In this contribution, a Modified gray wolf algorithm for use in engineering applications is presented. The grey wolf algorithm is one of the meta-heuristic optimization methods that has recently been widely used by researchers due to its good capabilities. The mechanism is free of derivation, simple in execution and implementation, and only needs target function as input of the problem, among other things that make the gray wolf algorithm popular and of interest. But the problem that can be mentioned about it is that the decreasing factor used in it is linear and in some non-linear problems, it may cause more error or late convergence to the original solution. This bottleneck is solved by presenting a Modified grey wolf algorithm. Then the results are compared in the form of an applied numerical example in engineering sciences with the classic grey wolf algorithm and some similar proposed coefficients to determine the efficiency of the Modified algorithm.

The huge amount of data created constantly with increasing rate from different sources such as smart phones, social media, imaging technologies and etc. becomes difficult to be analyzed by conventional data analytic tools. For this reason a new field of research called Big Data Analytics is growing faster in the research and industrial communities. Clustering big datasets is one of the important challenges which attracts more and more attentions among researchers. In this paper first a method for non-automatic big data clustering (when the number of clusters is known) and then a two-stage method for big data automatic clustering (able in finding the number of clusters) based on grey wolf optimization algorithm are introduced. In the first stage the algorithm tries to find the number of clusters using a tree structure and in the second stage the main algorithm searches the solution space to find the position of centroids. The methodology is tested on 13 synthetics and 2 real big mobility datasets. The achieved results show its effectiveness in big data clustering.

Many real-world optimization problems are complex and high-dimensional problems. In the problems, the search space grows exponentially as the problem dimension increases. Therefore, exact algorithms are not able to find the best solution in a reasonable time. As a result, approximate algorithms are applied to solve these problems. Among these algorithms, meta-heuristic algorithms have been shown a good performance in solving these problems. The grey wolf Optimizer (GWO) algorithm is one of the meta-heuristic algorithms. However, the structure of the algorithm limits its exploration capability and it may fall in local optima. In this case, the diversity of the population gradually decreases and sometimes, the algorithm is not able to escape from the local optima. To enhance the performance of GWO, an improved GWO algorithm called Condition-based Gray wolf optimization (Cb-GWO) algorithm is proposed in this study. In Cb-GWO, the exploration phase has been separated from the exploitation one and also some mechanisms have been considered to achieve better positions per iteration. Moreover, the balance between exploration and exploitation has been improved. The performance of proposed algorithm has been compared with several improved GWO algorithms, as well as Particle Swarm optimization (PSO), Spotted Hyena Optimizer (SHO), Harris Hawk optimization (HHO), Wild Horse Optimizer (WHO), Aquila Optimizer (AO), African Vultures optimization Algorithm (AVOA), which are among the newest meta-heuristic algorithms. These algorithms have been evaluated by CEC2018 benchmark optimization functions and the pressure vessel design to find the best results. The experimental results showed the significant improvement of efficiency of the proposed algorithm compared with other competitor algorithms.

Some civil engineering-based infrastructures are planned for the structural health monitoring (SHM) system based on their importance. Identifiction and detecting damage automatically at the right time are one of the major objectives this system faces. One of the methods to meet this objective is model updating whit use of optimization algorithms in structures.This paper is aimed to evaluate the location and severity of the damage combining two being-updated parameters of the flexibility matrix and the static strain energy of the structure using augmented grey wolf optimization (AGWO) and only with extracting the data of damaged structure, by applying 5 percent noise. The error between simulated and estimated results in average of ten runs and each damage scenario was less than 3 percent which proves the proper performance of this method in detection of the all damages of the 37-member three-dimensional frame and the 33-member two-dimensional truss. Moreover, they indicate that AGWO can provide a reliable tool to accurately identify the damage in compare with the particle swarm optimizer (PSO) and grey wolf optimizer (GWO).

Objective: In the present era, businesses have developed to a large extent which has, in turn, forced them to manage their resources and expenditures wisely for the sake of competition. This is mainly because the competitive market has severely reduced the flexibility of companies, which means that their ability respond to different economic situations has reduced and this puts most firms at the constant risk of bankruptcy and contraction. Therefore, in this study, we have tried to predict the bankruptcy of manufacturing companies through preventing the occurrence of such risks. methods: In this study, the "Kernel Extreme Learning Machine" has been used as one of the artificial intelligence models for predicting bankruptcy. Given that machine learning methods require an optimization algorithm we have used one of the most up-to-date, "Gray wolf Algorithm" which has been introduced in 2014. Results: The above model has been implemented on the 136 samples that were collected from the Tehran Stock Exchange between 2015 and 2018. All of the performance evaluation criteria including the classification, accuracy, type error, second-order error and area under the ROC curve showed better performance than the genetic algorithm which was presented and its significance was confirmed by t-test. Conclusion: Considering the gray wolf algorithm’ s high accuracy and its performance compared to the genetic algorithm, it is necessary to use the gray wolf algorithm to predict the bankruptcy of Iranian manufacturing companies either for investment purposes and for validation purposes, or for using internal management of the company.

