This paper introduces the Surrogate-assisted Multi-objective Grey Wolf Optimizer(SMOGWO)as a novel methodology for addressing the complex problem of empty-heavy train allocation,with a focus on line utilization balanc...This paper introduces the Surrogate-assisted Multi-objective Grey Wolf Optimizer(SMOGWO)as a novel methodology for addressing the complex problem of empty-heavy train allocation,with a focus on line utilization balance.By integrating surrogate models to approximate the objective functions,SMOGWO significantly improves the efficiency and accuracy of the optimization process.The effectiveness of this approach is evaluated using the CEC2009 multi-objective test function suite,where SMOGWO achieves a superiority rate of 76.67%compared to other leading multi-objective algorithms.Furthermore,the practical applicability of SMOGWO is demonstrated through a case study on empty and heavy train allocation,which validates its ability to balance line capacity,minimize transportation costs,and optimize the technical combination of heavy trains.The research highlights SMOGWO's potential as a robust solution for optimization challenges in railway transportation,offering valuable contributions toward enhancing operational efficiency and promoting sustainable development in the sector.展开更多
Medical image segmentation is a challenging task especially in multimodality medical image analysis.In this paper,an improved pulse coupled neural network based on multiple hybrid features grey wolf optimizer(MFGWO-PC...Medical image segmentation is a challenging task especially in multimodality medical image analysis.In this paper,an improved pulse coupled neural network based on multiple hybrid features grey wolf optimizer(MFGWO-PCNN)is proposed for multimodality medical image segmentation.Specifically,a two-stage medical image segmentation method based on bionic algorithm is presented,including image fusion and image segmentation.The image fusion stage fuses rich information from different modalities by utilizing a multimodality medical image fusion model based on maximum energy region.In the stage of image segmentation,an improved PCNN model based on MFGWO is proposed,which can adaptively set the parameters of PCNN according to the features of the image.Two modalities of FLAIR and TIC brain MRIs are applied to verify the effectiveness of the proposed MFGWO-PCNN algorithm.The experimental results demonstrate that the proposed method outperforms the other seven algorithms in subjective vision and objective evaluation indicators.展开更多
Detecting communities in real and complex networks is a highly contested topic in network analysis.Although many metaheuristic-based algorithms for community detection have been proposed,they still cannot effectively ...Detecting communities in real and complex networks is a highly contested topic in network analysis.Although many metaheuristic-based algorithms for community detection have been proposed,they still cannot effectively fulfill large-scale and real-world networks.Thus,this paper presents a new discrete version of the Improved Grey Wolf Optimizer(I-GWO)algorithm named DI-GWOCD for effectively detecting communities of different networks.In the proposed DI-GWOCD algorithm,I-GWO is first armed using a local search strategy to discover and improve nodes placed in improper communities and increase its ability to search for a better solution.Then a novel Binary Distance Vector(BDV)is introduced to calculate the wolves’distances and adapt I-GWO for solving the discrete community detection problem.The performance of the proposed DI-GWOCD was evaluated in terms of modularity,NMI,and the number of detected communities conducted by some well-known real-world network datasets.The experimental results were compared with the state-of-the-art algorithms and statistically analyzed using the Friedman and Wilcoxon tests.The comparison and the statistical analysis show that the proposed DI-GWOCD can detect the communities with higher quality than other comparative algorithms.展开更多
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 worke...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.展开更多
The process of selecting features or reducing dimensionality can be viewed as a multi-objective minimization problem in which both the number of features and error rate must be minimized.While it is a multi-objective ...The process of selecting features or reducing dimensionality can be viewed as a multi-objective minimization problem in which both the number of features and error rate must be minimized.While it is a multi-objective problem,current methods tend to treat feature selection as a single-objective optimization task.This paper presents enhanced multi-objective grey wolf optimizer with Lévy flight and mutation phase(LMuMOGWO)for tackling feature selection problems.The proposed approach integrates two effective operators into the existing Multi-objective Grey Wolf optimizer(MOGWO):a Lévy flight and a mutation operator.The Lévy flight,a type of random walk with jump size determined by the Lévy distribution,enhances the global search capability of MOGWO,with the objective of maximizing classification accuracy while minimizing the number of selected features.The mutation operator is integrated to add more informative features that can assist in enhancing classification accuracy.As feature selection is a binary problem,the continuous search space is converted into a binary space using the sigmoid function.To evaluate the classification performance of the selected feature subset,the proposed approach employs a wrapper-based Artificial Neural Network(ANN).The effectiveness of the LMuMOGWO is validated on 12 conventional UCI benchmark datasets and compared with two existing variants of MOGWO,BMOGWO-S(based sigmoid),BMOGWO-V(based tanh)as well as Non-dominated Sorting Genetic Algorithm II(NSGA-II)and Multi-objective Particle Swarm Optimization(BMOPSO).The results demonstrate that the proposed LMuMOGWO approach is capable of successfully evolving and improving a set of randomly generated solutions for a given optimization problem.Moreover,the proposed approach outperforms existing approaches in most cases in terms of classification error rate,feature reduction,and computational cost.展开更多
