Grey Wolf Optimization Method Research Articles

Soil water content estimation by using ground penetrating radar data full waveform inversion with grey wolf optimizer algorithm

AbstractSoil water content (SWC) estimation is important for many areas including hydrology, agriculture, soil science, and environmental science. Ground penetrating radar (GPR) is a promising geophysical method for SWC estimation. However, at present, most of the studies are based on partial information of GPR, like travel time or amplitude information, to invert the SWC. Full waveform inversion (FWI) can use the information of the entire waveform, which can improve the accuracy of parameter estimation. This study proposes a novel SWC estimation scheme by using the FWI of GPR, optimized by the grey wolf optimizer (GWO) algorithm. The proposed scheme includes a petrophysical relationship to link the SWC with the relative dielectric permittivity, 1D GPR forward modeling, and a GWO optimization algorithm. First, numerical modeling was carried out, and the proposed scheme was applied to both noise‐free and noisy data to verify its applicability. Then, the proposed method was applied to data collected from a field experimental site. These results, derived from both synthetic and real datasets, show that the proposed inversion scheme resulted in a good match between the observed and calculated GPR data. In the numerical modeling, it was observed that the SWC could be inverted accurately, even when noise was present in the data. These demonstrate that the GWO method can be applied for the quantitative interpretation of GPR data. The proposed scheme shows potential for SWC estimation by using GPR full waveform data.

Automatic lip-reading classification using deep learning approaches and optimized quaternion meixner moments by GWO algorithm

Lip-reading classification has received a lot of interest in recent decades because it is widely used in a variety of fields. It plays an important role in interpreting spoken words in noisy situations and reconstructing communication processes for those with hearing impairments. Despite significant advancements in this field, there are still several drawbacks in existing work such as feature extraction and Model capability for visual speech recognition. For these reasons, the current paper suggests an Optimized Quaternion Meixner Moments Convolutional Neural Network (OQMMs-CNN) method that intends to develop a Visual Speech Recognition (VSR) system based only on video images. This unique method combines OQMMs optimized for the GWO algorithm and convolutional neural networks taken from deep learning techniques with the aim of recognizing digits, words, or letters displayed as input videos.The OQMMs are used here as descriptors with the purpose of identifying, holding, and extracting essential information from video images (lips images) and generating moments for CNN input. The latter uses Meixner polynomials, which are defined by local parameters α and β. Then, the Grey Wolf optimization method (GWO) is applied to enssure excellent classification accuracy by optimizing those local parameters. After being tested on three public datasets such as AVLetters, Grid, AVDigits, and LRW, and comparing to several ways using complicated models and deep architecture, the method emerges as an excellent solution for reducing the high dimensionality of video pictures and training time.

An optimized model based on adaptive convolutional neural network and grey wolf algorithm for breast cancer diagnosis.

Medical image classification (IC) is a method for categorizing images according to the appropriate pathological stage. It is a crucial stage in computer-aided diagnosis (CAD) systems, which were created to help radiologists with reading and analyzing medical images as well as with the early detection of tumors and other disorders. The use of convolutional neural network (CNN) models in the medical industry has recently increased, and they achieve great results at IC, particularly in terms of high performance and robustness. The proposed method uses pre-trained models such as Dense Convolutional Network (DenseNet)-121 and Visual Geometry Group (VGG)-16 as feature extractor networks, bidirectional long short-term memory (BiLSTM) layers for temporal feature extraction, and the Support Vector Machine (SVM) and Random Forest (RF) algorithms to perform classification. For improved performance, the selected pre-trained CNN hyperparameters have been optimized using a modified grey wolf optimization method. The experimental analysis for the presented model on the Mammographic Image Analysis Society (MIAS) dataset shows that the VGG16 model is powerful for BC classification with overall accuracy, sensitivity, specificity, precision, and area under the ROC curve (AUC) of 99.86%, 99.9%, 99.7%, 97.1%, and 1.0, respectively, on the MIAS dataset and 99.4%, 99.03%, 99.2%, 97.4%, and 1.0, respectively, on the INbreast dataset.

