Optimizing Grey Wolf Optimization: A Novel Agents’ Positions Updating Technique for Enhanced Efficiency and Performance

Grey Wolf Optimization (GWO) is a nature-inspired metaheuristic algorithm that has gained popularity for solving optimization problems. In GWO, the success of the algorithm heavily relies on the efficient updating of the agents’ positions relative to the leader wolves. In this paper, we provide a brief overview of the Grey Wolf Optimization technique and its significance in solving complex optimization problems. Building upon the foundation of GWO, we introduce a novel technique for updating agents’ positions, which aims to enhance the algorithm’s effectiveness and efficiency. To evaluate the performance of our proposed approach, we conduct comprehensive experiments and compare the results with the original Grey Wolf Optimization technique. Our comparative analysis demonstrates that the proposed technique achieves superior optimization outcomes. These findings underscore the potential of our approach in addressing optimization challenges effectively and efficiently, making it a valuable contribution to the field of optimization algorithms.

Enhancing Hyper-Spectral Image Classification with Reinforcement Learning and Advanced Multi-Objective Binary Grey Wolf Optimization

Hyperspectral(HS)image classification plays a crucial role in numerous areas including remote sensing(RS),agriculture,and the monitoring of the environment.Optimal band selection in HS images is crucial for improving the efficiency and accuracy of image classification.This process involves selecting the most informative spectral bands,which leads to a reduction in data volume.Focusing on these key bands also enhances the accuracy of classification algorithms,as redundant or irrelevant bands,which can introduce noise and lower model performance,are excluded.In this paper,we propose an approach for HS image classification using deep Q learning(DQL)and a novel multi-objective binary grey wolf optimizer(MOBGWO).We investigate the MOBGWO for optimal band selection to further enhance the accuracy of HS image classification.In the suggested MOBGWO,a new sigmoid function is introduced as a transfer function to modify the wolves’position.The primary objective of this classification is to reduce the number of bands while maximizing classification accuracy.To evaluate the effectiveness of our approach,we conducted experiments on publicly available HS image datasets,including Pavia University,Washington Mall,and Indian Pines datasets.We compared the performance of our proposed method with several state-of-the-art deep learning(DL)and machine learning(ML)algorithms,including long short-term memory(LSTM),deep neural network(DNN),recurrent neural network(RNN),support vector machine(SVM),and random forest(RF).Our experimental results demonstrate that the Hybrid MOBGWO-DQL significantly improves classification accuracy compared to traditional optimization and DL techniques.MOBGWO-DQL shows greater accuracy in classifying most categories in both datasets used.For the Indian Pine dataset,the MOBGWO-DQL architecture achieved a kappa coefficient(KC)of 97.68%and an overall accuracy(OA)of 94.32%.This was accompanied by the lowest root mean square error(RMSE)of 0.94,indicating very precise predictions with minimal error.In the case of the Pavia University dataset,the MOBGWO-DQL model demonstrated outstanding performance with the highest KC of 98.72%and an impressive OA of 96.01%.It also recorded the lowest RMSE at 0.63,reinforcing its accuracy in predictions.The results clearly demonstrate that the proposed MOBGWO-DQL architecture not only reaches a highly accurate model more quickly but also maintains superior performance throughout the training process.

Hybrid Dipper Throated and Grey Wolf Optimization for Feature Selection Applied to Life Benchmark Datasets

Selecting the most relevant subset of features from a dataset is a vital step in data mining and machine learning.Each feature in a dataset has 2n possible subsets,making it challenging to select the optimum collection of features using typical methods.As a result,a new metaheuristicsbased feature selection method based on the dipper-throated and grey-wolf optimization(DTO-GW)algorithms has been developed in this research.Instability can result when the selection of features is subject to metaheuristics,which can lead to a wide range of results.Thus,we adopted hybrid optimization in our method of optimizing,which allowed us to better balance exploration and harvesting chores more equitably.We propose utilizing the binary DTO-GW search approach we previously devised for selecting the optimal subset of attributes.In the proposed method,the number of features selected is minimized,while classification accuracy is increased.To test the proposed method’s performance against eleven other state-of-theart approaches,eight datasets from the UCI repository were used,such as binary grey wolf search(bGWO),binary hybrid grey wolf,and particle swarm optimization(bGWO-PSO),bPSO,binary stochastic fractal search(bSFS),binary whale optimization algorithm(bWOA),binary modified grey wolf optimization(bMGWO),binary multiverse optimization(bMVO),binary bowerbird optimization(bSBO),binary hysteresis optimization(bHy),and binary hysteresis optimization(bHWO).The suggested method is superior 4532 CMC,2023,vol.74,no.2 and successful in handling the problem of feature selection,according to the results of the experiments.

