Research on Grey Wolf Optimization Algorithm Based on Adaptive Adjustment Strategy

The grey wolf optimization (GWO) algorithm, one of the recently proposed bio-inspired algorithms, simulates the leadership hierarchy and hunting mechanism of grey wolves in nature. The GWO has a good performance in some optimization tasks, but its search capacity decreases with the increasing search scope and dimension. This paper proposes an improved GWO (IGWO) algorithm, in which Levy flight strategy and a sine cosine operator with adaptive step are incorporated to significantly improve the performance of the algorithm. The Levy flight strategy is used to strengthen the efficiency of global search. The adaptive sine cosine operator is introduced to improve the local search ability. Experimental results based on twenty unconstrained benchmark problems show the superiority of the proposed IGWO. Furthermore, the IGWO is utilized in PID controller design. The comparison results show that the IGWO algorithm is better than, or at least comparable to, other well-established swarm intelligence algorithms.

To overcome the limitations of low hydrogen production efficiency in conventional control approaches for proton exchange membrane (PEM) electrolysis systems, a novel multivariable model predictive control (MPC) strategy integrated with an improved gray wolf optimization (IGWO) algorithm is proposed in this paper. First, a comprehensive mathematical model of the PEM electrolysis system is established, incorporating a dynamic coupling model that captures the complex interactions among current density, operating temperature, system pressure, and hydrogen production efficiency. Second, the nonlinear efficiency model is linearized through a robust weighted least squares approach, incorporating operational constraints for temperature and pressure. This linearized framework facilitates the development of a state-space model with current density, temperature, and pressure as manipulated variables, targeting hydrogen production efficiency as the controlled output. Third, the optimization problem of hydrogen production efficiency is transformed into a quadratic programming problem through the MPC framework enhancement. An upgraded gray wolf optimization algorithm featuring a dynamic convergence factor adjustment mechanism that improves computational efficiency of weight matrix optimization in MPC is proposed. The integration of the IGWO algorithm with the MPC framework establishes a dual-loop collaborative control architecture (IGWO-MPC) that synergistically combines predictive modeling with intelligent optimization. Finally, the performance improvements are validated by simulation experiments. Compared to conventional proportional-integral-derivative control, the IGWO-MPC architecture achieves 4.6% higher hydrogen production power, 5.3% reduction in thermal power loss, 5.3% efficiency enhancement over 24 h, and a 6.7% increase in daily hydrogen yield. When benchmarked against traditional MPC, IGWO-MPC maintains superior performance with 1.9% greater hydrogen production power, 2.1% lower thermal losses, 2.4% efficiency improvement, and 4.89% higher daily output.

The present article proposes a novel hybrid approach for addressing the synthesis problem of rectangular planar arrays under multiple constraints, through joint optimization of the weight function and the improved grey wolf optimization (IGWO) algorithm. Firstly, the grey wolf optimization (GWO) algorithm is improved by using tent chaotic mapping, nonlinear convergence factor, dominant wolf dynamic belief strategy, and opposition‐based learning strategy to increase the population diversity and the ability to jump out of the local optimum. Secondly, the array elements are weighted using the weight function to generate the position distribution matrix, which reduces the thinned matrix optimization time and improves the optimization efficiency. Finally, the position distribution matrix is used to generate the thinned array, and the IGWO algorithm is applied to perform the sparse optimization with multiple constraints. The effectiveness of the method is verified through numerical simulation and full‐wave simulation experiments, demonstrating its capability to enhance array antenna performance and reduce peak sidelobe level (PSLL). These experimental results hold significant engineering implications and provide valuable references for addressing the array distribution problem under multiple constraints.

