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Mining Implicit Equations From Data Using gene expression programming

IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTING 2022年第2期10卷 1058-1074页

作者： Zhong, Jinghui Yang, Jiaquan Chen, Yongliang Liu, Wei-Li Feng, Liang South China Univ Technol Sch Comp Sci & Engn Guangzhou 510641 Guangdong Peoples R China City Univ Hong Kong Dept Comp Sci Hong Kong Peoples R China Guangdong Polytech Normal Univ Sch Comp Sci Guangzhou 510665 Guangdong Peoples R China Chongqing Univ Coll Comp Sci Chongqing 400044 Peoples R China

Symbolic regression is an active research topic that has various applications in data mining and knowledge discovery. Existing methods for symbolic regression mainly focus on mining explicit equations. In contrast, implicit equations are more flexible and powerful than explicit equations with regard to describing the relationships between variables in the given dataset. However, evaluating the quality of an implicit equation is more difficult than evaluating an explicit equation. The traditional method for implicit equation evaluation is based on derivative calculation, which requires much time consumption and dense training data. To address the above issues, this article proposes a new evolutionary framework to efficiently mine implicit equations from data. In the proposed framework, a new mechanism (named CL-FEM) is proposed to evaluate implicit equations, and it can efficiently evaluate the accuracy and validity of implicit equations. In addition, a multiple sub-chromosome encoding method based on a least-squares estimator is proposed in the framework to further improve its search efficiency. Based on the proposed evolutionary framework, an efficient algorithm named gene expression programming with a least-squares estimator (LSE-GEP) is developed to mine implicit equations from data. Experimental results demonstrate that the proposed LSE-GEP method performs much better than the recently published methods, in terms of its success rate, accuracy and readability.

关键词： Mathematical model programming gene expression Encoding Data mining Biological cells Time complexity gene expression programming symbolic regression problem implicit equation evaluation mechanism multiple sub-chromosomes encoding method least-squares estimator

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Using gene expression programming to estimate sonic log distributions based on the natural gamma ray and deep resistivity logs: A case study from the Anadarko Basin, Oklahoma

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JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING 2010年第3-4期70卷 243-255页

作者： Cranganu, Constantin Bautu, Elena CUNY Brooklyn Coll Dept Geol Brooklyn NY 11210 USA Alexandru Ioan Cuza Univ Fac Comp Sci Iasi Romania

In the oil and gas industry, characterization of pore-I'll-lid pressures and rock lithology, along with estimation of porosity, permeability, fluid saturation and other physical properties is of crucial importance for successful exploration and exploitation. Along with other well logging methods, the compressional acoustic (Sonic) log (DT) is often used as a predictor because it responds to changes in porosity or compaction and, in turn. DT data are used to estimate formation porosity, to map abnormal pore-fluid pressure. or to perform petrophysical studies. However, despite its intrinsic value, the sonic log is not routinely recorded during well logging. Here we propose the use of a soft computing method - gene expression programming (GEP) - to synthesize missing DT logs when only common logs (such as natural gamma ray - GR, or deep resistivity - REID) are present. The gene expression programming approach can be divided into three steps: (1) supervised training of the model: (2) confirmation and validation of the model by blind-testing the results in wells containing both the predictor (GR, REID) and the target (DT) values used in the supervised training;and (3) applying the predicted model to wells containing the predictor data and obtaining the synthetic (simulated) DT log. GEP methodology offers significant advantages over traditional deterministic methods. It does not require a precise mathematical model equation describing the dependency between the predictor values and the target Values. Unlike linear regression techniques, GEP does not overpredict mean values and thereby preserves original data variability. GEP also deals greatly with uncertainty associated with the data, the immense size of the data and the diversity of the data type. A case study from the Anadarko Basin, Oklahoma, involving estimating the presence of overpressured zones, is presented. The results are promising and encouraging. (C) 2009 Elsevier B.V. All rights reserved.

