A true triaxial strength criterion for rocks by gene expression programming

Rock strength is a crucial factor to consider when designing and constructing underground projects.This study utilizes a gene expression programming(GEP)algorithm-based model to predict the true triaxial strength of rocks,taking into account the influence of rock genesis on their mechanical behavior during the model building process.A true triaxial strength criterion based on the GEP model for igneous,metamorphic and magmatic rocks was obtained by training the model using collected data.Compared to the modified Weibols-Cook criterion,the modified Mohr-Coulomb criterion,and the modified Lade criterion,the strength criterion based on the GEP model exhibits superior prediction accuracy performance.The strength criterion based on the GEP model has better performance in R2,RMSE and MAPE for the data set used in this study.Furthermore,the strength criterion based on the GEP model shows greater stability in predicting the true triaxial strength of rocks across different types.Compared to the existing strength criterion based on the genetic programming(GP)model,the proposed criterion based on GEP model achieves more accurate predictions of the variation of true triaxial strength(s1)with intermediate principal stress(s2).Finally,based on the Sobol sensitivity analysis technique,the effects of the parameters of the three obtained strength criteria on the true triaxial strength of the rock are analysed.In general,the proposed strength criterion exhibits superior performance in terms of both accuracy and stability of prediction results.

Rules Mining-Based Gene Expression Programming for the Multi-Skill Resource Constrained Project Scheduling Problem

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 environment.To solve MS-RCPSP,it is an efficient method to use dispatching rules combined with a parallel scheduling mechanism to generate a scheduling scheme.This 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 IGEP.The backward traversal decoding mechanism dramatically reduces the space complexity in the decoding process,and improves the algorithm’s performance.Several neighborhood operators improve the exploration of the potential search space.The experiment takes the intelligent multi-objective project scheduling environment(iMOPSE)benchmark dataset as the training set and testing set of IGEP.Ten newly dispatching rules are discovered and extracted by IGEP,and eight out of ten are superior to other typical dispatching rules.

A worldwide SPT-based soil liquefaction triggering analysis utilizing gene expression programming and Bayesian probabilistic method

In this context,two different approaches of soil liquefaction evaluation using a soft computing technique based on the worldwide standard penetration test(SPT) databases have been studied.Gene expression programming(GEP) as a gray-box modeling approach is used to develop different deterministic models in order to evaluate the occurrence of soil liquefaction in terms of liquefaction field performance indicator(LI) and factor of safety(FS) in logistic regression and classification concepts.The comparative plots illustrate that the classification concept-based models show a better performance than those based on logistic regression.In the probabilistic approach,a calibrated mapping function is developed in the context of Bayes’ theorem in order to capture the failure probabilities(PL) in the absence of the knowledge of parameter uncertainty.Consistent results obtained from the proposed probabilistic models,compared to the most well-known models,indicate the robustness of the methodology used in this study.The probability models provide a simple,but also efficient decision-making tool in engineering design to quantitatively assess the liquefaction triggering thresholds.

Scheduling Rules Based on Gene Expression Programming for Resource-Constrained Project Scheduling Problem

In order to minimize the project duration of resourceconstrained project scheduling problem( RCPSP), a gene expression programming-based scheduling rule( GEP-SR) method is proposed to automatically discover and select the effective scheduling rules( SRs) which are constructed using the project status and attributes of the activities. SRs are represented by the chromosomes of GEP, and an improved parallel schedule generation scheme( IPSGS) is used to transform the SRs into explicit schedules. The framework of GEP-SR for RCPSP is designed,and the effectiveness of the GEP-SR approach is demonstrated by comparing with other methods on the same instances.