The wind tunnel balance signal detection system is widely employed in aerospace applications for the accurate and automated measurement of aerodynamic forces and moments. However, measurement errors arise under different environmental temperature. This paper addresses the issue of measurement accuracy under different temperature conditions by proposing a temperature compensation method based on an improved gray wolf optimization (IGWO) algorithm and optimized extreme learning machine (ELM). The IGWO algorithm is enhanced by improving the initial population position, convergence factor, and iteration weights of the gray wolf optimization algorithm. Subsequently, the IGWO algorithm is employed to determine the optimal network parameters for the ELM. The calibration decoupling experiment and high-low temperature experiment are designed and carried out. On this basis, ELM, GWO-ELM, PSO-ELM, GWO-RBFNN and IGWO-ELM are used for temperature compensation experiments. The experimental results show that IGWO-ELM has a good temperature compensation effect, reducing the measurement error from 20%FS to within 0.04%FS. Consequently, the accuracy and stability of the wind tunnel balance signal detection system under different temperature environments are enhanced.

This research article thoroughly examines the implementation of an enhanced Grey Wolf Optimization (GWO) method for Multi-Objective Power Flow Optimization (MO-PFO) in the IEEE-118 bus test system. Given the growing complexity and uncertainty in modern power systems, power flow optimization presents a crucial challenge. The suggested enhanced GWO algorithm improves the performance of the traditional GWO for MO-PFO issues while addressing its inherent flaws.
 The goal of this study is to obtain optimal solutions concurrently for multiple objectives, including the reduction of power losses, voltage variations, and the enhancement of system stability. In the Related Works section, I review the research on power flow optimization in the literature, which also showcases the improvements achieved by applying various optimization techniques and discusses the benefits and drawbacks of traditional optimization methods and their effectiveness in dealing with MO-PFO issues.
 The improved GWO algorithm, designed specifically for MO-PFO, is described in detail in the Methodology section. I explain the adjustments made to the regular GWO algorithm and introduce a cutting-edge method for handling multiple objectives. In the IEEE-118 bus test system, I present the mathematical model of the MO-PFO problem and develop fitness functions for each objective.
 Furthermore, I describe the implementation of the enhanced GWO algorithm, including parameter settings and termination criteria. The proposed algorithm demonstrates its capability to effectively handle the multi-objective nature of power flow optimization, thereby paving the way for future power system operations that are more dependable and sustainable

Unmanned combat system is one of the important means to capture information superiority, carry out precision strike and accomplish special combat tasks in information war. Unmanned attack strategy plays a crucial role in unmanned combat system, which has to ensure the attack by unmanned surface vehicles (USVs) from failure. To meet the challenge, we propose a task allocation algorithm called distributed auction mechanism task allocation with grey wolf optimization (DAGWO). The traditional grey wolf optimization (GWO) algorithm is improved with a distributed auction mechanism (DAM) to constrain the initialization of wolves, which improves the optimization process according to the actual situation. In addition, one unmanned aerial vehicle (UAV) is employed as the central control system to establish task allocation model and construct fitness function for the multiple constraints of US V attack problem. The proposed DAGWO algorithm can not only ensure the diversity of wolves, but also avoid the local optimum problem. Simulation results show that the proposed DAGWO algorithm can effectively solve the problem of attack task allocation among multiple USVs.

Optimizing the crop cultivation pattern, in order to reduce water consumption, in arid and semi-arid regions such as Iran, due to water scarcity and food intake, is an essential solution for food intakes needs. Optimizing the crop cultivation pattern, in order to reduce water consumption, in arid and semi-arid regions such as Iran, due to water scarcity and food intake, is an essential solution for food intakes needs. In this study, new methods based on the election algorithms (EA) and gray wolf optimizer (GWO) algorithms were used to determine the optimal cultivation pattern in Moghan plain during the statistical years of 2007-2016. The objective function in the agricultural sector was based on each product and its yield, net from each product and the cultivar. Then, maximization of the objective function was performed using GWO and EA algorithm. The results of using GWO algorithm in determining the optimal crop pattern in Moghan plain showed that using economic policies such as changing the cultivar pattern, we can obtain a better result compared to EA algorithm in the agricultural sector. In general, the results of GWO algorithm showed that in the Moghan plain with 0.9, 140 billion rials, that is, about 42 % will have economic growth. In sum, the results showed that GWO algorithm with high values of statistical criteria (R2=0.96, RMSE=0.022 and NSE=0.75) has a higher efficiency in optimizing the crop cultivation pattern of Moghan plain, which can be applied to the correct planning for other cultivation areas to be employed.