关键词： gene expression programming soft computing sonic log Anadarko Basin overpressured zones

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Compressive strength prediction of concrete blended with carbon nanotubes using gene expression programming and random forest: hyper-tuning and optimization

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JOURNAL OF MATERIALS RESEARCH AND TECHNOLOGY-JMR&T 2023年 24卷 7198-7218页

作者： Yang, Dawei Xu, Ping Zaman, Athar Alomayri, Thamer Houda, Moustafa Alaskar, Abdulaziz Javed, Muhammad Faisal Xian Technol Univ Civil & Architecture Engn Xian 710021 Peoples R China Shaanxi Inst Urban & Rural Planning & Design Urban Renewal Res Inst Xian 710048 Peoples R China Capital Univ Sci & Technol Islamabad Islamabad Pakistan Umm Al Qura Univ Fac Appl Sci Dept Phys Mecca 21955 Saudi Arabia Amer Univ Middle East Coll Engn & Technol Kuwait Kuwait King Saud Univ Coll Engn Dept Civil Engn Riyadh 11451 Saudi Arabia COMSATS Univ Islamabad Dept Civil Engn Abbottabad 22060 Pakistan

The strength of carbon nanotubes (CNTs) and cement composites is dependent on multiple variables. In addition, CNTs added to a cement-based matrix can boost its strength. However, the information related to CNTs characteristics is limited and scarce. Their incorporation may substantially enhance the mechanical and durability properties of cementitious mixtures. Despite challenges such as high cost and workability problems. Therefore, proper consumption of these materials must be used to attain desired qualities. The principal plan of this investigation is to create predictive framework by utilizing machine-learning algorithms. gene expression programming (GEP), and the random forest algorithm (RFA) is employed to estimate the compressive strength of concrete mixed with CNTs. GEP is used as an individual approach, and RFA is used as an ensemble method to depict the most influential model. The outcomes of the two models are assessed by employing external K-fold cross-validation, and a comparison is done. A comprehensive database is established comprising 282 data points for the CS with blended CNTs. The model is then calibrated using six inputs, including curing time (CT), water-to-cement ratio (W/C), fine aggregate (FA), carbon nanotube content (CNTs), cement content (CC), and coarse aggregate (CA). In addition, the predicted results are validated using k-fold cross-validation, and performance metrics, such as mean absolute error (MAE), root squared error (RSE), correlation coefficient (R-2), root mean square error (RMSE), and relative root mean square error (RRMSE). The result shows that RF regression with the nth estimator shows robust accuracy by showing minimal errors as analyzed to individual RF and GEP models. Likewise, the nth model depicts higher R-2 = 0.96, and validation results demonstrate low errors. Moreover, the GEP model excels in terms of prediction through the empirical equation. In addition, Shapley analysis (SHAP) is performed to check the distribu

关键词： Carbon nanotubes gene expression programming Random forest K-fold cross-validation Statistical measures

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Modelling of expansion ratio and half-life of foamed bitumen using gene expression programming

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INTERNATIONAL JOURNAL OF PAVEMENT ENGINEERING 2021年第3期22卷 369-381页

作者： Eleyedath, Abhary Kar, Siksha Swaroopa Swamy, Aravind Krishna Indian Inst Technol Delhi Dept Civil Engn New Delhi India CSIR Cent Rd Res Inst Pavement Engn Area New Delhi India

