
Citation: Thomas Rauen, Rose Tanui, Christof Grewer. Structural and functional dynamics of Excitatory Amino Acid Transporters (EAAT)[J]. AIMS Molecular Science, 2014, 1(3): 99-125. doi: 10.3934/molsci.2014.3.99
[1] | Yong Xiong, Lin Pan, Min Xiao, Han Xiao . Motion control and path optimization of intelligent AUV using fuzzy adaptive PID and improved genetic algorithm. Mathematical Biosciences and Engineering, 2023, 20(5): 9208-9245. doi: 10.3934/mbe.2023404 |
[2] | Yongqiang Yao, Nan Ma, Cheng Wang, Zhixuan Wu, Cheng Xu, Jin Zhang . Research and implementation of variable-domain fuzzy PID intelligent control method based on Q-Learning for self-driving in complex scenarios. Mathematical Biosciences and Engineering, 2023, 20(3): 6016-6029. doi: 10.3934/mbe.2023260 |
[3] | Jiahao Zhang, Zhengming Gao, Suruo Li, Juan Zhao, Wenguang Song . Improved intelligent clonal optimizer based on adaptive parameter strategy. Mathematical Biosciences and Engineering, 2022, 19(10): 10275-10315. doi: 10.3934/mbe.2022481 |
[4] | Dongning Chen, Jianchang Liu, Chengyu Yao, Ziwei Zhang, Xinwei Du . Multi-strategy improved salp swarm algorithm and its application in reliability optimization. Mathematical Biosciences and Engineering, 2022, 19(5): 5269-5292. doi: 10.3934/mbe.2022247 |
[5] | Hong Lu, Hongxiang Zhan, Tinghua Wang . A multi-strategy improved snake optimizer and its application to SVM parameter selection. Mathematical Biosciences and Engineering, 2024, 21(10): 7297-7336. doi: 10.3934/mbe.2024322 |
[6] | Dashe Li, Xueying Wang, Jiajun Sun, Huanhai Yang . AI-HydSu: An advanced hybrid approach using support vector regression and particle swarm optimization for dissolved oxygen forecasting. Mathematical Biosciences and Engineering, 2021, 18(4): 3646-3666. doi: 10.3934/mbe.2021182 |
[7] | Sijie Wang, Shihua Zhou, Weiqi Yan . An enhanced whale optimization algorithm for DNA storage encoding. Mathematical Biosciences and Engineering, 2022, 19(12): 14142-14172. doi: 10.3934/mbe.2022659 |
[8] | Zijiao Zhang, Chong Wu, Shiyou Qu, Jiaming Liu . A hierarchical chain-based Archimedes optimization algorithm. Mathematical Biosciences and Engineering, 2023, 20(12): 20881-20913. doi: 10.3934/mbe.2023924 |
[9] | Huangjing Yu, Yuhao Wang, Heming Jia, Laith Abualigah . Modified prairie dog optimization algorithm for global optimization and constrained engineering problems. Mathematical Biosciences and Engineering, 2023, 20(11): 19086-19132. doi: 10.3934/mbe.2023844 |
[10] | Chengjun Wang, Xingyu Yao, Fan Ding, Zhipeng Yu . A trajectory planning method for a casting sorting robotic arm based on a nature-inspired Genghis Khan shark optimized algorithm. Mathematical Biosciences and Engineering, 2024, 21(2): 3364-3390. doi: 10.3934/mbe.2024149 |
A metaheuristic optimization algorithm is a novel population-based global search algorithm, and is more suitable for solving complex problems [1,2]. Rao et al. proposed a teaching-learning-based optimization (TLBO) algorithm to solve large-scale optimization problems. The simulation results of the standard test function showed that the TLBO algorithm effectively solves complex optimization problems [3]. To solve a complex constrained optimization problem, Sayed E et al. proposed a decomposition evolutionary algorithm [4]. Mohapatra et al. proposed a competitive swarm optimizer algorithm [5]. To overcome the shortcoming of particle swarm optimization (PSO) falling easily into a local optimum, an improved quantum PSO algorithm with the cultural gene algorithm and memory mechanism was proposed to solve continuous nonlinear problems [6,7]. Ali et al. presented a multi-population differential evolution global optimization algorithm [1]. Ant colony optimization, proposed by Ismkhan, has been applied to solving complex problems [8]. Using the symbiotic organism search algorithm for fractional fuzzy controllers [9] and so on.
In an industrial control system, the proportional integral derivative (PID) controller has been widely applied. It accounts for more than 90% of the actual control system [10]. The PID parameter tuning problem proposed by Ziegler and Nichols has caused extensive concern. However, the traditional PID parameter tuning method has the following problems: The control performance index is not ideal and, typically, the method has a large overshoot and long adjustment time. The control effect of an intelligent optimization algorithm in PID parameter tuning is better than that of the traditional tuning method, and it can avoid some shortcomings of traditional methods [11]. Jiang et al. proposed a PID tuning premature with a genetic algorithm (GA) to enhance the search and convergence speed, but there were problems of premature convergence and parameter dependence [12]. Yu et al. proposed seeker search algorithm optimization PID controller parameters; improved the control precision of the system; accelerated the response speed and robustness of the system; and optimized the optimal parameters for the control system PID, but the optimization formula complex, need to set more parameters [13]. P. B. de Moura Oliveira, et al. designed Posicast PID control systems using a gravitational search algorithm (GSA) [14]. Guo-qiang Zeng et al. designed multivariable PID controllers using real-coded population-based extremal optimization [15]. A. Belkadi et al. proposed a PSO-based approach on the robust PID adaptive controller for exoskeletons [16]. M. Gheisarnejad proposed an effective hybrid harmony search (HS) and cuckoo optimization algorithm-based fuzzy PID controller for load frequency control [17]. Amal Moharam, et al. designed an optimal PID controller using hybrid differential evolution and PSO with an aging leader and challengers [18].
The spotted hyena optimizer (SHO) [19] is a novel intelligence algorithm proposed by Dhiman and Kumar in 2017. It was inspired by the social and collaborative behavior of spotted hyenas, which exist in nature. Spotted hyenas typically perform four processes: Search, encirclement, hunt, and attack prey. The SHO has the characteristics of simple, easy to implement programming and adjust the parameters set less features. Since the SHO was proposed, there have been various improved versions of the SHO algorithm. For example, N. Panda, et al. used an improved SHO (ISHO) with space transformational search to train a pi-sigma higher-order neural network [20]. H. Moayedi et al. proposed using the SHO and ant lion optimization to predict the shear strength of soil [21]. Q. Luo, et al. proposed using the SHO with lateral inhibition for image matching [22]. G. Dhiman et al. proposed a multi-objective optimization algorithm for engineering problems [23] and used the SHO to solve the nonlinear economic load power dispatch problem [24]. Xu Y, et al. proposed an enhanced moth-flame optimizer with a mutation strategy for global optimization [25].
In function optimization and engineering optimization, it has been proved that the performance of the SHO is superior to that of the grey wolf optimizer (GWO), binary GWO [26], PSO, moth-flame optimization (MFO), multi-verse optimizer, sine cosine algorithm (SCA), GSA, GA, HS, Harris hawks optimization [27], bacterial foraging optimization [28], and flower pollination algorithm [29] in terms of precision and the convergence speed [22]. In this paper, an ISHO algorithm is applied to solve PID parameter problems in an automatic voltage regulator (AVR).
The remainder of the paper is organized as follows: The basic SHO algorithm is presented in Section 2. In Section 3, the ISHO is introduced. In Section 4, the ISHO is proposed to optimize PID parameters and compared with well-known algorithms. Finally, conclusions are provided in Section 5.
The social relationships and habits of animals are the source of inspiration for our work. This social behavior is also present in the spotted hyena, whose scientific name is Crocuta. According to llany et al. [30], spotted hyenas typically live in groups, with as many as 100 group members, and they have mutual trust and interdependence. The communication between spotted hyenas is typically posed, and given a special signal, they track prey using sight, hearing, and smell. There are four main steps for a spotted hyena to attack prey: Search for prey, encircle prey, hunt prey, and attack prey. To generate a mathematical model for encircling, the equations are as follows [31]:
$\vec D = \left| {\vec B \cdot {{\vec X}_p}\left( t \right) - \vec X\left( t \right)} \right| {\rm{ }}$ | (2.1) |
$\vec X\left( {t + 1} \right) = {\vec X_p}\left( t \right) - \vec E \cdot \vec D, $ | (2.2) |
where $t$ is the current iteration, $\vec B$ and $\vec E$ are the coefficient vectors, ${\vec X_p}$ is the position vector of the prey, $\vec X$ is the position vector, $\vec D$ is the distance between the prey and spotted hyena, and ${\rm{||}} \bullet {\rm{||}}$ represents the absolute value.
The coefficient vectors $\vec B$ and $\vec E$ are calculated as follows:
$\vec B = 2 \cdot r{\vec d_1}$ | (2.3) |
$\vec E = 2\vec h \cdot r{\vec d_2} - \vec h$ | (2.4) |
$\vec h = 5 - (t*(5/T)), $ | (2.5) |
where $t = 1, 2, 3, \cdots, T$ to balance exploration and exploitation, $\vec h$ linearly decreases from 5 to 0, and $r{\vec d_1}$ and $r{\vec d_2}$ are random vectors in [0, 1].
To define the spotted hyena behavior mathematically, the best search agent represents the location of the prey. The other search agents move toward the best search agent and save the best solutions obtained thus far to update their positions. The mathematical model can be formulated as follows:
${\vec D_h} = \left| {\vec B \cdot {{\vec X}_h} - {{\vec X}_k}} \right|$ | (2.6) |
${\vec X_k} = {\vec X_h} - \vec E \cdot {\vec D_h}$ | (2.7) |
${\vec C_h} = {\vec X_k} + {\vec X_{k + 1}} + \cdots + {\vec X_{k + N}}$ | (2.8) |
$N = coun{t_{nos}}({\vec X_h}, {\vec X_{h + 1}}, {\vec X_{h + 2}}, \cdots , (\vec X{}_h + \vec M)), $ | (2.9) |
where ${\vec X_h}$ is the position of the best spotted hyena, ${\vec X_k}$ is the position of other spotted hyena, N is the number of spotted hyenas, $\vec M$ is a random vector in [0.5, 1], $nos$ is the number of solutions, $coun{t_{nos}}$ is the count of all candidate solutions, and ${\vec C_h}$ is a cluster of N optimal solutions.
