As a critical component of the in situ stress state,determination of the minimum horizontal principal stress plays a significant role in both geotechnical and petroleum engineering.To this end,a gene expression progra...As a critical component of the in situ stress state,determination of the minimum horizontal principal stress plays a significant role in both geotechnical and petroleum engineering.To this end,a gene expression programming(GEP)algorithm-based model,in which the data of borehole breakout size,vertical principal stress,and rock strength characteristics are used as the inputs,is proposed to predict the minimum horizontal principal stress.Seventy-nine(79)samples with seven features are collected to construct the minimum horizontal principal stress dataset used for training models.Twenty-four(24)GEP model hyperparameter sets were configured to explore the key parameter combinations among the inputs and their potential relationships with the minimum horizontal principal stresses.Model performance was evaluated using root mean squared error(RMSE),mean absolute error(MAE),mean absolute percentage error(MAPE),and coefficient of determination(R^(2)).By comparing predictive performance and parameter composition,two models were selected from 24 GEP models that demonstrated excellent predictive performance and simpler parameter composition.Compared with prevalent models,the results indicate that the two selected GEP models have better performance on the test set(R^(2)=0.9568 and 0.9621).Additionally,the results conducted by SHapley Additive exPlanations(SHAP)sensitivity analysis and Local Interpretable Model-agnostic Explanations(LIME)demonstrate that the vertical principal stress is the most influential parameter in both GEP models.The two GEP models have simple parameter compositions as well as stable and excellent prediction performance,which is a viable method for predicting the minimum horizontal principal stresses.展开更多
Assessing the stability of pillars in underground mines(especially in deep underground mines)is a critical concern during both the design and the operational phases of a project.This study mainly focuses on developing...Assessing the stability of pillars in underground mines(especially in deep underground mines)is a critical concern during both the design and the operational phases of a project.This study mainly focuses on developing two practical models to predict pillar stability status.For this purpose,two robust models were developed using a database including 236 case histories from seven underground hard rock mines,based on gene expression programming(GEP)and decision tree-support vector machine(DT-SVM)hybrid algorithms.The performance of the developed models was evaluated based on four common statistical criteria(sensitivity,specificity,Matthews correlation coefficient,and accuracy),receiver operating characteristic(ROC)curve,and testing data sets.The results showed that the GEP and DT-SVM models performed exceptionally well in assessing pillar stability,showing a high level of accuracy.The DT-SVM model,in particular,outperformed the GEP model(accuracy of 0.914,sensitivity of 0.842,specificity of 0.929,Matthews correlation coefficient of 0.767,and area under the ROC of 0.897 for the test data set).Furthermore,upon comparing the developed models with the previous ones,it was revealed that both models can effectively determine the condition of pillar stability with low uncertainty and acceptable accuracy.This suggests that these models could serve as dependable tools for project managers,aiding in the evaluation of pillar stability during the design and operational phases of mining projects,despite the inherent challenges in this domain.展开更多
Given the growing concern over global warming and the critical role of carbon dioxide(CO_(2))in this phenomenon,the study of CO_(2)-induced alterations in coal strength has garnered significant attention due to its im...Given the growing concern over global warming and the critical role of carbon dioxide(CO_(2))in this phenomenon,the study of CO_(2)-induced alterations in coal strength has garnered significant attention due to its implications for carbon sequestration.A large number of experiments have proved that CO_(2) interaction time(T),saturation pressure(P)and other parameters have significant effects on coal strength.However,accurate evaluation of CO_(2)-induced alterations in coal strength is still a difficult problem,so it is particularly important to establish accurate and efficient prediction models.This study explored the application of advancedmachine learning(ML)algorithms and Gene Expression Programming(GEP)techniques to predict CO_(2)-induced alterations in coal strength.Sixmodels were developed,including three metaheuristic-optimized XGBoost models(GWO-XGBoost,SSA-XGBoost,PO-XGBoost)and three GEP models(GEP-1,GEP-2,GEP-3).Comprehensive evaluations using multiple metrics revealed that all models demonstrated high predictive accuracy,with the SSA-XGBoost model achieving the best performance(R2—Coefficient of determination=0.99396,RMSE—Root Mean Square Error=0.62102,MAE—Mean Absolute Error=0.36164,MAPE—Mean Absolute Percentage Error=4.8101%,RPD—Residual Predictive Deviation=13.4741).Model interpretability analyses using SHAP(Shapley Additive exPlanations),ICE(Individual Conditional Expectation),and PDP(Partial Dependence Plot)techniques highlighted the dominant role of fixed carbon content(FC)and significant interactions between FC and CO_(2) saturation pressure(P).Theresults demonstrated that the proposedmodels effectively address the challenges of CO_(2)-induced strength prediction,providing valuable insights for geological storage safety and environmental applications.展开更多
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(G...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.展开更多
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 p...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.展开更多
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...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.展开更多