At an early point,the diagnosis of pancreatic cancer is mediocre,since the radiologist is skill deficient.Serious threats have been posed due to the above reasons,hence became mandatory for the need of skilled technici...At an early point,the diagnosis of pancreatic cancer is mediocre,since the radiologist is skill deficient.Serious threats have been posed due to the above reasons,hence became mandatory for the need of skilled technicians.However,it also became a time-consuming process.Hence the need for automated diagnosis became mandatory.In order to identify the tumor accurately,this research pro-poses a novel Convolution Neural Network(CNN)based superior image classi-fication technique.The proposed deep learning classification strategy has a precision of 97.7%,allowing for more effective usage of the automatically exe-cuted feature extraction technique to diagnose cancer cells.Comparative analysis with CNN-Grey Wolf Optimization(GWO)is carried based on varied testing and training outcomes.The suggested study is carried out at a rate of 90%–10%,80%–20%,and 70%–30%,indicating the robustness of the proposed research work.Outcomes show that the suggested method is effective.GWO-CNN is reli-able and accurate relative to other detection methods available in the literatures.展开更多
The scope of this paper is to forecast wind speed. Wind speed, temperature, wind direction, relative humidity, precipitation of water content and air pressure are the main factors make the wind speed forecasting as a ...The scope of this paper is to forecast wind speed. Wind speed, temperature, wind direction, relative humidity, precipitation of water content and air pressure are the main factors make the wind speed forecasting as a complex problem and neural network performance is mainly influenced by proper hidden layer neuron units. This paper proposes new criteria for appropriate hidden layer neuron unit’s determination and attempts a novel hybrid method in order to achieve enhanced wind speed forecasting. This paper proposes the following two main innovative contributions 1) both either over fitting or under fitting issues are avoided by means of the proposed new criteria based hidden layer neuron unit’s estimation. 2) ELMAN neural network is optimized through Modified Grey Wolf Optimizer (MGWO). The proposed hybrid method (ELMAN-MGWO) performance, effectiveness is confirmed by means of the comparison between Grey Wolf Optimizer (GWO), Adaptive Gbest-guided Gravitational Search Algorithm (GGSA), Artificial Bee Colony (ABC), Ant Colony Optimization (ACO), Cuckoo Search (CS), Particle Swarm Optimization (PSO), Evolution Strategy (ES), Genetic Algorithm (GA) algorithms, meanwhile proposed new criteria effectiveness and precise are verified comparison with other existing selection criteria. Three real-time wind data sets are utilized in order to analysis the performance of the proposed approach. Simulation results demonstrate that the proposed hybrid method (ELMAN-MGWO) achieve the mean square error AVG ± STD of 4.1379e-11 ± 1.0567e-15, 6.3073e-11 ± 3.5708e-15 and 7.5840e-11 ± 1.1613e-14 respectively for evaluation on three real-time data sets. Hence, the proposed hybrid method is superior, precise, enhance wind speed forecasting than that of other existing methods and robust.展开更多
The grey wolf optimizer(GWO)is a swarm-based intelligence optimization algorithm by simulating the steps of searching,encircling,and attacking prey in the process of wolf hunting.Along with its advantages of simple pr...The grey wolf optimizer(GWO)is a swarm-based intelligence optimization algorithm by simulating the steps of searching,encircling,and attacking prey in the process of wolf hunting.Along with its advantages of simple principle and few parameters setting,GWO bears drawbacks such as low solution accuracy and slow convergence speed.A few recent advanced GWOs are proposed to try to overcome these disadvantages.However,they are either difficult to apply to large-scale problems due to high time complexity or easily lead to early convergence.To solve the abovementioned issues,a high-accuracy variable grey wolf optimizer(VGWO)with low time complexity is proposed in this study.VGWO first uses the symmetrical wolf strategy to generate an initial population of individuals to lay the foundation for the global seek of the algorithm,and then inspired by the simulated annealing algorithm and the differential evolution algorithm,a mutation operation for generating a new mutant individual is performed on three wolves which are randomly selected in the current wolf individuals while after each iteration.A vectorized Manhattan distance calculation method is specifically designed to evaluate the probability of selecting the mutant individual based on its status in the current wolf population for the purpose of dynamically balancing global search and fast convergence capability of VGWO.A series of experiments are conducted on 19 benchmark functions from CEC2014 and CEC2020 and three real-world engineering cases.For 19 benchmark functions,VGWO’s optimization results place first in 80%of comparisons to the state-of-art GWOs and the CEC2020 competition winner.A further evaluation based on the Friedman test,VGWO also outperforms all other algorithms statistically in terms of robustness with a better average ranking value.展开更多
Global optimization is an essential approach to any inversion problem.Recently,the grey wolf optimizer(GWO)has been proposed to optimize the global minimum,which has been quickly used in a variety of inv-ersion proble...Global optimization is an essential approach to any inversion problem.Recently,the grey wolf optimizer(GWO)has been proposed to optimize the global minimum,which has been quickly used in a variety of inv-ersion problems.In this study,we proposed a parameter-shifted grey wolf optimizer(psGWO)based on the conven-tional GWO algorithm to obtain the global minimum.Com-pared with GWO,the novel psGWO can effectively search targets toward objects without being trapped within the local minimum of the zero value.We confirmed the effectiveness of the new method in searching for uniform and random objectives by using mathematical functions released by the Congress on Evolutionary Computation.The psGWO alg-orithm was validated using up to 10,000 parameters to dem-onstrate its robustness in a large-scale optimization problem.We successfully applied psGWO in two-dimensional(2D)synthetic earthquake dynamic rupture inversion to obtain the frictional coefficients of the fault and critical slip-weakening distance using a homogeneous model.Furthermore,this alg-orithm was applied in inversions with heterogeneous dist-ributions of dynamic rupture parameters.This implementation can be efficiently applied in 3D cases and even in actual earthquake inversion and would deepen the understanding of the physics of natural earthquakes in the future.展开更多
