CC BY
0ПРИБОРОСТРОЕНИЕ, МЕТРОЛОГИЯ И ИНФОРМАЦИОННО-ИЗМЕРИТЕЛЬНЫЕ ПРИБОРЫ И СИСТЕМЫ
ВЕСТНИК ТОГУ. 2023. № 2 (69)
ИГ
УДК 519.8
Qin Hongwu, Wang Lizheng, Liu Zhengi, Chye En Un, V.V. Voronin
RESEARCH ON SEAGULL OPTIMIZATION ALGORITHM BASED ON ADAPTIVE WEIGHT
Qin Hongwu - PhD, Professor, School of Electronic and Information Engineering, Changchun University, Changchun, email: hongwuqin@live.cn (China); Wang Lizheng - Master of engineering, School of Electronic and Information Engineering, Changchun University, Changchun, email: 971656545@qq.com (China); Liu Zhengi - Master of engineering, School of Electronic and Information Engineering, Changchun University, Changchun, email: 603976139@qq.com (China); Chye En Un - Pacific National University, Khabarovsk, Russian Federation; Voronin V. V. - Pacific National University, Khabarovsk, Russian Federation
Seagull Optimization Algorithm (SOA) is an intelligent optimization algorithm with a simple structure, easy implementation, and excellent global and local search capabilities. However, the SOA also has some disadvantages, such as its easy fall into local optimization, dependence on the optimal individual, and low accuracy of solution. To solve these problems, this paper proposes an improved Seagull Optimization Algorithm (ISAO) based on adaptive weight. Aiming at the SOA search ability, convergence speed, and over-reliance on the best individual, the SOA is improved by using multiple excellent individuals, increasing the position update weight, and improving the control factor. The experimental results show that the accuracy and precision of the improved method are higher than those of the standard Seagull optimization algorithm.
Keywords: Seagull optimization algorithm, weight, control factor, intelligent algorithm.
Introduction
Nowadays, swarm intelligence optimization algorithms are often widely used in time series prediction [1], path planning [2], clustering analysis [3] and other problems because of their advantages of simple structure, fast convergence speed and few adjustment parameters. As an intelligent optimization algorithm, the Seagull optimization algorithm has attracted wide attention due to its simple structure, easy implementation, and excellent global search and local search capabilities. However, SOA is also prone to fall into local optimization, premature convergence, and low accuracy, which makes it have a lot of room for improvement. Abdelhamid et al [4] proposed an improved bionic optimization algorithm. The algorithm is developed
© Qin Hongwu, Wang Lizheng, Liu Zhengi, Chye En Un, Voronin V.V., 2023
ВЕСТНИК ТОГУ. 2023. № 2 (69)
based on three technologies, including a collaborative optimization strategy, simulation of the generation of new birds, and rearrangement of subgroups, which improves the accuracy of the algorithm. Xu et al [5] proposed a seagull optimization algorithm (MSOA) with a memory function to solve the equations. The memory function is introduced to improve the solution ability of the algorithm and avoid the algorithm falling into local optimization. The results show that the algorithm has advantages in terms of quantity and quality of solutions. Zhang et al [6] by redefining the representation and update strategy of seagull position, the seagull optimization algorithm is converted from continuous domain to discrete domain, and the discrete seagull optimization algorithm is established. At the same time, the random variation factor is introduced to make the seagull have the ability to jump out of the local optimal value. The test results show that it has strong application potential in spatial analysis. Li et al [7] proposed a seagull optimization algorithm (ESOA) integrating multiple strategies to improve the performance of the algorithm. Yan et al [8] proposed three improvement strategies to improve the optimization ability of SOA algorithm in view of the slow convergence speed of seagull optimization algorithm and easy to fall into local optimization. The results show that the proposed improvement strategy can significantly improve the convergence speed and accuracy of the SOA. Qin et al [9] proposed a sea-european optimization algorithm based on inertia weight, the position of seagulls is adjusted by calculating the value of additional variable A with nonlinear decreasing inertia weight, and the randomness of seagull flight is increased by Levy flight and random index value. The results show that the proposed optimization algorithm has fast convergence speed, high solution accuracy, and global convergence ability.
The seagull optimization algorithm is prone to falling into local optimization, depends on the optimal individual, and has low accuracy. This paper quotes nonlinear control factors, adopts multiple excellent individuals, increases the position update weight, improves SOA in view of search ability, convergence speed, and overdependence on the optimal individual, and proposes a seagull optimization algorithm based on adaptive weight.