Recognizing Ancient South Indian Language Using Opposition Based Grey Wolf Optimization

Recognizing signs and fonts of prehistoric language is a fairly difficult job that requires special tools.This stipulation make the dispensation period over-riding,difficult and tiresome to calculate.This paper present a technique for recognizing ancient south Indian languages by applying Artificial Neural Network(ANN)associated with Opposition based Grey Wolf Optimization Algorithm(OGWA).It identifies the prehistoric language,signs and fonts.It is an apparent from the ANN system that arbitrarily produced weights or neurons linking various layers play a significant role in its performance.For adaptively determining these weights,this paper applies various optimization algorithms such as Opposition based Grey Wolf Optimization,Particle Swarm Optimization and Grey Wolf Opti-mization to the ANN system.Performance results are illustrated that the proposed ANN-OGWO technique achieves superior accuracy over the other techniques.In test case 1,the accuracy value of OGWO is 94.89%and in test case 2,the accu-racy value of OGWO is 92.34%,on average,the accuracy of OGWO achieves 5.8%greater accuracy than ANN-GWO,10.1%greater accuracy than ANN-PSO and 22.1%greater accuracy over conventional ANN technique.

A Grey Wolf Optimization-Based Tilt Tri-rotor UAV Altitude Control in Transition Mode

To solve the problem of altitude control of a tilt tri-rotor unmanned aerial vehicle(UAV)in the transition mode,this study presents a grey wolf optimization(GWO)based neural network adaptive control scheme for a tilt trirotor UAV in the transition mode.Firstly,the nonlinear model of the tilt tri-rotor UAV is established.Secondly,the tilt tri-rotor UAV altitude controller and attitude controller are designed by a neural network adaptive control method,and the GWO algorithm is adopted to optimize the parameters of the neural network and the controllers.Thirdly,two altitude control strategies are designed in the transition mode.Finally,comparative simulations are carried out to demonstrate the effectiveness and robustness of the proposed control scheme.

Proportion integral-type active disturbance rejection generalized predictive control for distillation process based on grey wolf optimization parameter tuning

The high-purity distillation column system is strongly nonlinear and coupled,which makes it difficult to control.Active disturbance rejection control(ADRC)has been widely used in distillation systems,but it has limitations in controlling distillation systems with large time delays since ADRC employs ESO and feedback control law to estimate the total disturbance of the system without considering the large time delays.This paper designs a proportion integral-type active disturbance rejection generalized predictive control(PI-ADRGPC)algorithm to control the distillation column system with large time delay.It replaces the PD controller in ADRC with a proportion integral-type generalized predictive control(PI-GPC),thereby improving the performance of control systems with large time delays.Since the proposed controller has many parameters and is difficult to tune,this paper proposes to use the grey wolf optimization(GWO)to tune these parameters,whose structure can also be used by other intelligent optimization algorithms.The performance of GWO tuned PI-ADRGPC is compared with the control performance of GWO tuned ADRC method,multi-verse optimizer(MVO)tuned PI-ADRGPC and MVO tuned ADRC.The simulation results show that the proposed strategy can track reference well and has a good disturbance rejection performance.

Feature Selection Using Grey Wolf Optimization with Random Differential Grouping

Big data are regarded as a tremendous technology for processing a huge variety of data in a short time and with a large storage capacity.The user’s access over the internet creates massive data processing over the internet.Big data require an intelligent feature selection model by addressing huge varieties of data.Traditional feature selection techniques are only applicable to simple data mining.Intelligent techniques are needed in big data processing and machine learning for an efficient classification.Major feature selection algorithms read the input features as they are.Then,the features are preprocessed and classified.Here,an algorithm does not consider the relatedness.During feature selection,all features are misread as outputs.Accordingly,a less optimal solution is achieved.In our proposed research,we focus on the feature selection by using supervised learning techniques called grey wolf optimization(GWO)with decomposed random differential grouping(DrnDG-GWO).First,decomposition of features into subsets based on relatedness in variables is performed.Random differential grouping is performed using a fitness value of two variables.Now,every subset is regarded as a population in GWO techniques.The combination of supervised machine learning with swarm intelligence techniques produces best feature optimization results in this research.Once the features are optimized,we classify using advanced kNN process for accurate data classification.The result of DrnDGGWO is compared with those of the standard GWO and GWO with PSO for feature selection to compare the efficiency of the proposed algorithm.The accuracy and time complexity of the proposed algorithm are 98%and 5 s,which are better than the existing techniques.