Basic oxygen furnace(BOF)steelmaking end-point control using soft measurement models has essential value for economy and environment.However,the high-dimensional and redundant data of the BOF collected by the sensors ...Basic oxygen furnace(BOF)steelmaking end-point control using soft measurement models has essential value for economy and environment.However,the high-dimensional and redundant data of the BOF collected by the sensors will hinder the performance of models.The traditional feature selection results based on meta-heuristic algorithms cannot meet the stability of actual industrial applications.In order to eliminate the negative impact of feature selection application in the BOF steelmaking,an improved grey wolf optimizer(IGWO)for feature selection was proposed,and it was applied to the BOF data set.Firstly,the proposed algorithm preset the size of the feature subset based on the new encoding scheme,rather than the traditional uncertain number strategy.Then,opposition-based learning was used to initialize the grey wolf population so that the initial population was closer to the potential optimal solution.In addition,a novel population update method retained the features closely related to the best three grey wolves and probabilistically updated irrelevant features through measurement or random methods.These methods were used to search feature subsets to maximize search capability and stability of algorithm on BOF steelmaking data.Finally,the proposed algorithm was compared with other feature selection algorithms on the BOF data sets.The results show that the proposed IGWO can stably select the feature subsets that are conductive to the end-point regression accuracy control of BOF temperature and carbon content,which can improve the performance of the BOF steelmaking.展开更多
In the standard grey wolf optimizer(GWO), the search wolf must wait to update its current position until the comparison between the other search wolves and the three leader wolves is completed. During this waiting per...In the standard grey wolf optimizer(GWO), the search wolf must wait to update its current position until the comparison between the other search wolves and the three leader wolves is completed. During this waiting period, the standard GWO is seen as the static GWO. To get rid of this waiting period, two dynamic GWO algorithms are proposed: the first dynamic grey wolf optimizer(DGWO1) and the second dynamic grey wolf optimizer(DGWO2). In the dynamic GWO algorithms, the current search wolf does not need to wait for the comparisons between all other search wolves and the leading wolves, and its position can be updated after completing the comparison between itself or the previous search wolf and the leading wolves. The position of the search wolf is promptly updated in the dynamic GWO algorithms, which increases the iterative convergence rate. Based on the structure of the dynamic GWOs, the performance of the other improved GWOs is examined, verifying that for the same improved algorithm, the one based on dynamic GWO has better performance than that based on static GWO in most instances.展开更多
Due to its simplicity and ease of use, the standard grey wolf optimizer （GWO） is attracting much attention. However, due to its imperfect search structure and possible risk of being trapped in local optima, its appl...Due to its simplicity and ease of use, the standard grey wolf optimizer （GWO） is attracting much attention. However, due to its imperfect search structure and possible risk of being trapped in local optima, its application has been limited. To perfect the performance of the algorithm, an optimized GWO is proposed based on a mutation operator and eliminating-reconstructing mechanism （MR-GWO）. By analyzing GWO, it is found that it conducts search with only three leading wolves at the core, and balances the exploration and exploitation abilities by adjusting only the parameter a, which means the wolves lose some diversity to some extent. Therefore, a mutation operator is introduced to facilitate better searching wolves, and an eliminating- reconstructing mechanism is used for the poor search wolves, which not only effectively expands the stochastic search, but also accelerates its convergence, and these two operations complement each other well. To verify its validity, MR-GWO is applied to the global optimization experiment of 13 standard continuous functions and a radial basis function （RBF） network approximation experiment. Through a comparison with other algorithms, it is proven that MR-GWO has a strong advantage.展开更多
With the advancement of technology,gas shales have become one of the most prominent energy sources all over the world.Therefore,estimating the amount of adsorbed gas in shale resources is necessary for the technical a...With the advancement of technology,gas shales have become one of the most prominent energy sources all over the world.Therefore,estimating the amount of adsorbed gas in shale resources is necessary for the technical and economic foresight of the production operations.This paper presents a novel machine learning method called grey wolf optimizer support vector machine(GWO-SVM)to predict adsorbed gas.For this purpose,a data set containing temperature,pressure,total organic carbon(TOC),and humidity has been collected from several sources,and the GWO-SVM model was created based on it.The results show that this model has R-squared and root mean square error equal to 0.982 and 0.08,respectively.Also,the results ensure that the proposed model gives an excellent prediction of the amount of adsorbed gas compared to previously proposed models.Besides,according to the sensitivity analysis,among the input parameters,humidity has the highest effect on gas adsorption.展开更多