For spotted hyenas in the attack prey stage, to determine the optimal solution, it is necessary to continuously reduce the value of $\vec h$, where $\vec h$ is the step size that the spotted hyena takes to attack prey, and it is clear that, when looking for prey, the spotted hyena continues to increase the number of steps gain steps. The formulation for attacking prey is
$\vec X(t + 1) = \frac{{{{\vec C}_h}}}{N}, $ | (2.10) |
where $\vec X(t + 1)$ is the position of the current solution and $t$ is the number of iterations. The SHO allows its agents to update their positions in the direction of the prey.
Algorithm 1 Pseudocode of the SHO |
1. Initialize the spotted hyena population ${X_i}$ $(i = 1, 2, \cdots, n)$ 2. Initialize h, B, E, and N 3. Calculate the fitness of each search agent 4. ${\vec X_h}$= best search agent 5. ${\vec C_h}$= group or cluster of all far optimal solutions 6. while (t < max number of iterations) 7. for each search agent do 8. Update the position of the current search agent by Eq (2.10) 9. end for 10. Update h, B, E and N 11. Check if any search agent goes beyond the search space and revamp it 12 Calculate the fitness of each search agent 13. Update ${P_h}$ if there is a better solution by Eqs (2.6) and (2.7) 14. t = t + 1 15. end while 16. Return ${\vec X_h}$ |
The parameters $\vec B$ and $\vec E$ oblige the SHO algorithm to explore and exploit the search space. As $\vec B$ decreases, half the iterations are dedicated to exploration (when $\left| {\vec E} \right| > 1$) and the remainder are dedicated to exploitation (when $\left| {\vec E} \right| < 1$) [32]. From the above, the $\vec B$ vector contains random values in [0, 2]. This component provides random weights for prey to stochastically emphasize ($\vec B > 1$) or deemphasize ($\vec B < 1$) the effect of prey in defining the distance in Eq (2.3). This helps the random behavior of the SHO to increase during the course of optimization, and favors exploration and local optima avoidance. The pseudocode of the SHO algorithm is as above.
Haupt et al. found that the initial population affects the algorithm’s accuracy and convergence speed [32]. The better than initial population can lay the foundation for the global search of the SHO algorithm [21]. However, without any prior knowledge of the global optimal solution of the problem, the SHO algorithm typically adopts a random method when generating the initial search agent, which thus affects the search efficiency. The opposition learning strategy is a new technology that has emerged in the field of intelligent computing. So far, the opposite learning strategy has been successfully applied to swarm intelligent algorithms, such as PSO, HS, and DE algorithms [33,34]. In this paper, the opposite learning strategy is embedded into the SHO for initialization.
Algorithm 2 Initialization method based on opposite learning |
Set the population size to N 1. for i=1 to N do 2. for j=1 to d do 3. $X_i^j = l_i^j + rand(0, 1) \cdot (u_i^j - l_i^j)$ 4. end for 5. end for 6. for i=1 to N do 7. for j=1 to d do 8. $\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{X} _i^j = l_i^j + u_i^j - X_i^j$ 9. end for 10. end for 11. Output $\left\{ {X(N) \cup \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{X} (N)} \right\}$, where N denotes the individuals with the best fitness selected as the initial population. |
Definition: Opposition-based [35]. Suppose$X$exists in $\left[{l, u} \right]$. The opposite point is $\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{X} = l + u - X$. Let $X = ({X_1}, {X_2}, \cdots, X{}_d)$ be a point in d-dimensional space, where ${X_1}, {X_2}, \cdots, {X_d} \in R$ and ${X_i} \in \left[{{l_i}, {u_i}} \right]$ $\forall i \in \left\{ {1, 2, \cdots, d} \right\}$. The opposition-based $\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{X} = \left({{{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{X} }_1}, {{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{X} }_2}, \cdots, {{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{X} }_d}} \right)$ is completely defined by its components:
${\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{X} _i} = {l_i} + {u_i} - {X_i}.$ | (3.1) |
According to the above definition, the specific steps for using the opposite learning strategy to generate the initial population are as above.
Similar to other group intelligent optimization algorithms based on population iteration, it is crucial for the SHO to coordinate its exploration and exploitation capabilities. During exploration, groups need to detect a wider search area and avoid the SHO algorithm becoming stuck in a local optimum. The exploitation capacity mainly uses the group’s existing information to search some local solution’s areas of the solution. The convergence rate of the SHO algorithm has a decisive influence. Clearly, robustness and fast convergence are achieved only when the SHO algorithm improves the coordination of the exploration and exploitation capabilities.
According to [21], the SHO algorithm’s exploration and exploitation abilities depend on the change of the convergence factor $\vec h$. The larger the convergence factor $\vec h$, the better the global search ability and the more likely the SHO algorithm avoids falling into a local optimum. The smaller the convergence factor $\vec h$, the stronger the local search ability, which speeds up the convergence of the SHO algorithm. However, in the basic SHO algorithm, the convergence factor $\vec h$ decreases linearly from 5 to 0 as the number of iterations increases. The linear decreasing strategy of the convergence factor $\vec h$ has a good global search ability in the early stages of the algorithm, but the convergence speed is slow. In the latter part of the algorithm to speed up the convergence rate, but easy to fall into a local optimum, particularly in multimode functions problems. Therefore, in the evolutionary search process, the convergence factor $\vec h$ with the number of iterations linearly decreasing strategy cannot fully reflect the actual optimization of the search process in the SHO algorithm [36]. In fact, the SHO is expected to have a strong global search ability in the pre-search period while maintaining a fast convergence rate. Additionally, Enns, et al. and Zeng, et al. found that performance improved if the control parameter was chosen as a nonlinearly decreasing quantity rather than using a linearly decreasing strategy [30,32]. Thus, the control parameter $\vec h$ is modified as follows:
$\vec h = {\vec h_{initial}} - ({\vec h_{initial}} - {\vec h_{final}}) \times {(\frac{{Max\_iteration - t}}{{Max\_iteration}})^u}, $ | (3.2) |
where $t$ is the current iteration, $Max\_iteration$ is the maximum number of iterations, $u$ is the nonlinear modulation index, and ${\vec h_{initial}}$ and ${h_{final}}$ are the initial value and final value of control parameter $\vec h$, respectively. According to [32], when ${\vec h_{initial}}$ is set to 5, ${h_{final}}$ becomes 0.
Figure 1 shows typical control parameter $\vec h$ variations with iterations for different values of $u$. We conducted several SHO experiments with a nonlinear modulation index $u$ in the interval (0, 2.0). On average, the results are better than those of existing algorithms: The larger the value of u (u > 2.0), the greater the failed convergence rate.
Similar to other population-based intelligent optimization algorithms, in the late iteration of the SHO, all the spotted hyenas move closer to the optimal individual region, which results in a reduction of population diversity. In this case, if the current optimal individual is the local optimal, then the SHO algorithm falls into a local optimum. This is also an inherent characteristic of other group intelligent optimization algorithms. To reduce the probability of premature convergence for the SHO algorithm, in this paper, a diversity mutation operation is performed on the current optimal spotted hyena individuals. The steps are as follows:
Assume that an individual ${X_i} = ({x_{i1}},{x_{i2}}, \cdots ,{x_{id}})$ of the spotted hyena species selects one element ${x_k}(k = 1,2, \cdots ,d)$ randomly from the individual with a probability of and randomly generates a real number in the range $[{l_i},{u_i}]$ instead of the element from the individual ${X_i}$, thus producing a new individual. $X_i^' = (x_{i1}^',x_{i2}^', \cdots ,x_{id}^'$ The variation mutation operation is
$X{'_i} = \left\{ {li+λ⋅(ui−li)i=kXiotherwise } \right., $
|
(3.3) |
where ${l_i}$ and u are the upper and lower bounds of the variable x, respectively, and $\lambda \in [0, 1]$ is a random. The ISHO optimizer steps are presented in Algorithm 3.
Algorithm 3 Pseudocode of the ISHO |
1. Set the population size N using the opposite learning strategy described in Algorithm 2 to generate an initialized spotted hyena population ${X_i}(i = 1, 2, \cdots, n)$ 2. Initialize the parameters $h$, $B$, $E$, and $N$ 3. Calculate the fitness of each agent 4. ${P_h}$ = best search agent 5. ${C_h}$ = group or cluster of all far optimal solutions 6. while $\left({t < {t_{{\rm{max}}}}} \right)$ do 7. for i =1 to N do 8. Using Eq (3.2), calculate the value of the convergence factor h Update the other parameters B and E using Eqs (2.3) and (2.4), respectively 9. if $\left({\left| E \right| \ge 1} \right)$ do 10. According to Eq (2.7), update the spotted hyena individual’s position 11. end if 12. if $\left({\left| E \right| \ge 1} \right)$ do 13. According to Eq (2.10), update the spotted hyena individual’s position 14. end if 15. end for 16. Perform diversity mutation on the current spotted hyena individual using Eq (3.3) 17. Calculate the fitness of each agent 18. Update ${X_i}$ if there is a better solution 19. t = t+1 20. end while 21.end |
Providing constancy and stability at rated voltage levels in electricity, the network is also one of the main problems in power system control. If the rated voltage level deviates from this value, then the performance degrades and the life expectancy reduces. Another important reason for this control is true line loss, which depends on the real and reactive power flow. The reactive power flow is largely dependent on the terminal voltage of the power system. However, it is necessary to reduce the loss caused by the solid line by controlling the rated voltage level. To solve these control problems, an AVR system is applied to power generation units [36]. The role of the AVR is to maintain the terminal voltage of the synchronous alternator at the rated voltage value.
Using the PID controller to improve the dynamic response while reducing or eliminating the steady-state error, the derivative controller adds a finite zero to the open-loop plant, which enables the improvement of the transient response. The PID controller transfer function is
$C(s) = {K_p} + \frac{{{K_i}}}{S} + {K_d}S.$ | (4.1) |
A simple AVR system has four parts: Amplifier, exciter, generator, and sensor. The mathematical transfer function of the above four components is considered as linear and time constant. To analyze the dynamic performance of an AVR, the transfer functions of these components are in [37,38].
The amplifier model is represented by a gain ${K_A}$ and time constant ${\tau _A}$. The transfer function is given by
$\frac{{{V_r}(s)}}{{{V_e}(s)}} = \frac{{{K_A}}}{{1 + {\tau _A}s}}, $ | (4.2) |
where the range of ${K_A}$ is [10,400] and the amplifier time constant ranges from 0.02–0.1 s.
The transfer function of an exciter is modeled by a gain ${K_E}$ and time constant ${\tau _E}$, and given by
$\frac{{{V_f}(s)}}{{{V_r}(s)}} = \frac{{{K_E}}}{{1 + {\tau _E}s}}, $ | (4.3) |
where ${K_E}$ is typically in the range [10,400] and the time constant ${\tau _E}$ is in the range 0.5–1.0 s.
