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0ПРИБОРОСТРОЕНИЕ, МЕТРОЛОГИЯ И ИНФОРМАЦИОННО-ИЗМЕРИТЕЛЬНЫЕ
ВЕСТНИК ТСГУ. 2023. № 3 (70)
ПРИБОРЫ И СИСТЕМЫ
YflK 517.977.57
Fu Yu, Qin Hongwu, Wang Tianze, Zhang Ziyang, Chye En Un, V. V. Voronin
AN IMPROVED PELICAN OPTIMIZATION ALGORITHM BASED ON CONDOR
Fu Yu - School of Electronic and Information Engineering, Changchun University, Changchun, email: 1315914111@qq.com (China); Qin Hongwu - PhD, Professor, School of Electronic and Information Engineering, Changchun University, Changchun, email: hongwuqin@live.cn (China); Wang Tianze - School of Electronic and Information Engineering, Changchun University, Changchun, email: 568260932@qq.com (China); Zhang Ziyang - School of Electronic and Information Engineering, Changchun University, Changchun, email: zhangziyang3@qq.com (China); Chye En Un - Doctor of Technical Sciences, Professor, Head of the Department of Automation and System Engineering, Pacific National University, Khabarovsk, Russian Federation, e-mail: 000487@pnu.ed.ru; Voronin V.V. - Doctor of Technical Sciences, Professor, Department of Automation and System Engineering, Pacific National University, Khabarovsk, Russian Federation, e-mail: 004183@pnu.edu.ru
For the original Pelican Optimization Algorithm (POA), the local search ability is strong and the local optimal situation is easy to occur. Based on the hunting behavior of Condor, an improved Pelican algorithm (BPOA) is proposed in this paper to optimize the hunting mode of pelicans and to achieve high search capability and accuracy. Through standard benchmark function test, compared with the original Pelican Algorithm and Grey Wolf Optimization Algorithm (GWO), the results show that BPOA has faster convergence speed and better global search ability.
Keywords: optimization algorithm, Pelican optimization algorithm, Condor optimization algorithm, Grey Wolf optimization algorithm
Introduction
In recent years, with the continuous update and iteration of intelligent optimization, more and more intelligent optimization algorithms are known by people. At present, the widely recognized swarm intelligent optimization algorithm is particle swarm optimization (PSO) algorithm [1], ant colony optimization (ACO) [2], Grey Wolf optimization algorithm [3], etc. Many scholars apply different algorithms to various practical problems on the social surface. Aiming at the transmission function in the design of two-dimensional (2-D) finite impulse long response (FIR) digital filter, a transmission function phase interval optimization design algorithm based on cuckoo optimization algorithm is proposed. An optimized Back Propagation (BP)
© Fu Yu, Qin Hongwu, Wang Tianze, Zhang Ziyang, Chye En Un, Voronin V.V., 2023
BECTHHK TOry. 2023. № 3 (70)
neural network based on the improved Firefly Algorithm (FA) [4] was constructed to estimate the State of Health (SOH) of Li-ion battery. The global optimization ability and fast convergence speed of firefly algorithm are utilized to optimize the weights and thresholds of BP neural network [5], and Levy Flight is introduced to enhance the global search ability, expand the search scope, and improve the estimation accuracy [6]. In the process of navigation and obstacle avoidance, the wall crawling robot cannot accurately determine the position of obstacle nodes, resulting in poor obstacle avoidance effect. Therefore, some scholars proposed a navigational obstacle avoidance method of wall crawling robot based on locust optimization algorithm [7]. With the increasing difficulty and complexity of the problem, the accuracy and speed of the algorithm are required to be higher and higher. The improved Pelican algorithm proposed in this paper speeds up the iteration speed of the algorithm while improving the accuracy.
Pelican Optimization Algorithm
The main idea of pelican optimization algorithm is to simulate the natural behavior of pelicans in the process of hunting. In pelican optimization algorithm, the search agent is the pelican looking for food sources, and then a mathematical model of pelican optimization algorithm is proposed to solve the optimization problem. The proposed POA is a population-based algorithm in which pelicans are members of the population [8]. In a population-based algorithm, each population member implies a candidate solution [9]. Each population member proposes a value for the optimization problem variable based on its position in the search space. Pelican populations can be represented by the following population matrix:
where X is the population matrix of pelican, xWmis the new status of the Nth pelican in the mth dimension. N is the population number of pelicans. m is the dimension of solving the problem. Formula (2) is used to initialize the population members randomly according to the lower and upper bounds of the problem.
Where lj is the lower bound, uj is the upper bound, N is the population number of pelicans; m is the dimension of solving the problem.
The POA simulates the pelican's behavior and strategies when attacking and hunting prey to update candidate solutions. There are two stages to this hunting strategy, the exploration stage and the extraction stage.