Prediction of mode I fracture toughness of rock using linear multiple regression and gene expression programming

Prediction of mode I fracture toughness(KIC) of rock is of significant importance in rock engineering analyses. In this study, linear multiple regression(LMR) and gene expression programming(GEP)methods were used to provide a reliable relationship to determine mode I fracture toughness of rock. The presented model was developed based on 60 datasets taken from the previous literature. To predict fracture parameters, three mechanical parameters of rock mass including uniaxial compressive strength(UCS), Brazilian tensile strength(BTS), and elastic modulus(E) have been selected as the input parameters. A cluster of data was collected and divided into two random groups of training and testing datasets.Then, different statistical linear and artificial intelligence based nonlinear analyses were conducted on the training data to provide a reliable prediction model of KIC. These two predictive methods were then evaluated based on the testing data. To evaluate the efficiency of the proposed models for predicting the mode I fracture toughness of rock, various statistical indices including coefficient of determination(R2),root mean square error(RMSE), and mean absolute error(MAE) were utilized herein. In the case of testing datasets, the values of R2, RMSE, and MAE for the GEP model were 0.87, 0.188, and 0.156,respectively, while they were 0.74, 0.473, and 0.223, respectively, for the LMR model. The results indicated that the selected GEP model delivered superior performance with a higher R2value and lower errors.

Hybrid Gene Expression Programming-Based Sensor Data Correlation Mining

This paper deals with the reflectance estimation model issue to improve the estimation accuracy. We propose a model containing two core procedures: dimensionality reduction and model mining. First, the dimensionality reduction algorithm of hyperspectral data based on dependence degree(DRNDDD) is proposed to reduce the redundant hyperspectral band. DRND-DD solves the selection of suitable hyperspectral band via rough set theory. Furthermore, to improve the computation speed and accuracy of the model, based on DRND-DD, this paper proposes reflectance estimation model mining of leaf nitrogen concentration(LNC) for hyperspectral data by using hybrid gene expression programming(REMLNC-HGEP). Experimental results on three datasets demonstrate that the DRND-DD algorithm can obtain good results with a very short running time compared with principal component analysis(PCA), singular value decomposition(SVD), a dimensionality reduction algorithm based on the positive region(AR-PR) and a dimensionality reduction algorithm based on a discernable matrix(ARDM), and REMLNC-HGEP has low average time-consumption, high model mining success ratio and estimation accuracy. It was concluded that the REMLNC-HGEP performs better than the regression methods.

Modeling viscosity of methane,nitrogen,and hydrocarbon gas mixtures at ultra-high pressures and temperatures using group method of data handling and gene expression programming techniques

Accurate gas viscosity determination is an important issue in the oil and gas industries.Experimental approaches for gas viscosity measurement are timeconsuming,expensive and hardly possible at high pressures and high temperatures(HPHT).In this study,a number of correlations were developed to estimate gas viscosity by the use of group method of data handling(GMDH)type neural network and gene expression programming(GEP)techniques using a large data set containing more than 3000 experimental data points for methane,nitrogen,and hydrocarbon gas mixtures.It is worth mentioning that unlike many of viscosity correlations,the proposed ones in this study could compute gas viscosity at pressures ranging between 34 and 172 MPa and temperatures between 310 and 1300 K.Also,a comparison was performed between the results of these established models and the results of ten wellknown models reported in the literature.Average absolute relative errors of GMDH models were obtained 4.23%,0.64%,and 0.61%for hydrocarbon gas mixtures,methane,and nitrogen,respectively.In addition,graphical analyses indicate that the GMDH can predict gas viscosity with higher accuracy than GEP at HPHT conditions.Also,using leverage technique,valid,suspected and outlier data points were determined.Finally,trends of gas viscosity models at different conditions were evaluated.

Rapid Prototype Development Approach for Genetic Programming

Genetic Programming (GP) is an important approach to deal with complex problem analysis and modeling, and has been applied in a wide range of areas. The development of GP involves various aspects, including design of genetic operators, evolutionary controls and implementations of heuristic strategy, evaluations and other mechanisms. When designing genetic operators, it is necessary to consider the possible limitations of encoding methods of individuals. And when selecting evolutionary control strategies, it is also necessary to balance search efficiency and diversity based on representation characteristics as well as the problem itself. More importantly, all of these matters, among others, have to be implemented through tedious coding work. Therefore, GP development is both complex and time-consuming. To overcome some of these difficulties that hinder the enhancement of GP development efficiency, we explore the feasibility of mutual assistance among GP variants, and then propose a rapid GP prototyping development method based on πGrammatical Evolution (πGE). It is demonstrated through regression analysis experiments that not only is this method beneficial for the GP developers to get rid of some tedious implementations, but also enables them to concentrate on the essence of the referred problem, such as individual representation, decoding means and evaluation. Additionally, it provides new insights into the roles of individual delineations in phenotypes and semantic research of individuals.

