Synthesis of sparse rectangular planar arrays with weight function and improved grey wolf optimization algorithm

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.

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.

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.

Due to insufficient absolute positioning accuracy, industrial robots frequently face challenges in efficiently performing drilling and riveting operations during the assembly of aircraft and other large-scale workpieces. To enhance the absolute positioning accuracy of industrial robots, this paper proposes a novel kinematic calibration method for industrial robots based on the Improved Grey Wolf Optimization (IGWO) algorithm. Specifically, the method employs an enhanced selection and update strategy to avoid convergence stagnation and local optimum traps. The proposed method features a novel boundary search strategy, which leverages the Dimension-oriented Learning (DL) search strategy to enhance search speed and stability. Through parameter identification and calibration experiments, the effectiveness of the method was validated using an ABB IRB4600 industrial robot and a Leica laser tracker. Additionally, compared with the Levenberg–Marquardt (LM) algorithm, Particle Swarm Optimization (PSO), and Genetic Algorithm (GA), the IGWO algorithm demonstrates faster convergence and superior optimization performance. According to the calibration experimental results, by applying the IGWO algorithm, the absolute positioning accuracy of the industrial robot is ultimately improved from 1.918 mm to 0.475 mm and the absolute positioning accuracy is improved by 75.2%.

A grey wolf optimization algorithm based on an adaptive adjustment strategy (Improvements-Grey Wolf Optimization, IGWO) is proposed in this paper to address the issues with the Grey Wolf Optimization (GWO) algorithm, which has a slow convergence speed in the later stages and where the local search and global search cannot be taken into effective balance. First, a chaotic logistic map is used to initialize the population. Next, an inverse trigonometric function-based mathematical model is developed to achieve convergence purposes. Finally, a new location update method is used to update the next-generation location to improve search traversability. Additionally, the CEC2013-Benchmark standard test function was used to evaluate the benefits of performance compared to the standard GWO, PSO, and DEGWO (DE-Grey wolf optimization) algorithms. The improved GWO algorithm has greatly increased the convergence speed, search capability, and stability. It performs better than the other three algorithms as well.

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.

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.

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

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.

Improved DV-HOP localization algorithm based on grey wolf optimization

The grey wolf optimization (GWO) algorithm was proposed in 2014 and after several years of applications, it was used worldwide and all over the subjects which involved computation. Various improvements have been raised to increase the capability of optimization. Based on the best performance of the slimd mould (SM) algorithm in optimization, a hybridization of the SM and GWO algorithms was proposed about the updating equations, and the GWO algorithm with multiple tunnels for individuals to update their positions during iterations was revised. Simulation experiments were carried out and comparisons were made between the GWO algorithm with variable weights and our proposed new one. Better performance were confirmed and reported as conclusions.

This paper introduces an application of the dandelion optimization (DO) algorithm in antenna arrays. This is the first time that the DO algorithm has been used for optimizing antenna arrays. For antenna array optimization, sidelobe level (SLL) and deep nulls are key technical indicators. A lower SLL can improve the signal-to-noise ratio and reduce the impact of clutter signals outside the main beam. Deep nulls need to be aligned with the direction of interference to eliminate the influence of interference sources. The combination of the two can effectively improve the anti-interference ability of the entire system. Therefore, antenna arrays with ultra-low sidelobes and ultra-deep nulls are currently hot in the field of antenna array design and are also some of the key technologies needed to achieve modern high-performance radar systems. As a new type of evolutionary algorithm inspired by nature, the DO algorithm is inspired by the wind propagation behavior of dandelions in nature. This algorithm iteratively updates the population from three stages of ascent, descent, and landing, ultimately finding the optimal position. It has good optimization ability in solving complex problems such as those involving nonlinearity, discreteness, and non-convexity, and the antenna array pattern synthesis optimization problem belongs to multivariate nonlinear problems. Therefore, the DO algorithm can be effectively applied in the field of antenna array optimization. In this work, we use the following method to obtain an optimized pattern of a linear array with the lowest sidelobe level (SLL), null placement in particular directions, and a lower notch in particular directions: by controlling the antenna array’s element spacing and leaving the phase unchanged to optimize the current amplitudes and by controlling the excitation current and phase fixation of the antenna array and changing the element spacing. In the first and second examples, different algorithms are used to reduce the SLL of the antenna. In the first example, the DO algorithm reduces the SLL to −33.37 dB, which is 2.67 dB, 2.67 dB, 3.77 dB, 2.74 dB, and 2.52 dB lower than five other algorithms. In the second example, the SLL optimized by the DO algorithm is −42.56 dB, which is 5.04 dB and 1.48 dB lower than two other algorithms. In both examples, the DO algorithm reduces the SLL lower than other algorithms when the main lobe of the antenna is not significantly widened. Examples 3, 4, and 5 use the DO algorithm to optimize the amplitude of the current, generating deep nulls and deep notches in specific directions. In Example 3, the DO algorithm obtains a depth of nulls equal to −187.6 dB, which is 66.7 dB and 44.3 dB lower than that of the flower pollination algorithm (FPA) and the chaotic colony predation algorithm (CCPA), respectively. In Example 4, the deep null obtained by the DO algorithm is as low as −98.69 dB, which is 6.67 dB lower than the deep null obtained by the grey wolf optimization (GWO) algorithm. In Example 5, the deep notch obtained by the DO algorithm is as low as −63.1 dB, which is 6.4 dB and 1.9 dB lower than the spider monkey optimization (SMO) algorithm and the grasshopper optimization algorithm (GOA), respectively. The data prove that the DO algorithm produces deeper nulls and notches than other algorithms. The last two examples involve reducing sidelobe levels and generating deep nulls by optimizing the spacing between elements. In Example 5, the SLL obtained using the DO algorithm is −22.8766 dB, which is 0.1998 dB lower than the lowest SLL of −22.6768 dB among other algorithms. In Example 6, the SLL obtained using the DO algorithm is −20.1012 dB, and the null depth is −125.1 dB, which is 1.592 dB lower than the SLL obtained by the cat swarm optimization (CSO) algorithm and 19.1 dB lower than the deep null obtained by the GWO algorithm, respectively. In summary, the results of six simulation experiments indicate that the DO algorithm has better optimization ability in linear array optimization than other evolutionary algorithms.

Biodiesel manufacturing from renewable feedstocks has received a lot of attention as a viable alternative to fossil fuels. The Box-Behnken design, analysis of variance (ANOVA), and the Grey Wolf Optimizer (GWO) algorithm were used in this work to optimise biodiesel production from Nahar oil. The goal was to determine the best operating parameters for maximising biodiesel yield. The Box-Behnken design is used, with four essential parameters taken into account: molar ratio, reaction duration and temperature, and catalyst weight percentage. The response surface is studied in this design, and the key factors influencing biodiesel yield are discovered. The gathered data is given to ANOVA analysis to determine the statistical significance. ANOVA analysis is performed on the acquired data to determine the statistical significance of the components and their interactions. The GWO algorithm is used to better optimise the biodiesel production process. Based on the data provided, the GWO algorithm obtains an optimised yield of 91.6484% by running the reaction for 200 minutes, using a molar ratio of 7, and a catalyst weight percentage of 1.2. As indicated by the lower boundaries, the reaction temperature ranges from 50 °C. The results show that the Box-Behnken design, ANOVA, and GWO algorithm were successfully integrated for optimising biodiesel production from Nahar oil. This method offers useful insights into process optimisation and indicates the possibilities for increasing the efficiency and sustainability of biodiesel production. Further study can broaden the use of these strategies to various biodiesel production processes and feedstocks, advancing sustainable energy technology.