The generator model is represented by a gain ${K_G}$ and time constant ${\tau _G}$. The transfer function is given by
$\frac{{{V_t}(s)}}{{{V_f}(s)}} = \frac{{{K_{\rm{G}}}}}{{1 + {\tau _G}s}}, $ | (4.4) |
where ${K_R}$ is in the range [0.7, 1.0] and ${\tau _R}$ is in the range 1.0–2.0 s. The generator gain ${K_R}$ and time constant ${\tau _R}$ are load dependent.
The sensor is modeled by a gain ${K_R}$ and time constant ${\tau _R}$. The transfer function is given by
$\frac{{{V_s}(s)}}{{{V_t}(s)}} = \frac{{{K_R}}}{{1 + {\tau _R}s}}, $ | (4.5) |
where ${K_R}$ is in the range [10,400] and ${\tau _R}$ is in the range 0.001–0.06 s.
The complete transfer function model of the AVR system is given in Figure 2. In the work of Gozde and Taplanmacioglu [37], the parameters of the AVR system were ${K_A} = 10.0$, ${\tau _A} = 0.1$, ${K_E} = 1.0$, ${\tau _E} = 0.4$, ${K_G} = 1.0$, ${\tau _G} = 1.0$, ${K_R} = 1.0$, and ${\tau _R} = 0.01$.
The transformer function of the AVR system with the above parameters is
$\frac{{\Delta {V_t}(s)}}{{\Delta {V_{ref}}(s)}} = \frac{{0.1s + 10}}{{0.0004{s^4} + 0.045{s^3} + 0.555{s^2} + 1.51{s^2} + 1.51s + 11}}.$ | (4.6) |
To improve the dynamic response of the AVR system and maintain the terminal voltage at 1.0 pu, a PID controller is included, as shown in Figure 2.
With the PID controller, the transfer function of the AVR system of Figure 2 becomes
$\frac{{\Delta {V_t}(s)}}{{\Delta {V_{ref}}(s)}} = \frac{{0.1{K_d}{s^2} + (0.1{K_p} + 10{K_d}){s^2} + (0.1{K_i} + 10{K_p})s + 10{K_i}}}{{0.0004{s^5} + 0.045{s^4} + 0.555{s^3} + (1.51 + 10{K_d}){s^2} + (1 + 10{K_p})s + 10{K_i}}}.$ | (4.7) |
An AVR system with a PID controller tuned by the ISHO algorithm is shown in Figure 2. The gains of the PID controller are regulated by the ISHO algorithm. If the proportional gain is too high, then the system becomes unstable and the proportional gain becomes too low, which results in a larger error and lower sensitivity. For an AVR system, the ranges commonly used in the literature are [0.0, 1.5] and [0.2, 2.0] in [38,39]. To increase the search space for better optimization gains, the resulting lower and upper bounds are chosen to be 0.01 and 2, respectively.
To improve the performance control, the optimal PID parameters use the ISHO. The maximum overshoot, rise time, steady state error as a typical time domain analysis method index, and integral time multiplied by the absolute error (ITAE) are considered as control performance indicators in the design. The ITAE is the objective function with time value:
$ITAE = \int_0^t {t\left| {{V_t} - {V_{ref}}} \right|} dt.$ | (4.8) |
An ISHO-PID controller is presented for searching the optimal or near optimal controller parameters ${K_p}$, ${K_i}$, and ${K_d}$ using the ISHO algorithm. Each individual K contains three members: ${K_p}$, ${K_i}$, and ${K_d}$. The searching procedures of the proposed ISHO-PID controller are presented in Algorithm 4. The three controller parameters set in the algorithm are shown in Table 1.
Algorithm 4 ISHO solution for the PID control system algorithm |
1. Determine the parameters of the PID, proportional gain ${K_p}$, integral gain ${K_i}$, and differential gain ${K_d}$. 2. Randomly initialize population $X$ of $N$ individuals (solutions), $iter = 0$, and set the parameters of the ISHO, $h$, $B$, and $E$, and maximum number of iterations $ite{r_{\max }}$. 3. Set the lower and upper bounds of the three controller parameters for each individual, apply the PID controller with gains specified by that individual to the PID controller, run all the system steps, and calculate the fitness value of each individual using Eq (4.8). 4. Determine the optimal spotted hyena individual. while stop if the termination criterion is not satisfied do 5. for each individual $x \in X$ do 5.1. Propagate each spotted hyena individual $x$ to a new individual ${x'}$ using Eq (2.7). 5.2. if $f(x') > f(x)$ then 6. Update the position of all individuals using Eq (2.10). 7. Calculate each individual fitness function using Eq (4.8). 8. $iter = iter + 1$. 9. if $iter < ite{r_{\max }}$, then go to step 5. 10. Output the best solution and the optimal controller parameters. |
Controller parameters | Min. value | Max. value |
${K_p}$ | 0 | 1.5 |
${K_i}$ | 0 | 1.0 |
${K_d}$ | 0 | 1.0 |
The ISHO algorithm was applied to optimize the PID controller for an AVR system and determine a set of optimal gains that minimize the value of the objective function. To prove the superiority of the ISHO algorithm, we compared the ISHO with other algorithms that contain the SHO [19], GWO [40], PSOGSA [41], FPA [42], and SCA [43]. The results showed that the ISHO performed better than the other algorithms. All the parameters set in the algorithms are given in Table 2.
Algorithms | Parameter values |
SCA | ${r_2} \in [0, 2\pi]$, $a = 2$, ${r_4} \in [0, 1]$. The population size is 50. |
FPA | The proximity probability p = 0.8, the population size is 50. |
PSOGSA | ${c_1} = {c_2} = 2$, ${\omega _{\max }} = 0.3, {\omega _{\min }} = 0.1$, ${G_0} = 1$, $\alpha = 5$ the population size is 50. |
GWO | Components $\vec \alpha \in [0, 2]$ over the course of iterations. The population size is 50. |
SHO | The parameter is $\vec h \in [0, 5]$ over the course of iterations, the population size is 50. |
ISHO | ${\vec h_{initial}} = 5$, ${h_{final}} = 0$, $u \in [0, 2.0]$. The population size is 50. |
Setting the six algorithms’ parameters, we obtained the best parameter values for each algorithm to optimize the PID parameters using the population size of 50, 20 iterations, and 20 runs independently. "Best" is the optimal fitness value, "Worst" is the worst fitness value, "Mean" is the mean fitness value, and "Std." is the standard deviation. Table 3 shows that the best fitness value of ISHO was significantly better than those of the other algorithms, and the standard error of the ISHO was the smallest. It is thus proved that the ISHO is better than the standard SHO and other algorithms (SCA, FPA, PSOGSA, and GWO) in terms of obtaining the optimal PID parameters.
Algorithms | SCA | FPA | PSOGSA | GWO | SHO | ISHO |
${K_p}$ | 1.4155 | 1.4230 | 1.4012 | 1.3168 | 1.3079 | 1.0263 |
${K_i}$ | 0.9721 | 0.9974 | 0.9602 | 0.9051 | 0.9234 | 0.7115 |
${K_d}$ | 0.4546 | 0.4302 | 0.4601 | 0.4219 | 0.3985 | 0.3154 |
Best | 0.0328 | 0.0329 | 0.0328 | 0.0329 | 0.0334 | 0.0327 |
Worst | 0.0382 | 0.0380 | 0.0333 | 0.0369 | 0.0370 | 0.0331 |
Ave | 0.0344 | 0.0341 | 0.0330 | 0.0344 | 0.0347 | 0.0328 |
Std | 0.0015 | 0.0012 | 1.5427 × 10−4 | 0.0012 | 9.8111 × 10−4 | 8.4078 × 10−5 |
In Table 2, we label the optimal PID parameters with the optimal fitness values, and the minimum standard error is indicated by the black bold line. The table shows that, although the PSOGSA algorithm is also a hybrid of the PSO and GSA algorithms, the effect of optimally searching for PID parameters was still not as good as that of the ISHO algorithm.
Algorithms | SCA | FPA | PSOGSA | GWO | SHO | ISHO |
Maximum overshoots | 1.1751 | 1.1601 | 1.1383 | 1.1767 | 1.2017 | 1.120 |
Peak time (s) | 0.3821 | 0.3923 | 0.3883 | 0.3924 | 0.3951 | 0.4160 |
Settling time (s) | 0.6930 | 1.003 | 0.9723 | 0.9494 | 0.9288 | 0.8481 |
Rise time (s) | 0.2382 | 0.2207 | 0.2883 | 0.2274 | 0.2010 | 0.3021 |
The transient and steady-state behavior of the system can be analyzed from the transient analysis of the ISHO optimized PID controller in the AVR system, as shown in Figure 4. For comparison, responses for the SCA, FPA, PSOGSA, GWO, and SHO algorithms are shown in Table 8. The figure shows that the maximum overshoot for the ISHO algorithm is 5% less than that of the SCA algorithm, 3.5% less than that of the FPA algorithm, 4.82% less than that of the GWO algorithm, and 6.8% less than that of the SHO algorithm. The peak time for the ISHO algorithm is more than that of the SHO, GWO, PSOGSA, FPA, and SCA algorithms. The maximum overshoot and settling time for the ISHO algorithm are better than those of the SHO, GWO, PSOGSA, FPA, and SCA algorithms, and are major factors for comparing the stability analysis of systems.
The convergence characteristics are shown in Figure 4. The figure shows that the ISHO algorithm’s fitness value decreases the fastest compared with those of the other algorithms. This shows that the ISHO algorithm has a strong global search capability and higher precision. The ISHO algorithm is considered as an optimization of the PID controller parameters in the AVR system, which has promising potential applications.
The SHO was inspired by the social behavior of a spotted hyena swarm. Its mathematical model is relatively simple, but the control parameter directly affects the balance between the global search ability and local search ability in the SHO algorithm. Based on the analysis of the above characteristics of the SHO, in this paper, a nonlinear adjustment strategy was adopted for the control parameters and the mutation strategy was used to deal with the update of the intelligent individual position. The performance of the improved algorithm was verified by a simulation. The ISHO quickly approached the theoretical value and significantly improved the convergence speed and optimization efficiency. The ISHO algorithm was used to determine the parameters of the PID controller for an AVR system. It is clear from the results that the proposed ISHO algorithm avoided the shortcoming of the premature convergence of the SHO, GWO, PSOGSA, FPA, and SCA algorithms and obtained global solutions with better computation efficiency.
This work was supported by the Project of China University of Political Science and Law Research Innovation under Grant No. 10818441 and the Young Scholar Fund of China University of Political Science and Law under Grant No. 10819144. We thank Maxine Garcia, PhD, from Liwen Bianji, Edanz Group China (www.liwenbianji.cn/ac) for editing the English text of a draft of this manuscript.
