This paper presents a method used to the numeral eddy current sensor modelling based on the genetic neural network to settle its nonlinear problem. The principle and algorithms of genetic neural network are introduced...This paper presents a method used to the numeral eddy current sensor modelling based on the genetic neural network to settle its nonlinear problem. The principle and algorithms of genetic neural network are introduced. In this method, the nonlinear model parameters of the numeral eddy current sensor are optimized by genetic neural network (GNN) according to measurement data. So the method remains both the global searching ability of genetic algorithm and the good local searching ability of neural network. The nonlinear model has the advantages of strong robustness, on-line modelling and high precision. The maximum nonlinearity error can be reduced to 0.037% by using GNN. However, the maximum nonlinearity error is 0.075% using the least square method.展开更多
In this paper,we present a method used to the numeral eddy current sensor modeling based on genetic neural network to settle its nonlinear problem.The principle and algorithms of genetic neural network are introduced....In this paper,we present a method used to the numeral eddy current sensor modeling based on genetic neural network to settle its nonlinear problem.The principle and algorithms of genetic neural network are introduced.In this method, the nonlinear model parameters of the numeral eddy current sensor are optimized by genetic neural network (GNN) according to measurement data.So the method remains both the global searching ability of genetic algorithm and the good local searching ability of neural network.The nonlinear model has the advantages of strong robustness,on-line scaling and high precision.The maximum nonlinearity error can be reduced to 0.037% using GNN.However,the maximum nonlinearity error is 0.075% using least square method (LMS).展开更多
Considering the indefinite character of the value of design parameters and being satisfied with load-bearing capacity and stiffness, the fuzzy optimization mathematical model is set up to minimize the volume of tooth ...Considering the indefinite character of the value of design parameters and being satisfied with load-bearing capacity and stiffness, the fuzzy optimization mathematical model is set up to minimize the volume of tooth corona of a worm gear in an elevator mechanism. The method of second-class comprehensive evaluation was used based on the optimal level cut set, thus the optimal level value of every fuzzy constraint can be attained; the fuzzy optimization is transformed into the usual optimization. The Fast Back Propagation of the neural networks algorithm are adopted to train feed-forward networks so as to fit a relative coefficient. Then the fitness function with penalty terms is built by a penalty strategy, a neural networks program is recalled, and solver functions of the Genetic Algorithm Toolbox of Matlab software are adopted to solve the optimization model.展开更多
After the consideration of the nonlinear nature changes of monsoon index,and the subjective determination of network structure in traditional artificial neural network prediction modeling,monthly and seasonal monsoon ...After the consideration of the nonlinear nature changes of monsoon index,and the subjective determination of network structure in traditional artificial neural network prediction modeling,monthly and seasonal monsoon intensity index prediction is studied in this paper by using nonlinear genetic neural network ensemble prediction(GNNEP)modeling.It differs from traditional prediction modeling in the following aspects: (1)Input factors of the GNNEP model of monsoon index were selected from a large quantity of preceding period high correlation factors,such as monthly sea temperature fields,monthly 500-hPa air temperature fields,monthly 200-hPa geopotential height fields,etc.,and they were also highly information-condensed and system dimensionality-reduced by using the empirical orthogonal function(EOF)method,which effectively condensed the useful information of predictors and therefore controlled the size of network structure of the GNNEP model.(2)In the input design of the GNNEP model,a mean generating function(MGF)series of predictand(monsoon index)was added as an input factor;the contrast analysis of results of predic- tion experiments by a physical variable predictor-predictand MGF GNNEP model and a physical variable predictor GNNEP model shows that the incorporation of the periodical variation of predictand(monsoon index)is very effective in improving the prediction of monsoon index.(3)Different from the traditional neural network modeling,the GNNEP modeling is able to objectively determine the network structure of the GNNNEP model,and the model constructed has a better generalization capability.In the case of identical predictors,prediction modeling samples,and independent prediction samples,the prediction accuracy of our GNNEP model combined with the system dimensionality reduction technique of predictors is clearly higher than that of the traditional stepwise regression model using the traditional treatment technique of predictors,suggesting that the GNNEP model opens up a vast range of possibilities for operational weather prediction.展开更多