Modelling reference evapotranspiration using gene expression programming and artificial neural network at Pantnagar,India

Evapotranspiration is an essential component of the hydrological cycle that is of particular interest for water resource planning.Its quantification is helpful in irrigation scheduling,water balance studies,water allocation,etc.Modelling of reference evapotranspiration(ET0)using both gene expression programming(GEP)and artificial neural network(ANN)techniques was done using the daily meteorological data of the Pantnagar region,India,from 2010 to 2019.A total of 15 combinations of inputs were used in developing the ET0 models.The model with the least number of inputs consisted of maximum and minimum air temperatures,whereas the model with the highest number of inputs consisted of maximum air temperature,minimum air temperature,mean relative humidity,number of sunshine hours,wind speed at 2mheight and extra-terrestrial radiation as inputs and with ET0 as the output for all the models.All the GEP models were developed for a single functional set and pre-defined genetic operator values,while the best structure in each ANN model was found based on the performance during the testing phase.It was found that ANN models were superior to GEP models for the estimation purpose.It was evident from the reduction in RMSE values ranging from 2%to 56%during training and testing phases in all the ANN models compared with GEP models.The ANN models showed an increase of about 0.96%to 9.72%of R2 value compared to the respective GEP models.The comparative study of these models with multiple linear regression(MLR)depicted that the ANN and GEP models were superior to MLR models.

Prediction of Enhancement Effect of Nitroimidazoles on Irradiation by Gene Expression Programming

A novel machine learning method, gene expression programming（GEP）, was employed to build quatitative structure-activity relationship（QSAR） models for predicting the enhancement effect of nitroimidazole compounds on irradiation. The models were based on descriptors which were calculated from the molecular structures. Four descriptors were selected from the pool of descriptors by best multiple linear regression（BMLR） method. After that, three regression methods, multiple linear regression（MLR）, support vector machine（SVM） and GEP, were used to build QSAR models. Compared to MLR and SVM, GEP produced a better model with the square of correlation coefficient（R2）, 0.9203 and 0.9014, and the root mean square error（RMSE）, 0.6187 and 0.6875, for training set and test set, respectively. The results show that the GEP model has better predictive ability and more reliable than the MLR and SVM models. This indicates that GEP is a promising method on relevant researches in radiation area.

Smart prediction of liquefaction-induced lateral spreading

The prediction of liquefaction-induced lateral spreading/displacement(Dh)is a challenging task for civil/geotechnical engineers.In this study,a new approach is proposed to predict Dh using gene expression programming(GEP).Based on statistical reasoning,individual models were developed for two topographies:free-face and gently sloping ground.Along with a comparison with conventional approaches for predicting the Dh,four additional regression-based soft computing models,i.e.Gaussian process regression(GPR),relevance vector machine(RVM),sequential minimal optimization regression(SMOR),and M5-tree,were developed and compared with the GEP model.The results indicate that the GEP models predict Dh with less bias,as evidenced by the root mean square error(RMSE)and mean absolute error(MAE)for training(i.e.1.092 and 0.815;and 0.643 and 0.526)and for testing(i.e.0.89 and 0.705;and 0.773 and 0.573)in free-face and gently sloping ground topographies,respectively.The overall performance for the free-face topology was ranked as follows:GEP>RVM>M5-tree>GPR>SMOR,with a total score of 40,32,24,15,and 10,respectively.For the gently sloping condition,the performance was ranked as follows:GEP>RVM>GPR>M5-tree>SMOR with a total score of 40,32,21,19,and 8,respectively.Finally,the results of the sensitivity analysis showed that for both free-face and gently sloping ground,the liquefiable layer thickness(T_(15))was the major parameter with percentage deterioration(%D)value of 99.15 and 90.72,respectively.

