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Software defect prediction (SDP) is a critical aspect of software quality assurance, aiming to identify and manage potential defects in software systems. In this paper, we have proposed a novel hybrid approach that combines Gray Wolf Optimization with Feature Selection (GWOFS) and multilayer perceptron (MLP) for SDP. The GWOFS-MLP hybrid model is designed to optimize feature selection, ultimately enhancing the accuracy and efficiency of SDP. Gray Wolf Optimization, inspired by the social hierarchy and hunting behavior of gray wolves, is employed to select a subset of relevant features from an extensive pool of potential predictors. This study investigates the key challenges that traditional SDP approaches encounter and proposes promising solutions to overcome time complexity and the curse of the dimensionality reduction problem.

The integration of GWOFS and MLP results in a robust hybrid model that can adapt to diverse software datasets. This feature selection process harnesses the cooperative hunting behavior of wolves, allowing for the exploration of critical feature combinations. The selected features are then fed into an MLP, a powerful artificial neural network (ANN) known for its capability to learn intricate patterns within software metrics. MLP serves as the predictive engine, utilizing the curated feature set to model and classify software defects accurately.

The performance evaluation of the GWOFS-MLP hybrid model on a real-world software defect dataset demonstrates its effectiveness. The model achieves a remarkable training accuracy of 97.69% and a testing accuracy of 97.99%. Additionally, the receiver operating characteristic area under the curve (ROC-AUC) score of 0.89 highlights the model’s ability to discriminate between defective and defect-free software components.

Experimental implementations using machine learning-based techniques with feature reduction are conducted to validate the proposed solutions. The goal is to enhance SDP’s accuracy, relevance and efficiency, ultimately improving software quality assurance processes. The confusion matrix further illustrates the model’s performance, with only a small number of false positives and false negatives.

This paper aims at studying meta-heuristic algorithms. One of the common meta-heuristic optimization algorithms is called grey wolf optimization (GWO). The key aim is to enhance the limitations of the wolves’ searching process of attacking gray wolves.

The development of meta-heuristic algorithms has increased by researchers to use them extensively in the field of business, science and engineering. In this paper, the K-means clustering algorithm is used to enhance the performance of the original GWO; the new algorithm is called K-means clustering gray wolf optimization (KMGWO).

Results illustrate the efficiency of KMGWO against to the GWO. To evaluate the performance of the KMGWO, KMGWO applied to solve CEC2019 benchmark test functions.

Results prove that KMGWO is superior to GWO. KMGWO is also compared to cat swarm optimization (CSO), whale optimization algorithm-bat algorithm (WOA-BAT), WOA and GWO so KMGWO achieved the first rank in terms of performance. In addition, the KMGWO is used to solve a classical engineering problem and it is superior.

The paper has proposed to implement gray wolf optimization (GWO)-based filter-type proportional derivative with (FPD) plus (1+ proportional integral) multistage controller in a three-area integrated source-type interlinked power network for achieving automatic generation control.

For analysis, a three area interconnected power system of which each area comprises three different generating units where thermal and hydro system as common. Micro sources like wind generator, diesel generator and gas unit are integrated with area1, area2 and area3 respectively. For realization of system nonlinearity some physical constraints like generation rate constraint, governor dead band and boiler dynamics are effected in the system.

The supremacy of multistage controller structure over simple proportional integral (PI), proportional integral, derivative (PID) and GWO technique over genetic algorithm, differential evolution techniques has been demonstrated. A comparison is made on performances of different controllers and sensitivity analysis on settling times, overshoots and undershoots of different dynamic responses of system as well as integral based error criteria subsequent a step load perturbation (SLP). Finally, sensitive analysis has been analyzed by varying size of SLP and network parameters in range ±50 per cent from its nominal value.

Design and implementation of a robust FPD plus (1 + PI) controller for AGC of nonlinear power system. The gains of the proposed controller are optimized by the application of GWO algorithm. An investigation has been done on the dynamic performances of the suggested system by conducting a comparative analysis with conventional PID controller tuned by various optimization techniques to verify its supremacy. Establishment of the robustness and sensitiveness of the controller by varying the size and position of the SLP, varying the loading of the system randomly and varying the time constants of the system.

This paper aims to resolve the sizing issues of analog circuit design by using proposed metaheuristic optimization algorithm.

The hybridization of whale optimization algorithm and modified gray wolf optimization (WOA-mGWO) algorithm is proposed, and the same is applied for the automated design of analog circuits.

The proposed hybrid WOA-mGWO algorithm demonstrates better performance in terms of convergence rates and average fitness of the function after testing it with 23 classical benchmark functions. Moreover, a rigorous performance evaluation is done with 20 independent runs using Wilcoxon rank-sum test.

For evaluating the performance of the proposed algorithm, a conventional two-stage operational amplifier is considered. The aspect ratios calculated by simulating the algorithm in MATLAB are later used to design the operational amplifier in Cadence environment using 180nm CMOS standard process.