In order to overcome the system non-linearity and uncertainty inherent in magnetic bearing systems, a GA(genetic algnrithm)-based PID neural network controller is designed and trained tO emulate the operation of a c...In order to overcome the system non-linearity and uncertainty inherent in magnetic bearing systems, a GA(genetic algnrithm)-based PID neural network controller is designed and trained tO emulate the operation of a complete system (magnetic bearing, controller, and power amplifiers). The feasibility of using a neural network to control nonlinear magnetic bearing systems with unknown dynamics is demonstrated. The key concept of the control scheme is to use GA to evaluate the candidate solutions (chromosomes), increase the generalization ability of PID neural network and avoid suffering from the local minima problem in network learning due to the use of gradient descent learning method. The simulation results show that the proposed architecture provides well robust performance and better reinforcement learning capability in controlling magnetic bearing systems.展开更多
A new improved genetic BP algorithm was put forward in the paper. To determine whether the network falls into local minimum point, a discriminant of local minimum was put forth in the training process of a neural netw...A new improved genetic BP algorithm was put forward in the paper. To determine whether the network falls into local minimum point, a discriminant of local minimum was put forth in the training process of a neural network. A genetic algorithm was used to revise the weights of the neural network if the BP algorithm fell into minimums. The mechanical faults were diagnosed using the algorithm put forward in the paper, which verified the validity of this improved genetic BP algorithm.展开更多
Computational fluid dynamics(CFD) can give a lot of potentially very useful information for hydraulic optimization design of pumps, however, it cannot directly state what kind of modification should be made to impro...Computational fluid dynamics(CFD) can give a lot of potentially very useful information for hydraulic optimization design of pumps, however, it cannot directly state what kind of modification should be made to improve such hydrodynamic performance. In this paper, a more convenient and effective approach is proposed by combined using of CFD, multi-objective genetic algorithm(MOGA) and artificial neural networks(ANN) for a double-channel pump's impeller, with maximum head and efficiency set as optimization objectives, four key geometrical parameters including inlet diameter, outlet diameter, exit width and midline wrap angle chosen as optimization parameters. Firstly, a multi-fidelity fitness assignment system in which fitness of impellers serving as training and comparison samples for ANN is evaluated by CFD, meanwhile fitness of impellers generated by MOGA is evaluated by ANN, is established and dramatically reduces the computational expense. Then, a modified MOGA optimization process, in which selection is performed independently in two sub-populations according to two optimization objectives, crossover and mutation is performed afterword in the merged population, is developed to ensure the global optimal solution to be found. Finally, Pareto optimal frontier is found after 500 steps of iterations, and two optimal design schemes are chosen according to the design requirements. The preliminary and optimal design schemes are compared, and the comparing results show that hydraulic performances of both pumps 1 and 2 are improved, with the head and efficiency of pump 1 increased by 5.7% and 5.2%, respectively in the design working conditions, meanwhile shaft power decreased in all working conditions, the head and efficiency of pump 2 increased by 11.7% and 5.9%, respectively while shaft power increased by 5.5%. Inner flow field analyses also show that the backflow phenomenon significantly diminishes at the entrance of the optimal impellers 1 and 2, both the area of vortex and intensity of vortex decreases in the whole flow channel. This paper provides a promising tool to solve the hydraulic optimization problem of pumps' impellers.展开更多
The leaf area index(LAI)is an important agroecological physiological parameter affecting vegetation growth.To apply the genetic algorithms neural network model(GANNM)to the remote sensing inversion of winter wheat LAI...The leaf area index(LAI)is an important agroecological physiological parameter affecting vegetation growth.To apply the genetic algorithms neural network model(GANNM)to the remote sensing inversion of winter wheat LAI throughout the growth cycle and based on GaoFen-3 Synthetic aperture radar(GF-3 SAR)images and GaoFen-1 Wide Field of View(GF-1 WFV)images,the Xiangfu District in the east of Kaifeng City,Henan Province,was selected as the testing region.Winter wheat LAI data from five growth stages were combined,and optical and microwave polarization decomposition vegetation index models were used.The backscattering coefficient was extracted by modified water cloud model(MWCM),and the LAI was obtained by MWCM inversion as input factors to construct GANNM to invert LAI.The root mean square error(RMSE)and determination coefficient(R2)were used as evaluation indicators of the model.The fitting accuracy of winter wheat LAI in five growth stages by GANNM inversion was better than that of the BP neural network model;the R2 was higher than 0.8,and RMSE was lower than 0.3,indicating that the model could accurately invert the growth status of winter wheat in five growth stages.展开更多
