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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 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.

Efficient resource utilization in wireless sensor networks is an important issue. Clustering structure has an important effect on the efficient use of energy, which is one of the most critical resources. However, it is extremely vital to choose efficient and suitable cluster head (CH) elements in these structures to harness their benefits. Selecting appropriate CHs and finding optimal coefficients for each parameter of a relevant fitness function in CHs election is a non-deterministic polynomial-time (NP-hard) problem that requires additional processing. Therefore, the purpose of this paper is to propose efficient solutions to achieve the main goal by addressing the related issues.

This paper draws inspiration from three metaheuristic-based algorithms; gray wolf optimizer (GWO), incremental GWO and expanded GWO. These methods perform various complex processes very efficiently and much faster. They consist of cluster setup and data transmission phases. The first phase focuses on clusters formation and CHs election, and the second phase tries to find routes for data transmission. The CH selection is obtained using a new fitness function. This function focuses on four parameters, i.e. energy of each node, energy of its neighbors, number of neighbors and its distance from the base station.

The results obtained from the proposed methods have been compared with HEEL, EESTDC, iABC and NR-LEACH algorithms and are found to be successful using various analysis parameters. Particularly, I-HEELEx-GWO method has provided the best results.

This paper proposes three new methods to elect optimal CH that prolong the networks lifetime, save energy, improve overhead along with packet delivery ratio.

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).

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.

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.

The advancements in the cloud computing has gained the attention of several researchers to provide on-demand network access to users with shared resources. Cloud computing is important a research direction that can provide platforms and softwares to clients using internet. However, handling huge number of tasks in cloud infrastructure is a complicated task. Thus, it needs a load balancing (LB) method for allocating tasks to virtual machines (VMs) without influencing system performance. This paper aims to develop a technique for LB in cloud using optimization algorithms.

This paper proposes a hybrid optimization technique, named elephant herding-based grey wolf optimizer (EHGWO), in the cloud computing model for LB by determining the optimal VMs for executing the reallocated tasks. The proposed EHGWO is derived by incorporating elephant herding optimization (EHO) in grey wolf optimizer (GWO) such that the tasks are allocated to the VM by eliminating the tasks from overloaded VM by maintaining the system performance. Here, the load of physical machine (PM), capacity and load of VM is computed for deciding whether the LB has to be done or not. Moreover, two pick factors, namely, task pick factor (TPF) and VM pick factor (VPF), are considered for choosing the tasks for reallocating them from overloaded VM to underloaded VM. The proposed EHGWO decides the task to be allocated in the VM based on the newly derived fitness functions.

The minimum load and makespan obtained in the existing methods, constraint measure based LB (CMLB), fractional dragonfly based LB algorithm (FDLA), EHO, GWO and proposed EHGWO for the maximum number of VMs is illustrated. The proposed EHGWO attained minimum makespan with value 814,264 ns and minimum load with value 0.0221, respectively. Meanwhile, the makespan values attained by existing CMLB, FDLA, EHO, GWO, are 318,6896 ns, 230,9140 ns, 1,804,851 ns and 1,073,863 ns, respectively. The minimum load values computed by existing methods, CMLB, FDLA, EHO, GWO, are 0.0587, 0.026, 0.0248 and 0.0234. On the other hand, the proposed EHGWO with minimum load value is 0.0221. Hence, the proposed EHGWO attains maximum performance as compared to the existing technique.

This paper illustrates the proposed LB algorithm using EHGWO in a cloud computing model using two pitch factors, named TPF and VPF. For initiating LB, the tasks assigned to the overloaded VM are reallocated to under loaded VMs. Here, the proposed LB algorithm adapts capacity and loads for the reallocation. Based on TPF and VPF, the tasks are reallocated from VMs using the proposed EHGWO. The proposed EHGWO is developed by integrating EHO and GWO algorithm using a new fitness function formulated by load of VM, migration cost, load of VM, capacity of VM and makespan. The proposed EHGWO is analyzed based on load and makespan.

The paper aims to provide an efficient dispatching schedule for ready-mix concrete (RMC) trucks and create a balance between batch plants and construction sites.

The paper focused on developing a new metaheuristic swarm intelligence algorithm using Java code. The paper used statistical criterion: mean, standard deviation, running time to verify the effectiveness of the proposed optimization method and compared its derivatives with other algorithms, such as genetic algorithm (GA), Tabu search (TS), bee colony optimization (BCO), ant lion optimizer (ALO), grey wolf optimizer (GWO), dragonfly algorithm (DA) and particle swarm optimization (PSO).

The paper proved that integrating GWO and DA yields better results than independent algorithms and some selected algorithms in the literature. It also suggests that multi-independent batch plants could effectively cooperate in a system to deliver RMC to various construction sites.

The paper provides a compelling new hybrid swarm intelligence algorithm and a model allowing multi-independent batch plants to work in a system to deliver RMC. It fulfills an identified need to study how batch plant managers can expand their dispatching network, increase their competitiveness and improve their supply chain operations.

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.

Partial shading causes significant power decreases in the PV systems. The purpose of this paper is to address this problem, connectivity regulation is designed to reduce partial shading problems.

In this approach, the partial shading was estimated and dispersed evenly on the whole array by global shade dispersion technique (GSD). The grey wolf algorithm was implemented for the interconnection of arrays by an efficient switching matrix.

After the implementation of the GSD technique using a grey wolf algorithm, the performance under different shading conditions was analyzed using the MatLab simulation tool. The results were compared with total cross-tied (TCT), Su Do Ku and the proposed method of reconfiguration, where the proposed method improves the maximum power of the PV system appropriately.

This methodology uses any size of PV systems.

Replacement of conventional energy systems with renewable energy systems such as solar helps the environment clean and green.

The GSD interconnection scheme using the grey wolf optimization algorithm has proved an improved output performance compared with the existing TCT and Sudoku based reconfiguration techniques. By comparing with existing techniques in literature, the proposed method is more advantageous for reducing mismatch losses between the modules of any size of the PV array with less operating time.