The authors declare no conflict of interest.
[1] |
Zerangue N, Kavanaugh MP (1996) Flux coupling in a neuronal glutamate transporter. Nature 383: 634-637. doi: 10.1038/383634a0
![]() |
[2] |
Danbolt NC (2001) Glutamate uptake. Prog Neurobiol 65: 1-105. doi: 10.1016/S0301-0082(00)00067-8
![]() |
[3] | Hertz L (1979) Functional interactions between neurons and astrocytes. I. Turnover and metabolism of putative amino acid transmitters. ProgNeurobiol 13: 277-323. |
[4] |
Broer S, Brookes N (2001) Transfer of glutamine between astrocytes and neurons. J Neurochem 77: 705-719. doi: 10.1046/j.1471-4159.2001.00322.x
![]() |
[5] | Drejer J, Larsson OM, Schousboe A (1982) Characterization of L-glutamate uptake into and release from astrocytes and neurons cultured from differnt brain regions. ExpBrain Res 47: 259-269. |
[6] | Schousboe A, Hertz L (1981) Role of astroglial cells in glutamate homeostasis. Adv Biochem Psychopharmacol 27: 103-113. |
[7] | Rauen T, Taylor WR, Kuhlbrodt K, et al. (1998) High-affinity glutamate transporters in the rat retina: a major role of the glial glutamate transporter GLAST-1 in transmitter clearance. Cell Tissue Res 291: 19-31. |
[8] |
Rauen T, Wiessner M (2000) Fine tuning of glutamate uptake and degradation in glial cells: common transcriptional regulation of GLAST1 and GS. Neurochem Int 37: 179-189. doi: 10.1016/S0197-0186(00)00021-8
![]() |
[9] |
Furness DN, Dehnes Y, Akhtar AQ, et al. (2008) A quantitative assessment of glutamate uptake into hippocampal synaptic terminals and astrocytes: new insights into a neuronal role for excitatory amino acid transporter 2 (EAAT2). Neuroscience 157: 80-94. doi: 10.1016/j.neuroscience.2008.08.043
![]() |
[10] |
Pines G, Danbolt NC, Bjoras M, et al. (1992) Cloning and expression of a rat brain L-glutamate transporter. Nature 360: 464-467. doi: 10.1038/360464a0
![]() |
[11] |
Storck T, Schulte S, Hofmann K, et al. (1992) Structure, expression, and functional analysis of a Na(+)-dependent glutamate/aspartate transporter from rat brain. Proc Natl Acad Sci U S A 89: 10955-10959. doi: 10.1073/pnas.89.22.10955
![]() |
[12] | Arriza JL, Fairman WA, Wadiche JI, et al. (1994) Functional comparisons of three glutamate transporter subtypes cloned from human motor cortex. J Neurosci 14: 5559-5569. |
[13] |
Tanaka K, Watase K, Manabe T, et al. (1997) Epilepsy and exacerbation of brain injury in mice lacking the glutamate transporter GLT-1. Science 276: 1699-1702. doi: 10.1126/science.276.5319.1699
![]() |
[14] |
Bjornsen LP, Hadera MG, Zhou Y, et al. (2014) The GLT-1 (EAAT2; slc1a2) glutamate transporter is essential for glutamate homeostasis in the neocortex of the mouse. J Neurochem 128: 641-649. doi: 10.1111/jnc.12509
![]() |
[15] |
Rauen T, Wiessner M, Sullivan R, et al. (2004) A new GLT1 splice variant: cloning and immunolocalization of GLT1c in the mammalian retina and brain. Neurochem Int 45: 1095-1106. doi: 10.1016/j.neuint.2004.04.006
![]() |
[16] |
Sullivan R, Rauen T, Fischer F, et al. (2004) Cloning, transport properties, and differential localization of two splice variants of GLT-1 in the rat CNS: Implications for CNS glutamate homeostasis. Glia 45: 155-169. doi: 10.1002/glia.10317
![]() |
[17] |
Lee A, Anderson AR, Beasley SJ, et al. (2012) A new splice variant of the glutamate-aspartate transporter: cloning and immunolocalization of GLAST1c in rat, pig and human brains. J Chem Neuroanat 43: 52-63. doi: 10.1016/j.jchemneu.2011.10.005
![]() |
[18] |
Grewer C, Gameiro A, Rauen T (2014) SLC1 glutamate transporters. Pflugers Arch 466: 3-24. doi: 10.1007/s00424-013-1397-7
![]() |
[19] |
Rauen T (2000) Diversity of glutamate transporter expression and function in the mammalian retina. Amino Acids 19: 53-62. doi: 10.1007/s007260070033
![]() |
[20] |
Rauen T, Kanner BI (1994) Localization of the glutamate transporter GLT-1 in rat and macaque monkey retinae. Neurosci Lett 169: 137-140. doi: 10.1016/0304-3940(94)90375-1
![]() |
[21] |
Wiessner M, Fletcher EL, Fischer F, et al. (2002) Localization and possible function of the glutamate transporter, EAAC1, in the rat retina. Cell Tissue Res 310: 31-40. doi: 10.1007/s00441-002-0612-1
![]() |
[22] |
Holmseth S, Dehnes Y, Huang YH, et al. (2012) The density of EAAC1 (EAAT3) glutamate transporters expressed by neurons in the mammalian CNS. J Neurosci 32: 6000-6013. doi: 10.1523/JNEUROSCI.5347-11.2012
![]() |
[23] | Dehnes Y, Chaudhry FA, Ullensvang K, et al. (1998) The glutamate transporter EAAT4 in rat cerebellar Purkinje cells: a glutamate-gated chloride channel concentrated near the synapse in parts of the dendritic membrane facing astroglia. J Neurosci 18: 3606-3619. |
[24] |
Mim C, Balani P, Rauen T, et al. (2005) The Glutamate Transporter Subtypes EAAT4 and EAATs 1-3 Transport Glutamate with Dramatically Different Kinetics and Voltage Dependence but Share a Common Uptake Mechanism. J Gen Physiol 126: 571-589. doi: 10.1085/jgp.200509365
![]() |
[25] |
Gincel D, Regan MR, Jin L, et al. (2007) Analysis of cerebellar Purkinje cells using EAAT4 glutamate transporter promoter reporter in mice generated via bacterial artificial chromosome-mediated transgenesis. Exp Neurol 203: 205-212. doi: 10.1016/j.expneurol.2006.08.016
![]() |
[26] |
Kovermann P, Machtens JP, Ewers D, et al. (2010) A conserved aspartate determines pore properties of anion channels associated with excitatory amino acid transporter 4 (EAAT4). J Biol Chem 285: 23676-23686. doi: 10.1074/jbc.M110.126557
![]() |
[27] |
Arriza JL, Eliasof S, Kavanaugh MP, et al. (1997) Excitatory amino acid transporter 5, a retinal glutamate transporter coupled to a chloride conductance. Proc Natl Acad Sci U S A 94: 4155-4160. doi: 10.1073/pnas.94.8.4155
![]() |
[28] |
Wersinger E, Schwab Y, Sahel JA, et al. (2006) The glutamate transporter EAAT5 works as a presynaptic receptor in mouse rod bipolar cells. J Physiol 577: 221-234. doi: 10.1113/jphysiol.2006.118281
![]() |
[29] |
Gameiro A, Braams S, Rauen T, et al. (2011) The Discovery of Slowness: Low-Capacity Transport and Slow Anion Channel Gating by the Glutamate Transporter EAAT5. Biophysical journal 100: 2623-2632. doi: 10.1016/j.bpj.2011.04.034
![]() |
[30] | Hediger MA, Kanai Y, You G, et al. (1995) Mammalian ion-coupled solute transporters. JPhysiolLond 482: 7S-17S. |
[31] |
Bailey CG, Ryan RM, Thoeng AD, et al. (2011) Loss-of-function mutations in the glutamate transporter SLC1A1 cause human dicarboxylic aminoaciduria. J Clin Invest 121: 446-453. doi: 10.1172/JCI44474
![]() |
[32] |
Duerson K, Woltjer RL, Mookherjee P, et al. (2009) Detergent-insoluble EAAC1/EAAT3 aberrantly accumulates in hippocampal neurons of Alzheimer's disease patients. Brain Pathol 19: 267-278. doi: 10.1111/j.1750-3639.2008.00186.x
![]() |
[33] |
Revett TJ, Baker GB, Jhamandas J, et al. (2013) Glutamate system, amyloid ss peptides and tau protein: functional interrelationships and relevance to Alzheimer disease pathology. J Psychiatry Neurosci 38: 6-23. doi: 10.1503/jpn.110190
![]() |
[34] | Rothstein JD (2009) Current hypotheses for the underlying biology of amyotrophic lateral sclerosis. Ann Neurol 65 Suppl 1: S3-9. |
[35] |
Lang UE, Borgwardt S (2013) Molecular Mechanisms of Depression: Perspectives on New Treatment Strategies. Cell Physiol Biochem 31: 761-777. doi: 10.1159/000350094
![]() |
[36] |
Crino PB, Jin H, Shumate MD, et al. (2002) Increased expression of the neuronal glutamate transporter (EAAT3/EAAC1) in hippocampal and neocortical epilepsy. Epilepsia 43: 211-218. doi: 10.1046/j.1528-1157.2002.35001.x
![]() |
[37] |
Estrada-Sanchez AM, Rebec GV (2012) Corticostriatal dysfunction and glutamate transporter 1 (GLT1) in Huntington's disease: interactions between neurons and astrocytes. Basal Ganglia 2: 57-66. doi: 10.1016/j.baga.2012.04.029
![]() |
[38] | Rao VL, Dogan A, Todd KG, et al. (2001) Antisense knockdown of the glial glutamate transporter GLT-1, but not the neuronal glutamate transporter EAAC1, exacerbates transient focal cerebral ischemia-induced neuronal damage in rat brain. J Neurosci 21: 1876-1883. |
[39] |
Grewer C, Gameiro A, Zhang Z, et al. (2008) Glutamate forward and reverse transport: from molecular mechanism to transporter-mediated release after ischemia. IUBMB Life 60: 609-619. doi: 10.1002/iub.98
![]() |
[40] |
Ketheeswaranathan P, Turner NA, Spary EJ, et al. (2011) Changes in glutamate transporter expression in mouse forebrain areas following focal ischemia. Brain Res 1418: 93-103. doi: 10.1016/j.brainres.2011.08.029