In order to investigate the boron removal effect in slag refining process,intermediate frequency furnace was used to purify boron in SiO2-CaO-Na3 AlF6-CaSiO3 slag system at 1,550℃,and back propagation(BP)neural netwo...In order to investigate the boron removal effect in slag refining process,intermediate frequency furnace was used to purify boron in SiO2-CaO-Na3 AlF6-CaSiO3 slag system at 1,550℃,and back propagation(BP)neural network was used to model the relationship between slag compositions and boron content in SiO2-CaO-Na3 AlF6-CaSiO3 slag system.The BP neural network predicted error is below 2.38%.The prediction results show that the slag composition has a significant influence on boron removal.Increasing the basicity of slag by adding CaO or Na3 AlF6 to CaSiO3-based slag could contribute to the boron removal,and the addition of Na3 AlF6 has a better removal effect in comparison with the addition of CaO.The oxidizing characteristic of CaSiO3 results in the ineffective removal with the addition of SiO2.The increase of oxygen potential(pO2)in the CaO-Na3 AlF6-CaSiO3 slag system by varying the SiO2 proportion can also contribute to the boron removal in silicon ingot.The best slag composition to remove boron was predicted by BP neural network using genetic algorithm(GA).The predicted results show that the mass fraction of boron in silicon reduces from 14.0000×10-6 to0.4366×10-6 after slag melting using 23.12%SiO2-10.44%CaO-16.83%Na3 AlF6-49.61%CaSiO3 slag system,close to the experimental boron content in silicon which is below 0.5×10-6.展开更多
Genetic algorithm and partial least square(GA-PLS),kernel PLS(KPLS) and Levenberg-Marquardt artificial neural network(L-M ANN) techniques were used to investigate the correlation between retention time(RT) and...Genetic algorithm and partial least square(GA-PLS),kernel PLS(KPLS) and Levenberg-Marquardt artificial neural network(L-M ANN) techniques were used to investigate the correlation between retention time(RT) and descriptors for 15 nanoparticle compounds obtained by the comprehensive two-dimensional gas chromatography system(GC × GC).Application of the dodecanethiol monolayer-protected gold nanoparticle(MPN) column was for a high-speed separation as the second column of GC × GC.The L-M ANN model with the final optimum network architecture of [13-5-1] gave a significantly better performance than the other models.This is the first research on the quantitative structure-retention relationship(QSRR) of nanoparticle compounds using the GA-PLS,GA-KPLS and L-M ANN.展开更多
Pollution flashover accidents occur frequently in railway OCS in saline-alkali areas.To accurately predict the pollution flashover voltage of insulators,a pollution flashover warning should be made in advance.Accordin...Pollution flashover accidents occur frequently in railway OCS in saline-alkali areas.To accurately predict the pollution flashover voltage of insulators,a pollution flashover warning should be made in advance.According to the operating environment of insulators along the Qinghai-Tibet railway,the pollution flashover experiments were designed for the cantilever composite insulator FQBG-25/12.Through the experiments,the flashover voltage under the influence of soluble contaminant density(SCD)of different pollution components,non-soluble deposit density(NSDD),temperature(T),and atmospheric pressure(P)was obtained.On this basis,the GA-BP neural network prediction model was established.P,SCD,NSDD,CaSO_(4) mass fraction(w(CaSO_(4))),and T were taken as input parameters,50%flashover voltage(U_(50%))of the insulator was taken as output parameters.The results showed that the prediction deviation was less than 10%,which meets the basic engineering requirements.The results could not only provide early warning for the anti-pollution flashover work of the railway power supply department,but also be used as an auxiliary contrast to verify the accuracy of the results of the experiments,and provide a theoretical basis for the classification of pollution levels in different regions.展开更多
Since the overall prediction error of a classifier on imbalanced problems can be potentially misleading and bi- ased, alternative performance measures such as G-mean and F-measure have been widely adopted. Various tec...Since the overall prediction error of a classifier on imbalanced problems can be potentially misleading and bi- ased, alternative performance measures such as G-mean and F-measure have been widely adopted. Various techniques in- cluding sampling and cost sensitive learning are often em- ployed to improve the performance of classifiers in such sit- uations. However, the training process of classifiers is still largely driven by traditional error based objective functions. As a result, there is clearly a gap between the measure accord- ing to which the classifier is evaluated and how the classifier is trained. This paper investigates the prospect of explicitly using the appropriate measure itself to search the hypothesis space to bridge this gap. In the case studies, a standard three- layer neural network is used as the classifier, which is evolved by genetic algorithms (GAs) with G-mean as the objective function. Experimental results on eight benchmark problems show that the proposed method can achieve consistently fa- vorable outcomes in comparison with a commonly used sam- pling technique. The effectiveness of multi-objective opti- mization in handling imbalanced problems is also demon- strated.展开更多