Grey Wolf Optimization Based Tuning of Terminal Sliding Mode Controllers for a Quadrotor

The research on Unmanned Aerial Vehicles(UAV)has intensified considerably thanks to the recent growth in the fields of advanced automatic control,artificial intelligence,and miniaturization.In this paper,a Grey Wolf Optimization(GWO)algorithm is proposed and successfully applied to tune all effective parameters of Fast Terminal Sliding Mode(FTSM)controllers for a quadrotor UAV.A full control scheme is first established to deal with the coupled and underactuated dynamics of the drone.Controllers for altitude,attitude,and position dynamics become separately designed and tuned.To work around the repetitive and time-consuming trial-error-based procedures,all FTSM controllers’parameters for only altitude and attitude dynamics are systematically tuned thanks to the proposed GWO metaheuristic.Such a hard and complex tuning task is formulated as a nonlinear optimization problem under operational constraints.The performance and robustness of the GWO-based control strategy are compared to those based on homologous metaheuristics and standard terminal sliding mode approaches.Numerical simulations are carried out to show the effectiveness and superiority of the proposed GWO-tuned FTSM controllers for the altitude and attitude dynamics’stabilization and tracking.Nonparametric statistical analyses revealed that the GWO algorithm is more competitive with high performance in terms of fastness,non-premature convergence,and research exploration/exploitation capabilities.

Forecasting Multi-Step Ahead Monthly Reference Evapotranspiration Using Hybrid Extreme Gradient Boosting with Grey Wolf Optimization Algorithm

It is important for regional water resources management to know the agricultural water consumption information several months in advance.Forecasting reference evapotranspiration(ET_(0))in the next few months is important for irrigation and reservoir management.Studies on forecasting of multiple-month ahead ET_(0) using machine learning models have not been reported yet.Besides,machine learning models such as the XGBoost model has multiple parameters that need to be tuned,and traditional methods can get stuck in a regional optimal solution and fail to obtain a global optimal solution.This study investigated the performance of the hybrid extreme gradient boosting(XGBoost)model coupled with the Grey Wolf Optimizer(GWO)algorithm for forecasting multi-step ahead ET_(0)(1-3 months ahead),compared with three conventional machine learning models,i.e.,standalone XGBoost,multi-layer perceptron(MLP)and M5 model tree(M5)models in the subtropical zone of China.The results showed that theGWO-XGB model generally performed better than the other three machine learning models in forecasting 1-3 months ahead ET_(0),followed by the XGB,M5 and MLP models with very small differences among the three models.The GWO-XGB model performed best in autumn,while the MLP model performed slightly better than the other three models in summer.It is thus suggested to apply the MLP model for ET_(0) forecasting in summer but use the GWO-XGB model in other seasons.

Multi-Objective Grey Wolf Optimization Algorithm for Solving Real-World BLDC Motor Design Problem

The first step in the design phase of the Brushless Direct Current(BLDC)motor is the formulation of the mathematical framework and is often used due to its analytical structure.Therefore,the BLDC motor design problem is considered to be an optimization problem.In this paper,the analytical model of the BLDC motor is presented,and it is considered to be a basis for emphasizing the optimization methods.The analytical model used for the experimentation has 78 non-linear equations,two objective functions,five design variables,and six non-linear constraints,so the BLDC motor design problem is considered as highly non-linear in electromagnetic optimization.Multi-objective optimization becomes the forefront of the current research to obtain the global best solution using metaheuristic techniques.The bio-inspired multi-objective grey wolf optimizer(MOGWO)is presented in this paper,and it is formulated based on Pareto optimality,dominance,and archiving external.The performance of theMOGWO is verified on standard multi-objective unconstraint benchmark functions and applied to the BLDC motor design problem.The results proved that the proposedMOGWO algorithm could handle nonlinear constraints in electromagnetic optimization problems.The performance comparison in terms of Generational Distance,inversion GD,Hypervolume-matrix,scattered-matrix,and coverage metrics proves that the MOGWO algorithm can provide the best solution compared to other selected algorithms.The source code of this paper is backed up with extra online support at https://premkumarmanoharan.wixsite.com/mysite and https://www.mathworks.com/matlabcentral/fileexchange/75259-multiobjective-non-sorted-grey-wolf-mogwo-nsgwo.