![]() |
[41] |
Seki Y, Feustel PJ, Keller RW, et al. (1999) Inhibition of ischemia-induced glutamate release in rat striatum by dihydrokinate and an anion channel blocker. Stroke 30: 433-440. doi: 10.1161/01.STR.30.2.433
![]() |
[42] | Azami Tameh A, Clarner T, Beyer C, et al. (2013) Regional regulation of glutamate signaling during cuprizone-induced demyelination in the brain. Ann Anat. |
[43] |
Karlsson RM, Tanaka K, Heilig M, et al. (2008) Loss of glial glutamate and aspartate transporter (excitatory amino acid transporter 1) causes locomotor hyperactivity and exaggerated responses to psychotomimetics: rescue by haloperidol and metabotropic glutamate 2/3 agonist. Biol Psychiatry 64: 810-814. doi: 10.1016/j.biopsych.2008.05.001
![]() |
[44] |
Karlsson RM, Tanaka K, Saksida LM, et al. (2009) Assessment of glutamate transporter GLAST (EAAT1)-deficient mice for phenotypes relevant to the negative and executive/cognitive symptoms of schizophrenia. Neuropsychopharmacology 34: 1578-1589. doi: 10.1038/npp.2008.215
![]() |
[45] |
Adamczyk A, Gause CD, Sattler R, et al. (2011) Genetic and functional studies of a missense variant in a glutamate transporter, SLC1A3, in Tourette syndrome. Psychiatr Genet 21: 90-97. doi: 10.1097/YPG.0b013e328341a307
![]() |
[46] |
Reyes N, Ginter C, Boudker O (2009) Transport mechanism of a bacterial homologue of glutamate transporters. Nature 462: 880-885. doi: 10.1038/nature08616
![]() |
[47] |
Verdon G, Boudker O (2012) Crystal structure of an asymmetric trimer of a bacterial glutamate transporter homolog. Nat Struct Mol Biol 19: 355-357. doi: 10.1038/nsmb.2233
![]() |
[48] |
Yernool D, Boudker O, Jin Y, et al. (2004) Structure of a glutamate transporter homologue from Pyrococcus horikoshii. Nature 431: 811-818. doi: 10.1038/nature03018
![]() |
[49] |
Jardetzky O (1966) Simple allosteric model for membrane pumps. Nature 211: 969-970. doi: 10.1038/211969a0
![]() |
[50] |
Owe SG, Marcaggi P, Attwell D (2006) The ionic stoichiometry of the GLAST glutamate transporter in salamander retinal glia. J Physiol 577: 591-599. doi: 10.1113/jphysiol.2006.116830
![]() |
[51] |
Kanai Y, Nussberger S, Romero MF, et al. (1995) Electrogenic properties of the epithelial and neuronal high affinity glutamate transporter. J Biol Chem 270: 16561-16568. doi: 10.1074/jbc.270.28.16561
![]() |
[52] | Wadiche JI, Kavanaugh MP (1998) Macroscopic and microscopic properties of a cloned glutamate transporter/chloride channel. J Neurosci 18: 7650-7661. |
[53] | Otis TS, Kavanaugh MP (2000) Isolation of current components and partial reaction cycles in the glial glutamate transporter EAAT2. J Neurosci 20: 2749-2757. |
[54] | Otis TS, Jahr CE (1998) Anion currents and predicted glutamate flux through a neuronal glutamate transporter. J Neurosci 18: 7099-7110. |
[55] | Bergles DE, Tzingounis AV, Jahr CE (2002) Comparison of coupled and uncoupled currents during glutamate uptake by GLT-1 transporters. J Neurosci 22: 10153-10162. |
[56] |
Grewer C, Watzke N, Wiessner M, et al. (2000) Glutamate translocation of the neuronal glutamate transporter EAAC1 occurs within milliseconds. Proc Natl Acad Sci U S A 97: 9706-9711. doi: 10.1073/pnas.160170397
![]() |
[57] |
Watzke N, Bamberg E, Grewer C (2001) Early intermediates in the transport cycle of the neuronal excitatory amino acid carrier EAAC1. J Gen Physiol 117: 547-562. doi: 10.1085/jgp.117.6.547
![]() |
[58] | Mwaura J, Tao Z, James H, et al. (2012) Protonation state of a conserved acidic amino acid involved in Na(+) binding to the glutamate transporter EAAC1. ACS Chem Neurosci 12: 1073-1083. |
[59] | Diamond JS, Jahr CE (1997) Transporters buffer synaptically released glutamate on a submillisecond time scale. J Neurosci 17: 4672-4687. |
[60] |
Mim C, Tao Z, Grewer C (2007) Two conformational changes are associated with glutamate translocation by the glutamate transporter EAAC1. Biochemistry 46: 9007-9018. doi: 10.1021/bi7005465
![]() |
[61] |
Wadiche JI, Arriza JL, Amara SG, et al. (1995) Kinetics of a human glutamate transporter. Neuron 14: 1019-1027. doi: 10.1016/0896-6273(95)90340-2
![]() |
[62] |
Loo DD, Hazama A, Supplisson S, et al. (1993) Relaxation kinetics of the Na+/glucose cotransporter. Proc Natl Acad Sci U S A 90: 5767-5771. doi: 10.1073/pnas.90.12.5767
![]() |
[63] | Lu CC, Hilgemann DW (1999) GAT1 (GABA:Na+:Cl-) cotransport function. Kinetic studies in giant Xenopus oocyte membrane patches. J Gen Physiol 114: 445-457. |
[64] |
Grewer C, Zhang Z, Mwaura J, et al. (2012) Charge compensation mechanism of a Na+-coupled, secondary active glutamate transporter. J Biol Chem 287: 26921-26931. doi: 10.1074/jbc.M112.364059
![]() |
[65] |
Zhang Z, Tao Z, Gameiro A, et al. (2007) Transport direction determines the kinetics of substrate transport by the glutamate transporter EAAC1. Proc Natl Acad Sci U S A 104: 18025-18030. doi: 10.1073/pnas.0704570104
![]() |
[66] |
Wadiche JI, Amara SG, Kavanaugh MP (1995) Ion fluxes associated with excitatory amino acid transport. Neuron 15: 721-728. doi: 10.1016/0896-6273(95)90159-0
![]() |
[67] |
Eliasof S, Jahr CE (1996) Retinal glial cell glutamate transporter is coupled to an anionic conductance. Proc Natl Acad Sci U S A 93: 4153-4158. doi: 10.1073/pnas.93.9.4153
![]() |
[68] | Billups B, Rossi D, Attwell D (1996) Anion conductance behavior of the glutamate uptake carrier in salamander retinal glial cells. J Neurosci 16: 6722-6731. |
[69] |
Fairman WA, Vandenberg RJ, Arriza JL, et al. (1995) An excitatory amino-acid transporter with properties of a ligand-gated chloride channel. Nature 375: 599-603. doi: 10.1038/375599a0
![]() |
[70] |
Larsson HP, Picaud SA, Werblin FS, et al. (1996) Noise analysis of the glutamate-activated current in photoreceptors. Biophysl J 70: 733-742. doi: 10.1016/S0006-3495(96)79613-3
![]() |
[71] |
Melzer N, Biela A, Fahlke C (2003) Glutamate modifies ion conduction and voltage-dependent gating of excitatory amino acid transporter-associated anion channels. J Biol Chem 278: 50112-50119. doi: 10.1074/jbc.M307990200
![]() |
[72] | Picaud SA, Larsson HP, Grant GB, et al. (1995) Glutamate-gated chloride channel with glutamate-transporter-like properties in cone photoreceptors of the tiger salamander. J Neurophys 74: 1760-1771. |
[73] |
Watzke N, Grewer C (2001) The anion conductance of the glutamate transporter EAAC1 depends on the direction of glutamate transport. FEBS Lett 503: 121-125. doi: 10.1016/S0014-5793(01)02715-6
![]() |
[74] |
Tao Z, Grewer C (2007) Cooperation of the conserved aspartate 439 and bound amino acid substrate is important for high-affinity Na+ binding to the glutamate transporter EAAC1. J Gen Physiol 129: 331-344. doi: 10.1085/jgp.200609678
![]() |
[75] |
Boudker O, Ryan RM, Yernool D, et al. (2007) Coupling substrate and ion binding to extracellular gate of a sodium-dependent aspartate transporter. Nature 445: 387-393. doi: 10.1038/nature05455
![]() |
[76] |
Cater RJ, Vandenberg RJ, Ryan RM (2014) The domain interface of the human glutamate transporter EAAT1 mediates chloride permeation. Biophys J 107: 621-629. doi: 10.1016/j.bpj.2014.05.046
![]() |
[77] |
Huang Z, Tajkhorshid E (2008) Dynamics of the extracellular gate and ion-substrate coupling in the glutamate transporter. Biophys J 95: 2292-2300. doi: 10.1529/biophysj.108.133421
![]() |
[78] |
Shrivastava IH, Jiang J, Amara SG, et al. (2008) Time-resolved mechanism of extracellular gate opening and substrate binding in a glutamate transporter. J Biol Chem 283: 28680-28690. doi: 10.1074/jbc.M800889200
![]() |
[79] |
Huang Z, Tajkhorshid E (2010) Identification of the third Na+ site and the sequence of extracellular binding events in the glutamate transporter. Biophys J 99: 1416-1425. doi: 10.1016/j.bpj.2010.06.052
![]() |
[80] |
Bastug T, Heinzelmann G, Kuyucak S, et al. (2012) Position of the third Na+ site in the aspartate transporter GltPh and the human glutamate transporter, EAAT1. PLoS One 7: e33058. doi: 10.1371/journal.pone.0033058
![]() |
[81] |
Groeneveld M, Slotboom DJ (2010) Na(+):aspartate coupling stoichiometry in the glutamate transporter homologue Glt(Ph). Biochemistry 49: 3511-3513. doi: 10.1021/bi100430s
![]() |
[82] |
Larsson HP, Wang X, Lev B, et al. (2010) Evidence for a third sodium-binding site in glutamate transporters suggests an ion/substrate coupling model. Proc Natl Acad Sci U S A 107: 13912-13917. doi: 10.1073/pnas.1006289107
![]() |
[83] |