A typical foamed bituminous mixture design process involves production and evaluation of foamed bitumen over a range of foaming temperatures and water contents. Such a process of elaborate testing (over a range of temperatures and water contents) is a time- and resource-consuming exercise. This work presents a novel gene expression programming-based approach to predict the expansion ratio and half-life of foamed bitumen. To develop these predictive models, a database that consists of foamed bitumen characteristics (i.e. expansion ratio and half-life) and physico-chemical properties of bitumen was developed using six distinct binders (of different viscosity grades). Initially, all binders were tested for their physical properties and chemical composition. Furthermore, foamed bitumen characteristics of these binders were measured over the range of test temperatures (110 degrees C to 200 degrees C) and water contents (2% to 11%). The final database consisted of 166 observations (arising out of different combinations of 6 binder types, 6 water contents, and 8 test temperatures and an average of 3 replicates for each condition). expressions to predict foamed bitumen characteristics have been developed based on temperature, water content, viscosity, and chemical composition using this database through the gene expression programming technique. The numerical values of goodness of fit parameters indicated that models based on physical properties are able to predict expansion ratio and half-life with reasonable accuracy. Furthermore, the use of information regarding chemical composition along with physical properties improved the accuracy of predictive models significantly. These expressions can be used to identify the feasible range of test conditions for the production of foamed bitumen before actual testing is commenced.

关键词： Cold mix technology foamed bitumen expansion ratio half-life gene expression programming

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A new approach for predicting and collaborative evaluating the cutting force in face milling based on gene expression programming

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JOURNAL OF NETWORK AND COMPUTER APPLICATIONS 2013年第6期36卷 1540-1550页

作者： Yang, Yang Li, Xinyu Gao, Liang Shao, Xinyu Huazhong Univ Sci & Technol Sch Mech Sci & Engn State Key Lab Digital Mfg Equipment & Technol Wuhan 430074 Peoples R China

Cutting force is one of the fundamental elements that can provide valuable insight in the investigation of cutter breakage, tool wear, machine tool chatter, and surface finish in face milling. Analyzing the relationship between process factors and cutting force is helpful to set the process parameters of the future cutting operation and further improve production quality and efficiency. Since cutting force is impacted by the inherent uncertainties in the machining process, how to predict the cutting force presents a significant challenge. In the meantime, face milling is a complex process involving multiple experts with different domain knowledge, collaborative evaluation of the cutting force model should be conducted to effectively evaluate the constructed predictive model. gene expression programming (GEP) combines the advantages of the genetic Algorithm (GA) and genetic programming (GP), and has been successfully applied in function mining and formula finding. In this paper, a new approach to predict the face milling cutting force based on GEP is proposed. At the basis of defining a GEP environment for the cutting force prediction, an explicit predictive model has been constructed. To verify the effectiveness of the proposed approach, a case study has been conducted. The comparisons between the proposed approach and some previous works show that the constructed model fits very well with the experimental data and can predict the cutting force with a high accuracy. Moreover, in order to better apply the constructed predictive models in actual face milling process, a collaborative model evaluation method is proposed to provide a distributed environment for geographical distributed experts to evaluate the constructed predictive model collaboratively, and four kinds of collaboration mode are discussed. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Cutting force modeling gene expression programming Face milling Collaborative model evaluation

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Rules Mining-Based gene expression programming for the Multi-Skill Resource Constrained Project Scheduling Problem

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Computer Modeling in Engineering & Sciences 2023年第9期136卷 2815-2840页

作者： Min Hu Zhimin Chen Yuan Xia Liping Zhang Qiuhua Tang Key Laboratory of Metallurgical Equipment and Control Technology Ministry of EducationWuhan University of Science and TechnologyWuhan430081China Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering Wuhan University of Science and TechnologyWuhan430081China Precision Manufacturing Institute Wuhan University of Science and TechnologyWuhan430081China China Ship Development and Design Center Wuhan430060China

Themulti-skill resource-constrained project scheduling problem(MS-RCPSP)is a significantmanagement science problem that extends from the resource-constrained project scheduling problem(RCPSP)and is integrated with a real project and production *** solve MS-RCPSP,it is an efficient method to use dispatching rules combined with a parallel scheduling mechanism to generate a scheduling *** paper proposes an improved gene expression programming(IGEP)approach to explore newly dispatching rules that can broadly solve MS-RCPSP.A new backward traversal decoding mechanism,and several neighborhood operators are applied in *** backward traversal decoding mechanism dramatically reduces the space complexity in the decoding process,and improves the algorithm’s *** neighborhood operators improve the exploration of the potential search *** experiment takes the intelligent multi-objective project scheduling environment(iMOPSE)benchmark dataset as the training set and testing set of *** newly dispatching rules are discovered and extracted by IGEP,and eight out of ten are superior to other typical dispatching rules.

