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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.

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.

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.

Generation scheduling (GS) is the most prominent and hard-hitting problem in the electrical power industry especially in an integrated power system. Countless techniques have been used so far to solve this GS problem for proper functioning of the units in the power system to dispatch the load economically to consumers at once. Therefore, this work aims to study for the best possible function of integrated power plants to obtain the most favourable solution to the GS problem.

An appropriate method works in a proper way and assures to give the best solution to the GS problem. The finest function of incorporated power plants should be mathematically devised as a problem and via that the aim of the GS problem to minimize the total fuel cost subject to different constraints will be achieved. In this research work, the latest meta-heuristic and swarm intelligence-based technique called grey wolf optimization (GWO) technique is used as an optimization tool that will work along with the formulated problem for correct scheduling of generating units and thus achieve the objective function.

The recommended GWO technique provides the best feasible solution which is optimal in its performance for different test cases in the GS problem of integrated power plant. It is further found that the obtained solutions using GWO method are better than the former reports of other traditional methods in terms of solution excellence. The GWO method is found to be unique in its performance and having superior computational efficiency.

Decision making is significant for effective operation of integrated power plants in an electrical power system. The recommended tactic implements a modern meta-heuristic procedure that is applied to diverse test systems. The method that is proposed is efficient in providing the best solutions of solving GS problems. The suggested method surpasses the early techniques by offering the most excellent feasible solutions. Thus, it is obvious that the proposed method may be the appropriate substitute to attain the optimal operation of GS problem.

Renewable energy sources are discontinuous and infrequent in nature, and it is tough to predict them in general. Further, integrating renewable energy source-based plants with the conventional plant is extremely difficult to operate and maintain. Operation of integrated power system is full of challenges and complications. To handle those complications and challenges, the GWO algorithm is suggested for solving the GS problem and thus obtain the optimal solution in integrated power systems by considering the reserve requirement, load balance, equality and inequality constraints.

The proposed system should be further tested on diverse test systems to evaluate its performance in solving a GS problem and the results should be compared. Computation results reveal that the proposed GWO method is efficient in attaining best solution in GS problem. Further, its performance is effectively established by comparing the result obtained by GWO with other traditional methods.

Smooth and autonomous navigation of mobile robot in a cluttered environment is the main purpose of proposed technique. That includes localization and path planning of mobile robot. These are important aspects of the mobile robot during autonomous navigation in any workspace. Navigation of mobile robots includes reaching the target from the start point by avoiding obstacles in a static or dynamic environment. Several techniques have already been proposed by the researchers concerning navigational problems of the mobile robot still no one confirms the navigating path is optimal.

Therefore, the modified grey wolf optimization (GWO) controller is designed for autonomous navigation, which is one of the intelligent techniques for autonomous navigation of wheeled mobile robot (WMR). GWO is a nature-inspired algorithm, which mainly mimics the social hierarchy and hunting behavior of wolf in nature. It is modified to define the optimal positions and better control over the robot. The motion from the source to target in the highly cluttered environment by negotiating obstacles. The controller is authenticated by the approach of V-REP simulation software platform coupled with real-time experiment in the laboratory by using Khepera-III robot.

During experiments, it is observed that the proposed technique is much efficient in motion control and path planning as the robot reaches its target position without any collision during its movement. Further the simulation through V-REP and real-time experimental results are recorded and compared against each corresponding results, and it can be seen that the results have good agreement as the deviation in the results is approximately 5% which is an acceptable range of deviation in motion planning. Both the results such as path length and time taken to reach the target is recorded and shown in respective tables.

After literature survey, it may be said that most of the approach is implemented on either mathematical convergence or in mobile robot, but real-time experimental authentication is not obtained. With a lack of clear evidence regarding use of MGWO (modified grey wolf optimization) controller for navigation of mobile robots in both the environment, such as in simulation platform and real-time experimental platforms, this work would serve as a guiding link for use of similar approaches in other forms of robots.

This paper aims to examine the design and control of a symmetric multilevel inverter (MLI) using grey wolf optimization and differential evolution algorithms.

