Consequently, we impose these as 'soft' constraints, penalizing expressions for constraint violation, without outright rejecting them. References [14,15] also found soft constraints to be more effective than hard constraints. This approach (as implemented in PySR) is detailed in algorithm 1 (in SI).…”

Section: Checking Thermodynamic Constraintsmentioning

confidence: 99%

Incorporating background knowledge in symbolic regression using a computer algebra system

Fox,

Tran,

Nacion

et al. 2024

Mach. Learn.: Sci. Technol.

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Symbolic Regression (SR) can generate interpretable, concise expressions that fit a given dataset, allowing for more human understanding of the structure than black-box approaches. The addition of background knowledge (in the form of symbolic mathematical constraints) allows for the generation of expressions that are meaningful with respect to theory while also being consistent with data. We specifically examine the addition of constraints to traditional genetic algorithm (GA) based SR (PySR) as well as a Markov-chain Monte Carlo (MCMC) based Bayesian SR architecture (Bayesian Machine Scientist), and apply these to rediscovering adsorption equations from experimental, historical datasets.We find that, while hard constraints prevent GA and MCMC SR from searching, soft constraints can lead to improved performance both in terms of search effectiveness and model meaningfulness, with computational costs increasing by about an order of magnitude. If the constraints do not correlate well with the dataset or expected models, they can hinder the search of expressions. We find incorporating these constraints in Bayesian SR (as the Bayesian prior) is better than by modifying the fitness function in the GA.

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“…Over the course of the evolutionary cycle of GP, some variables will survive and have higher probability to appear in later generations, while variables with less impact will gradually disappear. To determine the most important features in the developed GP tree models, the approach will be referred to as the measurement of "relative impact" of input variables [39,40]. The relative impact on an input variable is measured according to the number of references to this variable in all generated GP models starting from the initial population until the last generation.…”

Section: -3-identification Of the Most Relevant Featuresmentioning

confidence: 99%

Evolving Genetic Programming Tree Models for Predicting the Mechanical Properties of Green Fibers

AL-Oqla,

Faris,

Habib

et al. 2023

Emerg Sci J

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Advanced modern technology and the industrial sustainability theme have contributed to the implementation of composite materials for various industrial applications. Bio-composites are among the desired alternatives for green products. However, to properly control the performance of bio-composites, predicting their constituent properties is of paramount importance. This work introduces an innovative, evolving genetic programming tree model for predicting the mechanical properties of natural fibers for the first time based upon several inherent chemical and physical properties. Cellulose, hemicellulose, lignin, and moisture contents, as well as the Microfibrillar angle of various natural fibers, were considered to establish the prediction models. A one-hold-out methodology was applied for the training/testing phases. Robust models were developed utilizing evolving genetic programming tree models to predict the tensile strength, Young’s modulus, and the elongation at break properties of the natural fibers. It was revealed that the Microfibrillar angle was dominant and capable of determining the ultimate tensile strength of the natural fibers by 44.7%, comparable to other considered properties, while the impact of cellulose content in the model was only 35.6%. This would facilitate utilizing artificial intelligence to predict the overall mechanical properties of natural fibers without exhausting experimental efforts and cost to enhance the development of better green composite materials for various industrial applications. Doi: 10.28991/ESJ-2023-07-06-02 Full Text: PDF

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Shape-constrained multi-objective genetic programming for symbolic regression

Cited by 14 publications

References 25 publications

Forecasting Selected Commodities’ Prices with the Bayesian Symbolic Regression

Forecasting Selected Commodities’ Prices with the Bayesian Symbolic Regression

Incorporating background knowledge in symbolic regression using a computer algebra system

Evolving Genetic Programming Tree Models for Predicting the Mechanical Properties of Green Fibers

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