The hybrid WOA-mGWO algorithm is tailored to improve the exploration ability of the algorithm by combining the abilities of two metaheristic algorithms, i.e. whale optimization algorithm and modified gray wolf optimization algorithm. To build further credence and to prove its profound existence in the latest state of the art, a statistical study is also conducted over 20 independent runs, for the robustness of the proposed algorithm, resulting in best, mean and worst solutions for analog IC sizing problem. A comparison of the best solution with other significant sizing tools proving the efficiency of hybrid WOA-mGWO algorithm is also provided. Montecarlo simulation and corner analysis are also performed to validate the endurance of the design.

The interval multi-objective optimization problems (IMOPs) are universal and vital uncertain optimization problems. In this study, an interval multi-objective grey wolf optimization algorithm (GWO) based on fuzzy system is proposed to solve IMOPs effectively.

First, the classical genetic operators are embedded into the interval multi-objective GWO as local search strategies, which effectively balanced the global search ability and local development ability. Second, by constructing a fuzzy system, an effective local search activation mechanism is proposed to save computing resources as much as possible while ensuring the performance of the algorithm. The fuzzy system takes hypervolume, imprecision and number of iterations as inputs and outputs the activation index, local population size and maximum number of iterations. Then, the fuzzy inference rules are defined. It uses the activation index to determine whether to activate the local search process and sets the population size and the maximum number of iterations in the process.

The experimental results show that the proposed algorithm achieves optimal hypervolume results on 9 of the 10 benchmark test problems. The imprecision achieved on 8 test problems is significantly better than other algorithms. This means that the proposed algorithm has better performance than the commonly used interval multi-objective evolutionary algorithms. Moreover, through experiments show that the local search activation mechanism based on fuzzy system proposed in this study can effectively ensure that the local search is activated reasonably in the whole algorithm process, and reasonably allocate computing resources by adaptively setting the population size and maximum number of iterations in the local search process.

This study proposes an Interval multi-objective GWO, which could effectively balance the global search ability and local development ability. Then an effective local search activation mechanism is developed by using fuzzy inference system. It closely combines global optimization with local search, which improves the performance of the algorithm and saves computing resources.

Intelligent prediction of node localization in wireless sensor networks (WSNs) is a major concern for researchers. The huge amount of data generated by modern sensor array systems required computationally efficient calibration techniques. This paper aims to improve localization accuracy by identifying obstacles in the optimization process and network scenarios.

The proposed method is used to incorporate distance estimation between nodes and packet transmission hop counts. This estimation is used in the proposed support vector machine (SVM) to find the network path using a time difference of arrival (TDoA)-based SVM. However, if the data set is noisy, SVM is prone to poor optimization, which leads to overlapping of target classes and the pathways through TDoA. The enhanced gray wolf optimization (EGWO) technique is introduced to eliminate overlapping target classes in the SVM.

The performance and efficacy of the model using existing TDoA methodologies are analyzed. The simulation results show that the proposed TDoA-EGWO achieves a higher rate of detection efficiency of 98% and control overhead of 97.8% and a better packet delivery ratio than other traditional methods.

The proposed method is successful in detecting the unknown position of the sensor node with a detection rate greater than that of other methods.

Supply chains (SCs) have been growingly virtualized in response to the market challenges and opportunities that are presented by new and cost-effective internet-based technologies today. This paper designed a virtual closed-loop supply chain (VCLSC) network based on multiperiod, multiproduct and by using the Internet of Things (IoT). The purpose of the paper is the optimization of the VCLSC network.

The proposed model considers the maximization of profit. For this purpose, costs related to virtualization such as security, energy consumption, recall and IoT facilities along with the usual costs of the SC are considered in the model. Due to real-world demand fluctuations, in this model, demand is considered fuzzy. Finally, the problem is solved using the Grey Wolf algorithm and Firefly algorithm. A numerical example and sensitivity analysis on the main parameters of the model are used to describe the importance and applicability of the developed model.

The findings showed that the Firefly algorithm performed better and identified more profit for the SC in each period. Also, the results of the sensitivity analysis using the IoT in a VCLSC showed that the profit of the virtual supply chain (VSC) is higher compared to not using IoT due to tracking defective parts and identifying reversible products. In proposed model, chain members can help improve chain operations by tracking raw materials and products, delivering products faster and with higher quality to customers, bringing a new level of SC efficiency to industries. As a result, VSCs can be controlled, programmed and optimized remotely over the Internet based on virtual objects rather than direct observation.

There are limited researches on designing and optimizing the VCLSC network. This study is one of the first studies that optimize the VSC networks considering minimization of virtual costs and maximization of profits. In most researches, the theory of VSC and its advantages have been described, while in this research, mathematical optimization and modeling of the VSC have been done, and it has been tried to apply SC virtualization using the IoT. Considering virtual costs in VSC optimization is another originality of this research. Also, considering the uncertainty in the SC brings the issue closer to the real world. In this study, virtualization costs including security, recall and energy consumption in SC optimization are considered.