The optimal modulation index along with the switching angles are calculated for an 11 level inverter. Harmonics are used to estimate the quality of output voltage and measuring the improvement of the power quality.

The simulation is carried out in MATLAB/Simulink for 11 levels of symmetric MLI and compared with the conventional inverter design. A solar photovoltaic array-based experimental setup is considered to provide the input for symmetric MLI. Field Programmable Gate Array (FPGA) based controller is used to provide the switching pulses for the inverter switches.

Attempted to develop a system with different optimization techniques.

The combined heat and power dispatch (CHPD) aims to optimize the outputs of online units in a power plant consisting thermal generators, co-generators and heat-only units. Identifying the operating point of a co-generator within its feasible operating region (FOR) is difficult. This paper aims to solve the CHPD problem in static and dynamic environments.

The CHPD plant operation is formulated as an optimization problem under static and dynamic load conditions with the objectives of minimizations of cost and emissions subject to various system and operational constraints. A novel bio-inspired search technique, grey wolf optimization (GWO) algorithm is used as an optimization tool.

The GWO-based algorithm has been developed to determine the preeminent power and heat dispatch of operating units within the FOR region. The proposed methodology provides fuel cost savings and lesser pollutant emissions than those in earlier reports. Particularly, the GWO always keeps the co-generator’s operating point within the FOR, whereas most of the existing methods fail.

The GWO is applied for the first time to solve the CHPD problems. New dispatch schedules are reported for 7-unit system with the objectives of total fuel cost and emission minimizations, 24-unit system for economic operation and 11-unit system in dynamic environment. The simulation experiments reveal that GWO converges quickly, consistent and the statistical performance clears its applicability to CHPD problems.

This paper aims to find the minimum possible number of phasor measurement units (PMUs) to achieve maximum and complete observability of the power system and improve the redundancy of measurements, in normal cases (with and without zero injection bus [ZIB]), and then in conditions of a single PMU failure and outage of a single line.

An efficient approach operates adequately and provides the optimal solutions for the PMUs placement problem. The finest function of optimal PMUs placement (OPP) should be mathematically devised as a problem, and via that, the aim of the OPP problem is to identify the buses of the power system to place the PMU devices to ensure full observability of the system. In this paper, the grey wolf optimizer (GWO) is used for training multi-layer perceptrons (MLPs), which is known as Grey Wolf Optimizer (GWO) based Neural Network (“GW-NN”) to place the PMUs in power grids optimally.

Following extensive simulation tests with MATLAB/Simulink, the results obtained for the placement of PMUs provide system measurements with less or at most the same number of PMUs, but with a greater degree of observability than other approaches.

The efficiency of the suggested method is tested on the IEEE 14-bus, 24-bus, New England 39-bus and Algerian 114-bus systems.

This paper proposes a new method for placing PMUs in the power grids as a multi-objective to reduce the cost and improve the observability of these grids in normal and faulty cases.

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).

The purpose of this paper is to focus on the cost-effective and environmentally sustainable operation of thermal power systems to allocate optimum active power generation resultant for a feasible solution in diverse load patterns using the grey wolf optimization (GWO) algorithm.

The economic dispatch problem is formulated as a bi-objective optimization subjected to several operational and practical constraints. A normalized price penalty factor approach is used to convert these objectives into a single one. The GWO algorithm is adopted as an optimization tool in which the exploration and exploitation process in search space is carried through encircling, hunting and attacking.

A linear interpolated price penalty model is developed based on simple analytical geometry equations that perfectly blend two non-commensurable objectives. The desired GWO algorithm reports a new optimum thermal generation schedule for a feasible solution for different operational strategies. These are better than the earlier reports regarding solution quality.

The proposed method seems to be a promising optimization tool for the utilities, thereby modifying their operating strategies to generate electricity at minimum energy cost and pollution levels. Thus, a strategic balance is derived among economic development, energy cost and environmental sustainability.

A single optimization tool is used in both quadratic and non-convex cost characteristics thermal modal. The GWO algorithm has discovered the best, cost-effective and environmentally sustainable generation dispatch.