关键词： Project scheduling multi-skill gene expression programming dispatching rules

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Numerical assessment of rectangular tunnels configurations using support vector machine (SVM) and gene expression programming (GEP)

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ENGINEERING WITH COMPUTERS 2022年第SUPPL 4期38卷 3581-3597页

作者： Zhang, Jun Shi, Ruoli Shi, Shaohua Alzo'ubi, A. K. Roco-Videla, Angel Hussein, Mohamed M. A. Khan, Afrasyab Yunnan Univ Sch Architecture & Planning Kunming 650091 Yunnan Peoples R China Sichuan Univ Arts & Sci Sch Architectural Engn Dazhou 635000 Sichuan Peoples R China Abu Dhabi Univ Civil Engn Dept Abu Dhabi U Arab Emirates Univ Bernardo OHiggins Fac Ciencias Salud Programa Magister Ciencias Quim Biol Santiago Chile Univ Catolica Santisima Concepcion Fac Ingn Dept Ingn Civil Concepcion Chile Sohag Univ Fac Engn Civil Engn Dept Sohag Egypt South Ural State Univ Inst Engn & Technol Dept Hydraul & Hydraul & Pneumat Syst Lenin Prospect 76 Chelyabinsk 454080 Russia

Rectangular tunnel boring machine (TBM) is applied for the tunnels' excavation including a cross section of circular and rectangular shape within the various rocks and soil strata. Excessive structural forces, which is produced within tunnel linings, might affect the serviceability and safety of tunnels whose forces acting on tunnels linings during the initial design period have to be accurately calculated. Few numerical studies have been conducted on different soil-rectangular tunnel systems to clarify the critical response characteristics of cut-and-cover (rectangular) tunnels adjusted to transversal ground shaking. In this case, predicting the soil dynamic shear stresses developed around the tunnel is an elaborate task due to the interaction of TBM in the rectangular form and the rock. Despite doing the empirical studies in analyzing the rectangular tunnels systems, using artificial intelligence (AI) methods could significantly develop the optimization of TBM tunneling and decreasing the cost, error percentages, disturbance, and time-consuming complications related to tunneling. In this study, two algorithms, namely, support vector machine (SVM) and gene expression programming (GEP), were used to accurately predict the soil dynamic shear stresses developed around the tunnel. The models were developed and measured resulting that SVM can indicate a high-performance capacity in predicting the soil dynamic shear stresses developed around the tunnel through the rectangular TBM excavation machine.

关键词： Rectangular TBM Artificial intelligence Excavation Support vector machine gene expression programming

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Prediction and minimization of blast-induced flyrock using gene expression programming and firefly algorithm

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NEURAL COMPUTING & APPLICATIONS 2018年第6期29卷 269-281页

作者： Faradonbeh, Roohollah Shirani Armaghani, Danial Jahed Amnieh, Hassan Bakhshandeh Mohamad, Edy Tonnizam Tarbiat Modares Univ Dept Min Fac Engn Tehran 14115143 Iran UTM Dept Geotech & Transportat Fac Civil Engn Skudai 81310 Johor Malaysia Univ Tehran Sch Min Coll Engn Tehran 111554563 Iran