Identification of partial differential equations from noisy data with integrated knowledge discovery and embedding using evolutionary neural networks

Identification of underlying partial differential equations(PDEs)for complex systems remains a formidable challenge.In the present study,a robust PDE identification method is proposed,demonstrating the ability to extract accurate governing equations under noisy conditions without prior knowledge.Specifically,the proposed method combines gene expression programming,one type of evolutionary algorithm capable of generating unseen terms based solely on basic operators and functional terms,with symbolic regression neural networks.These networks are designed to represent explicit functional expressions and optimize them with data gradients.In particular,the specifically designed neural networks can be easily transformed to physical constraints for the training data,embedding the discovered PDEs to further optimize the metadata used for iterative PDE identification.The proposed method has been tested in four canonical PDE cases,validating its effectiveness without preliminary information and confirming its suitability for practical applications across various noise levels.

Energy Consumption Prediction of a CNC Machining Process With Incomplete Data

Energy consumption prediction of a CNC machining process is important for energy efficiency optimization strategies.To improve the generalization abilities,more and more parameters are acquired for energy prediction modeling.While the data collected from workshops may be incomplete because of misoperation,unstable network connections,and frequent transfers,etc.This work proposes a framework for energy modeling based on incomplete data to address this issue.First,some necessary preliminary operations are used for incomplete data sets.Then,missing values are estimated to generate a new complete data set based on generative adversarial imputation nets(GAIN).Next,the gene expression programming(GEP)algorithm is utilized to train the energy model based on the generated data sets.Finally,we test the predictive accuracy of the obtained model.Computational experiments are designed to investigate the performance of the proposed framework with different rates of missing data.Experimental results demonstrate that even when the missing data rate increases to 30%,the proposed framework can still make efficient predictions,with the corresponding RMSE and MAE 0.903 k J and 0.739 k J,respectively.

An Evolutionary Algorithm for Non-Destructive Reverse Engineering of Integrated Circuits

In hardware Trojan detection technology, destructive reverse engineering can restore an original integrated circuitwith the highest accuracy. However, this method has a much higher overhead in terms of time, effort, and cost thanbypass detection. This study proposes an algorithm, called mixed-feature gene expression programming, whichapplies non-destructive reverse engineering to the chip with bypass detection data. It aims to recover the originalintegrated circuit hardware, or else reveal the unknown circuit design in the chip.

Local vs. cross station simulation of suspended sediment load in successive hydrometric stations: heuristic modeling approach

The present paper aims at modeling suspended sediment load(SSL) using heuristic data driven methodologies, e.g. Gene Expression Programming(GEP) and Support Vector Machine(SVM) in three successive hydrometric stations of Housatonic River in U.S. The simulations were carried out through local and cross-station data management scenarios to investigate the interrelations between the SSL values of upstream/downstream stations. The available scenarios were applied to predict SSL values using GEP to obtain the best models. Then, the best models were predicted by SVM approach and the obtained results were compared with those of GEP. The comparison of the results revealed that the SVM technique is more capable than the GEP for modeling the SSL through the both local and cross-station data management strategies. Besides, local application seems to be better than cross-station application for modeling SSL. Nevertheless, the cross-station application demonstrated to be a valid methodology for simulating SSL, which would be of interest for the stations with lack of observational data. Also, the prediction capability of conventional Sediment Rating Curve(SRC) method was compared with those of GEPand SVM techniques. The obtained results revealed the superiority of GEP and SVM-based models over the traditional SRC technique in the studied stations.

Modeling of shear wave velocity in limestone by soft computing methods

The main purpose of current study is development of an intelligent model for estimation of shear wave velocity in limestone. Shear wave velocity is one of the most important rock dynamic parameters. Because rocks have complicated structure, direct determination of this parameter takes time, spends expenditure and requires accuracy. On the other hand, there are no precise equations for indirect determination of it; most of them are empirical. By using data sets of several dams of Iran and neuro-genetic, adaptive neuro-fuzzy inference system （ANFIS）, and gene expression programming （GEP） methods, models are rendered for prediction of shear wave velocity in limestone. Totally, 516 sets of data has been used for modeling. From these data sets, 413 ones have been utilized for building the intelligent model, and 103 have been used for their performance evaluation. Compressional wave velocity （Vp）, density （7） and porosity （.n）, were considered as input parameters. Respectively, the amount of R for neuro-genetic and ANFIS networks was 0.959 and 0.963. In addition, by using GEP, three equations are obtained; the best of them has 0.958R. ANFIS shows the best prediction results, whereas GEP indicates proper equations. Because these equations have accuracy, they could be used for prediction of shear wave velocity for limestone in the future.

