Hybrid Particle Swarm Research Articles

ADAPTIVE HYBRID DIFFERENTIAL EVOLUTION PARTICLE SWARM OPTIMIZATION ALGORITHM FOR OPTIMIZATION DISTRIBUTED GENERATION IN DISTRIBUTION NETWORKS

The incorporation of Distributed Generation (DG) into the Radial Distribution System (RDS) aids in resolving power system issues such as power loss. However, finding the ideal location and size for DG is challenging yet crucial for maximizing these advantages. Inappropriate location and sizing of DG can negatively impact its benefits, highlighting the need for effective optimization methods. To address these challenges, metaheuristic methods like Particle Swarm Optimization (PSO), Differential Evolution (DE), and Firefly algorithms are particularly useful. This research aims to determine the best location and size of DG to minimize active power losses in the RDS. Despite the success of DE and PSO in previous works, a gap remains in achieving optimal convergence performance and computational efficiency. Building on the success of DE and PSO, this study presents a hybrid optimization approach, Adaptive Hybrid Differential Evolution and Particle Swarm Optimization (AHDEPSO), to reduce power loss in RDS. This approach combines the strengths of DE and PSO, enhancing exploration and exploitation capabilities while improving convergence performance. The effectiveness of this approach is demonstrated through testing on the IEEE 33 and IEEE 69 bus systems using MATLAB software, showing that AHDEPSO can achieve optimal computational time and best fitness function, being 38.3% faster than other algorithms. This hybrid approach offers a significant improvement over traditional methods, filling the research gap and providing a more efficient solution.

Research on Fire Detection of Cotton Picker Based on Improved Algorithm.

According to the physical characteristics of cotton and the work characteristics of cotton pickers in the field, during the picking process, there is a risk of cotton combustion. The cotton picker working environment is complex, cotton ignition can be hidden, and fire is difficult to detect. Therefore, in this study, we designed an improved algorithm for multi-sensor data fusion; built a cotton picker fire detection system by using infrared temperature sensors, CO sensors, and the upper computer; and proposed a BP neural network model based on improved mutation operator hybrid gray wolf optimizer and particle swarm optimization (MGWO-PSO) algorithm based on the BP neural network model. This algorithm includes the introduction of a mutation operator in the gray wolf algorithm to improve the search ability of the algorithm, and, at the same time, we introduce the PSO algorithm idea. The improved fusion algorithm is used as a learning algorithm to optimize the BP neural network, and the optimized network is used to process and predict the data collected from temperature and gas sensors, which effectively improves the accuracy of fire prediction. The sensor measurements were compared with the actual values to verify the effectiveness of the GWO-PSO-optimized BP neural network model. Once experimentally verified, the improved GWO-PSO algorithm achieves a correlation coefficient R of 0.96929, a prediction accuracy rate of 96.10%, and a prediction error rate of only 3.9%, while the system monitors an accurate early warning rate of 96.07%, and the false alarm and omission rates are both less than 5%. This study can detect cotton picker fires in real time and provide timely warnings, which provides a new method for the accurate detection of fires during the field operation of cotton pickers.

Optimal Dimensional Synthesis of Ackermann Steering Mechanisms for Three-Axle, Six-Wheeled Vehicles

This study employs four metaheuristic optimization methods to optimize the dimensional synthesis of Ackermann steering mechanisms for three-axle, six-wheeled vehicles with front-axle steering mode and reverse-phase steering mode. The employed optimization methods include Particle Swarm Optimization (PSO), Hybrid Particle Swarm Optimization (HPSO), Differential Evolution with golden ratio (DE-gr), and Linearly Ensemble of Parameters and Mutation Strategies in Differential Evolution (L-EPSDE). With a front-wheel steering angle range of 70 degrees, two hundred optimization experiments were conducted for each method, and statistical analyses revealed that DE-gr and L-EPSDE methods outperformed PSO and HPSO methods in terms of standard deviation, mean value, and minimum error. These two methods exhibited superior convergence stability, faster convergence, and higher accuracy compared to PSO and HPSO. Reverse-phase (K = 1) steering mode outperformed front-axle steering mode, delivering reduced steering errors and turning radii. Considering the transmission ratio of front to rear axle (K) as a design variable in reverse-phase steering mode increased design flexibility and significantly lowered steering errors for the front and rear axle steering mechanisms. However, this comes with a slight increase in the turning radius of the vehicle’s front part compared to when K = 1. The optimized mechanism, designed using the DE-gr method, was validated through kinematic simulations and steering analyses using MSC-ADAMS v2015 software, further confirming the effectiveness and reliability of the proposed design.