Generally, optimization is defined as the process of determining the minimum or maximum value that depends on the function of the goal, even now there are many problems regarding optimization. One of them is the problem regarding the selection of goods to be included in a limited storage medium called Knapsack problem. Knapsack problems have different types and variations. This study will solve the problem of bounded knapsack multiple constraints by implementing the Grey Wolf Optimizer (GWO) algorithm. The problem of bounded knapsack multiple constraints has more than one subject with the items that are inserted into the dimension storage media can be partially or completely inserted, but the number of objects is limited. The aim of this study is to determine the results of using the Grey Wolf Optimizer (GWO) algorithm for solving the problem of multiple constraints bounded knapsack and compare the optimal solutions obtained by the simplex method using the Solver Add-In in Microsoft Excel. The data used in this study is primary data. There are two parameters to be tested, namely population parameters and maximum iteration. The test results of the two parameters show that the population parameters and maximum iterations have the same effect, where the greater the value of the population parameters and the maximum iteration, the results obtained are also getting closer to the optimal value. In addition, based on the results of the final experiment it is known that the comparison of the results of the GWO algorithm and the simplex method has a fairly small percentage deviation which indicates that the GWO algorithm produces results that are close to the optimal value.
 Keywords: GWO algorithm, Knapsack, Multiple Constraints Bounded Knapsack.

Feature selection is an important part of data mining, image recognition and other fields. The efficiency and accuracy of classification algorithm can be improved by selecting the best feature subset. The classical feature selection technology has some limitations, and heuristic optimization algorithm for feature selection is an alternative method to solve these limitations and find the optimal solution. In this paper, we proposed a Multi Strategy Grey Wolf Optimizer algorithm (MSGWO) based on random guidance, local search and subgroup cooperation strategies for feature selection, which solves the problem that the traditional grey wolf optimizer algorithm (GWO) is easy to fall into local optimization with a single search strategy. Among them, the random guidance strategy can make full use of the random characteristics to enhance the global search ability of the population, and the local search strategy makes grey wolf individuals make full use of the search space around the current best solution, and the subgroup cooperation strategy is very important to balance the global search and local search of the algorithm in the iterative process. MSGWO algorithm cooperates with each other in three strategies to update the location of grey wolf individuals, and enhances the global and local search ability of grey wolf individuals. Experimental results show that MSGWO can quickly find the optimal feature combination and effectively improve the performance of the classification model.

The emergence of wireless sensor network (WSN) makes the communication between people and things more extensive, and provides a new way for people to obtain information and more accurate real‐time communication. However, the regional distance in WSN is still a big problem. This method can not only optimize the cluster structure, but also reduce the number of member nodes in the cluster, the cluster head receiving energy, and reduce the data transmission distance between nodes. At the same time, the number of packets received by the base station increases, so that more sensing information can be obtained. The simulation results showed that compared with the smart Ethernet protection (SEP) protocol and the low energy adaptive clustering hierarchy (LEACH) protocol, the number of first node deaths (FND) of the grey wolf optimizer (GWO) algorithm was 153 and 233 times different from those of the SEP and LEACH protocols respectively at 100m*100m. In the case of 200m*200m, compared with that of SEP and LEACH, the number of FND of GWO was 152 and 200 times different. Finally, in the case of 300m*300m, compared with that of SEP and LEACH, the number of FND of GWO was 142 and 158 times different. The GWO algorithm has a higher node ARE ratio in a wider region. In the same 1000 rounds, the node ARE of GWO was 61%, while the node ARE of SEP and LEACH protocols were 7% and 3%, respectively. From the above results, it can be found that the GWO algorithm has been greatly improved in terms of network energy efficiency, network lifetime, etc., and can still work normally under larger scale monitoring. The innovation of this article lies in the localization problem of fixed node mobile sensor networks, proposing a mobile sensor network localization method based on mobile error nodes. This can optimize the distance between nodes and improve the positioning accuracy of the algorithm in both distributed and centralized situations. This article is protected by copyright. All rights reserved.