We design a grey wolf optimizer hybridized with an interior point algorithm to correct a faulty antenna array. If a single sensor fails, the radiation power pattern of the entire array is disturbed in terms of sidelob...We design a grey wolf optimizer hybridized with an interior point algorithm to correct a faulty antenna array. If a single sensor fails, the radiation power pattern of the entire array is disturbed in terms of sidelobe level(SLL) and null depth level(NDL), and nulls are damaged and shifted from their original locations. All these issues can be solved by designing a new fitness function to reduce the error between the preferred and expected radiation power patterns and the null limitations. The hybrid algorithm has been designed to control the array's faulty radiation power pattern. Antenna arrays composed of 21 sensors are used in an example simulation scenario. The MATLAB simulation results confirm the good performance of the proposed method, compared with the existing methods in terms of SLL and NDL.展开更多
In fifth-generation wireless communication system(5G),more connections are built between metaheuristics and electromagnetic equipment design.In this paper,we propose a self-adaptive grey wolf optimizer(SAGWO)combined ...In fifth-generation wireless communication system(5G),more connections are built between metaheuristics and electromagnetic equipment design.In this paper,we propose a self-adaptive grey wolf optimizer(SAGWO)combined with a novel optimization model of a 5G frequency selection surface(FSS)based on FSS unit nodes.SAGWO includes three improvement strategies,improving the initial distribution,increasing the randomness,and enhancing the local search,to accelerate the convergence and effectively avoid local optima.In benchmark tests,the proposed optimizer performs better than the five other optimization algorithms:original grey wolf optimizer(GWO),genetic algorithm(GA),particle swarm optimizer(PSO),improved grey wolf optimizer(IGWO),and selective opposition based grey wolf optimization(SOGWO).Due to its global searchability,SAGWO is suitable for solving the optimization problem of a 5G FSS that has a large design space.The combination of SAGWO and the new FSS optimization model can automatically obtain the shape of the FSS unit with electromagnetic interference shielding capability at the center operating frequency.To verify the performance of the proposed method,a double-layer ring FSS is designed with the purpose of providing electromagnetic interference shielding features at28 GHz.The results show that the optimized FSS has better electromagnetic interference shielding at the center frequency and has higher angular stability.Finally,a sample of the optimized FSS is fabricated and tested.展开更多
We propose a competitive binary multi-objective grey wolf optimizer(CBMOGWO)to reduce the heavy computational burden of conventional multi-objective antenna topology optimization problems.This method introduces a popu...We propose a competitive binary multi-objective grey wolf optimizer(CBMOGWO)to reduce the heavy computational burden of conventional multi-objective antenna topology optimization problems.This method introduces a population competition mechanism to reduce the burden of electromagnetic(EM)simulation and achieve appropriate fitness values.Furthermore,we introduce a function of cosine oscillation to improve the linear convergence factor of the original binary multi-objective grey wolf optimizer(BMOGWO)to achieve a good balance between exploration and exploitation.Then,the optimization performance of CBMOGWO is verified on 12 standard multi-objective test problems(MOTPs)and four multi-objective knapsack problems(MOKPs)by comparison with the original BMOGWO and the traditional binary multi-objective particle swarm optimization(BMOPSO).Finally,the effectiveness of our method in reducing the computational cost is validated by an example of a compact high-isolation dual-band multiple-input multiple-output(MIMO)antenna with high-dimensional mixed design variables and multiple objectives.The experimental results show that CBMOGWO reduces nearly half of the computational cost compared with traditional methods,which indicates that our method is highly efficient for complex antenna topology optimization problems.It provides new ideas for exploring new and unexpected antenna structures based on multi-objective evolutionary algorithms(MOEAs)in a flexible and efficient manner.展开更多
The technical advancement in information systems contributes towards the massive availability of the documents stored in the electronic databases such as e-mails,internet and web pages.Therefore,it becomes a complex t...The technical advancement in information systems contributes towards the massive availability of the documents stored in the electronic databases such as e-mails,internet and web pages.Therefore,it becomes a complex task for arranging and browsing the required document.This paper proposes an approach for incremental clustering using the BatGrey Wolf Optimizer(BAGWO).The input documents are initially subjected to the pre-processing module to obtain useful keywords,and then the feature extraction is performed based on wordnet features.After feature extraction,feature selection is carried out using entropy function.Subsequently,the clustering is done using the proposed BAGWO algorithm.The BAGWO algorithm is designed by integrating the Bat Algorithm(BA)and Grey Wolf Optimizer(GWO)for generating the different clusters of text documents.Hence,the clustering is determined using the BAGWO algorithm,yielding the group of clusters.On the other side,upon the arrival of a new document,the same steps of pre-processing and feature extraction are performed.Based on the features of the test document,the mapping is done between the features of the test document,and the clusters obtained by the proposed BAGWO approach.The mapping is performed using the kernel-based deep point distance and once the mapping terminated,the representatives are updated based on the fuzzy-based representative update.The performance of the developed BAGWO outperformed the existing techniques in terms of clustering accuracy,Jaccard coefficient,and rand coefficient with maximal values 0.948,0.968,and 0.969,respectively.展开更多
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 O...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.展开更多
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 import...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.展开更多
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 ...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.展开更多
基金supported by the National Natural Science Foundation of China(Project No.5217232152102391)+2 种基金Sichuan Province Science and Technology Innovation Talent Project(2024JDRC0020)China Shenhua Energy Company Limited Technology Project(GJNY-22-7/2300-K1220053)Key science and technology projects in the transportation industry of the Ministry of Transport(2022-ZD7-132).