Seagull Optimization Algorithm
Seagull is a kind of seabird that spreads all over the world, with a wide variety and different sizes. They live in groups and use group intelligence to find and attack prey. An intelligent optimization algorithm inspired by biology, Seagull Optimization Algorithm [ 10] (SOA), was proposed by Indian scholar Gaurav Dhiman in 2018. The main inspiration for this algorithm comes from the migration and attack behavior of seagulls in nature. These behaviors can be explored and utilized in a given search space after mathematical modeling and implementation.
ВЕСТНИК ТОГУ. 2023. № 2 (69)
Migration: that is, the seagull moves from the current position to the next target position, and the migration behavior simulates the position movement process of the seagull population. The whole migration behavior needs to meet three requirements:
1) Avoidance of collision: build a model with an additional variable A to avoid collision between adjacent seagulls. The algorithm iterates to calculate and update the seagull position with additional control factor variable A, expression is
C = A^X(t), (1)
where, C refers to the position where there is no collision with adjacent seagulls; T represents the number of iterations; X (t) represents the current iteration position of seagulls; A represents the movement behavior of seagulls in the given search space, and the expression is
A = fc — fc
t
Maxjter ’
(2)
where, fc is used to control the variation range of additional variable A, and fc is generally taken as 2; Maxjter represents the maximum number of iterations.
2) Determine the direction of movement: after determining the position to avoid collision, the seagull will move towards the current best seagull position, and the expression is
D = B^[Xp(t)—X(t)\, (3)
where, D represents the relative position between the individual seagull and the current best seagull; Xp (t) indicates the current best seagull position; B is the convergence factor of coordination search, and the expression is
В = 2^ A2 •r1, (4)
where, r1 is the random value of random vector between [0, 1].
3) Close to the best position: after determining the collision avoidance position and moving direction, the individual seagull moves to the direction of the current best seagull. The expression is
U=ID + CI, (5)
where, U represents the distance between the individual seagull and the current best seagull.
Attack: the behavior of seagulls attacking prey can be expressed by spiral motion on the xyz plane, and the specific expression is f r = ekv,
) x = r • со s(k),
I у = r • sin(k), z = r • к,
where r is the flying radius of seagulls; u and и are the coefficients that control the shape of the spiral, and u and и are generally taken as 1; к represents the random
ВЕСТНИК ТОГУ. 2023. № 2 (69)
attack angle within the range of [0, 2k]; The new position expression after attacking the prey is
X(t + 1) — xyz^U + Xp(t), (7)
where, X (t+1) is the individual position of the seagull updated after the attack. That is, the position after iteration.
Improved Seagull Optimization Algorithm
The Seagull algorithm has strong applicability and good competitiveness in engineering optimization problems. Many scholars have studied and improved the Seagull algorithm and applied it in many fields. According to the existing research at home and abroad, the improvement of the Seagull algorithm mainly includes the improvement of population initialization, the improvement of the search method, parameter optimization, and mixed improvements of multiple algorithms.
In the optimization process of the seagull algorithm, only a single optimal individual is often used to update the seagull position. The result is that it is easy to cause local optimization and mislead the seagull population to deviate from the migration route. This paper adds two additional optimal solutions to this problem. Improve the algorithm to reduce the impact of local optimization on the algorithm.
In addition, the control factor A of Seagull algorithm changes in a linearly decreasing manner, which will lead to an unstable transition between exploration and development of the algorithm and poor optimization accuracy. To solve this problem, this paper cites an improved nonlinear control factor algorithm to improve the accuracy of the algorithm. Expression is
A = fc-fc • I \ . (8)
yj Maxjter
The Seagull algorithm adopts the local search method of random spiral, which is too dependent on the selection of spiral coefficient, which will reduce the local search ability. To solve this problem, at last, when updating the location, two new optimal solutions are added in the early stage of the algorithm, and three optimal locations X are calculated according to formula (7) Xx, X2, X3. After that, the adaptive weight strategy is used to build a new location update formula. Expression
is X(t 1 1) _ (ш1^1 + ш2^2+ш3^з)
where ш1, ш2, ш3 expression is
^ 1Ы 1 |*l| + |*2| + |*3|’ (10)
^ 1Ы 2 |*l|+|*2|+|*3|' (11)
|*3| 3 |*l|+|*2|+|*3| (12)
ВЕСТНИК ТОГУ. 2023. № 2 (69)
General steps of seagull optimization algorithm based on adaptive weight:
(1) Perform seagull position initialization within the specified range;
(2) Calculate the fitness value of seagulls;
(3) Assign the best three values to three seagulls;
(4) Seagull migration;
(5) Seagull attack;
(6) Whether the number of iterations is the maximum. If not, skip to (2). Yes, next step
(7) Formula (9) updates and outputs X (t+1).