Settlement modeling in central core rockfill dams by new approaches

One of the most important reasons for the serious damage of embankment dams is their impermissible settlement.Therefore,it can be stated that the prediction of settlement of a dam is of paramount importance.This study aims to apply intelligent methods to predict settlement after constructing central core rockfill dams.Attempts were made in this research to prepare models for predicting settlement of these dams using the information of 35 different central core rockfill dams all over the world and Adaptive Neuro-Fuzzy Interface System(ANFIS) and Gene Expression Programming(GEP) methods.Parameters such as height of dam(H) and compressibility index(Ci) were considered as the input parameters.Finally,a form was designed using visual basic software for predicting dam settlement.With respect to the accuracy of the results obtained from the intelligent methods,they can be recommended for predicting settlement after constructing central core rockfill dams for the future plans.

An innovative model for predicting the displacement and rotation of column-tree moment connection under fire

In this study,we carried out nonlinear finite element simulations to predict the performance of a columntree moment connection(CTMC)under fire and static loads.We also conducted a detailed parameter study based on five input variables,including the applied temperature,number of flange bolts,number of web bolts,length of the beam,and applied static loads.The first variable is changed among seven levels,whereas the other variables are changed among three levels.Employing the Taguchi method for variables 2-5 and their levels,9 samples were designed for the parameter study,where each sample was exposed to 7 different temperatures yielding 63 outputs.The related variables for each output are imported for the training and testing of different surrogate models.These surrogate models include a multiple linear regression(MLR),multiple Ln equation regression(MLnER),an adaptive network-based fuzzy inference system(ANFIS),and gene expression programming(GEP).44 samples were used for training randomly while the remaining samples were employed for testing.We show that GEP outperforms MLR,MLnER,and ANFIS.The results indicate that the rotation and deflection of the CTMC depend on the temperature.In addition,the fire resistance increases with a decrease in the beam length;thus,a shorter beam can increase the fire resistance of the building.The numbers of flanges and web bolts slightly affect the rotation and displacement of the CTMCs at temperatures of above 400℃.

Applying extended intrinsic mean spin tensor in evolution algorithm for RANS modelling of turbulent rotating channel flow

We present a machine learning based method for RANS modeling in the rotating frame of reference(RFR).The extended intrinsic mean spin tensor(EIMST)is adopted in a novel expansion of the evolution algorithm,named multi-dimensional gene expression programming(MGEP).Based on DNS data,a constrain free model for Reynolds stress is created by considering system rotating.The anisotropy behavior of Reynolds stress is considered in the model,which is then for the first time applied for modeling turbulent flow inside a rotating channel.Compared with the traditional RANS model,the new model can predict the non-symmetric profile of Reynolds stress.Meanwhile,the Taylor-Gortler vortex is captured in our simulations with the new model.It is demonstrated that the application of EIMST in MGEP can be successfully adopted for RANS modeling in the RFR.

Real-Time Hybrid Flow Shop Scheduling Approach in Smart Manufacturing Environment

Smart manufacturing in the“Industry 4.0”strategy promotes the deep integration of manufacturing and information technologies,which makes the manufacturing system a ubiquitous environment.However,the real-time scheduling of such a manufacturing system is a challenge faced by many decision makers.To deal with this challenge,this study focuses on the real-time hybrid flow shop scheduling problem(HFSP).First,the characteristic of the hybrid flow shop in a smart manufacturing environment is analyzed,and its scheduling problem is described.Second,a real-time scheduling approach for the HFSP is proposed.The core module is to employ gene expression programming to construct a new and efficient scheduling rule according to the real-time status in the hybrid flow shop.With the scheduling rule,the priorities of the waiting job are calculated,and the job with the highest priority will be scheduled at this decision time point.A group of experiments are performed to prove the performance of the proposed approach.The numerical experiments show that the real-time scheduling approach outperforms other single-scheduling rules and the back-propagation neural network method in optimizing most objectives for different size instances.Therefore,the contribution of this study is the proposal of a real-time scheduling approach,which is an effective approach for real-time hybrid flow shop scheduling in a smart manufacturing environment.