文摘This paper introduces the Surrogate-assisted Multi-objective Grey Wolf Optimizer(SMOGWO)as a novel methodology for addressing the complex problem of empty-heavy train allocation,with a focus on line utilization balance.By integrating surrogate models to approximate the objective functions,SMOGWO significantly improves the efficiency and accuracy of the optimization process.The effectiveness of this approach is evaluated using the CEC2009 multi-objective test function suite,where SMOGWO achieves a superiority rate of 76.67%compared to other leading multi-objective algorithms.Furthermore,the practical applicability of SMOGWO is demonstrated through a case study on empty and heavy train allocation,which validates its ability to balance line capacity,minimize transportation costs,and optimize the technical combination of heavy trains.The research highlights SMOGWO's potential as a robust solution for optimization challenges in railway transportation,offering valuable contributions toward enhancing operational efficiency and promoting sustainable development in the sector.
基金This research is supported by the National Key Research and Development Program of China(2018YFB0804202,2018YFB0804203)Regional Joint Fund of NSFC(U19A2057),the National Natural Science Foundation of China(61672259,61876070)and the Jilin Province Science and Technology Development Plan Project(20190303134SF,20180201064SF).
文摘Medical image segmentation is a challenging task especially in multimodality medical image analysis.In this paper,an improved pulse coupled neural network based on multiple hybrid features grey wolf optimizer(MFGWO-PCNN)is proposed for multimodality medical image segmentation.Specifically,a two-stage medical image segmentation method based on bionic algorithm is presented,including image fusion and image segmentation.The image fusion stage fuses rich information from different modalities by utilizing a multimodality medical image fusion model based on maximum energy region.In the stage of image segmentation,an improved PCNN model based on MFGWO is proposed,which can adaptively set the parameters of PCNN according to the features of the image.Two modalities of FLAIR and TIC brain MRIs are applied to verify the effectiveness of the proposed MFGWO-PCNN algorithm.The experimental results demonstrate that the proposed method outperforms the other seven algorithms in subjective vision and objective evaluation indicators.
文摘Detecting communities in real and complex networks is a highly contested topic in network analysis.Although many metaheuristic-based algorithms for community detection have been proposed,they still cannot effectively fulfill large-scale and real-world networks.Thus,this paper presents a new discrete version of the Improved Grey Wolf Optimizer(I-GWO)algorithm named DI-GWOCD for effectively detecting communities of different networks.In the proposed DI-GWOCD algorithm,I-GWO is first armed using a local search strategy to discover and improve nodes placed in improper communities and increase its ability to search for a better solution.Then a novel Binary Distance Vector(BDV)is introduced to calculate the wolves’distances and adapt I-GWO for solving the discrete community detection problem.The performance of the proposed DI-GWOCD was evaluated in terms of modularity,NMI,and the number of detected communities conducted by some well-known real-world network datasets.The experimental results were compared with the state-of-the-art algorithms and statistically analyzed using the Friedman and Wilcoxon tests.The comparison and the statistical analysis show that the proposed DI-GWOCD can detect the communities with higher quality than other comparative algorithms.
基金supported by the Natural Science Foundation of Anhui Province(Grant Number 2208085MG181)the Science Research Project of Higher Education Institutions in Anhui Province,Philosophy and Social Sciences(Grant Number 2023AH051063)the Open Fund of Key Laboratory of Anhui Higher Education Institutes(Grant Number CS2021-ZD01).
文摘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.
基金supported by Universiti Teknologi PETRONAS,under the Yayasan Universiti Teknologi PETRONAS (YUTP)Fundamental Research Grant Scheme (YUTPFRG/015LC0-274)support by Researchers Supporting Project Number (RSP-2023/309),King Saud University,Riyadh,Saudi Arabia.
文摘The process of selecting features or reducing dimensionality can be viewed as a multi-objective minimization problem in which both the number of features and error rate must be minimized.While it is a multi-objective problem,current methods tend to treat feature selection as a single-objective optimization task.This paper presents enhanced multi-objective grey wolf optimizer with Lévy flight and mutation phase(LMuMOGWO)for tackling feature selection problems.The proposed approach integrates two effective operators into the existing Multi-objective Grey Wolf optimizer(MOGWO):a Lévy flight and a mutation operator.The Lévy flight,a type of random walk with jump size determined by the Lévy distribution,enhances the global search capability of MOGWO,with the objective of maximizing classification accuracy while minimizing the number of selected features.The mutation operator is integrated to add more informative features that can assist in enhancing classification accuracy.As feature selection is a binary problem,the continuous search space is converted into a binary space using the sigmoid function.To evaluate the classification performance of the selected feature subset,the proposed approach employs a wrapper-based Artificial Neural Network(ANN).The effectiveness of the LMuMOGWO is validated on 12 conventional UCI benchmark datasets and compared with two existing variants of MOGWO,BMOGWO-S(based sigmoid),BMOGWO-V(based tanh)as well as Non-dominated Sorting Genetic Algorithm II(NSGA-II)and Multi-objective Particle Swarm Optimization(BMOPSO).The results demonstrate that the proposed LMuMOGWO approach is capable of successfully evolving and improving a set of randomly generated solutions for a given optimization problem.Moreover,the proposed approach outperforms existing approaches in most cases in terms of classification error rate,feature reduction,and computational cost.