The flow chart of seagull optimization algorithm based on adaptive weight is shown in Fig.l.
Fig 1. Flowchart of the ISOA
Experimental results and analysis
In order to test the ISOA, this paper uses the standard benchmark function to conduct a comprehensive optimization test on the improved Seagull optimization algorithm. The standard reference functions are shown in Table 1. In addition, this paper also tested the competitiveness of ISOA. The standard seagull optimization algorithm, particle swarm optimization algorithm, gray wolf optimization algorithm, and ISOA are used for comparative experiments. In order to achieve the verification purpose, 30 independent tests were conducted, and 500 iterations were set for the experiment. Take the average value and standard deviation to indicate the accuracy
ВЕСТНИК ТОГУ. 2023. № 2 (69)
of the experiment, and the test results have a certain guiding role. The comparison of experimental results is shown in Table 2.
It can be seen from Table 2 that the ISOA has achieved the closest results to the real values on the functions ft, f2, f3, f4, f5 and f6. That is, the test result is closer to the actual value. Compared with the other three algorithms, the improved algorithm in this paper is several orders of magnitude higher than the other algorithms. The analysis of experimental results shows that ISOA has more obvious optimization results. In general, the optimization effect of seagull optimization algorithm based on adaptive weight is more obvious, and the optimization accuracy is significantly improved. In the stability analysis, by deliberately observing the best position of 500 iterations in the experiment, we can find that the standard deviation of ISOA is the most stable in all functions, that is, the stability is the best. In addition, the convergence rate curve of the standard benchmark function is shown in Fig. 2. As can be seen from Fig. 2, compared with the other three algorithms, the ISOA has significantly faster convergence speed and better accuracy in processing ft ... ft; functions. According to the above analysis, ISOA has better performance in terms of convergence speed and accuracy.
Table 1
Standard benchmark functions
Function expression Dim Search interval Optim al value
n fi(x) = £ = 1 30 [-100, 100] 0
n n /2М = + П|Х;| £=1 £=1 30 [-10, 10] 0
= |(b) 30 [-100, 100] 0
f4(x) = maXj{|Xj| , 1 < i < n] 30 [-100, 100] 0
n fs(x) = ^ txf + random [0,1) i=1 30 [-1.28, 1.28] 0
s Й N 1 II * 30 [-500, 500] 418.98 *5
ВЕСТНИК ТОГУ. 2023. № 2 (69)
Table 2
Comparative experimental results
SOA GWO PSO ISOA
fi mean 6.60E-12 1.97E-27 1.24E-04 1.47E- 287
std 1.37E-11 2.24E-27 1.10E-04 0.00E+00
f2 mean 1.86E-08 9.95E-17 2.92E-02 5.75E- 147
std 1.83E-08 7.26E-17 3.82E-02 7.10E- 147
f3 mean 1.94E-05 1.27E-05 8.77E+01 6.07E- 272
std 3.34E-05 2.91E-05 3.00E+01 0.00E+00
f mean 1.24E-02 1.82E-06 1.12E+00 1.26E- 138
std 2.52E-02 2.13E-06 2.70E-01 1.76E- 138
f mean 2.70E-03 1.60E-03 1.96E-01 1.02E-04
std 1.60E-03 7.28E-04 7.57E-02 1.08E-04
fe mean -5.19E+03 -6.22E+03 -5.29E+03 4.26E+03
std 7.44E+02 1.13E+03 1.05E+03 5.11E+02
fi
f2
ВЕСТНИК ТОГУ. 2023. № 2 (69)
f4
Objective space
Objective space
-2000
£
о -2500
«
тз
a)
S -3000
|
о -3500 2
8 -4000
w
M -4500 * -5000 -5500 -6000 -6500 -7000
100 200 300 400 500
Iteration
f6
Fig 2. Convergence diagram of functionf1 ... f6 curve
Conclusion
This paper proposes to use multiple excellent individuals and update the iterative position with an adaptive weight strategy based on the standard seagull optimization algorithm, combined with the nonlinear control factor, and proposes the seagull optimization algorithm based on adaptive weight (ISOA). It effectively improves the shortcomings of SOA, such as its easy fall into local optimization, dependence on the optimal individual, and low solution accuracy. The test results of the standard reference function show that ISOA has stronger comprehensive perfor-
ВЕСТНИК ТОГУ. 2023. № 2 (69)
mance, faster convergence speed, and better robustness. through comparative experiments with the standard seagull optimization algorithm, the particle swarm optimization algorithm, and the Gray Wolf optimization algorithm. The ISOA optimization method has higher accuracy and precision.