Optimal sizing of grid connected multi-microgrid system using grey wolf optimization

Renewable distributed energy resources (DERs) offer a promising and environmentally sustainable solution for providing energy. Nowadays, there has been significant attention in wind, solar Photovoltaic (PV), and hydrogen-based fuel cell (FC) systems due to their ability to provide cost-effective energy to replace conventional generations. However, the intermittent nature of renewable energy sources presents challenges and operational issues for fully renewable energy systems. To address this, integrating energy storage systems and effectively managing uncertainties related to both load and generation resources are crucial for mitigating such challenges. This paper proposes a hybrid grid-connected PV-wind-FC generation-based Multi-microgrid (MMG) system integrated with a Battery Energy Storage System (BESS) to meet the entire load demand of the adopted MMG-based IEEE 14-bus system. The aim is to ensure cost-effectiveness and enable energy trading with the main grid by optimizing system configurations. The study incorporates stochastic analysis to handle uncertainties related to load, meteorological data, and energy prices to optimize the configuration of DERs and BESS in the MMGs. A Grey Wolf Optimization (GWO) algorithm is employed to determine the optimal sizing of the proposed grid-connected MMG. The proposed algorithm has reduced the NPC from $431.796 million to $428.832 million and LCOE to 0.267$/kWh when load and generation data uncertainty and dynamic energy price has considered. The robustness of the proposed approach is evaluated by comparing results with those obtained using Particle Swarm Optimization (PSO) and JAYA algorithms. The GWO method demonstrates superior performance, resulting in lower total Net Present Cost (NPC), lower system capacity, and a lower Levelized Cost of Energy (LCOE) compared to its counterparts. Moreover, the GWO algorithm exhibits the fastest convergence, indicating its accuracy and robustness compared to PSO and JAYA algorithms.

Advanced CKD detection through optimized metaheuristic modeling in healthcare informatics

Data categorization is a top concern in medical data to predict and detect illnesses; thus, it is applied in modern healthcare informatics. In modern informatics, machine learning and deep learning models have enjoyed great attention for categorizing medical data and improving illness detection. However, the existing techniques, such as features with high dimensionality, computational complexity, and long-term execution duration, raise fundamental problems. This study presents a novel classification model employing metaheuristic methods to maximize efficient positives on Chronic Kidney Disease diagnosis. The medical data is initially massively pre-processed, where the data is purified with various mechanisms, including missing values resolution, data transformation, and the employment of normalization procedures. The focus of such processes is to leverage the handling of the missing values and prepare the data for deep analysis. We adopt the Binary Grey Wolf Optimization method, a reliable subset selection feature using metaheuristics. This operation is aimed at improving illness prediction accuracy. In the classification step, the model adopts the Extreme Learning Machine with hidden nodes through data optimization to predict the presence of CKD. The complete classifier evaluation employs established measures, including recall, specificity, kappa, F-score, and accuracy, in addition to the feature selection. Data related to the study show that the proposed approach records high levels of accuracy, which is better than the existing models.

Three-Dimensional Path Planning for Post-Disaster Rescue UAV by Integrating Improved Grey Wolf Optimizer and Artificial Potential Field Method

The path planning of unmanned aerial vehicles (UAVs) is crucial in UAV search and rescue operations to ensure efficient and safe search activities. However, most existing path planning algorithms are not suitable for post-disaster mountain rescue mission scenarios. Therefore, this paper proposes the IGWO-IAPF algorithm based on the fusion of the improved grey wolf optimizer (GWO) and the improved artificial potential field (APF) algorithm. This algorithm builds upon the grey wolf optimizer and introduces several improvements. Firstly, a nonlinear adjustment strategy for control parameters is proposed to balance the global and local search capabilities of the algorithm. Secondly, an optimized individual position update strategy is employed to coordinate the algorithm’s search ability and reduce the probability of falling into local optima. Additionally, a waypoint attraction force is incorporated into the traditional artificial potential field algorithm based on the force field to fulfill the requirements of three-dimensional path planning and further reduce the probability of falling into local optima. The IGWO is used to generate an initial path, where each point is assigned an attraction force, and then the IAPF is utilized for subsequent path planning. The simulation results demonstrate that the improved IGWO exhibits approximately a 60% improvement in convergence compared to the conventional GWO. Furthermore, the integrated IGWO-IAPF algorithm shows an approximately 10% improvement in path planning effectiveness compared to other traditional algorithms. It possesses characteristics such as shorter flight distance and higher safety, making it suitable for meeting the requirements of post-disaster rescue missions.