Multilevel image thresholding is essential for segmenting images. Expectation Maximization (EM) is effective for finding thresholds; but, it is sensitive to starting points. The grey wolf Optimizer (GWO) is fast at finding thresholds but can get stuck in local optima. This paper presents a new algorithm, EM+GWO, combining both methods to improve segmentation. EM estimates Gaussian Mixture Model (GMM) coefficients, while GWO finds better solutions when EM is stuck. GWO adjusts GMM parameters using Root Mean Square Error (RMSE) for the best fit. The algorithm was tested on nine standard images, evaluating global fitness, PSNR, SSIM, FSIM, and computational time. The results show that EM+GWO significantly enhances image segmentation effectiveness. Statistical tools indicate that RCG achieves the best RMSE and PSNR in 7 out of 9 test images, and it holds the highest rank in both SSIM and FSIM. The average execution time of each algorithm was calculated, showing that EM+GWO has an acceptable running time compared to EM and GWO. This balance between computational efficiency and improved segmentation performance makes the proposed EM+GWO algorithm a robust and effective solution for image segmentation tasks. Overall, the combination of EM and GWO methods provides a more reliable and accurate approach to optimizing image segmentation, avoiding local optima, and enhancing overall performance.

Metaheuristic algorithms are used to solve NP-hard optimization problems. These algorithms have two main components, i. e. exploration and exploitation, and try to strike a balance between exploration and exploitation to achieve the best possible near-optimal solution. The bat algorithm is one of the metaheuristic algorithms with poor exploration and exploitation. In this paper, exploration and exploitation processes of Gray wolf Optimizer (GWO) algorithm are applied to some of the solutions produced by the bat algorithm. Therefore, part of the population of the bat algorithm is changed by two processes (i. e. exploration and exploitation) of GWO; the new population enters the bat algorithm population when its result is better than that of the exploitation and exploration operators of the bat algorithm. Thereby, better new solutions are introduced into the bat algorithm at each step. In this paper, 20 mathematic benchmark functions are used to evaluate and compare the proposed method. The simulation results show that the proposed method outperforms the bat algorithm and other metaheuristic algorithms in most implementations and has a high performance.

This paper presents the optimization of a system of square cascades for separating the middle components of xenon. It also presents the optimal use of square cascades in this system. As an example, the separation of 130 Xe, an element whose middle isotope is much more complex than any of the other isotopes of xenon, is provided. The grey wolf Algorithm is applied for optimization. and the parameters of cascade feed flow rate, cut off the cascade, feed location, feed flow of gas centrifuges (GC), and the cut of the first stage are optimized in such a way that the maximum recovery of the target isotope and the maximum cascade capacity are achieved. Based on the optimization results, the more steps the cascade has, the fewer separation steps are needed for the nine selected cascades with 180 GCs. As a result, both the recovery factor and the amount of product increase.

Stock market forecasting is a challenging task for investors and researchers in the financial market due to highly noisy, nonparametric, volatile, complex, non-linear, dynamic and chaotic nature of stock price time series. With the development of computationally intelligent method, it is possible to predict stock price time series more accurately. Artificial neural networks (ANNs) are one of the most promising biologically inspired techniques. ANNs have been widely used to make predictions in various research. The performance of ANNs is very dependent on the learning technique utilized to train the weight and bias vectors. The proposed study aims to predict daily Tehran Exchange Dividend Price Index (TEDPIX) via the hybrid multilayer perceptron (MLP) neural networks and metaheuristic algorithms which consist of genetic algorithm (GA), particle swarm optimization (PSO), black hole (BH), grasshopper optimization algorithm (GOA) and grey wolf optimization (GWO). We have extracted 18 technical indicators based on the daily TEDPIX as input parameters. Therefore, the experimental result shows that grey wolf optimization has superior performance to train MLPs for predicting the stock market in metaheuristic-based.