文摘At an early point,the diagnosis of pancreatic cancer is mediocre,since the radiologist is skill deficient.Serious threats have been posed due to the above reasons,hence became mandatory for the need of skilled technicians.However,it also became a time-consuming process.Hence the need for automated diagnosis became mandatory.In order to identify the tumor accurately,this research pro-poses a novel Convolution Neural Network(CNN)based superior image classi-fication technique.The proposed deep learning classification strategy has a precision of 97.7%,allowing for more effective usage of the automatically exe-cuted feature extraction technique to diagnose cancer cells.Comparative analysis with CNN-Grey Wolf Optimization(GWO)is carried based on varied testing and training outcomes.The suggested study is carried out at a rate of 90%–10%,80%–20%,and 70%–30%,indicating the robustness of the proposed research work.Outcomes show that the suggested method is effective.GWO-CNN is reli-able and accurate relative to other detection methods available in the literatures.
文摘The scope of this paper is to forecast wind speed. Wind speed, temperature, wind direction, relative humidity, precipitation of water content and air pressure are the main factors make the wind speed forecasting as a complex problem and neural network performance is mainly influenced by proper hidden layer neuron units. This paper proposes new criteria for appropriate hidden layer neuron unit’s determination and attempts a novel hybrid method in order to achieve enhanced wind speed forecasting. This paper proposes the following two main innovative contributions 1) both either over fitting or under fitting issues are avoided by means of the proposed new criteria based hidden layer neuron unit’s estimation. 2) ELMAN neural network is optimized through Modified Grey Wolf Optimizer (MGWO). The proposed hybrid method (ELMAN-MGWO) performance, effectiveness is confirmed by means of the comparison between Grey Wolf Optimizer (GWO), Adaptive Gbest-guided Gravitational Search Algorithm (GGSA), Artificial Bee Colony (ABC), Ant Colony Optimization (ACO), Cuckoo Search (CS), Particle Swarm Optimization (PSO), Evolution Strategy (ES), Genetic Algorithm (GA) algorithms, meanwhile proposed new criteria effectiveness and precise are verified comparison with other existing selection criteria. Three real-time wind data sets are utilized in order to analysis the performance of the proposed approach. Simulation results demonstrate that the proposed hybrid method (ELMAN-MGWO) achieve the mean square error AVG ± STD of 4.1379e-11 ± 1.0567e-15, 6.3073e-11 ± 3.5708e-15 and 7.5840e-11 ± 1.1613e-14 respectively for evaluation on three real-time data sets. Hence, the proposed hybrid method is superior, precise, enhance wind speed forecasting than that of other existing methods and robust.
文摘The grey wolf optimizer(GWO)is a swarm-based intelligence optimization algorithm by simulating the steps of searching,encircling,and attacking prey in the process of wolf hunting.Along with its advantages of simple principle and few parameters setting,GWO bears drawbacks such as low solution accuracy and slow convergence speed.A few recent advanced GWOs are proposed to try to overcome these disadvantages.However,they are either difficult to apply to large-scale problems due to high time complexity or easily lead to early convergence.To solve the abovementioned issues,a high-accuracy variable grey wolf optimizer(VGWO)with low time complexity is proposed in this study.VGWO first uses the symmetrical wolf strategy to generate an initial population of individuals to lay the foundation for the global seek of the algorithm,and then inspired by the simulated annealing algorithm and the differential evolution algorithm,a mutation operation for generating a new mutant individual is performed on three wolves which are randomly selected in the current wolf individuals while after each iteration.A vectorized Manhattan distance calculation method is specifically designed to evaluate the probability of selecting the mutant individual based on its status in the current wolf population for the purpose of dynamically balancing global search and fast convergence capability of VGWO.A series of experiments are conducted on 19 benchmark functions from CEC2014 and CEC2020 and three real-world engineering cases.For 19 benchmark functions,VGWO’s optimization results place first in 80%of comparisons to the state-of-art GWOs and the CEC2020 competition winner.A further evaluation based on the Friedman test,VGWO also outperforms all other algorithms statistically in terms of robustness with a better average ranking value.
基金This study is supported by the National Natural Science Foundation of China(Nos.41922024 and 42174057)Shenzhen Key Laboratory of Deep Offshore Oil and Gas Exploration Technology(No.ZDS-YS20190902093007855)Shenzhen Science and Technology Program(No.KQTD20170810111725321).
文摘Global optimization is an essential approach to any inversion problem.Recently,the grey wolf optimizer(GWO)has been proposed to optimize the global minimum,which has been quickly used in a variety of inv-ersion problems.In this study,we proposed a parameter-shifted grey wolf optimizer(psGWO)based on the conven-tional GWO algorithm to obtain the global minimum.Com-pared with GWO,the novel psGWO can effectively search targets toward objects without being trapped within the local minimum of the zero value.We confirmed the effectiveness of the new method in searching for uniform and random objectives by using mathematical functions released by the Congress on Evolutionary Computation.The psGWO alg-orithm was validated using up to 10,000 parameters to dem-onstrate its robustness in a large-scale optimization problem.We successfully applied psGWO in two-dimensional(2D)synthetic earthquake dynamic rupture inversion to obtain the frictional coefficients of the fault and critical slip-weakening distance using a homogeneous model.Furthermore,this alg-orithm was applied in inversions with heterogeneous dist-ributions of dynamic rupture parameters.This implementation can be efficiently applied in 3D cases and even in actual earthquake inversion and would deepen the understanding of the physics of natural earthquakes in the future.