Energy-Saving Distributed Flexible Job Shop Scheduling Optimization with Dual Resource Constraints Based on Integrated Q-Learning Multi-Objective Grey Wolf Optimizer

The distributed flexible job shop scheduling problem(DFJSP)has attracted great attention with the growth of the global manufacturing industry.General DFJSP research only considers machine constraints and ignores worker constraints.As one critical factor of production,effective utilization of worker resources can increase productivity.Meanwhile,energy consumption is a growing concern due to the increasingly serious environmental issues.Therefore,the distributed flexible job shop scheduling problem with dual resource constraints(DFJSP-DRC)for minimizing makespan and total energy consumption is studied in this paper.To solve the problem,we present a multi-objective mathematical model for DFJSP-DRC and propose a Q-learning-based multi-objective grey wolf optimizer(Q-MOGWO).In Q-MOGWO,high-quality initial solutions are generated by a hybrid initialization strategy,and an improved active decoding strategy is designed to obtain the scheduling schemes.To further enhance the local search capability and expand the solution space,two wolf predation strategies and three critical factory neighborhood structures based on Q-learning are proposed.These strategies and structures enable Q-MOGWO to explore the solution space more efficiently and thus find better Pareto solutions.The effectiveness of Q-MOGWO in addressing DFJSP-DRC is verified through comparison with four algorithms using 45 instances.The results reveal that Q-MOGWO outperforms comparison algorithms in terms of solution quality.

Deformation resistance prediction of tandem cold rolling based on grey wolf optimization and support vector regression

In the traditional rolling force model of tandem cold rolling mills,the calculation of the deformation resistance of the strip head does not consider the actual size and mechanical properties of the incoming material,which results in a mismatch between the deformation resistance setting and the actual state of the incoming material and thus affects the accuracy of the rolling force during the low-speed rolling process of the strip head.The inverse calculation of deformation resistance was derived to obtain the actual deformation resistance of the strip head in the tandem cold rolling process,and the actual process parameters of the strip in the hot and cold rolling processes were integrated to create the cross-process dataset as the basis to establish the support vector regression(SVR)model.The grey wolf optimization(GWO)algorithm was used to optimize the hyperparameters in the SVR model,and a deformation resistance prediction model based on GWO–SVR was established.Compared with the traditional model,the GWO–SVR model shows different degrees of improvement in each stand,with significant improvement in stands S3–S5.The prediction results of the GWO–SVR model were applied to calculate the head rolling setting of a 1420 mm tandem rolling mill.The head rolling force had a similar degree of improvement in accuracy to the deformation resistance,and the phenomenon of low head rolling force setting from stands S3 to S5 was obviously improved.Meanwhile,the thickness quality and shape quality of the strip head were improved accordingly,and the application results were consistent with expectations.

Hybrid Grey Wolf and Dipper Throated Optimization in Network Intrusion Detection Systems

The Internet of Things(IoT)is a modern approach that enables connection with a wide variety of devices remotely.Due to the resource constraints and open nature of IoT nodes,the routing protocol for low power and lossy(RPL)networks may be vulnerable to several routing attacks.That’s why a network intrusion detection system(NIDS)is needed to guard against routing assaults on RPL-based IoT networks.The imbalance between the false and valid attacks in the training set degrades the performance of machine learning employed to detect network attacks.Therefore,we propose in this paper a novel approach to balance the dataset classes based on metaheuristic optimization applied to locality-sensitive hashing and synthetic minority oversampling technique(LSH-SMOTE).The proposed optimization approach is based on a new hybrid between the grey wolf and dipper throated optimization algorithms.To prove the effectiveness of the proposed approach,a set of experiments were conducted to evaluate the performance of NIDS for three cases,namely,detection without dataset balancing,detection with SMOTE balancing,and detection with the proposed optimized LSHSOMTE balancing.Experimental results showed that the proposed approach outperforms the other approaches and could boost the detection accuracy.In addition,a statistical analysis is performed to study the significance and stability of the proposed approach.The conducted experiments include seven different types of attack cases in the RPL-NIDS17 dataset.Based on the 2696 CMC,2023,vol.74,no.2 proposed approach,the achieved accuracy is(98.1%),sensitivity is(97.8%),and specificity is(98.8%).

