A Multi-Strategy Combined Grey Wolf Optimization Algorithm

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 Lypunov‐based Adaptive Backstepping Control (ABSC) approach is designed for a power Buck converter. This strategy is an advanced version of the Backstepping method utilising Lyapunov stability function to reach a higher stability and a better disturbance rejection behaviour in the practical applications. In addition, to reduce the computational burden and increase ease of implantation, Black‐box technique is considered assuming no accurate mathematical model for the system. Nonetheless, in real‐time environments, disturbances with wider ranges including: supply voltage variation, parametric variation, and noise can negatively impact the operation of this method. To compensate for this problem, the gains of the controller should be tuned again for better adaptability with the working condition. Therefore, to satisfy this need and enhance the controller's performance, a metaheuristic algorithm is applied in the control scheme called Grey Wolf Optimisation (GWO) algorithm. GWO is a well‐behaved nature‐inspired algorithm with faster decision‐making dynamics along with more accuracy over different optimisation algorithms. To better elaborate the merits of this approach, conventional BSM and PSO‐based PID schemes are also designed and tested in different situations.

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.

Grey-Wolf Optimizer (GWO) and Salp-Swarm Algorithm (SSA) are among the recent metaheuristic algorithms that have shown considerable potential in solving practical problems. Nevertheless, these optimisation methods usually suffer from a poor performance, especially when dealing with multimodal and high-dimensional problems. To overcome drawbacks of these algorithms, a new population-based global optimisation algorithm inspired by GWO and SSA is proposed in this paper. The basic idea behind the proposed approach is to divide the population into two groups that adopt new position updating strategies. The movement method of the first group is inspired by the hunting mechanism used in GWO algorithm. On the other hand, the population of the second group moves into the search space using a new strategy based on the position updating method employed by the follower salps in SSA. The performances of the proposed algorithm, named GW-SSA, have been studied through 23 benchmark functions of different types and dimensions. The obtained results were statistically analysed using Wilcoxon signed-rank. Furthermore, GW-SSA algorithm has been applied to solve four real engineering design problems. The experimental results show the superior performance of GW-SSA compared to GWO, SSA and other recently proposed optimisation algorithms.

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.

A Grey-Wolf optimization (GWO) algorithm served for fiber Bragg grating (FBG) strain sensor in structure detection is developed in this paper. A strain profile demodulation method of FBG reflection spectrum based on GWO algorithm is proposed, which uses an improved transfer matrix method for calculation. The GWO algorithm simulates the leadership and hunting mechanism of gray wolves in nature. For leadership, it has four types of gray wolves, such as α, β, δ, and ω wolves. Additionally, three main steps of hunting, searching, surrounding and attacking prey have also been simulated. On this basis, the reconstructed non-uniform strain profile by GWO algorithm was verified by a comprehensive numerical simulation. And the simulation results verify the accuracy and effectiveness of the GWO method. The calculation example shows that the target strain profile is in good agreement with the reconstructed strain profile.

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.

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.

The existing photovoltaic power generation multi-source collaborative control technology cannot improve the control effect of microgrid, resulting in high peak load balancing cost of microgrid. Therefore, the photovoltaic power generation multi-source collaborative control technology based on differential evolution (DE)-gray wolf optimization (GWO) algorithm is adopted. The main components of the microgrid system, such as photovoltaic power generation equipment, hydroelectric power generation equipment, and battery pack, are modeled. With the goal of minimum peak cost and maximum transmission power, collaborative control of water, light and energy storage is carried out. The gray Wolf algorithm is used to solve the multi-objective problem of water and light storage in microgrid, and the gray Wolf algorithm is optimized by DE algorithm. Experiments show that the convergence speed of the optimized DEVOLU-Gray Wolf algorithm is obviously accelerated, and the problem of falling into the local optimal solution is completely avoided. After the application of this method, the photovoltaic, hydraulic, and battery of the microgrid run in order, ensure the smooth operation of the microgrid, and improve the economic benefit of the microgrid.

To solve the problem of traversal multi-target path planning for an unmanned cruise ship in an unknown obstacle environment of lakes, this study proposed a hybrid multi-target path planning algorithm. The proposed algorithm can be divided into two parts. First, the multi-target path planning problem was transformed into a traveling salesman problem, and an improved Grey Wolf Optimization (GWO) algorithm was used to calculate the multi-target cruise sequence. The improved GWO algorithm optimized the convergence factor by introducing the Beta function, which can improve the convergence speed of the traditional GWO algorithm. Second, based on the planned target sequence, an improved D* Lite algorithm was used to implement the path planning between every two target points in an unknown obstacle environment. The heuristic function in the D* Lite algorithm was improved to reduce the number of expanded nodes, so the search speed was improved, and the planning path was smoothed. The proposed algorithm was verified by experiments and compared with the other four algorithms in both ordinary and complex environments. The experimental results demonstrated the strong applicability and high effectiveness of the proposed method.

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.

With the wide application of industrial manipulators, the research of its moving trajectory control method has become more and more important content. In this paper, the motor closed-loop control strategy of an industrial 6R manipulator was briefly introduced, the proportional, integral, and differential ( (PID) algorithm commonly used in motor control was analyzed, and its shortcomings were pointed out. Then, the incremental PID algorithm was introduced to design a grey wolf optimization (IGWO) algorithm to achieve parameter tuning. Simulation experiments were carried out in a MATLAB environment. The results showed that the incremental PID algorithm generated a smaller control deviation than the PID algorithm. The average deviation of the three axes of the incremental PID algorithm undergoing IGWO parameter tuning was less than 0.2 mm, and the moving time was between 1.1 s and 1.3 s. The control accuracy and efficiency of the incremental PID algorithm undergoing IGWO parameter tuning were better than those of the incremental PID algorithm whose parameters were tuned using the trial-and-error method and the grey wolf optimization algorithm respectively. Moreover, better stability and anti-interference were observed in step response and sinusoidal response. The results prove that the incremental PID algorithm combined with the IGWO algorithm is reliable in the moving trajectory control of industrial manipulators and can be applied in practice.

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.

Requirement prioritization is one of the most important approach in the process of requirement engineering due to use it in order to prioritize the execution sort of requirements with taking into account the viewpoints of stakeholders. Thus, in this study, grey wolf optimization (GWO) algorithm is applied in order to prioritize the requirements of a software project. GWO imitates the hunting behavior of grey wolves in nature. Which distinct from others that it has dominant leadership hierarchy which contains four main types; alpha, beta delta and omega wolves. In this paper, a proposed algorithm is presented to prioritize the requirements into ordered list. Furthermore, it is compared and evaluated with analytical hierarchy process (AHP) technique in terms of average running time and dataset size. The findings display that the RP-GWO performs better than AHP mechanism by approximately (30%).

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.