基金supported by the National Natural Science Foundation of China(Grant No.61863018)the Applied Basic Research Programs of Yunnan Science and Technology Department(Grant No.202001AT070038).
文摘Basic oxygen furnace(BOF)steelmaking end-point control using soft measurement models has essential value for economy and environment.However,the high-dimensional and redundant data of the BOF collected by the sensors will hinder the performance of models.The traditional feature selection results based on meta-heuristic algorithms cannot meet the stability of actual industrial applications.In order to eliminate the negative impact of feature selection application in the BOF steelmaking,an improved grey wolf optimizer(IGWO)for feature selection was proposed,and it was applied to the BOF data set.Firstly,the proposed algorithm preset the size of the feature subset based on the new encoding scheme,rather than the traditional uncertain number strategy.Then,opposition-based learning was used to initialize the grey wolf population so that the initial population was closer to the potential optimal solution.In addition,a novel population update method retained the features closely related to the best three grey wolves and probabilistically updated irrelevant features through measurement or random methods.These methods were used to search feature subsets to maximize search capability and stability of algorithm on BOF steelmaking data.Finally,the proposed algorithm was compared with other feature selection algorithms on the BOF data sets.The results show that the proposed IGWO can stably select the feature subsets that are conductive to the end-point regression accuracy control of BOF temperature and carbon content,which can improve the performance of the BOF steelmaking.
基金Project supported by the Scientific Research Plan Projects of Shaanxi Education Department (No. 20JK0972)the Natural Science Basic Research Project of Shaanxi Province (No. 2021JM-517)the Educational and Teaching Reform Research Project of Xianyang Normal University (No. 2017Y004)。
文摘In the standard grey wolf optimizer(GWO), the search wolf must wait to update its current position until the comparison between the other search wolves and the three leader wolves is completed. During this waiting period, the standard GWO is seen as the static GWO. To get rid of this waiting period, two dynamic GWO algorithms are proposed: the first dynamic grey wolf optimizer(DGWO1) and the second dynamic grey wolf optimizer(DGWO2). In the dynamic GWO algorithms, the current search wolf does not need to wait for the comparisons between all other search wolves and the leading wolves, and its position can be updated after completing the comparison between itself or the previous search wolf and the leading wolves. The position of the search wolf is promptly updated in the dynamic GWO algorithms, which increases the iterative convergence rate. Based on the structure of the dynamic GWOs, the performance of the other improved GWOs is examined, verifying that for the same improved algorithm, the one based on dynamic GWO has better performance than that based on static GWO in most instances.
基金supported by the National High-Tech R&D Program(863)of China(No.2015AA7041003)the Scientific Research Plan Projects of Shanxi Education Department(No.17JK0825)the Scientific Research Plan Projects of Xianyang Normal University(No.15XSYK036)
文摘Due to its simplicity and ease of use, the standard grey wolf optimizer （GWO） is attracting much attention. However, due to its imperfect search structure and possible risk of being trapped in local optima, its application has been limited. To perfect the performance of the algorithm, an optimized GWO is proposed based on a mutation operator and eliminating-reconstructing mechanism （MR-GWO）. By analyzing GWO, it is found that it conducts search with only three leading wolves at the core, and balances the exploration and exploitation abilities by adjusting only the parameter a, which means the wolves lose some diversity to some extent. Therefore, a mutation operator is introduced to facilitate better searching wolves, and an eliminating- reconstructing mechanism is used for the poor search wolves, which not only effectively expands the stochastic search, but also accelerates its convergence, and these two operations complement each other well. To verify its validity, MR-GWO is applied to the global optimization experiment of 13 standard continuous functions and a radial basis function （RBF） network approximation experiment. Through a comparison with other algorithms, it is proven that MR-GWO has a strong advantage.
文摘With the advancement of technology,gas shales have become one of the most prominent energy sources all over the world.Therefore,estimating the amount of adsorbed gas in shale resources is necessary for the technical and economic foresight of the production operations.This paper presents a novel machine learning method called grey wolf optimizer support vector machine(GWO-SVM)to predict adsorbed gas.For this purpose,a data set containing temperature,pressure,total organic carbon(TOC),and humidity has been collected from several sources,and the GWO-SVM model was created based on it.The results show that this model has R-squared and root mean square error equal to 0.982 and 0.08,respectively.Also,the results ensure that the proposed model gives an excellent prediction of the amount of adsorbed gas compared to previously proposed models.Besides,according to the sensitivity analysis,among the input parameters,humidity has the highest effect on gas adsorption.