The shear stress distribution in circular channels was modeled in this study using gene expression programming(GEP). 173 sets of reliable data were collected under four flow conditions for use in the training and test...The shear stress distribution in circular channels was modeled in this study using gene expression programming(GEP). 173 sets of reliable data were collected under four flow conditions for use in the training and testing stages. The effect of input variables on GEP modeling was studied and 15 different GEP models with individual, binary, ternary, and quaternary input combinations were investigated. The sensitivity analysis results demonstrate that dimensionless parameter y/P, where y is the transverse coordinate, and P is the wetted perimeter, is the most influential parameter with regard to the shear stress distribution in circular channels. GEP model 10, with the parameter y/P and Reynolds number(Re) as inputs, outperformed the other GEP models, with a coefficient of determination of 0.7814 for the testing data set. An equation was derived from the best GEP model and its results were compared with an artificial neural network(ANN) model and an equation based on the Shannon entropy proposed by other researchers. The GEP model, with an average RMSE of 0.0301, exhibits superior performance over the Shannon entropy-based equation, with an average RMSE of 0.1049, and the ANN model, with an average RMSE of 0.2815 for all flow depths.展开更多
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 r...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.展开更多
In recent years,feature selection(FS)optimization of high-dimensional gene expression data has become one of the most promising approaches for cancer prediction and classification.This work reviews FS and classificati...In recent years,feature selection(FS)optimization of high-dimensional gene expression data has become one of the most promising approaches for cancer prediction and classification.This work reviews FS and classification methods that utilize evolutionary algorithms(EAs)for gene expression profiles in cancer or medical applications based on research motivations,challenges,and recommendations.Relevant studies were retrieved from four major academic databases-IEEE,Scopus,Springer,and ScienceDirect-using the keywords‘cancer classification’,‘optimization’,‘FS’,and‘gene expression profile’.A total of 67 papers were finally selected with key advancements identified as follows:(1)The majority of papers(44.8%)focused on developing algorithms and models for FS and classification.(2)The second category encompassed studies on biomarker identification by EAs,including 20 papers(30%).(3)The third category comprised works that applied FS to cancer data for decision support system purposes,addressing high-dimensional data and the formulation of chromosome length.These studies accounted for 12%of the total number of studies.(4)The remaining three papers(4.5%)were reviews and surveys focusing on models and developments in prediction and classification optimization for cancer classification under current technical conditions.This review highlights the importance of optimizing FS in EAs to manage high-dimensional data effectively.Despite recent advancements,significant limitations remain:the dynamic formulation of chromosome length remains an underexplored area.Thus,further research is needed on dynamic-length chromosome techniques for more sophisticated biomarker gene selection techniques.The findings suggest that further advancements in dynamic chromosome length formulations and adaptive algorithms could enhance cancer classification accuracy and efficiency.展开更多
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 allo...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.展开更多
基金partially supported by the National Natural Science Foundation of China(Grant Nos.42177164 and 52474121)the Distinguished Youth Science Foundation of Hunan Province of China(Grant No.2022JJ10073).
文摘As a critical component of the in situ stress state,determination of the minimum horizontal principal stress plays a significant role in both geotechnical and petroleum engineering.To this end,a gene expression programming(GEP)algorithm-based model,in which the data of borehole breakout size,vertical principal stress,and rock strength characteristics are used as the inputs,is proposed to predict the minimum horizontal principal stress.Seventy-nine(79)samples with seven features are collected to construct the minimum horizontal principal stress dataset used for training models.Twenty-four(24)GEP model hyperparameter sets were configured to explore the key parameter combinations among the inputs and their potential relationships with the minimum horizontal principal stresses.Model performance was evaluated using root mean squared error(RMSE),mean absolute error(MAE),mean absolute percentage error(MAPE),and coefficient of determination(R^(2)).By comparing predictive performance and parameter composition,two models were selected from 24 GEP models that demonstrated excellent predictive performance and simpler parameter composition.Compared with prevalent models,the results indicate that the two selected GEP models have better performance on the test set(R^(2)=0.9568 and 0.9621).Additionally,the results conducted by SHapley Additive exPlanations(SHAP)sensitivity analysis and Local Interpretable Model-agnostic Explanations(LIME)demonstrate that the vertical principal stress is the most influential parameter in both GEP models.The two GEP models have simple parameter compositions as well as stable and excellent prediction performance,which is a viable method for predicting the minimum horizontal principal stresses.
文摘Assessing the stability of pillars in underground mines(especially in deep underground mines)is a critical concern during both the design and the operational phases of a project.This study mainly focuses on developing two practical models to predict pillar stability status.For this purpose,two robust models were developed using a database including 236 case histories from seven underground hard rock mines,based on gene expression programming(GEP)and decision tree-support vector machine(DT-SVM)hybrid algorithms.The performance of the developed models was evaluated based on four common statistical criteria(sensitivity,specificity,Matthews correlation coefficient,and accuracy),receiver operating characteristic(ROC)curve,and testing data sets.The results showed that the GEP and DT-SVM models performed exceptionally well in assessing pillar stability,showing a high level of accuracy.The DT-SVM model,in particular,outperformed the GEP model(accuracy of 0.914,sensitivity of 0.842,specificity of 0.929,Matthews correlation coefficient of 0.767,and area under the ROC of 0.897 for the test data set).Furthermore,upon comparing the developed models with the previous ones,it was revealed that both models can effectively determine the condition of pillar stability with low uncertainty and acceptable accuracy.This suggests that these models could serve as dependable tools for project managers,aiding in the evaluation of pillar stability during the design and operational phases of mining projects,despite the inherent challenges in this domain.