X =
(1)
•v* -y ... •v*
Xij =lj+rand(uj - lj), i= 1,2,..., N, j= 1,2,..., m (2)
AN IMPROVED PELICAN OPTIMIZATION -
ALGORITHM BASED ON CONDOR BECIHHK TOrY 2023 № 3
In the first stage, the pelican identifies the location of its prey and then moves towards this identified area. Modeling the pelican's strategy led to the search space scanning and the exploration capabilities of the proposed POA in discovering different areas of the search space. One of the most important aspects of POA is that the location of prey is randomly generated in the search space. This increases the POA's ability to explore the space for precise search solutions. In formula (3), the above concepts and the pelican's strategy of moving to the prey position are mathematically simulated.
PI - i Xi'j + rand * (Pi - IXi'iFp < Fi l' 1 ( Xi'j + rand * (Xij — Pj), else,
where x[1jis the new status of the ith pelican in the jth dimension, I is a random number which is equal to one or two, Pj is the location of prey in the j-th dimension, and FP is its objective function value. The parameter I is a number that can be randomly equal to 1 or 2. This parameter is randomly selected for each iteration and for each member. When the value of this parameter is equal to two, it brings more displacement for a member, which can lead that member to newer areas of the search space. Therefore, parameter I affects the POA exploration power to accurately scan the search space.
In the POA, the pelican's new position is accepted if the value of the objective function is improved at that position. In this type of update, which is called a valid update, the algorithm cannot move to a non-optimal region. This process is modeled using formula
Hf: Ffl 2 ' (4)
where Xf1 is the current individual, Xi is the best individual, Ff1 is the objective function value of the current individual, and Ft is the current optimal objective function value.
In the second stage, after the pelicans reach the surface, they spread their wings above the water, move the fish upward, and then place the prey in their throat pouch. This strategy results in more fish being caught by pelicans in the areas being attacked. Modeling this behavior in pelicans, the POA converges to a better point in the hunting area. This process improves the POA's local search capability and the ability to utilize sensors. From a mathematical point of view, the algorithm must examine points near the pelican position in order to converge to a better solution. In formula (5), this behavior of pelicans during hunting is mathematically simulated.
4,2j=Hi+0.02(1-1-)(2 * rand — 1) * xtJ (5)
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Fu Yu, Qin Hongwu, Wang Tianze, BECI™KTOry. 2023 № 3 (70) Zhang Ziyang, Chye En Un, Voronin V^
Where Xij is the current individual, t is the number of current iterations, and T is the maximum number of iterations, rand is a random number between 0 and 1.
At this stage, valid updates are also used to accept or reject the new pelican location, which is modeled in formula (4).
The improved Pelican algorithm
The exploration phase remains unchanged, and the original exploration method is adopted for modeling, namely, as shown in formula (3) and formula (4), to explore the possible optimal solution. In the mining phase, swooping strategy is introduced, taking into account the different movements of pelicans when they hunt. The random number is multiplied by the pelican in the best position at the moment, which is the best solution at the moment. In addition, to describe the trajectory in polar coordinates, first calculate the current poles of the X and Y axes, multiply the difference between the current point and the average point by the extreme point of the X axis plus the difference between the current point and the optimal point by the pole of the Y axis, in which the average and the optimal point need to be multiplied by a random number to increase the pelican's approach to the optimal point and the center point. Finally, the contemporary optimal solution is obtained. As shown in formula (6) -(8).
xf2j =Xij+(-R+2rand) * Xij (6)
R=0.02*(1 - (7)
xf2j- =rand * Xij + x(i) * step + y(i) + stepl (8)
Where, rand is a random matrix form generated by random numbers, y(i) is extreme point obtained through the calculation of polar coordinates, and step and stepl are the distances from y(i) to x andy, respectively. By modifying the original production stage, the pelican is closer to the optimal solution and improves its performance. General steps of the algorithm:
1. Input population number, problem dimension, number of iterations, relevant parameters;
2. Initialize population and corresponding fitness value;
3. For t=1 to T;
4. Generate random pelicans ;
5. Record the best pelicans of the first generation and the best position;
6. For i=1 to N;
7. Start the first stage - exploration stage, and compare the fitness values calculated by formulas (3) and (4);
8. With the best of the first generation to renew pelican population;
AN IMPROVED PELICAN OPTIMIZATION -
ALGORITHM BASED ON CONDOR BEC™K TOry 2023 № 3 C70)
9. Start the second stage - mining stage, formula (6) ~ (8) was used to update the population;
10. End;
11. Output contemporary optimal individuals;
12. End;
13. Output global optimal individuals;
Fig. 1. Algorithm flow chart
Experiment and conclusion
In order to fully verify the superiority of the algorithm, 13 widely used standard functions are selected in this paper for optimization testing. The test functions are shown in Table 1, among which f ... f7 is a single-peak standard reference function, f -fn is a multi-mode standard reference function. Single-peak function can test the local optimization ability of the algorithm, while multi-peak function can test the global search ability of the algorithm. The test results are instructive.