基金Project supported by the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province,Chinathe Foundation of Huaiyin Teachers College Professor,China(Grant Nos07KJD510027 and 06HSJS020)
文摘This paper presents a method used to the numeral eddy current sensor modelling based on the genetic neural network to settle its nonlinear problem. The principle and algorithms of genetic neural network are introduced. In this method, the nonlinear model parameters of the numeral eddy current sensor are optimized by genetic neural network (GNN) according to measurement data. So the method remains both the global searching ability of genetic algorithm and the good local searching ability of neural network. The nonlinear model has the advantages of strong robustness, on-line modelling and high precision. The maximum nonlinearity error can be reduced to 0.037% by using GNN. However, the maximum nonlinearity error is 0.075% using the least square method.
文摘In this paper,we present a method used to the numeral eddy current sensor modeling based on genetic neural network to settle its nonlinear problem.The principle and algorithms of genetic neural network are introduced.In this method, the nonlinear model parameters of the numeral eddy current sensor are optimized by genetic neural network (GNN) according to measurement data.So the method remains both the global searching ability of genetic algorithm and the good local searching ability of neural network.The nonlinear model has the advantages of strong robustness,on-line scaling and high precision.The maximum nonlinearity error can be reduced to 0.037% using GNN.However,the maximum nonlinearity error is 0.075% using least square method (LMS).
文摘Considering the indefinite character of the value of design parameters and being satisfied with load-bearing capacity and stiffness, the fuzzy optimization mathematical model is set up to minimize the volume of tooth corona of a worm gear in an elevator mechanism. The method of second-class comprehensive evaluation was used based on the optimal level cut set, thus the optimal level value of every fuzzy constraint can be attained; the fuzzy optimization is transformed into the usual optimization. The Fast Back Propagation of the neural networks algorithm are adopted to train feed-forward networks so as to fit a relative coefficient. Then the fitness function with penalty terms is built by a penalty strategy, a neural networks program is recalled, and solver functions of the Genetic Algorithm Toolbox of Matlab software are adopted to solve the optimization model.
基金the New Technology Extension Project of China Meteorological Administration under Grant No.GMATG2008M49the National Natural Science Foundation of China under Grant No.40675023
文摘After the consideration of the nonlinear nature changes of monsoon index,and the subjective determination of network structure in traditional artificial neural network prediction modeling,monthly and seasonal monsoon intensity index prediction is studied in this paper by using nonlinear genetic neural network ensemble prediction(GNNEP)modeling.It differs from traditional prediction modeling in the following aspects: (1)Input factors of the GNNEP model of monsoon index were selected from a large quantity of preceding period high correlation factors,such as monthly sea temperature fields,monthly 500-hPa air temperature fields,monthly 200-hPa geopotential height fields,etc.,and they were also highly information-condensed and system dimensionality-reduced by using the empirical orthogonal function(EOF)method,which effectively condensed the useful information of predictors and therefore controlled the size of network structure of the GNNEP model.(2)In the input design of the GNNEP model,a mean generating function(MGF)series of predictand(monsoon index)was added as an input factor;the contrast analysis of results of predic- tion experiments by a physical variable predictor-predictand MGF GNNEP model and a physical variable predictor GNNEP model shows that the incorporation of the periodical variation of predictand(monsoon index)is very effective in improving the prediction of monsoon index.(3)Different from the traditional neural network modeling,the GNNEP modeling is able to objectively determine the network structure of the GNNNEP model,and the model constructed has a better generalization capability.In the case of identical predictors,prediction modeling samples,and independent prediction samples,the prediction accuracy of our GNNEP model combined with the system dimensionality reduction technique of predictors is clearly higher than that of the traditional stepwise regression model using the traditional treatment technique of predictors,suggesting that the GNNEP model opens up a vast range of possibilities for operational weather prediction.