SummaryThe search for an effective nature‐inspired optimization technique has certainly continued for decades. This work proposes a novel robust multi‐user detection algorithm based on Grey wolf optimization and differential evolution algorithm to overcome the problem of high bit error rate (BER) in multi‐user detection under an impulse noise environment. The simulation results show that the iteration times of the multi‐user detector based on the proposed algorithm is less than those of genetic algorithm, differential evolution algorithm, Grey wolf optimization algorithm, salp swarm algorithm, grasshopper optimisation algorithm, and whale optimization algorithm with the lowerst BER value.

Optimal design of mixed dielectric coaxial-annular TSV using GWO algorithm based on artificial neural network

In order to overcome the drawbacks of falling into local extremum and lower optimization precision of standard particle swarm optimization (PSO) algorithm, multipopulation strategy, adaptive dynamic adjustment strategy and co-evolution mode are introduced into the standard PSO algorithm in order to propose an improved coevolutionary PSO(MPACEPSO) algorithm based on multi-strategy evolution mode and multi-population co-evolutionary mechanism. In the evolutionary process of MPACEPSO algorithm, the multi-population strategy is used to divide the population into several subpopulations, which use different co-evolutionary model to evolve. These sub-populations are influenced and promoted each other in order to realize the exchange of information and co-evolution among the sub-populations, improve the convergence speed and search precision of MPACEPSO algorithm, and effectively suppress the appearance of the local optimum. The adaptive dynamic adjustment strategy of inertia weight is used to keep the diversity of population, reduce the probability of falling into the local extremum. Finally, the ZDT functions are selected to test the optimization performance of proposed MPACEPSO algorithm. The experimental results show that the proposed MPACEPSO algorithm has faster convergence speed, stronger global search ability, higher solving precision and better dynamic optimization performance. The experimental result analysis shows that the proposed MPACEPSO algorithm is insensitive to parameters and easy to be used in solving the complex optimization problems.

This paper presents the recently developed Grey Wolf Optimization (GWO) algorithm, which is based on the food collecting behavior of grey wolves to determining the feasible optimal solution of the multi objective environmental economic dispatch (MOEED) problem. Nonlinear characteristics of alternators and exponential emissions and loss minimization are considered in the problem. While searching for a better solution, GWO does not require any statistics about the gradient of the objective function. The GWO algorithm effectiveness has been tested on four different systems as 6-unit (IEEE 30-bus), 10-unit, 11-unit and 14-unit (IEEE 118-bus) test systems to solve the MOEED problems. The result of the test systems shows, for practical power systems GWO as a better option to solve the MOEED problems. Both the optimality of the solution to test systems and the convergence speed of the GWO algorithm are promising.

A weighing error compensation method using IGWO–LMBPNN, which combines an improved gray wolf optimization algorithm (IGWO) with the Levenberg–Marquardt backpropagation neural network (LMBPNN), is proposed to enhance truck scale accuracy. It uses output signals from multiple load cells as inputs to the neural network for establishing the error compensation model. The IGWO algorithm is used to initialize the weights and biases of the model, while the LMBPNN algorithm further optimizes these parameters. To evaluate the effectiveness of the IGWO–LMBPNN method, it was compared with the existing compensation methods, including BPNN, LMBPNN, gray wolf optimization with LMBPNN (GWO–LMBPNN), particle swarm optimization with LMBPNN (PSO–LMBPNN), and Fine Gaussian SVM. The experimental results demonstrate a significant improvement in error reduction for truck scale weighing. The mean absolute error (MAE) of IGWO–LMBPNN is 8.5 kg, which was reduced by 38.8%, 29.2%, 19%, 21.3%, and 33.1% compared with BPNN, LMBPNN, GWO–LMBPNN, PSO–LMBPNN, and Fine Gaussian SVM, respectively. These findings not only verify the efficacy of the IGWO–LMBPNN in enhancing weighing accuracy but also highlight its potential for other practical applications.