The main objective of blasting operations is to provide proper rock fragmentation and to avoid undesirable environmental impacts such as flyrock. Flyrock is the source of most of the injuries and property damage in a majority of blasting accidents in surface mines. Therefore, proper prediction and subsequently optimization of flyrock distance may reduce the possible damages. The first objective of this study is to develop a new predictive model based on gene expression programming (GEP) for predicting flyrock distance. To achieve this aim, three granite quarry sites in Malaysia were investigated and a database composed of blasting data of 76 operations was prepared for modelling. Considering changeable GEP parameters, several GEP models were constructed and the best one among them was selected. Coefficient of determination values of 0.920 and 0.924 for training and testing datasets, respectively, demonstrate that GEP predictive equation is capable enough of predicting flyrock. The second objective of this study is to optimize blasting data for minimization purpose of flyrock. To do this, a new non-traditional optimization algorithm namely firefly algorithm (FA) was selected and used. For optimization purposes, a series of analyses were performed on the FA parameters. As a result, implementing FA algorithm, a reduction of about 34 % in results of flyrock distance (from 60 to 39.793 m) was observed. The obtained results of this study are useful to minimize possible damages caused by flyrock.

关键词： Flyrock gene expression programming Firefly algorithm Optimization purpose

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Permeability Prediction in Tight Carbonate Rocks Using gene expression programming (GEP)

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ROCK MECHANICS AND ROCK ENGINEERING 2021年第5期54卷 2581-2593页

作者： Wei, Yufeng Xue, Xinhua Chengdu Univ Technol State Key Lab Geohazard Prevent & Geoenvironm Pro Chengdu 610059 Peoples R China Sichuan Univ Coll Water Resource & Hydropower Chengdu 610065 Peoples R China

Figures 12, 13 and 14 plot the variations of three input variables (e.g., HT ht , HT F ht and HT dPT ht ) against the permeability HT k ht predicted by the GEP model. The constants of the first gene HT c2 ht , HT c7... 详细信息

Figures 12, 13 and 14 plot the variations of three input variables (e.g., HT

ht , HT

F

ht and HT

d_{PT}

ht ) against the permeability HT

k

ht predicted by the GEP model. The constants of the first gene HT

c_{2}

ht , HT

c_{7}

ht and HT

c_{8}

ht are -8.833, -8.661 and -6.561, respectively. 3 can be written mathematically as HT

(x \times 5) - (cos)

ht . The constants of the second gene HT

c_{2}

ht and HT

c_{5}

ht are -9.067 and 3.056, respectively. [Extracted from the article]

关键词： gene expression programming Permeability Tight carbonate rocks Artificial neural network Conventional models genetic algorithms

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An algorithm evaluation for discovering classification rules with gene expression programming

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INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS 2016年第2期9卷 263-280页

作者： Guerrero-Enamorado, Alain Morell, Carlos Noaman, Amin Y. Ventura, Sebastian Univ Ciencias Informat Havana Cuba Univ Cent Las Villas Villa Clara Cuba King Abdulaziz Univ Jeddah 21413 Saudi Arabia Univ Cordoba UCO Cordoba Spain

In recent years, evolutionary algorithms have been used for classification tasks. However, only a limited number of comparisons exist between classification genetic rule-based systems and gene expression programming rule-based systems. In this paper, a new algorithm for classification using gene expression programming is proposed to accomplish this task, which was compared with several classical state-of-the-art rule-based classifiers. The proposed classifier uses a Michigan approach;the evolutionary process with elitism is guided by a token competition that improves the exploration of fitness surface. Individuals that cover instances, covered previously by others individuals, are penalized. The fitness function is constructed by the multiplying three factors: sensibility, specificity and simplicity. The classifier was constructed as a decision list, sorted by the positive predictive value. The most numerous class was used as the default class. Until now, only numerical attributes are allowed and a mono objective algorithm that combines the three fitness factors is implemented. Experiments with twenty benchmark data sets have shown that our approach is significantly better in validation accuracy than some genetic rule-based state-of-the-art algorithms (i.e., SLAVE, HIDER, Tan, Falco, Bojarczuk and CORE) and not significantly worse than other better algorithms (i.e., GASSIST, LOGIT-BOOST and UCS).

关键词： genetic programming gene expression programming Classification rules Discriminant functions

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