3Tl
Table 1
Classic benchmark functions
Expression D Section Best
f1(x) = V" x2 Sphere 30 [-100, 100] 0
f (x) = V" Ixl + n" Ixl J^ ' A Hi-1 «1 Schwefel2.22 30 [-10, 10] 0
f3(x) = IL (E, xj )2 Schwefel1.2 30 [-100, 100] 0
f4(x) = max« {|x«| , 1 <« < "} Schwefel2.21 30 [-100, 100] 0
f5 (x)=i":; [100 (x«,1 - xf )2+(x -1)2 ] Rosenbrock 30 [-30, 30] 0
2 f6( x) = I"-1 ([ x + 0.5]) Step 30 [-100, 100] 0
f (x) = I" 11x4 + random[0, 1) 30 [-1.28, 1.28] 0
f8(x) = I":1 -x sin ) 30 [-500, 500] -418.98 *5
f (x) = V" [x2 - 10cos (2nx.) + 1öl Ii-i L ' V ,J J Rastrigin 30 [-5.12, 5.12] 0
f0 (x) = -20exp(-0.2^1 / "I" j x,2 -exp(1/"I" j cos(2^x. ))+20+e Ackley 30 [-32, 32] 0
fu(x) = 1/4000l":1 xf -n^-1cos(x,/4i) +1 Griewank 30 [-600, 600] 0
f2( x) = */n {wan^) + (y -1)2 [1 + sin(^yj] + (yn -1)2} + I" u(x. ,10,100,4) y -1 + x« +1 30 [-50, 50] 0
f3 (x) = 0.1{sin(3^x) + (x, -1)2 [1+sin(3^x, +1)] + (x -1)2[1+sin(2^x„)]} +I"._u(xI ,5,100,4) 30 [-50, 50] 0
ik(%i — a)m, Xi > a,
0, — a < xt < a, k(—Xi — a)m, Xi < —a.
Fu Yu, Qin Hongwu, Wang Tianze, HECIIfflK Tory. 2023. № 3 (70) ^ ziyang, Chye En Un, Voronin V^
AN IMPROVED PELICAN OPTIMIZATION -
ALGORITHM BASED ON CONDOR BEC™K TOry 2023 № 3 C70)
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Fig. 2. Experimental result chart
Conclusion
Under the premise that the population size of the three optimization algorithms is 30 and the number of iterations is 500, the experimental results show that the convergence rate and the optimal solution of the BPOA proposed in this paper are superior to the original POA and GWO algorithms in both single-peak function and multi-peak function. It shows that the improved algorithm in this paper is effective in function, and it needs to be further perfected in practical application.
Acknowledgements
This work was supported by the project of Jilin Provincial Science and Technology Department (20210402081GH), the Project of Jilin Provincial Development and Reform Commission (2023C042-4), the Innovation and Entrepreneurship Talent Funding Project of Jilin Province (2023RY17) and the Changchun University Climbing Program (Project No. 2021JBD33L39).
AN IMPROVED PELICAN OPTIMIZATION -
ALGORITHM BASED ON CONDOR BEC™K TOry 2023 № 3 C70)
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ВЕСТНИК ТОГУ. 2023. № 3 (70)
Заглавие: Улучшенный алгоритм оптимизации PELICAN на основе CON-
Авторы:
Фу Юй - Чанчуньский университет (КНР)
Цинь Хуну - Чанчуньский университет (КНР)
Ван Тянзэ - Чанчуньский университет (КНР)
Чжан Цзыян - Чанчуньский университет (КНР)
Чье Ен Ун - Тихоокеанский государственный университет (Россия)
Воронин В.В. - Тихоокеанский государственный университет (Россия)
Аннотация: Оригинальный алгоритм оптимизации Pelican (POA) обладает хорошими возможностями локальной оптимизации. На основе охотничьего поведения кондора в этой статье предлагается улучшенный алгоритм Pelican (BPOA) для решения задач оптимизации с повышенной точностью поиска. Результаты стандартного эталонного функционального теста по сравнению с исходным алгоритмом Pelican и алгоритмом оптимизации Grey Wolf (GWO) показывают, что BPOA имеет более высокую скорость сходимости и лучшие возможности глобального поиска.
Ключевые слова: алгоритм оптимизации Pelican, алгоритм оптимизации Condor, алгоритм оптимизации Grey Wolf.
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