DeChancie J, Shrivastava IH, Bahar I (2011) The mechanism of substrate release by the aspartate transporter GltPh: insights from simulations. Mol Biosyst 7: 832-842. doi: 10.1039/C0MB00175A
![]() |
[84] |
Zomot E, Bahar I (2013) Intracellular gating in an inward-facing state of aspartate transporter Glt(Ph) is regulated by the movements of the helical hairpin HP2. J Biol Chem 288: 8231-8237. doi: 10.1074/jbc.M112.438432
![]() |
[85] |
Heinzelmann G, Kuyucak S (2014) Molecular dynamics simulations of the mammalian glutamate transporter EAAT3. PLoS One 9: e92089. doi: 10.1371/journal.pone.0092089
![]() |
[86] |
Jiang J, Shrivastava IH, Watts SD, et al. (2011) Large collective motions regulate the functional properties of glutamate transporter trimers. Proc Natl Acad Sci U S A 108: 15141-15146. doi: 10.1073/pnas.1112216108
![]() |
[87] |
Lezon TR, Bahar I (2012) Constraints imposed by the membrane selectively guide the alternating access dynamics of the glutamate transporter GltPh. Biophys J 102: 1331-1340. doi: 10.1016/j.bpj.2012.02.028
![]() |
[88] |
Das A, Gur M, Cheng MH, et al. (2014) Exploring the conformational transitions of biomolecular systems using a simple two-state anisotropic network model. PLoS Comput Biol 10: e1003521. doi: 10.1371/journal.pcbi.1003521
![]() |
[89] |
Stolzenberg S, Khelashvili G, Weinstein H (2012) Structural intermediates in a model of the substrate translocation path of the bacterial glutamate transporter homologue GltPh. J Phys Chem B 116: 5372-5383. doi: 10.1021/jp301726s
![]() |
[90] |
Grewer C, Watzke N, Rauen T, et al. (2003) Is the glutamate residue Glu-373 the proton acceptor of the excitatory amino acid carrier 1? J Biol Chem 278: 2585-2592. doi: 10.1074/jbc.M207956200
![]() |
[91] |
Heinzelmann G, Kuyucak S (2014) Molecular Dynamics Simulations Elucidate the Mechanism of Proton Transport in the Glutamate Transporter EAAT3. Biophys J 106: 2675-2683. doi: 10.1016/j.bpj.2014.05.010
![]() |
[92] |
Grewer C, Jager J, Carpenter BK, et al. (2000) A new photolabile precursor of glycine with improved properties: A tool for chemical kinetic investigations of the glycine receptor. Biochemistry 39: 2063-2070. doi: 10.1021/bi9919652
![]() |
[93] |
Grewer C, Rauen T (2005) Electrogenic glutamate transporters in the CNS: molecular mechanism, pre-steady-state kinetics, and their impact on synaptic signaling. J Membr Biol 203: 1-20. doi: 10.1007/s00232-004-0731-6
![]() |
[94] |
Gegelashvili G, Robinson MB, Trotti D, et al. (2001) Regulation of glutamate transporters in health and disease. Prog Brain Res 132: 267-286. doi: 10.1016/S0079-6123(01)32082-4
![]() |
[95] |
Santos SD, Carvalho AL, Caldeira MV, et al. (2009) Regulation of AMPA receptors and synaptic plasticity. Neuroscience 158: 105-125. doi: 10.1016/j.neuroscience.2008.02.037
![]() |
[96] |
Stephenson FA, Cousins SL, Kenny AV (2008) Assembly and forward trafficking of NMDA receptors (Review). Mol Membr Biol 25: 311-320. doi: 10.1080/09687680801971367
![]() |
[97] | Robinson MB (2002) Regulated trafficking of neurotransmitter transporters: common notes but different melodies. J Neurochem 80: 1-11. |
[98] |
Gonzalez MI, Robinson MB (2004) Protein KINASE C-Dependent Remodeling of Glutamate Transporter Function. Mol Intervent 4: 48-58. doi: 10.1124/mi.4.1.48
![]() |
[99] |
Sheldon AL, Robinson MB (2007) The role of glutamate transporters in neurodegenerative diseases and potential opportunities for intervention. Neurochem Int 51: 333-355. doi: 10.1016/j.neuint.2007.03.012
![]() |
[100] | Beart PM, O'Shea RD (2007) Transporters for L-glutamate: an update on their molecular pharmacology and pathological involvement. Br J Pharmacol 150: 5-17. |
[101] |
Poitry-Yamate CL, Vutskits L, Rauen T (2002) Neuronal-induced and glutamate-dependent activation of glial glutamate transporter function. J Neurochem 82: 987-997. doi: 10.1046/j.1471-4159.2002.01075.x
![]() |
[102] |
Benediktsson AM, Marrs GS, Tu JC, et al. (2012) Neuronal activity regulates glutamate transporter dynamics in developing astrocytes. Glia 60: 175-188. doi: 10.1002/glia.21249
![]() |
[103] |
Gonzalez-Gonzalez IM, Garcia-Tardon N, Gimenez C, et al. (2008) PKC-dependent endocytosis of the GLT1 glutamate transporter depends on ubiquitylation of lysines located in a C-terminal cluster. Glia 56: 963-974. doi: 10.1002/glia.20670
![]() |
[104] |
Sheldon AL, Gonzalez MI, Krizman-Genda EN, et al. (2008) Ubiquitination-mediated internalization and degradation of the astroglial glutamate transporter, GLT-1. Neurochem Int 53: 296-308. doi: 10.1016/j.neuint.2008.07.010
![]() |
[105] |
Martinez-Villarreal J, Garcia Tardon N, Ibanez I, et al. (2012) Cell surface turnover of the glutamate transporter GLT-1 is mediated by ubiquitination/deubiquitination. Glia 60: 1356-1365. doi: 10.1002/glia.22354
![]() |
[106] |
Sheldon AL, Gonzalez MI, Robinson MB (2006) A carboxyl-terminal determinant of the neuronal glutamate transporter, EAAC1, is required for platelet-derived growth factor-dependent trafficking. J Biol Chem 281: 4876-4886. doi: 10.1074/jbc.M504983200
![]() |
[107] |
Garcia-Tardon N, Gonzalez-Gonzalez IM, Martinez-Villarreal J, et al. (2012) Protein kinase C (PKC)-promoted endocytosis of glutamate transporter GLT-1 requires ubiquitin ligase Nedd4-2-dependent ubiquitination but not phosphorylation. J Biol Chem 287: 19177-19187. doi: 10.1074/jbc.M112.355909
![]() |
[108] |
A DA, Soragna A, Di Cairano E, et al. (2010) The Surface Density of the Glutamate Transporter EAAC1 is Controlled by Interactions with PDZK1 and AP2 Adaptor Complexes. Traffic 11: 1455-1470. doi: 10.1111/j.1600-0854.2010.01110.x
![]() |
[109] |
Traub LM (2009) Tickets to ride: selecting cargo for clathrin-regulated internalization. Nat Rev Mol Cell Biol 10: 583-596. doi: 10.1038/nrm2751
![]() |
[110] |
Sato K, Otsu W, Otsuka Y, et al. (2013) Modulatory roles of NHERF1 and NHERF2 in cell surface expression of the glutamate transporter GLAST. Biochem Biophys Res Commun 430: 839-845. doi: 10.1016/j.bbrc.2012.11.059
![]() |
[111] | Shouffani A, Kanner BI (1990) Cholesterol is required for the reconstruction of the sodium- and chloride-coupled, gamma-aminobutyric acid transporter from rat brain. J Biol Chem 265: 6002-6008. |
[112] |
Butchbach ME, Guo H, Lin CL (2003) Methyl-beta-cyclodextrin but not retinoic acid reduces EAAT3-mediated glutamate uptake and increases GTRAP3-18 expression. J Neurochem 84: 891-894. doi: 10.1046/j.1471-4159.2003.01588.x
![]() |
[113] |
Simons K, Gerl MJ (2010) Revitalizing membrane rafts: new tools and insights. Nat Rev Mol Cell Biol 11: 688-699. doi: 10.1038/nrm2977
![]() |
[114] |
Butchbach ME, Tian G, Guo H, et al. (2004) Association of excitatory amino acid transporters, especially EAAT2, with cholesterol-rich lipid raft microdomains: importance for excitatory amino acid transporter localization and function. J Biol Chem 279: 34388-34396. doi: 10.1074/jbc.M403938200
![]() |
[115] |
Zschocke J, Bayatti N, Behl C (2005) Caveolin and GLT-1 gene expression is reciprocally regulated in primary astrocytes: association of GLT-1 with non-caveolar lipid rafts. Glia 49: 275-287. doi: 10.1002/glia.20116
![]() |
[116] |
Gonzalez MI, Krizman-Genda E, Robinson MB (2007) Caveolin-1 regulates the delivery and endocytosis of the glutamate transporter, excitatory amino acid carrier 1. J Biol Chem 282: 29855-29865. doi: 10.1074/jbc.M704738200
![]() |
[117] | Ledesma MD, Dotti CG (2005) The conflicting role of brain cholesterol in Alzheimer's disease: lessons from the brain plasminogen system. Biochem Soc Symp: 129-138. |
[118] |
Tian G, Kong Q, Lai L, et al. (2010) Increased expression of cholesterol 24S-hydroxylase results in disruption of glial glutamate transporter EAAT2 association with lipid rafts: a potential role in Alzheimer's disease. J Neurochem 113: 978-989. doi: 10.1111/j.1471-4159.2010.06661.x
![]() |
[119] |
Arriza JL, Eliasof S, Kavanaugh MP, et al. (1997) Excitatory amino acid transporter 5, a retinal glutamate transporter coupled to a chloride conductance. Proc Natl Acad Sci U S A 94: 4155-4160. doi: 10.1073/pnas.94.8.4155
![]() |
[120] | Arriza JL, Fairman WA, Wadiche JI, et al. (1994) Functional comparisons of three glutamate transporter subtypes cloned from human motor cortex. J Neurosci 14: 5559-5569. |
[121] | Bridges RJ, Stanley MS, Anderson MW, et al. (1991) Conformationally defined neurotransmitter analogues. Selective inhibition of glutamate uptake by one pyrrolidine-2,4-dicarboxylate diastereomer. J Med Chem 34: 717-725. |
[122] |