Prediction of Backfill Strength Based on Support Vector Regression Improved by Grey Wolf Optimization

In order to predict backfill strength rapidly with high accuracy and provide a new technical support for digitization and intelligentization of mine,a support vector regression(SVR)model improved by grey wolf optimization(GWO),GWO-SVR model,is established.First,GWO is used to optimize penalty term and kernel function parameter in SVR model with high accuracy based on the experimental data of uniaxial compressive strength of filling body.Subsequently,a prediction model which uses the best two parameters of best c and best g is established with the slurry density,cement dosage,ratio of artificial aggregate to tailings,and curing time taken as input factors,and uniaxial compressive strength of backfill as the output factor.The root mean square error of this GWO-SVR model in predicting backfill strength is 0.143 and the coefficient of determination is 0.983,which means that the predictive effect of this model is accurate and reliable.Compared with the original SVR model without the optimization of GWO and particle swam optimization(PSO)-SVR model,the performance of GWO-SVR model is greatly promoted.The establishment of GWO-SVR model provides a new tool for predicting backfill strength scientifically.

Allocation and sizing of reactive power compensators considering PV power and load demand uncertainty using beetle-antenna grey wolf optimization

Distributed photovoltaic(PV)systems play an important role in supplying many recent microgrids.The absence of reactive power support for these small-scale PV plants increases total microgrid losses and voltage-instability threats.Reactive power compensations(RPCs)should be integrated to enhance both microgrid losses and voltage profiles.RPC planning is a non-linear,complicated problem.In this paper,a combined RPC allocation and sizing algorithm is proposed.The RPC-integrating buses are selected using a new adaptive approach of loss sensitivity analysis.In the sizing process,the uncertainties in PV power and load demand are modelled using proper probability density functions.Three simulation techniques for handling uncertainties are compared to define the accurate and fast accurate method as follows:Monte Carlo simulation(MCS),scenario tree construction and reduction method,and point estimation method(PEM).The load flow equations are solved using the forward-backward sweep method.RPCs are optimally sized using the beetle-antenna-based strategy with grey wolf optimization(BGWO)to overcome the local minima problem that appeared in the other pre-proposed methods.Results have been compared using particle swarm optimization and conventional GWO.The proposed model is verified using the IEEE 33 radial bus system.The expected power loss has been reduced by 22% and 31% using compensation of 26% and 44%,respectively.The results obtained prove that the BGWO optimal power flow and PEM to handle the uncertainty can significantly reduce the computation time with sufficient accuracy.Under the study conditions,PEM reduces the computation time to 4 minutes compared with 4 hours for MCS,with only a 3% error compared with MCS as an uncertainty benchmark method.

Multi-UAV coordination control by chaotic grey wolf optimization based distributed MPC with event-triggered strategy

The paper proposes a new swarm intelligence-based distributed Model Predictive Control(MPC)approach for coordination control of multiple Unmanned Aerial Vehicles(UAVs).First,a distributed MPC framework is designed and each member only shares the information with neighbors.The Chaotic Grey Wolf Optimization(CGWO)method is developed on the basis of chaotic initialization and chaotic search to solve the local Finite Horizon Optimal Control Problem(FHOCP).Then,the distributed cost function is designed and integrated into each FHOCP to achieve multi-UAV formation control and trajectory tracking with no-fly zone constraint.Further,an event-triggered strategy is proposed to reduce the computational burden for the distributed MPC approach,which considers the predicted state errors and the convergence of cost function.Simulation results show that the CGWO-based distributed MPC approach is more computationally efficient to achieve multi-UAV coordination control than traditional method.