基金supported by the Ministry of Higher Education(MOHE)the Research Management Centre(RMC)+2 种基金the School of Postgraduate Studies(SPS)the Communication Engineering Department,the Faculty of Electrical Engineering(FKE)Universiti T¨ekùnolóogi Malaysia(UTM)Johor Bahru(Nos.12H09 and 03E20tan)
文摘We design a grey wolf optimizer hybridized with an interior point algorithm to correct a faulty antenna array. If a single sensor fails, the radiation power pattern of the entire array is disturbed in terms of sidelobe level(SLL) and null depth level(NDL), and nulls are damaged and shifted from their original locations. All these issues can be solved by designing a new fitness function to reduce the error between the preferred and expected radiation power patterns and the null limitations. The hybrid algorithm has been designed to control the array's faulty radiation power pattern. Antenna arrays composed of 21 sensors are used in an example simulation scenario. The MATLAB simulation results confirm the good performance of the proposed method, compared with the existing methods in terms of SLL and NDL.
基金Project supported by the Guangdong Basic and Applied Basic Research FoundationChina(No.2019A1515011783)the National Natural Science Foundation of China(No.52075184)。
文摘In fifth-generation wireless communication system(5G),more connections are built between metaheuristics and electromagnetic equipment design.In this paper,we propose a self-adaptive grey wolf optimizer(SAGWO)combined with a novel optimization model of a 5G frequency selection surface(FSS)based on FSS unit nodes.SAGWO includes three improvement strategies,improving the initial distribution,increasing the randomness,and enhancing the local search,to accelerate the convergence and effectively avoid local optima.In benchmark tests,the proposed optimizer performs better than the five other optimization algorithms:original grey wolf optimizer(GWO),genetic algorithm(GA),particle swarm optimizer(PSO),improved grey wolf optimizer(IGWO),and selective opposition based grey wolf optimization(SOGWO).Due to its global searchability,SAGWO is suitable for solving the optimization problem of a 5G FSS that has a large design space.The combination of SAGWO and the new FSS optimization model can automatically obtain the shape of the FSS unit with electromagnetic interference shielding capability at the center operating frequency.To verify the performance of the proposed method,a double-layer ring FSS is designed with the purpose of providing electromagnetic interference shielding features at28 GHz.The results show that the optimized FSS has better electromagnetic interference shielding at the center frequency and has higher angular stability.Finally,a sample of the optimized FSS is fabricated and tested.
基金supported by the National Natural Science Foundation of China(Nos.61801521 and 61971450)the Natural Science Foundation of Hunan Province,China(No.2018JJ2533)the Fundamental Research Funds for the Central Universities,China(Nos.2018gczd014and 20190038020050)。
文摘We propose a competitive binary multi-objective grey wolf optimizer(CBMOGWO)to reduce the heavy computational burden of conventional multi-objective antenna topology optimization problems.This method introduces a population competition mechanism to reduce the burden of electromagnetic(EM)simulation and achieve appropriate fitness values.Furthermore,we introduce a function of cosine oscillation to improve the linear convergence factor of the original binary multi-objective grey wolf optimizer(BMOGWO)to achieve a good balance between exploration and exploitation.Then,the optimization performance of CBMOGWO is verified on 12 standard multi-objective test problems(MOTPs)and four multi-objective knapsack problems(MOKPs)by comparison with the original BMOGWO and the traditional binary multi-objective particle swarm optimization(BMOPSO).Finally,the effectiveness of our method in reducing the computational cost is validated by an example of a compact high-isolation dual-band multiple-input multiple-output(MIMO)antenna with high-dimensional mixed design variables and multiple objectives.The experimental results show that CBMOGWO reduces nearly half of the computational cost compared with traditional methods,which indicates that our method is highly efficient for complex antenna topology optimization problems.It provides new ideas for exploring new and unexpected antenna structures based on multi-objective evolutionary algorithms(MOEAs)in a flexible and efficient manner.
文摘The technical advancement in information systems contributes towards the massive availability of the documents stored in the electronic databases such as e-mails,internet and web pages.Therefore,it becomes a complex task for arranging and browsing the required document.This paper proposes an approach for incremental clustering using the BatGrey Wolf Optimizer(BAGWO).The input documents are initially subjected to the pre-processing module to obtain useful keywords,and then the feature extraction is performed based on wordnet features.After feature extraction,feature selection is carried out using entropy function.Subsequently,the clustering is done using the proposed BAGWO algorithm.The BAGWO algorithm is designed by integrating the Bat Algorithm(BA)and Grey Wolf Optimizer(GWO)for generating the different clusters of text documents.Hence,the clustering is determined using the BAGWO algorithm,yielding the group of clusters.On the other side,upon the arrival of a new document,the same steps of pre-processing and feature extraction are performed.Based on the features of the test document,the mapping is done between the features of the test document,and the clusters obtained by the proposed BAGWO approach.The mapping is performed using the kernel-based deep point distance and once the mapping terminated,the representatives are updated based on the fuzzy-based representative update.The performance of the developed BAGWO outperformed the existing techniques in terms of clustering accuracy,Jaccard coefficient,and rand coefficient with maximal values 0.948,0.968,and 0.969,respectively.
文摘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.
基金This study was jointly supported by the National Natural Science Foundation of China(Nos.51879196,51790533,51709143)Jiangxi Natural Science Foundation of China(No.20181BAB206045).
文摘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.
文摘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.