Griffiths R, Dunlop J, Gorman A, et al. (1994) L-Trans-Pyrrolidine-2,4-Dicarboxylate and Cis-1-Aminocyclobutane-1,3-Dicarboxylate Behave as Transportable, Competitive Inhibitors of the High-Affinity Glutamate Transporters. Biochem Pharmacol 47: 267-274. doi: 10.1016/0006-2952(94)90016-7
![]() |
[123] | Vandenberg RJ, Mitrovic AD, Chebib M, et al. (1997) Contrasting modes of action of methylglutamate derivatives on the excitatory amino acid transporters, EAAT1 and EAAT2. Mol Pharmacol 51: 809-815. |
[124] |
Huang S, Ryan RM, Vandenberg RJ (2009) The role of cation binding in determining substrate selectivity of glutamate transporters. J Biol Chem 284: 4510-4515. doi: 10.1074/jbc.M808495200
![]() |
[125] |
Eliasof S, McIlvain HB, Petroski RE, et al. (2001) Pharmacological characterization of threo-3-methylglutamic acid with excitatory amino acid transporters in native and recombinant systems. J Neurochem 77: 550-557. doi: 10.1046/j.1471-4159.2001.00253.x
![]() |
[126] |
Kanai Y, Hediger MA (1992) Primary structure and functional characterization of a high-affinity glutamate transporter. Nature 360: 467-471. doi: 10.1038/360467a0
![]() |
[127] |
Rauen T, Jeserich G, Danbolt NC, et al. (1992) Comparative analysis of sodium-dependent L-glutamate transport of synaptosomal and astroglial membrane vesicles from mouse cortex. FEBS Lett 312: 15-20. doi: 10.1016/0014-5793(92)81401-7
![]() |
[128] | Zerangue N, Kavanaugh MP (1996) Interaction of L-cysteine with a human excitatory amino acid transporter. J Physiol 493 ( Pt 2): 419-423. |
[129] |
Roberts PJ, Watkins JC (1975) Structural requirements for the inhibition for L-glutamate uptake by glia and nerve endings. Brain Res 85: 120-125. doi: 10.1016/0006-8993(75)91016-1
![]() |
[130] | Wilson DF, Pastuszko A (1986) Transport of Cysteate by Synaptosomes Isolated from Rat-Brain - Evidence That It Utilizes the Same Transporter as Aspartate, Glutamate, and Cysteine Sulfinate. J Neurochem 47: 1091-1097. |
[131] |
Vandenberg RJ, Mitrovic AD, Johnston GAR (1998) Serine-O-sulphate transport by the human glutamate transporter, EAAT2. Br J Pharmacol 123: 1593-1600. doi: 10.1038/sj.bjp.0701776
![]() |
[132] |
Bender AS, Woodbury DM, White HS (1989) Beta-Dl-Methylene-Aspartate, an Inhibitor of Aspartate-Aminotransferase, Potently Inhibits L-Glutamate Uptake into Astrocytes. Neurochem Res 14: 641-646. doi: 10.1007/BF00964873
![]() |
[133] |
Mitrovic AD, Amara SG, Johnston GA, et al. (1998) Identification of functional domains of the human glutamate transporters EAAT1 and EAAT2. J Biol Chem 273: 14698-14706. doi: 10.1074/jbc.273.24.14698
![]() |
[134] |
Vandenberg RJ, Mitrovic AD, Johnston GA (1998) Serine-O-sulphate transport by the human glutamate transporter, EAAT2. Br J Pharmacol 123: 1593-1600. doi: 10.1038/sj.bjp.0701776
![]() |
[135] | Campiani G, De Angelis M, Armaroli S, et al. (2001) A rational approach to the design of selective substrates and potent nontransportable inhibitors of the excitatory amino acid transporter EAAC1 (EAAT3). New glutamate and aspartate analogues as potential neuroprotective agents. J Med Chem 44: 2507-2510. |
[136] |
Danbolt NC (2001) Glutamate uptake. Prog Neurobiol 65: 1-105. doi: 10.1016/S0301-0082(00)00067-8
![]() |
[137] |
Wang GJ, Chung HJ, Schnuer J, et al. (1998) Dihydrokainate-sensitive neuronal glutamate transport is required for protection of rat cortical neurons in culture against synaptically released glutamate. Eur J Neurosci 10: 2523-2531. doi: 10.1046/j.1460-9568.1998.00256.x
![]() |
[138] | Shimamoto K, Lebrun B, Yasuda-Kamatani Y, et al. (1998) DL-threo-beta-benzyloxyaspartate, a potent blocker of excitatory amino acid transporters. Mol Pharmacol 53: 195-201. |
[139] |
Boudker O, Verdon G (2010) Structural perspectives on secondary active transporters. Trends Pharmacol Sci 31: 418-426. doi: 10.1016/j.tips.2010.06.004
![]() |
[140] | Shigeri Y, Shimamoto K, Yasuda-Kamatani Y, et al. (2001) Effects of threo-beta-hydroxyaspartate derivatives on excitatory amino acid transporters (EAAT4 and EAAT5). J Neurochem 79: 297-302. |
[141] |
Shimamoto K, Shigeri Y, Yasuda-Kamatani Y, et al. (2000) Syntheses of optically pure beta-hydroxyaspartate derivatives as glutamate transporter blockers. Bioorg Med Chem Lett 10: 2407-2410. doi: 10.1016/S0960-894X(00)00487-X
![]() |
[142] |
Lebrun B, Sakaitani M, Shimamoto K, et al. (1997) New beta-hydroxyaspartate derivatives are competitive blockers for the bovine glutamate/aspartate transporter. J Biol Chem 272: 20336-20339. doi: 10.1074/jbc.272.33.20336
![]() |
[143] |
Shimamoto K, Sakai R, Takaoka K, et al. (2004) Characterization of novel L-threo-beta-benzyloxyaspartate derivatives, potent blockers of the glutamate transporters. Mol Pharmacol 65: 1008-1015. doi: 10.1124/mol.65.4.1008
![]() |
[144] | Shimamoto K, Otsubo Y, Shigeri Y, et al. (2007) Characterization of the tritium-labeled analog of L-threo-beta-benzyloxyaspartate binding to glutamate transporters. Mol Pharmacol 71: 294-302. |
[145] |
Martinov V, Dehnes Y, Holmseth S, et al. (2014) A novel glutamate transporter blocker, LL-TBOA, attenuates ischaemic injury in the isolated, perfused rat heart despite low transporter levels. Eur J Cardiothorac Surg 45: 710-716. doi: 10.1093/ejcts/ezt487
![]() |
[146] | Dunlop J, Eliasof S, Stack G, et al. (2003) WAY-855 (3-amino-tricyclo[2.2.1.02.6]heptane-1,3-dicarboxylic acid): a novel, EAAT2-preferring, nonsubstrate inhibitor of high-affinity glutamate uptake. Br J Pharmacol 140: 839-846. |
[147] |
Dunlop J, McIlvain HB, Carrick TA, et al. (2005) Characterization of novel aryl-ether, biaryl, and fluorene aspartic acid and diaminopropionic acid analogs as potent inhibitors of the high-affinity glutamate transporter EAAT2. Mol Pharmacol 68: 974-982. doi: 10.1124/mol.105.012005
![]() |
[148] |
Campiani G, Fattorusso C, De Angelis M, et al. (2003) Neuronal high-affinity sodium-dependent glutamate transporters (EAATs): targets for the development of novel therapeutics against neurodegenerative diseases. Curr Pharm Des 9: 599-625. doi: 10.2174/1381612033391261
![]() |
[149] | Funicello M, Conti P, De Amici M, et al. (2004) Dissociation of [3H]L-glutamate uptake from L-glutamate-induced [3H]D-aspartate release by 3-hydroxy-4,5,6,6a-tetrahydro-3aH-pyrrolo[3,4-d]isoxazole-4-carboxylic acid and 3-hydroxy-4,5,6,6a-tetrahydro-3aH-pyrrolo[3,4-d]isoxazole-6-carboxylic acid, two conformationally constrained aspartate and glutamate analogs. Mol Pharmacol 66: 522-529. |
[150] |
Callender R, Gameiro A, Pinto A, et al. (2012) Mechanism of inhibition of the glutamate transporter EAAC1 by the conformationally constrained glutamate analogue (+)-HIP-B. Biochemistry 51: 5486-5495. doi: 10.1021/bi3006048
![]() |
[151] |
Erichsen MN, Huynh TH, Abrahamsen B, et al. (2010) Structure-activity relationship study of first selective inhibitor of excitatory amino acid transporter subtype 1: 2-Amino-4-(4-methoxyphenyl)-7-(naphthalen-1-yl)-5-oxo-5,6,7,8-tetrahydro-4H-chromene-3-carbonitrile (UCPH-101). J Med Chem 53: 7180-7191. doi: 10.1021/jm1009154
![]() |
[152] |
Huynh THV, Shim I, Bohr H, et al. (2012) Structure-Activity Relationship Study of Selective Excitatory Amino Acid Transporter Subtype 1 (EAAT1) Inhibitor 2-Amino-4-(4-methoxyphenyl)-7-(naphthalen-1-yl)-5-oxo-5,6,7,8-tetrahydro-4H-chromene-3-carbonitrile (UCPH-101) and Absolute Configurational Assignment Using Infrared and Vibrational Circular Dichroism Spectroscopy in Combination with ab Initio Hartree-Fock Calculations. J Med Chem 55: 5403-5412. doi: 10.1021/jm300345z
![]() |
[153] |
Abrahamsen B, Schneider N, Erichsen MN, et al. (2013) Allosteric Modulation of an Excitatory Amino Acid Transporter: The Subtype-Selective Inhibitor UCPH-101 Exerts Sustained Inhibition of EAAT1 through an Intramonomeric Site in the Trimerization Domain. J Neurosci 33: 1068-1087. doi: 10.1523/JNEUROSCI.3396-12.2013
![]() |
[154] |
Rothstein JD, Patel S, Regan MR, et al. (2005) Beta-lactam antibiotics offer neuroprotection by increasing glutamate transporter expression. Nature 433: 73-77. doi: 10.1038/nature03180
![]() |
[155] |
Fontana AC, de Oliveira Beleboni R, Wojewodzic MW, et al. (2007) Enhancing glutamate transport: mechanism of action of Parawixin1, a neuroprotective compound from Parawixia bistriata spider venom. Mol Pharmacol 72: 1228-1237. doi: 10.1124/mol.107.037127
![]() |
[156] |
Fontana ACK, Guizzo R, Beleboni RD, et al. (2003) Purification of a neuroprotective component of Parawixia bistriata spider venom that enhances glutamate uptake. Br J Pharmacol 139: 1297-1309. doi: 10.1038/sj.bjp.0705352