Acknowledgments
This work was supported by the Project (20210402081GH) of Jilin Provincial Science and Technology Department, the Project (2023C042-4) of Jilin Provincial Development and Reform Commission, the Innovation and Entrepreneurship Talent Funding Project (2023RY17) of Jilin Province, and the Climbing Program Project (2021JBD33L39) of Changchun University.
References
1. Hu Xiaotong, Cheng Chen. Time series prediction based on multi-dimensional and cross-scale LSTM model // Computer Engineering and Design. 2023. № 44. P, 440-446.
2. Research on path planning of mobile robot based on improved ephemera algorithm / Zou Awei, Wang Lei, Li Weimin, et al. // Mechanical Science and Technology. 2023. Vol. 1.
3. Meng Rongjuan. Cluster analysis based on improved Drosophila algo-rithm/D. Ningxia University. 2022.
4. An improved seagull optimization algorithm for optimal coordination of distance and directional over-current relays / M. Abdelhamid, E.H. Houssein, M.A. Mahdy, et al. // Expert Systems with Application. 2022 (Aug.).
5. Xu Le, Mo Yuanbin, Lu Yanyue. Seagull optimization algorithm with memory function to solve equations // Computer Engineering and Design. 2021. Vol. 42. P. 3428-3437.
6. Analysis of path optimization algorithm using seagull theory / Zhang Tao, Yang Xiaofeng, Qin Kun, Li Feifei, Luo Wenshan // Surveying and Mapping Bulletin. 2022. Vol.12. P. 110-115.
7. Li Dahai, Xiong Wenqing, Wang Zhendong. A multi-strategy collaborative improvement seagull algorithm and its application // Computer application research. 2023. Vol. 1.
8. Yan Aijun, Hu Kaicheng. Improvement strategy and application to improve the optimization ability of seagull optimization algorithm // Information and Control. 2022. Vol. 51. P. 688-698.
9. Qin Weina, Zhang Damin, Yin Dexin, Cai Pengchen. A seagull optimization algorithm based on nonlv.inear inertia weight // Miniature Computer System. 2022. Vol. 43. P. 10-14.
10. Dhiman G., Kumar V. Seagull Optimization Algorithm: Theory and its Applications for Large Scale Industrial Engineering Problems // Knowledge-Based Systems. 2018.
ВЕСТНИК ТОГУ. 2023. № 2 (69)
Заглавие: Исследование алгоритма оптимизации Seagull на основе адаптивного выбора веса
Авторы:
Цинь Хуну - Чанчуньский университет (КНР)
Ван Личжэн - Чанчуньский университет (КНР)
Лю Чжэни - Чанчуньский университет (КНР)
Чье Ен Ун - Тихоокеанский государственный университет (Россия)
Воронин В.В. - Тихоокеанский государственный университет (Россия)
Аннотация: Алгоритм оптимизации Seagull (SOA), относится к алгоритмам оптимизации с простой структурой, легкой реализацией и с возможностями глобального и локального поиска. Однако SOA также имеет некоторые недостатки, такие как приверженность к локальной оптимизации, зависимость от выбора начальных условий и низкая точность решения. Для решения этих проблем в данной статье предлагается улучшенный алгоритм оптимизации Seagull (ISAO), основанный на адаптивном выборе веса и управления процессом оптимизации. Вычислительные эксперименты показывают, что точность улучшенного метода выше, чем у стандартного алгоритма оптимизации Seagull.
Ключевые слова: Алгоритм оптимизации Seagull, вес, управляющий коэффициент, интеллектуальный алгоритм.