PGL: A short-time model for ship trajectory prediction

Abstract Ship trajectory prediction plays a critical role in collision detection and risk assessment. To enhance prediction accuracy and efficiency, a novel hybrid particle swarm optimisation (PSO) and grey wolf optimisation (GWO) long, short-term memory (LSTM) network model is proposed (PGL model). The hybrid PSO-GWO optimisation method combines the algorithm's strengths and offers improved stability and performance. The hybrid algorithm is employed to optimise the hyperparameters of the LSTM neural networks to enhance prediction accuracy and efficiency. To demonstrate the superiority of the PGL model, the LSTM, PSO-LSTM and PGL are applied to the same dataset, and then prediction performance and processing time are compared. Experimental results indicate that the proposed PGL algorithm outperforms prediction accuracy and optimisation time.

Coupling Beams’ Shear Capacity Prediction by Hybrid Support Vector Regression and Particle Swarm Optimization

Coupling Beams’ Shear Capacity Prediction by Hybrid Support Vector Regression and Particle Swarm Optimization

Multi-objective Optimization of a Yoke-less Axial Flux Switching PM Motor based on Hybrid Particle Swarm Optimization

In this study, a hybrid particle swarm optimization (HPSO) approach is presented for enhancing the performance of a three-phase, 12-slot, 19-pole yoke-less axial-field flux-switching permanent magnet (YASA-AFFSPM) motor. The aim of the optimization process is to achieve a motor that demonstrates high efficiency and stable operation. To facilitate this, a finite element analysis model is developed, and a multi-objective optimization function utilizing weight coefficients is created. The variables in this study include the split ratio, stator axial length, sandwiching pole angle, rotor pole angle, permanent magnet arc, and the number of conductors per slot. The optimization objectives encompass efficiency, power factor, cogging torque, and average torque, evaluated under both no-load and load conditions. Findings indicate that the hybrid particle swarm optimization method excels in its search capabilities and convergence speed, resulting in motor designs that align closely with the intended specifications. Finite element simulations further validate the proposed methodology's effectiveness and practicality. Finally, experimental results are presented to confirm the reliability of the suggested algorithm.

Enhancing Underwater Object Recognition: Integrating Transfer Learning with Hybrid Optimization Techniques for Improved Detection Accuracy

Underwater object recognition presents unique challenges due to varying water conditions, low visibility, and the presence of noise. This research proposes an advanced methodology that combines transfer learning and hybrid optimization techniques to enhance recognition accuracy in underwater environments. Specifically, a pre-trained EfficientNet model is employed for feature extraction, leveraging its capacity to capture diverse features in underwater images. The model is then optimized using a hybrid Particle Swarm Optimization and Genetic Algorithm (PSOGA) to fine-tune hyperparameters such as learning rate, number of layers, and activation functions. This hybrid approach balances exploration and exploitation in the search space, allowing the model to converge on an optimal solution that maximizes accuracy. The model is evaluated against nine existing deep learning models, including ResNet-50, VGG-16, EfficientNet-B0, and MobileNetV2. The proposed PSOGA model achieves a superior accuracy of 98.32%, surpassing the best-performing models like EfficientNet-B0, which reached 95.89%. Furthermore, the model outperforms traditional optimizers like Adam, RMSprop, and AdaGrad, which attained lower accuracies. Precision, recall, and F1-score for the PSOGA model also demonstrate remarkable improvements, highlighting the model's effectiveness in underwater object recognition. The combination of transfer learning and hybrid optimization enables the model to generalize well across diverse underwater environments while maintaining computational efficiency.

A Hybrid Particle Swarm Optimisation Algorithm for Multi-Resource Constrained Flexible Job Shop Scheduling Problem with Transportation

A Hybrid Particle Swarm Optimisation Algorithm for Multi-Resource Constrained Flexible Job Shop Scheduling Problem with Transportation

Novel neural network classification of maternal fetal ultrasound planes through optimized feature selection