基金This project is supported by National Natural Science Foundation of China (No. 5880203).
文摘In order to overcome the system non-linearity and uncertainty inherent in magnetic bearing systems, a GA(genetic algnrithm)-based PID neural network controller is designed and trained tO emulate the operation of a complete system (magnetic bearing, controller, and power amplifiers). The feasibility of using a neural network to control nonlinear magnetic bearing systems with unknown dynamics is demonstrated. The key concept of the control scheme is to use GA to evaluate the candidate solutions (chromosomes), increase the generalization ability of PID neural network and avoid suffering from the local minima problem in network learning due to the use of gradient descent learning method. The simulation results show that the proposed architecture provides well robust performance and better reinforcement learning capability in controlling magnetic bearing systems.
文摘A new improved genetic BP algorithm was put forward in the paper. To determine whether the network falls into local minimum point, a discriminant of local minimum was put forth in the training process of a neural network. A genetic algorithm was used to revise the weights of the neural network if the BP algorithm fell into minimums. The mechanical faults were diagnosed using the algorithm put forward in the paper, which verified the validity of this improved genetic BP algorithm.
基金Supported by National Natural Science Foundation of China(Grant No.51109094)Priority Academic Program Development of Jiangsu Higher Education Institutions of China
文摘Computational fluid dynamics(CFD) can give a lot of potentially very useful information for hydraulic optimization design of pumps, however, it cannot directly state what kind of modification should be made to improve such hydrodynamic performance. In this paper, a more convenient and effective approach is proposed by combined using of CFD, multi-objective genetic algorithm(MOGA) and artificial neural networks(ANN) for a double-channel pump's impeller, with maximum head and efficiency set as optimization objectives, four key geometrical parameters including inlet diameter, outlet diameter, exit width and midline wrap angle chosen as optimization parameters. Firstly, a multi-fidelity fitness assignment system in which fitness of impellers serving as training and comparison samples for ANN is evaluated by CFD, meanwhile fitness of impellers generated by MOGA is evaluated by ANN, is established and dramatically reduces the computational expense. Then, a modified MOGA optimization process, in which selection is performed independently in two sub-populations according to two optimization objectives, crossover and mutation is performed afterword in the merged population, is developed to ensure the global optimal solution to be found. Finally, Pareto optimal frontier is found after 500 steps of iterations, and two optimal design schemes are chosen according to the design requirements. The preliminary and optimal design schemes are compared, and the comparing results show that hydraulic performances of both pumps 1 and 2 are improved, with the head and efficiency of pump 1 increased by 5.7% and 5.2%, respectively in the design working conditions, meanwhile shaft power decreased in all working conditions, the head and efficiency of pump 2 increased by 11.7% and 5.9%, respectively while shaft power increased by 5.5%. Inner flow field analyses also show that the backflow phenomenon significantly diminishes at the entrance of the optimal impellers 1 and 2, both the area of vortex and intensity of vortex decreases in the whole flow channel. This paper provides a promising tool to solve the hydraulic optimization problem of pumps' impellers.
基金funded by 2016 National Key Research and Development Plan(grant number 2016YFC0803103)Research on Key Technology of Agricultural Remote Sensing Monitoring(grant number 12210243)and Henan Provincial University Innovation Team Support Plan(grant number 14IRTSTHN026).
文摘The leaf area index(LAI)is an important agroecological physiological parameter affecting vegetation growth.To apply the genetic algorithms neural network model(GANNM)to the remote sensing inversion of winter wheat LAI throughout the growth cycle and based on GaoFen-3 Synthetic aperture radar(GF-3 SAR)images and GaoFen-1 Wide Field of View(GF-1 WFV)images,the Xiangfu District in the east of Kaifeng City,Henan Province,was selected as the testing region.Winter wheat LAI data from five growth stages were combined,and optical and microwave polarization decomposition vegetation index models were used.The backscattering coefficient was extracted by modified water cloud model(MWCM),and the LAI was obtained by MWCM inversion as input factors to construct GANNM to invert LAI.The root mean square error(RMSE)and determination coefficient(R2)were used as evaluation indicators of the model.The fitting accuracy of winter wheat LAI in five growth stages by GANNM inversion was better than that of the BP neural network model;the R2 was higher than 0.8,and RMSE was lower than 0.3,indicating that the model could accurately invert the growth status of winter wheat in five growth stages.