1. Investigates the role of IoT for virtual supply chain profit optimization and mathematical optimization of virtual closed-loop supply chain (VCLSC) based on multiperiod, multiproduct with emphasis on using the IoT under uncertainty.

2. Considering the most important costs of virtualization of supply chain include: cost of IoT information security, cost of IoT energy consumption, cost of recall the production department, cost of IoT facilities.

3. Selection of the optimal suppliers in each period and determination of the price of each returned product in virtual supply chain.

4. Solving and validating the proposed model with two meta-heuristic algorithms (the Grey Wolf algorithm and Firefly algorithm).

Investigates the role of IoT for virtual supply chain profit optimization and mathematical optimization of virtual closed-loop supply chain (VCLSC) based on multiperiod, multiproduct with emphasis on using the IoT under uncertainty.

Considering the most important costs of virtualization of supply chain include: cost of IoT information security, cost of IoT energy consumption, cost of recall the production department, cost of IoT facilities.

Selection of the optimal suppliers in each period and determination of the price of each returned product in virtual supply chain.

Solving and validating the proposed model with two meta-heuristic algorithms (the Grey Wolf algorithm and Firefly algorithm).

This paper aims to focus on the inclusion of the frequency behavior of grounding system effect on surge arrester (SA) model parameters’ estimation.

The grounding system impedance and its frequency behavior are the factors that have influence on the SA performance. Up to now, the grounding system impedance effect and the frequency behavior of the soil parameters have not been studied for the estimation of the parameters of the SA frequency-dependent model. In this paper, the grounding system’s influence on the SA dynamic model has been simulated for rod- and counterpoise-shaped electrodes. Particle swarm optimization with a grey wolf optimization algorithm has been implemented as an optimization algorithm to adjust the parameters of the SA dynamic model.

The results show that the frequency behavior of the grounding impedance and soil electrical parameters can impress the optimum parameters of the SA frequency-dependent model and should be considered for more reliable results. Also, the results evidence that the proposed optimization method provides more accurate results compared to other optimization methods.

To the best of the authors’ knowledge, this work is one of the first attempts to investigate the effect of frequency grounding system on SA frequency-dependent model parameters.

This paper aims to apply grey wolf optimizer (GWO) algorithm for steady state analysis of self-excited induction generators (SEIGs) supplying isolated loads.

Taking the equivalent circuit of SEIG, the impedances representing the stator, rotor and the connected load are reduced to a single loop impedance in terms of the unknown frequency, magnetizing reactance and core loss resistance for the given rotor speed. This loop impedance is taken as the objective function and minimized using GWO to solve for the unknown parameters. By including the value of the desired voltage as a constraint, the formulated objective function is also extended for estimating the required excitation capacitance.

The experimental results obtained on a three phase 415 V, 3.5 kW SEIG and the corresponding predetermined performance characteristics agree closely, thereby validating the proposed GWO method. Moreover, a comparative study of GWO with genetic algorithm and particle swarm optimization techniques reveals that GWO exhibits much quicker convergence of the objective function.

The important contributions of this paper are as follows: for the first time, GWO has been introduced for the SEIG performance predetermination and computation of the excitation capacitance for attaining the desired terminal voltage for the given load and speed; the predicted performance accuracy is improved by considering the variable core loss of the SEIG; and GWO does not require derivations of lengthy equations for calculating the SEIG performance.

This study aims to propose a more precise method for robust design optimization of mechanical structures with black-box problems, while also considering the efficiency of uncertainty analysis.

The method first introduces a dual adaptive chaotic flower pollination algorithm (DACFPA) to overcome the shortcomings of the original flower pollination algorithm (FPA), such as its susceptibility to poor accuracy and convergence efficiency when dealing with complex optimization problems. Furthermore, a DACFPA-Kriging model is developed by optimizing the relevant parameter of Kriging model via DACFPA. Finally, the dual Kriging model is constructed to improve the efficiency of uncertainty analysis, and a robust design optimization method based on DACFPA-Dual-Kriging is proposed.

The DACFPA outperforms the FPA, particle swarm optimization and gray wolf optimization algorithms in terms of solution accuracy, convergence speed and capacity to avoid local optimal solutions. Additionally, the DACFPA-Kriging model exhibits superior prediction accuracy and robustness contrasted with the original Kriging and FPA-Kriging. The proposed method for robust design optimization based on DACFPA-Dual-Kriging is applied to the motor hanger of the electric multiple units as an engineering case study, and the results confirm a significant reduction in the fluctuation of the maximum equivalent stress.

This study represents the initial attempt to enhance the prediction accuracy of the Kriging model using the improved FPA and to combine the dual Kriging model for uncertainty analysis, providing an idea for the robust optimization design of mechanical structure with black-box problem.