Ultrasound (US) imaging is an essential diagnostic technique in prenatal care, enabling enhanced surveillance of fetal growth and development. Fetal ultrasonography standard planes are crucial for evaluating fetal development parameters and detecting abnormalities. Real-time imaging, low cost, non-invasiveness, and accessibility make US imaging indispensable in clinical practice. However, acquiring fetal US planes with correct fetal anatomical features is a difficult and time-consuming task, even for experienced sonographers. Medical imaging using AI shows promise for addressing current challenges. In response to this challenge, a Deep Learning (DL)-based automated categorization method for maternal fetal US planes are introduced to enhance detection efficiency and diagnosis accuracy. This paper presents a hybrid optimization technique for feature selection and introduces a novel Radial Basis Function Neural Network (RBFNN) for reliable maternal fetal US plane classification. A large dataset of maternal–fetal screening US images was collected from publicly available sources and categorized into six groups: the four fetal anatomical planes, the mother's cervix, and an additional category. Feature extraction is performed using Gray-Level Co-occurrence Matrix (GLCM), and optimization methods such as Particle Swarm Optimization (PSO), Grey Wolf Optimization (GWO), and a hybrid Particle Swarm Optimization and Grey Wolf Optimization (PSOGWO) approach are utilized to select the most relevant features. The optimized features from each algorithm are then input into both conventional and proposed DL models. Experimental results indicate that the proposed approach surpasses conventional DL models in performance. Furthermore, the proposed model is evaluated against previously published models, showcasing its superior classification accuracy. In conclusion, our proposed approach provides a solid foundation for automating the classification of fetal US planes, leveraging optimization and DL techniques to enhance prenatal diagnosis and care.

Research on Planting Strategy Based on Game Theory Hybrid Particle Model

Hybrid particle swarm optimization (PSS) is an intelligent optimization method widely used in machine learning. In this paper, we combine evolutionary game theory and particle swarm optimization and apply them to the optimization of farm planting strategies. Firstly, a linear regression model was established by accurately modeling the output, sales volume and other relevant indicators of agricultural products. Then, by using the powerful global search ability of game theory and hybrid particle swarm optimization to solve the optimal solution under constraints. Subsequently, the Monte Carlo method is introduced to incorporate factors such as climate and geographic location into the model, which further improves the accuracy of the prediction. This study not only successfully applies game theory and hybrid particle swarm optimization to the optimization of farm planting strategy, which has high practical value, but also provides a useful reference for similar multi-dimensional programming problems.

New PSO-GWO-based model for enhancing power quality in electrical networks interconnected with photovoltaic sources

This research introduces an innovative model to enhance power quality within electrical networks interconnected with photovoltaic (PV) sources. The central concern addressed in this study revolves around the impact of PV source power quality on local electric networks. This research endeavors to elucidate how achieving a more refined power pattern in electric networks is attainable by considering the power quality of PV sources. A hybrid Particle Swarm Optimization-Gray Wolf Optimization (PSO-GWO) algorithm is proposed to obtain optimal solutions. Empirical findings underscore the significant impact of Unified Power Quality Conditioners (UPQC) on social welfare, reinforcing the potential benefits of improving power quality. The results reveal that localized price reductions primarily drive the enhancement of social welfare, and this socioeconomic advantage outweighs improvements in sustainability metrics.

Modeling and Analysis of College English from the Perspective of Connected Intelligent Algorithms

To explore the realm of English education through contemporary advancements in artificial intelligence (AI), language education methods have developed significantly traditional approaches that usually have trouble with individualized learning needs and cannot handle diverse proficiency levels. This paper reveals the most prominent problem of inefficiency and non-personalized learning experiences in college English as a significant concern in the existing literature. In response, it suggests a novel method called Artificial Intelligence based English Teaching Method (AI-ETM). It has linked intelligent algorithms that can dynamically adapt teaching strategies and learning materials according to individual student’s needs, rate of comprehension and proficiency levels. The main aim of AI-ETM is to integrate AI technologies with hybrid particle swarm optimization (PSO) into English language teaching to improve effectiveness and efficiency and provide personalized learning experiences for students. This paper expects several outcomes from the implementation of AI-ETM. Among these is enhanced student engagement and motivation due to personalized learning experiences customized according to personal preferences and level of competence. Additionally, AI-ETM is expected to improve learning outcomes by offering targeted feedback and adaptive learning resources. This paper suggests that once AI-ETM is introduced, efficiency in delivering language instruction services will improve, thereby optimizing the allocation of educational resources.