Research on spatial localization method of composite damage under strong noise

In this paper, a damage spatial imaging approach based on novel signal extraction is suggested to reconstruct the Lamb wave response signal under strong noise and realize the spatial localization of damage. First, the Variable Mode Decomposition (VMD) parameters are optimized by the improved Grey Wolf optimization method (IGWO) to decompose the response signal. To rebuild the response signal, the correlation coefficient is used to choose the optimal modal component and the residual. To give the best wavelet function and transform level for adaptive denoising of the reconstructed signal without a reference signal, an enhanced Discrete Wavelet Transform (DWT) based on Shannon entropy is proposed. To achieve damage localization imaging, a damage spatial localization model is built utilizing a reconstruction algorithm for probabilistic inspection of damage (RAPID) approach and a convolutional neural network (CNN). The suggested method may successfully increase the signal-to-noise ratio (SNR) of the reconstructed response signal and lower the error of spatial localization under strong noise through experiments. The spatial localization of composite damage using Lamb wave under strong noise is expanded in this paper.

الحجم الأمثل للنظام الهجين المستقل والمتجدد على أساس التكاليف باستخدام تقنية Gray Wolf Optimization

Ensuring low-cost and highly reliable electricity generation while meeting the demand load poses a significant challenge. Power plants operate continuously to produce power, with the Programmable Logic Controller (PLC) control system playing a crucial role in managing all the equipment. Power deficiencies in the PLC rooms can lead to equipment disturbances and potential damage to the plant. To address this problem and utilize the abundant solar energy in Libya, this study introduces the optimal sizing of an autonomous hybrid storage system using an optimization method. The Net Present Costs (NPC), Loss Power Supply Probability (LPSP), and Levelized Cost of Energy (LCOE) are employed to extract a suitable function database. The proposed system generates 7 kW of power to meet demand and is implemented in MATLAB. The Grey Wolf Optimization (GWO) method is applied to determine the optimal number of PV panels and BESS capacity for the autonomous hybrid system. The optimal solution obtained through GWO is determined to be 40 PV panels and a 60Ah BESS capacity.

Diabetic eye disease in computerised tomography of feature extraction and classification in hybrid neural network

ABSTRACT Blindness or loss of vision is primarily caused by diabetic retinopathy, or DR. It is a retinal condition that may cause harm to the eyes’ blood vessels.Due to the complicated eye structure, manually detecting diabetic retinopathy takes time and is prone to human mistake. There have been several automatic methods proposed for the diagnosis of diabetic retinopathy from fundus images.Using a combination of InceptionV3 and ResNet50, an optimised deep Convolutional Neural Network model of feature fusion is presented in this paper to categories diabetic retinopathy photos into five kinds. Concatenating results in the suggested model including both the Inception Modules and the Residual Blocks, this mitigates the gradient problem and reduces the number of parameters. Resnet50 and Inceptionv3, two different deep learning (DL) models, were used. The proposed hybrid InceptionV3 and ResNet50 based optimised deep CNN (IR_ODCNN) model gathers features from the data and joins them before sending them to the DCNN that has been optimised for classification. The hyper parameters for CNN layer training are optimised using the Grey Wolf Optimizer (GWO) method. An image dataset of the fundus is used to assess the suggested model. The experimental findings indicate that, when compared to the current approaches, In terms of classifying diabetic retinopathy, the proposed model performs better.

Using the Grey Wolf Aquila Synergistic Algorithm for Design Problems in Structural Engineering.

The Aquila Optimizer (AO) is a metaheuristic algorithm that is inspired by the hunting behavior of the Aquila bird. The AO approach has been proven to perform effectively on a range of benchmark optimization issues. However, the AO algorithm may suffer from limited exploration ability in specific situations. To increase the exploration ability of the AO algorithm, this work offers a hybrid approach that employs the alpha position of the Grey Wolf Optimizer (GWO) to drive the search process of the AO algorithm. At the same time, we applied the quasi-opposition-based learning (QOBL) strategy in each phase of the Aquila Optimizer algorithm. This strategy develops quasi-oppositional solutions to current solutions. The quasi-oppositional solutions are then utilized to direct the search phase of the AO algorithm. The GWO method is also notable for its resistance to noise. This means that it can perform effectively even when the objective function is noisy. The AO algorithm, on the other hand, may be sensitive to noise. By integrating the GWO approach into the AO algorithm, we can strengthen its robustness to noise, and hence, improve its performance in real-world issues. In order to evaluate the effectiveness of the technique, the algorithm was benchmarked on 23 well-known test functions and CEC2017 test functions and compared with other popular metaheuristic algorithms. The findings demonstrate that our proposed method has excellent efficacy. Finally, it was applied to five practical engineering issues, and the results showed that the technique is suitable for tough problems with uncertain search spaces.