基金partially supported by the National Natural Science Foundation of China(42177164,52474121)the Outstanding Youth Project of Hunan Provincial Department of Education(23B0008).
文摘Given the growing concern over global warming and the critical role of carbon dioxide(CO_(2))in this phenomenon,the study of CO_(2)-induced alterations in coal strength has garnered significant attention due to its implications for carbon sequestration.A large number of experiments have proved that CO_(2) interaction time(T),saturation pressure(P)and other parameters have significant effects on coal strength.However,accurate evaluation of CO_(2)-induced alterations in coal strength is still a difficult problem,so it is particularly important to establish accurate and efficient prediction models.This study explored the application of advancedmachine learning(ML)algorithms and Gene Expression Programming(GEP)techniques to predict CO_(2)-induced alterations in coal strength.Sixmodels were developed,including three metaheuristic-optimized XGBoost models(GWO-XGBoost,SSA-XGBoost,PO-XGBoost)and three GEP models(GEP-1,GEP-2,GEP-3).Comprehensive evaluations using multiple metrics revealed that all models demonstrated high predictive accuracy,with the SSA-XGBoost model achieving the best performance(R2—Coefficient of determination=0.99396,RMSE—Root Mean Square Error=0.62102,MAE—Mean Absolute Error=0.36164,MAPE—Mean Absolute Percentage Error=4.8101%,RPD—Residual Predictive Deviation=13.4741).Model interpretability analyses using SHAP(Shapley Additive exPlanations),ICE(Individual Conditional Expectation),and PDP(Partial Dependence Plot)techniques highlighted the dominant role of fixed carbon content(FC)and significant interactions between FC and CO_(2) saturation pressure(P).Theresults demonstrated that the proposedmodels effectively address the challenges of CO_(2)-induced strength prediction,providing valuable insights for geological storage safety and environmental applications.
文摘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.
文摘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.
基金The Spring Plan of Ministry of Education,China(No.Z2012017)
文摘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.
文摘The shear stress distribution in circular channels was modeled in this study using gene expression programming(GEP). 173 sets of reliable data were collected under four flow conditions for use in the training and testing stages. The effect of input variables on GEP modeling was studied and 15 different GEP models with individual, binary, ternary, and quaternary input combinations were investigated. The sensitivity analysis results demonstrate that dimensionless parameter y/P, where y is the transverse coordinate, and P is the wetted perimeter, is the most influential parameter with regard to the shear stress distribution in circular channels. GEP model 10, with the parameter y/P and Reynolds number(Re) as inputs, outperformed the other GEP models, with a coefficient of determination of 0.7814 for the testing data set. An equation was derived from the best GEP model and its results were compared with an artificial neural network(ANN) model and an equation based on the Shannon entropy proposed by other researchers. The GEP model, with an average RMSE of 0.0301, exhibits superior performance over the Shannon entropy-based equation, with an average RMSE of 0.1049, and the ANN model, with an average RMSE of 0.2815 for all flow depths.
基金supported by the National Natural Science Foundation of China(Grant No.42177164)the Distinguished Youth Science Foundation of Hunan Province of China(Grant No.2022JJ10073)the Innovation-Driven Project of Central South University(Grant No.2020CX040).
文摘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.
基金funded by the Ministry of Higher Education of Malaysia,grant number FRGS/1/2022/ICT02/UPSI/02/1.
文摘In recent years,feature selection(FS)optimization of high-dimensional gene expression data has become one of the most promising approaches for cancer prediction and classification.This work reviews FS and classification methods that utilize evolutionary algorithms(EAs)for gene expression profiles in cancer or medical applications based on research motivations,challenges,and recommendations.Relevant studies were retrieved from four major academic databases-IEEE,Scopus,Springer,and ScienceDirect-using the keywords‘cancer classification’,‘optimization’,‘FS’,and‘gene expression profile’.A total of 67 papers were finally selected with key advancements identified as follows:(1)The majority of papers(44.8%)focused on developing algorithms and models for FS and classification.(2)The second category encompassed studies on biomarker identification by EAs,including 20 papers(30%).(3)The third category comprised works that applied FS to cancer data for decision support system purposes,addressing high-dimensional data and the formulation of chromosome length.These studies accounted for 12%of the total number of studies.(4)The remaining three papers(4.5%)were reviews and surveys focusing on models and developments in prediction and classification optimization for cancer classification under current technical conditions.This review highlights the importance of optimizing FS in EAs to manage high-dimensional data effectively.Despite recent advancements,significant limitations remain:the dynamic formulation of chromosome length remains an underexplored area.Thus,further research is needed on dynamic-length chromosome techniques for more sophisticated biomarker gene selection techniques.The findings suggest that further advancements in dynamic chromosome length formulations and adaptive algorithms could enhance cancer classification accuracy and efficiency.
文摘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.