Battery Remaining Useful Life Estimation based on Particle Swarm Optimization-Neural Network

Determining the Remaining Useful Life (RUL) of a battery is essential for several purposes, including proactive maintenance planning, optimizing resource allocation, preventing unforeseen failures, improving safety, extending battery lifespan, and achieving accurate cost savings. Concerning that matter, this study proposed hybrid Particle Swarm Optimization–Neural Network (PSO-NN) for estimating battery RUL. In the evaluation of the proposed method, the effectiveness is assessed using the metrics of Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE). The dataset employed for this investigation comprises eight input parameters and one output variable, representing the battery RUL. In conducting an analysis, the performance of the PSO-NN model is compared with hybrid NN with Cultural Algorithm (CA-NN) and Harmony Search Algorithm (HSA-NN), as well as the standalone Autoregressive Integrated Moving Average (ARIMA). Upon examination of the findings, it becomes evident that the PSO-NN model outperforms the alternatives with an MAE of 2.7708 and an RMSE of 4.3468, significantly lower than HSA-NN (MAE: 22.0583, RMSE: 34.5154), CA-NN (MAE: 9.1189, RMSE: 22.4646), and ARIMA (MAE: 494.6275, RMSE: 584.3098). The PSO-NN also achieves the lowest maximum error of 104.7381 compared to 490.3125 for HSA-NN, 827.0163 for CA-NN, and 1,160.0000 for ARIMA. Additionally, the low two-tail probability values (P(T≤t)), all below the significance level of 0.05, indicate that the differences between PSO-NN and the other methods (HSA-NN, CA-NN, and ARIMA) are statistically significant. These results highlight the superior accuracy and robustness of the PSO-NN model in predicting battery RUL. This study contributes to the field by presenting the PSO-NN as a highly effective tool for accurate battery RUL estimation, as evidenced by its superior performance over alternative methods.

Mechanism Isomorphism Identification Based on Decision Tree Algorithm and Hybrid Particle Swarm Optimization Algorithm

Mechanism isomorphism identification is a typical quadratic assignment problem similar to traveling salesman and job-shop scheduling. For the complex mechanism with more components, common methods of isomorphism identification may fail due to low solving efficiency and reliability. Based on the decision tree algorithm and hybrid particle swarm optimization (HPSO) algorithm, the global-local search method is proposed to identify isomorphism of mechanisms. More precisely, based on the intrinsic relationship between links and vertices in the mechanism, the decision tree algorithm globally searches the characteristic path with mapping properties of different mechanisms. On this basis, HPSO algorithm combines genetic algorithm with particle swarm optimization algorithm to find the exact global optimal solution instead of local optimal solution. Some complex cases such as 14-link kinematic chains, 18-vertex topological graphs, and 8-vertex planetary gear trains are used to evaluate the efficiency and reliability of the proposed method. Results show that the proposed method can accurately identify isomorphism of mechanisms in a relatively short time. It can improve the solving efficiency of isomorphism identification in structural synthesis.

A Talent Cultivation and Performance Evaluation Model Based on a Fuzzy Control Algorithm

The Internet era has raised the demand for skilled workers in businesses and for economic expansion. Businesses find it difficult to expand when trained personnel are shortages. Evaluating and managing exceptionally gifted persons have become more difficult due to technological developments, which have slowed down technological progress and business expansion. The study suggests a technique to quantify how firms develop and employ talent to address this issue. An algorithm called the fuzzy optimized talent cultivation engine (FOTCE) is introduced to evaluate the effectiveness of talent development. The algorithm combines an adaptive neuro-Fuzzy Inference System with Adaptive Hybrid Particle Swarm Optimization. By considering factors including work-life balance, training, involvement, job performance, and satisfaction, the suggested FOTCE algorithm hopes to improve talent strategies and boost organizational competitiveness. The FOTCE algorithm assesses talent development on three levels: overall efficacy, major categories (such as job satisfaction and involvement), and individual indicators within each category. Fuzzy logic handles subjective viewpoints and unclear data in the study, allowing for a more comprehensive assessment. The technique uses fuzzy math to show different levels of employee retention by giving different factors different weights. The results show that the FOTCE technique helps evaluate and upgrade talent development programs and provides valuable insights for better people management when tested with accurate HR data from a company. The findings demonstrate that the suggested FOTCE algorithm outperformed state-of-the-art models like IAA-NRM (83% retention rate) and FAHP (87% retention rate) by a wide margin. Comparatively, FAHP had an EEI of 83% and DEA had 86%. The EEI for this organization achieved 95%. In addition, the FOTCE model showed a higher Talent Development Efficiency Score (TCDES) of 93%, proving that it boosts organizational competitiveness and employee happiness.