Advanced Frequency Control Technique Using GTO with Balloon Effect for Microgrids with Photovoltaic Source to Lower Harmful Emissions and Protect Environment

Renewable energy (RE) resources such as wind and PV solar power are crucial for transitioning to carbon-free and sustainable energy systems, especially for agricultural and domestic applications in the desert and rural areas. However, implementing RE resources may lead to frequency penetrations, especially in isolated microgrids (µGs). This study proposes an adaptive load frequency control (LFC) technique for power systems. An integral controller can be tuned online using an artificial gorilla troops optimization algorithm (GTO), which is supported using a balloon effect (BE) identifier. Adaptive control is used to control the system frequency in case of variable loads and fluctuation due to 6 MW photovoltaic (PV). Three other optimization methods have been compared with the GTO + BE technique, namely the Grey Wolf Optimization method (GWO), the standard artificial gorilla troops optimization (GTO) and the Jaya technique. Digital simulation tests approved the efficiency of (GTO + BE) during system difficulties such as load disturbance and system parameter variations. In addition, the same test conditions have been repeated using a real-time simulation platform. The real-time simulation results supported the digital outcomes.

Allocation and Sizing of DSTATCOM with Renewable Energy Systems and Load Uncertainty Using Enhanced Gray Wolf Optimization

Over the last decade, flexible alternating current transmission systems (FACTS) have been crucial in ensuring optimal power distribution within modern power systems. A vital component of FACTS devices is the distribution static compensator (DSTATCOM), which is essential for maintaining a reliable power supply. It is commonly used for reactive power compensation, voltage regulation, and harmonic reduction. Determining the appropriate size and placement of DSTATCOMs is vital to ensuring their efficiency. This study introduces the improved gray wolf optimizer (I-GWO), a refined version of the classical gray wolf optimization (GWO) method. The I-GWO incorporates a dimension learning-based hunting (DLH) strategy to preserve population diversity, balance exploration and exploitation, and prevent the premature convergence of classical GWO. In this research, the I-GWO was applied to determine the optimum allocation and sizing of the DSTATCOMs, considering system constraints, including those presented by the intermittent and stochastic nature of the load and renewable energy resources, specifically wind and solar energy. The suggested approach was successfully tested on 33-, 69-, and 85-bus distribution systems and then compared with existing studies. The results demonstrated the I-GWO-based approach’s superiority in terms of reducing power losses, improving voltage profiles, and enhancing voltage stability.

Optimization and inventory management under stochastic demand using metaheuristic algorithm.

This study considers multi-period inventory systems for optimizing profit and storage space under stochastic demand. A nonlinear programming model based on random demand is proposed to simulate the inventory operation. The effective inventory management system is realized using a multi-objective grey wolf optimization (MOGWO) method, reducing storage space while maximizing profit. Numerical outcomes are used to confirm the efficacy of the optimal solutions. The numerical analysis and tests for multi-objective inventory optimization are performed in the four practical scenarios. The inventory model's sensitivity analysis is performed to verify the optimal solutions further. Especially the proposed approach allows businesses to optimize profits while regulating the storage space required to operate in inventory management. The supply chain performance can be significantly enhanced using inventory management strategies and inventory management practices. Finally, the novel decision-making strategy can offer new insights into effectively managing digital supply chain networks against market volatility.

Novel grey wolf optimizer based parameters selection for GARCH and ARIMA models for stock price prediction.