基金financially supported by the National High Technology Research and Development Program of China (No.2012AA062302)。
文摘In order to investigate the boron removal effect in slag refining process,intermediate frequency furnace was used to purify boron in SiO2-CaO-Na3 AlF6-CaSiO3 slag system at 1,550℃,and back propagation(BP)neural network was used to model the relationship between slag compositions and boron content in SiO2-CaO-Na3 AlF6-CaSiO3 slag system.The BP neural network predicted error is below 2.38%.The prediction results show that the slag composition has a significant influence on boron removal.Increasing the basicity of slag by adding CaO or Na3 AlF6 to CaSiO3-based slag could contribute to the boron removal,and the addition of Na3 AlF6 has a better removal effect in comparison with the addition of CaO.The oxidizing characteristic of CaSiO3 results in the ineffective removal with the addition of SiO2.The increase of oxygen potential(pO2)in the CaO-Na3 AlF6-CaSiO3 slag system by varying the SiO2 proportion can also contribute to the boron removal in silicon ingot.The best slag composition to remove boron was predicted by BP neural network using genetic algorithm(GA).The predicted results show that the mass fraction of boron in silicon reduces from 14.0000×10-6 to0.4366×10-6 after slag melting using 23.12%SiO2-10.44%CaO-16.83%Na3 AlF6-49.61%CaSiO3 slag system,close to the experimental boron content in silicon which is below 0.5×10-6.
文摘Genetic algorithm and partial least square(GA-PLS),kernel PLS(KPLS) and Levenberg-Marquardt artificial neural network(L-M ANN) techniques were used to investigate the correlation between retention time(RT) and descriptors for 15 nanoparticle compounds obtained by the comprehensive two-dimensional gas chromatography system(GC × GC).Application of the dodecanethiol monolayer-protected gold nanoparticle(MPN) column was for a high-speed separation as the second column of GC × GC.The L-M ANN model with the final optimum network architecture of [13-5-1] gave a significantly better performance than the other models.This is the first research on the quantitative structure-retention relationship(QSRR) of nanoparticle compounds using the GA-PLS,GA-KPLS and L-M ANN.
基金Supported by the National Natural Science Foundation of China(51767014)the Scientific and Technological Research and Development Program of the China Railway(2017J010-C/2017).
文摘Pollution flashover accidents occur frequently in railway OCS in saline-alkali areas.To accurately predict the pollution flashover voltage of insulators,a pollution flashover warning should be made in advance.According to the operating environment of insulators along the Qinghai-Tibet railway,the pollution flashover experiments were designed for the cantilever composite insulator FQBG-25/12.Through the experiments,the flashover voltage under the influence of soluble contaminant density(SCD)of different pollution components,non-soluble deposit density(NSDD),temperature(T),and atmospheric pressure(P)was obtained.On this basis,the GA-BP neural network prediction model was established.P,SCD,NSDD,CaSO_(4) mass fraction(w(CaSO_(4))),and T were taken as input parameters,50%flashover voltage(U_(50%))of the insulator was taken as output parameters.The results showed that the prediction deviation was less than 10%,which meets the basic engineering requirements.The results could not only provide early warning for the anti-pollution flashover work of the railway power supply department,but also be used as an auxiliary contrast to verify the accuracy of the results of the experiments,and provide a theoretical basis for the classification of pollution levels in different regions.
文摘Since the overall prediction error of a classifier on imbalanced problems can be potentially misleading and bi- ased, alternative performance measures such as G-mean and F-measure have been widely adopted. Various techniques in- cluding sampling and cost sensitive learning are often em- ployed to improve the performance of classifiers in such sit- uations. However, the training process of classifiers is still largely driven by traditional error based objective functions. As a result, there is clearly a gap between the measure accord- ing to which the classifier is evaluated and how the classifier is trained. This paper investigates the prospect of explicitly using the appropriate measure itself to search the hypothesis space to bridge this gap. In the case studies, a standard three- layer neural network is used as the classifier, which is evolved by genetic algorithms (GAs) with G-mean as the objective function. Experimental results on eight benchmark problems show that the proposed method can achieve consistently fa- vorable outcomes in comparison with a commonly used sam- pling technique. The effectiveness of multi-objective opti- mization in handling imbalanced problems is also demon- strated.