Spectrum Sensing and Resource Allocation for Frequency Hopping Based CRN Using Hazelnut Tree Search Algorithm

This paper presents a novel spectrum sensing and resource allocation method for Cognitive Radio Networks (CRNs) using the Hazelnut Tree Search (HTS) algorithm in a frequency-hopping framework. CRNs enable secondary users (SUs) to utilize unused licensed spectrum without causing interference to primary users (PUs). The proposed Spectrum Sensing and Resource Allocation using Hazelnut Tree Search in CRN (SS-RA-HTS-CRN) method detects PU presence, prompting SUs to switch channels to avoid interference, guided by a designated guide node (GN). The HTS algorithm selects optimal sensing nodes and improves spectrum sensing, enhancing resource allocation reliability. Simulations in NS-3.26 show that SS-RA-HTS-CRN achieves delay reductions of 28.93%, 31.9%, and 22.45%, delivery ratio improvements of 28.21%, 17.41%, and 11.565%, and packet drop rate reductions of 35.4%, 44.3%, and 23.12% compared with Energy-Aware Resource Allocation with Backtracking Search Optimization (SS-RA-BSO-CRN), Spectrum Sensing with Hybrid Particle Swarm and Gravitational Search (SS-hybrid PSOGSA-CRN), and Spectrum Sensing using Modified Spider Monkey Optimization (SS-MSMO-CRN). The proposed SS-RA-HTS-CRN method significantly enhances efficiency, reliability, and adaptability in CRNs, making it a promising solution for dynamic spectrum management.

Optimized Energy Management Strategy for an Autonomous DC Microgrid Integrating PV/Wind/Battery/Diesel-Based Hybrid PSO-GA-LADRC Through SAPF

This study focuses on microgrid systems incorporating hybrid renewable energy sources (HRESs) with battery energy storage (BES), both essential for ensuring reliable and consistent operation in off-grid standalone systems. The proposed system includes solar energy, a wind energy source with a synchronous turbine, and BES. Hybrid particle swarm optimizer (PSO) and a genetic algorithm (GA) combined with active disturbance rejection control (ADRC) (PSO-GA-ADRC) are developed to regulate both the frequency and amplitude of the AC bus voltage via a load-side converter (LSC) under various operating conditions. This approach further enables efficient management of accessible generation and general consumption through a bidirectional battery-side converter (BSC). Additionally, the proposed method also enhances power quality across the AC link via mentoring the photovoltaic (PV) inverter to function as shunt active power filter (SAPF), providing the desired harmonic-current element to nonlinear local loads as well. Equipped with an extended state observer (ESO), the hybrid PSO-GA-ADRC provides efficient estimation of and compensation for disturbances such as modeling errors and parameter fluctuations, providing a stable control solution for interior voltage and current control loops. The positive results from hardware-in-the-loop (HIL) experimental results confirm the effectiveness and robustness of this control strategy in maintaining stable voltage and current in real-world scenarios.

Gravity data inversion for parameters assessment over geologically faulted structures—A hybrid particle swarm optimization and gravitational search algorithm technique

AbstractInterpreting gravity anomalies caused by fault formations is associated with hydrocarbon systems, mineralized areas and hazardous zones and is the main goal of this research. To achieve an effective and robust model over the geologically faulted structures from gravity anomalies, we present a nature‐inspired hybrid algorithm, which synergizes the physics of the particle swarm optimization and gravitational search algorithm with variable inertia weights. The basic principle of developed particle swarm optimization and gravitational search algorithm method is to synergistically use the exploratory strengths of gravitational search algorithm with the exploitation capacity of particle swarm optimization in order to optimize and enhance the effectiveness by both algorithms. The technique has been tested on synthetic gravity data with varying settings of noises over geologically faulted structure before being applied to field data taken from Ahiri‐Cherla and Aswaraopet master fault present in Pranhita–Godavari valley, India. The optimization process is further refined through normalized Gaussian probability density functions, confidence intervals, histograms and correlation matrices to quantify uncertainty, stability, sensitivity and resolution. When dealing with field data, the true model is never known; in these circumstances, the quality of the outcome can only be inferred from the uncertainty in the mean model. The research utilizes a 68.27% confidence intervals to identify a location where the probability density function is more dominant. This region is then used to evaluate the mean model, which is expected to be more appropriate and closer to the genuine model. Correlation matrices further provide a clear demonstration of the strong connection between layer parameters. The results suggest that particle swarm optimization and gravitational search algorithm is less affected by model parameters and yields geologically more consistent outcomes with little uncertainty in the model, aligning well with the available results. The analysed results show that the method we came up with works well and is stable when it comes to solving the two‐dimensional gravity inverse problem. Future research may involve extending the approach to three‐dimensional inversion problems, with potential improvements in computational efficiency and search accuracy for global optimization methods.