Stock price data often exhibit nonlinear patterns and dynamics in nature. The parameter selection in generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive integrated moving average (ARIMA) models is challenging due to stock price volatility. Most studies examined the manual method for parameter selection in GARCH and ARIMA models. These procedures are time-consuming and based on trial and error. To overcome this, we considered a GWO method for finding the optimal parameters in GARCH and ARIMA models. The motivation behind considering the grey wolf optimizer (GWO) is one of the popular methods for parameter optimization. The novel GWO-based parameters selection approach for GARCH and ARIMA models aims to improve stock price prediction accuracy by optimizing the parameters of ARIMA and GARCH models. The hierarchical structure of GWO comprises four distinct categories: alpha (α), beta (β), delta (δ) and omega (ω). The predatory conduct of wolves primarily encompasses the act of pursuing and closing in on the prey, tracing the movements of the prey, and ultimately launching an attack on the prey. In the proposed context, attacking prey is a selection of the best parameters for GARCH and ARIMA models. The GWO algorithm iteratively updates the positions of wolves to provide potential solutions in the search space in GARCH and ARIMA models. The proposed model is evaluated using root mean squared error (RMSE), mean squared error (MSE), and mean absolute error (MAE). The GWO-based parameter selection for GARCH and ARIMA improves the performance of the model by 5% to 8% compared to existing traditional GARCH and ARIMA models.

Mitigation of High Photovoltaic Penetration Effects in Electrical Grid Systems Using a Hybrid Particle Swarm and Grey Wolf Optimization Approach

The rising integration of photovoltaic (PV) systems into electrical grids has introduced significant challenges allied with voltage stability, power quality, and grid reliability, particularly beneath high PV penetration scenarios. This work presents a hybrid optimization approach combining particle swarm optimization (PSO) and grey wolf optimization (GWO) to mitigate these challenges effectively. The hybrid PSO–GWO method is not only applied to optimize the position and sizing of PV systems, but also the configuration of grid‐supportive devices like static synchronous compensators (STATCOMs), in Institute of Electrical and Electronics Institute (IEEE) 14‐test bus system. The proposed hybrid system led to a 42.2% power loss reduction, from 18.5 to 10.7 MW effectively enhancing efficiency of the grid, improves voltage profiles, all bus voltages maintained with in the acceptable range of 0.95–1.05 p.u. The study also identified optimal locations for PV units, with placements at bus 3, 6, and 9, where PV sizes were adjusted to 10, 12, and 8 MW, respectively. Additionally, the optimal placement of STATCOMs at bus 4, 7, and 10 provided reactive power support of up to 9 MVAR, further enhancing system stability. The findings suggest that the hybrid PSO–GWO optimization technique is a promising tool for managing the complexities of high PV penetration in modern electrical grids, ensuring proficient and reliable grid operation.

Fuzzy modelling approach and soft computing mechanism for predicting cognitive impairment in old people

Growing older is a phenomenon that is associated with increasingly complex health situations as a result of the coexistence of several chronic diseases. As a result, there is a downward tendency in both older people and their caretakers’ quality of life, which frequently results in frailty. There are numerous solutions available to treat the issue, which primarily affects older people. The basic and most popular imaging method for predicting cognitive impairment is magnetic resonance imaging. Furthermore, few of the earlier models had a definite level of accuracy when diagnosing the condition. Further, there is a critical need to put in place a stronger, more reliable approach to precise prediction. When compared to other procedures, using magnetic resonance images to predict cognitive decline is the safest and most straightforward. The advanced concept for a better optimized strategy to predict cognitive impairment at an early stage is presented in this research. The hybrid krill herd and grey wolf optimization method is offered as a solution to address the challenges in locating the impacted area. In a short amount of time, a significant number of MRI images are analyzed, and the results show a more precise or higher rate of recognition.

An intelligent PID controller tuning for speed control of BLDC motor using driving training-based optimization

Tuning of proportional-integral-derivative (PID) controller remains a matter of great concern for the control engineers as it plays a major role to obtain optimal performance of any system Due to their simplicity and excellent efficiency, metaheuristic algorithms have recently become extremely popular among researchers for handling a wide range of real-world optimization challenges. In order to optimize a PID controller for managing the speed of a BLDC motor, this work proposes a novel application of the driving training-based optimization (DTBO) algorithm, one of the latest and most recent human-based metaheuristic algorithms. The purpose of this present study is to optimize a PID controller for a BLDC motor speed control by DTBO method and evaluate its performance with a similar controller tuned by grey wolf optimization (GWO) method. Additionally, the suggested DTBO-PID controller's robustness analysis is being carried out with BLDC motor parameter modifications as well as a comparison to the GWO-PID controller. The comparison is carried out in MATLAB/Simulink, and the results are based on common step response metrics such rise time, settling time, and maximum overshoot. For easier comprehension, the results are presented in tabular and graphical form. The chosen BLDC motor drive system's selected DTBO-PID controller performs better and is more reliable than the GWO-PID controller, according to the final simulation findings.