Application of a simplified Grey Wolf optimization technique for adaptive fuzzy PID controller design for frequency regulation of a distributed power generation system

A Simplified Grey Wolf Optimizer(SGWO)is suggested for resolving optimization tasks.The simplification in the original Grey Wolf Optimizer(GWO)method is introduced by ignoring the worst category wolves while giving priority to the better wolves during the search process.The advantage of the presented SGWO over GWO is a better solution taking less execution time and is demonstrated by taking unimodal,multimodal,and fixed dimension test functions.The results are also contrasted to the Gravitational Search Algorithm,the Particle Swarm Optimization,and the Sine Cosine Algorithm and this shows the superiority of the proposed SGWO technique.Practical application in a Distributed Power Generation System(DPGS)with energy storage is then considered by designing an Adaptive Fuzzy PID(AFPID)controller using the suggested SGWO method for frequency control.The DPGS contains renewable generation such as photovoltaic,wind,and storage elements such as battery and flywheel,in addition to plug-in electric vehicles.It is demonstrated that the SGWO method is superior to the GWO method in the optimal controller design task.It is also seen that SGWO based AFPID controller is highly efficacious in regulating the frequency compared to the standard PID controller.A sensitivity study is also performed to examine the impact of the unpredictability in the parameters of the investigated system on system performance.Finally,the novelty of the paper is demonstrated by comparing with the existing publications in an extensively used two-area test system.

Short-term wind power prediction using an improved grey wolf optimization algorithm with back-propagation neural network

A short-term wind power prediction method is proposed in this paper with experimental results obtained from a wind farm located in Northeast China.In order to improve the accuracy of the prediction method using a traditional back-propagation(BP)neural network algorithm,the improved grey wolf optimization(IGWO)algorithm has been adopted to optimize its parameters.The performance of the proposed method has been evaluated by experiments.First,the features of the wind farm are described to show the fundamental information of the experiments.A single turbine with rated power of 1500 kW and power generation coefficient of 2.74 in the wind farm was introduced to show the technical details of the turbines.Original wind power data of the whole farm were preprocessed by using the quartile method to remove the abnormal data points.Then,the retained wind power data were predicted and analysed by using the proposed IGWO-BP algorithm.Analysis of the results proves the practicability and efficiency of the prediction model.Results show that the average accuracy of prediction is~11%greater than the traditional BP method.In this way,the proposed wind power prediction method can be adopted to improve the accuracy of prediction and to ensure the effective utilization of wind energy.

A hybrid machine learning optimization algorithm for multivariable pore pressure prediction

Pore pressure is essential data in drilling design,and its accurate prediction is necessary to ensure drilling safety and improve drilling efficiency.Traditional methods for predicting pore pressure are limited when forming particular structures and lithology.In this paper,a machine learning algorithm and effective stress theorem are used to establish the transformation model between rock physical parameters and pore pressure.This study collects data from three wells.Well 1 had 881 data sets for model training,and Wells 2 and 3 had 538 and 464 data sets for model testing.In this paper,support vector machine(SVM),random forest(RF),extreme gradient boosting(XGB),and multilayer perceptron(MLP)are selected as the machine learning algorithms for pore pressure modeling.In addition,this paper uses the grey wolf optimization(GWO)algorithm,particle swarm optimization(PSO)algorithm,sparrow search algorithm(SSA),and bat algorithm(BA)to establish a hybrid machine learning optimization algorithm,and proposes an improved grey wolf optimization(IGWO)algorithm.The IGWO-MLP model obtained the minimum root mean square error(RMSE)by using the 5-fold cross-validation method for the training data.For the pore pressure data in Well 2 and Well 3,the coefficients of determination(R^(2))of SVM,RF,XGB,and MLP are 0.9930 and 0.9446,0.9943 and 0.9472,0.9945 and 0.9488,0.9949 and 0.9574.MLP achieves optimal performance on both training and test data,and the MLP model shows a high degree of generalization.It indicates that the IGWO-MLP is an excellent predictor of pore pressure and can be used to predict pore pressure.

A Hybrid of Grey Wolf Optimization and Genetic Algorithm for Optimization of Hybrid Wind and Solar Renewable Energy System

In this paper,a hybrid of grey wolf optimization(GWO)and genetic algorithm(GA)has been implemented to minimize the annual cost of hybrid of wind and solar renewable energy system.It was named as hybrid of grey wolf optimization and genetic algorithm(HGWOGA).HGWOGA was applied to this hybrid problem through three procedures.First,the balance between the exploration and the exploitation process was done by grey wolf optimizer algorithm.Then,we divided the population into subpopulation and used the arithmetical crossover operator to utilize the dimension reduction and the population partitioning processes.At last,mutation operator was applied in the whole population in order to refrain from the premature convergence and trapping in local minima.MATLAB code was designed to implement the proposed methodology.The result of this algorithm is compared with the results of iteration method,GWO,GA,artificial bee colony(ABC)and particle swarm optimization(PSO)techniques.The results obtained by this algorithm are better when compared with those mentioned in the text.