Device optimization of all-perovskite triple-junction solar cells for realistic irradiation conditions

All-perovskite two-terminal tandem solar cells, comprising two or more junctions, offer high power conversion efficiencies (PCEs) that exceed the limits of single-junction photovoltaics. Realizing high-efficiency SCs requires carefully optimizing the photoactive layer, front electrodes, and functional layers. Here, we first aim to determine the optimal device architecture, i.e., the perovskites bandgaps and optimum layer thicknesses, for standard test conditions (STCs). We then optimize the energy yield (EY) under realistic outdoor conditions (ROCs), i.e., the overall electrical energy to be expected in one year at a specific location. In the first step, we reference our simulation with two terminal all-perovskite triple-junction SCs (2T3J-PSCs) to previously experimentally realized PSC with a PCE of 20.1% as a benchmark to derive the underlying diode parameters and use our in-house energy yield code combined with a hybrid particle swarm optimization and gravitational search algorithm (PSOGSA) to find the optimal bandgap combination and perovskite layer thicknesses. The optimized SCs with the optimal bandgap combination offer a PCE of 25.1% with a current density of 10.1 mA/cm2. Furthermore, the effect of the other functional layers, such as transparent conductive oxide (TCO), hole transport layer (HTL), and recombination junctions (RJs), is also investigated to enhance the cell performance further. The SCs with optimized layers exhibit improved parameters: PCE of 27.1%, with a relative improvement of 34.8% in the PCE compared with the fabricated cell, and a high current matching a of 10.8 mA/cm2. The numerical results showed that the reported cell can potentially achieve a PCE of 36% at an eVoc/EG ratio of 0.72. However, the optimal parameters may vary in real-world operating conditions due to variations in temperature, humidity, and light exposure. As a result, the optimal energy yield (EY) parameters may differ. Therefore, the energy yield optimizing process is also carried out by considering ROCs in Phoenix, AZ, USA, to find the best parameters under these conditions. We found that the optimum top layer bandgap under ROCs is lower than under STCs due to a bluer, more shifted spectrum in ROCs. After that, the optimized cell under ROCs is tested in several locations exhibiting different climatic conditions (Seattle, Honolulu, Los Angeles, Miami, and Milwaukee). The numerical results show that the optimized cell under ROCs offers an increase in energy yield in several locations compared to conventional single-junction crystalline Si-SCs (PCE = 23.6%) with a high energy yield of 648.2 kWh/m2 in Phoenix, with an improvement of 39.9% in the EY compared to the Si-SC counterpart. Our results provide design guidelines for fabricating a highly efficient triple-junction perovskite SC in the lab and outdoor applications and improve the efficiency of 2T3J-PSCs beyond the 30% limit.

Performance of PSO-GWO, VAGWO, and GWO optimization techniques for economic dispatch problem: studied case of the southeast algerian electrical network

Economic dispatch (ED) aims to identify the most cost-effective strategy for allocating power generation while meeting demand and adhering to the physical constraints of the power system. In this paper, three algorithms are proposed to solve the ED problem in power systems, including a hybrid Particle Swarm Optimization with Grey Wolf Optimizer (PSO-GWO), modified Velocity Aided Grey Wolf Optimizer (VAGWO), and Grey Wolf Optimizer (GWO). PSO is a meta-heuristic optimization technique designed to find the optimal solution to a problem by guiding the movement of particles within a defined exploration space. GWO is also a meta-heuristic optimization algorithm based on the natural behavior of grey wolves. In this paper, to enhance the performance of GWO, it is first combined with the PSO method. VAGWO is employed to refine the GWO formulation by optimizing the convergence steps. At the beginning of the iterations, the distance between the solutions (wolves) is increased to promote exploration of the search space. As the iterations progress, the step size is reduced, allowing for a more precise and efficient convergence toward the optimal solution. These algorithms will be implemented in Matlab software to minimize the fuel cost production of the following test networks: IEEE 30-bus network, Algerian 114-bus network, and Southeast Algerian network. These methods show that the PSO-GWO algorithm offers better results when compared through VAGWO and GWO.