![]() |
[157] |
Xing XC, Chang LC, Kong QM, et al. (2011) Structure-activity relationship study of pyridazine derivatives as glutamate transporter EAAT2 activators. Bioorg Med Chem Lett 21: 5774-5777. doi: 10.1016/j.bmcl.2011.08.009
![]() |
1. | Amirreza Naderipour, Zulkurnain Abdul-Malek, Mohammad Hajivand, Zahra Mirzaei Seifabad, Mohammad Ali Farsi, Saber Arabi Nowdeh, Iraj Faraji Davoudkhani, Spotted hyena optimizer algorithm for capacitor allocation in radial distribution system with distributed generation and microgrid operation considering different load types, 2021, 11, 2045-2322, 10.1038/s41598-021-82440-9 | |
2. | Nibedan Panda, Santosh Kumar Majhi, Rosy Pradhan, A Hybrid Approach of Spotted Hyena Optimization Integrated with Quadratic Approximation for Training Wavelet Neural Network, 2022, 47, 2193-567X, 10347, 10.1007/s13369-022-06564-4 | |
3. | Davut Izci, Serdar Ekinci, Hatice Lale Zeynelgil, Controlling an automatic voltage regulator using a novel Harris hawks and simulated annealing optimization technique, 2023, 2578-0727, 10.1002/adc2.121 | |
4. | Nikhil Paliwal, Laxmi Srivastava, Manjaree Pandit, Rao algorithm based optimal Multi‐term FOPID controller for automatic voltage regulator system , 2022, 43, 0143-2087, 1707, 10.1002/oca.2926 | |
5. | Serdar Ekinci, Davut Izci, Erdal Eker, Laith Abualigah, An effective control design approach based on novel enhanced aquila optimizer for automatic voltage regulator, 2023, 56, 0269-2821, 1731, 10.1007/s10462-022-10216-2 | |
6. | Abdelhakim Idir, Laurent Canale, Yassine Bensafia, Khatir Khettab, Design and Robust Performance Analysis of Low-Order Approximation of Fractional PID Controller Based on an IABC Algorithm for an Automatic Voltage Regulator System, 2022, 15, 1996-1073, 8973, 10.3390/en15238973 | |
7. | Shafih Ghafori, Farhad Soleimanian Gharehchopogh, Advances in Spotted Hyena Optimizer: A Comprehensive Survey, 2022, 29, 1134-3060, 1569, 10.1007/s11831-021-09624-4 | |
8. | Yi Zhang, XianBo Sun, Li Zhu, ShengXin Yang, YueFei Sun, Qingling Wang, Research on Three-Phase Unbalanced Commutation Strategy Based on the Spotted Hyena Optimizer Algorithm, 2022, 2022, 1099-0526, 1, 10.1155/2022/2092421 | |
9. | Chunhui Mo, Xiaofeng Wang, Lin Zhang, 2022, Chapter 10, 978-981-19-8151-7, 142, 10.1007/978-981-19-8152-4_10 | |
10. | Davut Izci, Serdar Ekinci, H. Lale Zeynelgil, John Hedley, Performance evaluation of a novel improved slime mould algorithm for direct current motor and automatic voltage regulator systems, 2022, 44, 0142-3312, 435, 10.1177/01423312211037967 | |
11. | Davut Izci, Serdar Ekinci, Seyedali Mirjalili, Optimal PID plus second-order derivative controller design for AVR system using a modified Runge Kutta optimizer and Bode’s ideal reference model, 2022, 2195-268X, 10.1007/s40435-022-01046-9 | |
12. | Nikhil Paliwal, Laxmi Srivastava, Manjaree Pandit, Equilibrium optimizer tuned novel FOPID‐DN controller for automatic voltage regulator system , 2021, 31, 2050-7038, 10.1002/2050-7038.12930 | |
13. | Muhammad Imran Nadeem, Kanwal Ahmed, Dun Li, Zhiyun Zheng, Hafsa Naheed, Abdullah Y. Muaad, Abdulrahman Alqarafi, Hala Abdel Hameed, SHO-CNN: A Metaheuristic Optimization of a Convolutional Neural Network for Multi-Label News Classification, 2022, 12, 2079-9292, 113, 10.3390/electronics12010113 | |
14. | Özay Can, Cenk Andiç, Serdar Ekinci, Davut Izci, Enhancing transient response performance of automatic voltage regulator system by using a novel control design strategy, 2023, 0948-7921, 10.1007/s00202-023-01777-8 | |
15. | Sudhakar Babu Thanikanti, T. Yuvaraj, R. Hemalatha, Belqasem Aljafari, Nnamdi I. Nwulu, Optimizing Radial Distribution System With Distributed Generation and EV Charging: A Spotted Hyena Approach, 2024, 12, 2169-3536, 113422, 10.1109/ACCESS.2024.3438456 | |
16. | Bora Çavdar, Erdinç Şahin, Erhan Sesli, On the assessment of meta-heuristic algorithms for automatic voltage regulator system controller design: a standardization process, 2024, 106, 0948-7921, 5801, 10.1007/s00202-024-02314-x | |
17. |
Bora Çavdar, Erdinç Şahin, Ömür Akyazı, Fatih Mehmet Nuroğlu,
A novel optimal PI\uplambda1I\uplambda2D\upmu1D\upmu2 controller using mayfly optimization algorithm for automatic voltage regulator system,
2023,
35,
0941-0643,
19899,
10.1007/s00521-023-08834-0
|
|
18. | Rohit Salgotra, Pankaj Sharma, Saravanakumar Raju, Amir H. gandomi, A Contemporary Systematic Review on Meta-heuristic Optimization Algorithms with Their MATLAB and Python Code Reference, 2024, 31, 1134-3060, 1749, 10.1007/s11831-023-10030-1 | |
19. | Ömer Öztürk, Bora Çavdar, Otomatik Gerilim Regülatörü Sistemi Denetleyici Tasarımı için Meta-Sezgisel Algoritmaların Performansı, 2024, 14, 2564-7377, 2258, 10.31466/kfbd.1558173 | |
20. | Tapas Si, Péricles B. C. Miranda, Utpal Nandi, Nanda Dulal Jana, Ujjwal Maulik, Saurav Mallik, Mohd Asif Shah, QSHO: Quantum spotted hyena optimizer for global optimization, 2025, 58, 1573-7462, 10.1007/s10462-024-11072-y | |
21. | Fei Dai, Tianli Ma, Song Gao, Optimal Design of a Fractional Order PIDD2 Controller for an AVR System Using Hybrid Black-Winged Kite Algorithm, 2025, 14, 2079-9292, 2315, 10.3390/electronics14122315 |
Controller parameters | Min. value | Max. value |
${K_p}$ | 0 | 1.5 |
${K_i}$ | 0 | 1.0 |
${K_d}$ | 0 | 1.0 |
Algorithms | Parameter values |
SCA | ${r_2} \in [0, 2\pi]$, $a = 2$, ${r_4} \in [0, 1]$. The population size is 50. |
FPA | The proximity probability p = 0.8, the population size is 50. |
PSOGSA | ${c_1} = {c_2} = 2$, ${\omega _{\max }} = 0.3, {\omega _{\min }} = 0.1$, ${G_0} = 1$, $\alpha = 5$ the population size is 50. |
GWO | Components $\vec \alpha \in [0, 2]$ over the course of iterations. The population size is 50. |
SHO | The parameter is $\vec h \in [0, 5]$ over the course of iterations, the population size is 50. |
ISHO | ${\vec h_{initial}} = 5$, ${h_{final}} = 0$, $u \in [0, 2.0]$. The population size is 50. |
Algorithms | SCA | FPA | PSOGSA | GWO | SHO | ISHO |
${K_p}$ | 1.4155 | 1.4230 | 1.4012 | 1.3168 | 1.3079 | 1.0263 |
${K_i}$ | 0.9721 | 0.9974 | 0.9602 | 0.9051 | 0.9234 | 0.7115 |
${K_d}$ | 0.4546 | 0.4302 | 0.4601 | 0.4219 | 0.3985 | 0.3154 |
Best | 0.0328 | 0.0329 | 0.0328 | 0.0329 | 0.0334 | 0.0327 |
Worst | 0.0382 | 0.0380 | 0.0333 | 0.0369 | 0.0370 | 0.0331 |
Ave | 0.0344 | 0.0341 | 0.0330 | 0.0344 | 0.0347 | 0.0328 |
Std | 0.0015 | 0.0012 | 1.5427 × 10−4 | 0.0012 | 9.8111 × 10−4 | 8.4078 × 10−5 |
Algorithms | SCA | FPA | PSOGSA | GWO | SHO | ISHO |
Maximum overshoots | 1.1751 | 1.1601 | 1.1383 | 1.1767 | 1.2017 | 1.120 |
Peak time (s) | 0.3821 | 0.3923 | 0.3883 | 0.3924 | 0.3951 | 0.4160 |
Settling time (s) | 0.6930 | 1.003 | 0.9723 | 0.9494 | 0.9288 | 0.8481 |
Rise time (s) | 0.2382 | 0.2207 | 0.2883 | 0.2274 | 0.2010 | 0.3021 |
Controller parameters | Min. value | Max. value |
${K_p}$ | 0 | 1.5 |
${K_i}$ | 0 | 1.0 |
${K_d}$ | 0 | 1.0 |
Algorithms | Parameter values |
SCA | ${r_2} \in [0, 2\pi]$, $a = 2$, ${r_4} \in [0, 1]$. The population size is 50. |
FPA | The proximity probability p = 0.8, the population size is 50. |
PSOGSA | ${c_1} = {c_2} = 2$, ${\omega _{\max }} = 0.3, {\omega _{\min }} = 0.1$, ${G_0} = 1$, $\alpha = 5$ the population size is 50. |
GWO | Components $\vec \alpha \in [0, 2]$ over the course of iterations. The population size is 50. |
SHO | The parameter is $\vec h \in [0, 5]$ over the course of iterations, the population size is 50. |
ISHO | ${\vec h_{initial}} = 5$, ${h_{final}} = 0$, $u \in [0, 2.0]$. The population size is 50. |
Algorithms | SCA | FPA | PSOGSA | GWO | SHO | ISHO |
${K_p}$ | 1.4155 | 1.4230 | 1.4012 | 1.3168 | 1.3079 | 1.0263 |
${K_i}$ | 0.9721 | 0.9974 | 0.9602 | 0.9051 | 0.9234 | 0.7115 |
${K_d}$ | 0.4546 | 0.4302 | 0.4601 | 0.4219 | 0.3985 | 0.3154 |
Best | 0.0328 | 0.0329 | 0.0328 | 0.0329 | 0.0334 | 0.0327 |
Worst | 0.0382 | 0.0380 | 0.0333 | 0.0369 | 0.0370 | 0.0331 |
Ave | 0.0344 | 0.0341 | 0.0330 | 0.0344 | 0.0347 | 0.0328 |
Std | 0.0015 | 0.0012 | 1.5427 × 10−4 | 0.0012 | 9.8111 × 10−4 | 8.4078 × 10−5 |
Algorithms | SCA | FPA | PSOGSA | GWO | SHO | ISHO |
Maximum overshoots | 1.1751 | 1.1601 | 1.1383 | 1.1767 | 1.2017 | 1.120 |
Peak time (s) | 0.3821 | 0.3923 | 0.3883 | 0.3924 | 0.3951 | 0.4160 |
Settling time (s) | 0.6930 | 1.003 | 0.9723 | 0.9494 | 0.9288 | 0.8481 |
Rise time (s) | 0.2382 | 0.2207 | 0.2883 | 0.2274 | 0.2010 | 0.3021 |