Surface Roughness Prediction of Titanium Alloy during Abrasive Belt Grinding Based on an Improved Radial Basis Function (RBF) Neural Network.

Titanium alloys have become an indispensable material for all walks of life because of their excellent strength and corrosion resistance. However, grinding titanium alloy is exceedingly challenging due to its pronounced material characteristics. Therefore, it is crucial to create a theoretical roughness prediction model, serving to modify the machining parameters in real time. To forecast the surface roughness of titanium alloy grinding, an improved radial basis function neural network model based on particle swarm optimization combined with the grey wolf optimization method (GWO-PSO-RBF) was developed in this study. The results demonstrate that the improved neural network developed in this research outperforms the classical models in terms of all prediction parameters, with a model-fitting R2 value of 0.919.

SSFSCE: Design of a Sleep Scheduling based Fan Shaped Clustering Model to enhance working Energy Efficiency of WSN

To enhance energy level in WSN is a research requirement, which assists in improving their lifetime over a series of communications. To achieve this target, a various variety of clustering & sleep scheduling models are discussed by researchers. Most of these models deploy static clustering & sleep scheduling operations, which limits their applicability & scalability levels. Moreover, dynamic clustering & scheduling models are highly complex, which reduces temporal QoS performance under real-time use cases. In order to reduce the probability of these issues, this text discusses design of the proposed Sleep Scheduling based Fan Shaped Clustering Model to enhance working Energy Efficiency of WSN. The proposed model initially deploys a Grey Wolf Optimization (GWO) Method for dynamic sleep scheduling via temporal performance analysis. The GWO Method models a fitness function that combines temporal usage levels, temporal Quality of Service (QoS), and temporal energy levels. Based on this modelling process, nodes were categorized into wake & sleep nodes, which were further clustered via destination-aware Fan Shaped Clustering (FSC), that assisted in improving QoS performance under multiple scenarios. The FSC Model was combined with a QoS-aware routing model, that assisted in selection of routing paths that can achieve low delay, high throughput, and high packet delivery with higher energy efficiency levels. Efficiency of the model was tested on node & network conditions, and its QoS performance was checked in terms of communication delay, consumption of energy, level of throughput, and Packet Delivery Ratio (PDR) levels. On the basis of these comparative evaluations, it is observed that the new proposed model is able to enhance end-to-end delay by 8.5%, reduce level of energy by 15.5%, while increasing throughput by 8.3%, and PDR by 1.5%, thus making it useful for a different real-time conditions.

An innovative process design of seawater desalination toward hydrogen liquefaction applied to a ship's engine: An economic analysis and intelligent data-driven learning study/optimization

Integrating heat recovery applications with heavy engines during transportation is critical for achieving sustainable production and reducing the irreversibility associated with the power production process of the engine. In this regard, the current paper introduces a novel waste heat recovery method utilizing the hot flue gas released by a 1-MW ship's engine to yield liquefied hydrogen from seawater desalination while simultaneously meeting the ship's air-conditioning requirement. In addition, a techno-economic analysis and an advanced feasibility study/optimization are conducted. The process employs reverse osmosis desalination to generate freshwater fed to a water electrolyzer for hydrogen production. The needed power is supplied from an organic flash cycle coupled with an ejector-based bi-evaporator refrigeration cycle. The first cooling loop of the refrigeration cycle offers air-conditioning, while the low-temperature loop yields cooling for the Claude hydrogen liquefaction cycle. A comprehensive feasibility assessment is conducted from the thermodynamic, economic, and environmental viewpoints, and accordingly, an intelligent data-driven learning approach is implemented for performing different multi-criteria optimization scenarios. This approach uses an artificial neural network with a multi-objective grey wolf optimization method. The LINMAP method is employed to reach the most favorable scenario and identify the optimal solution. The findings indicate that the flash temperature attains the highest mean sensitivity index measured at 0.377. Moreover, the best optimization scenario is associated with the exergy efficiency, CO2 emission reduction, and liquefied hydrogen cost as objective functions, calculated at 11.39 %, 22.31 kg/MWh, and 10.25 $/kg, respectively.