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Актуальные проблемы авиации и космонавтики - 2022. Том 2
УДК 519.8
ДВАЖДЫ УЛУЧШЕННЫЙ АЛГОРИТМ ОПТИМИЗАЦИИ НА ОСНОВЕ ИМИТАЦИИ ПОВЕДЕНИЯ КИТОВ
Ли Цзявэй Научный руководитель - Е. А. Сопов
Сибирский государственный университет науки и технологий имени академика М. Ф. Решетнева
Российская Федерация, 660037, г. Красноярск, просп. им. газ. «Красноярский рабочий»
*Е-шай 31levi.lijiawei@outlook.com
Традиционный алгоритм оптимизации на основе имитации поведения китов (WOA) склонен к локальной оптимальности, и его скорость сходимости низкая. В работе предлагается улучшенный алгоритм оптимизации для повышения точности и скорости сходимости по сравнению с традиционным алгоритмом WOA и другими интеллектуальными алгоритмами оптимизации.
Ключевые слова: глобальная оптимизация, алгоритм имитации поведения китов, скорость сходимости.
A DOUBLY IMPROVED APPROACH BASED ON WHALE OPTIMIZATION
ALGORITHM
Li Jiawei Scientific Supervisor - E. A. Sopov
Reshetnev Siberian State University of Science and Technology 31, Krasnoyarskii rabochii prospekt, Krasnoyarsk, 660037, Russian Federation *B-mail levi.lijiawei@outlook.com
The traditional Whale Optimization Algorithm (WOA) is prone to local optimality and its convergence speed is slow. An improved WOA is proposed to improve the accuracy and convergence speed in finding the optimal position compared to the traditional WOA and other intelligent optimization algorithms.
Keywords: global optimization, whale algorithm; convergence speed.
1 Double-improvement whale optimization algorithm.
WOA is slow to converge, prone to local optima and prone to premature convergence during computation, and is proposed to improve WOA using a non-linear convergence factor and adaptive weights [1]. The non-linear convergence factor is unbalanced between the global exploration and local exploitation capabilities of WOA in the process of finding the optimal solution [2]. For the analysis of the WOA, the convergence factor a decreases linearly from 2 to 0 as the number of
Секция «Математические методы моделирования, управления и анализа данных»
iterations increases, which also makes the speed of the iteration of the algorithm become relatively slow. In this paper, a nonlinear convergence factor is proposed [3] to address this problem. The specific formula is as follows:
d = 1-sin(t*(—-—)) (1)
v Max_iter v '
here Max_iter is the maximum number of iterations and t is the current iteration number of iterations.
Adaptive weighting strategy. WOA performs local position development at a later stage of the computation easily fall into local optimum, particularly prone to early convergence. For this reason, an adaptive weighting strategy is proposed:
M = 1 - (eMax-iter — lj/(e — 1), (2)
X(t + 1) = ¿3 •it *(t)-A • D, X(t + 1) = D • ebl •cost 2nl) + M • X*(t). (3)
2 Experimental results and analysis
2.1 Test functions. To verify the performance of the CWOA in seeking the optimal solution in this paper, four benchmark test functions selected with reference to the literature (Table 1).
Table 1
Test function
Test functions Range Theoretical optimal
[-100,100] 0
F2=If=1|xi|+^nr=1|xi| [-10,10] 0
F3 = ir=1(I"=1X;)2 [-100,100] 0
F4 = max{ |X(|},1 < i < n} [-100,100] 0
2.2 Parameter setting and analysis of experimental results. The parameters are set in the
modified WOA: k = 2, d = 0.5, b = 1,r = random[0; 1], and a decreases linearly from 2 to 0.
Two population intelligence algorithms were selected for the experiment, namely PSO [4], FFA and the basic WOA. All the used population size was set to 30, the maximum number of iterations that could be performed was set to 500.
The experimental results of the four test functions are shown in Table 2 and Figure 1.
Table 2
Comparison of experimental results
PSO FFA WOA CWOA
Functions Running Optimum Running Optimum Running Optimum Running Optimum
time value time value time value time value
Ft 0.94 51.57 0.66 5112.67 0.84 0 0.72 0
F2 1 20.35 0.74 45.69 0.90 0 0.73 0.01
Fs 1.22 5089.29 0.84 20492.72 1.10 110894 8.87 10005.10
F* 0.98 16.29 0 27.93 0.84 78.12 0.8 56.63
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(<=) F,
0 30
Iterations
( d) F,
Fig. 1. F1~F4. test function algorithm performance test diagram
Conclusions. WOA is a kind of optimization algorithm with bionic search, but it still has some limitations when optimizing some complex functions. The non-linear convergence factor solves the problem of imbalance between the algorithm's global exploration ability and local exploitation ability in computation, and the adaptive weighting strategy allows the algorithm to maintain population diversity and to jump out of the problem of falling into local optima in time. The results show that the improved WOA can break the restriction of being trapped in a local optimum, achieve faster convergence and solution accuracy, and provide better global search and local exploitation capabilities than the other three algorithms, demonstrating the effectiveness of the proposed improvements to the WOA.
References
1. Gharehchopogh, F. S., and Hojjat Gh. A Comprehensive Survey: Whale Optimization Algorithm and Its Applications. Swarm and Evolutionary Computation, vol. 48, 2019, pp. 1-24.
2. Qibing, J., Zhang, Y. Parameter Optimization of Active Disturbance Rejection Controller Using Adaptive Differential Ant-Lion Optimizer. Algorithms, vol. 15, no. 1, 2022, p. 19.
3. Saafan, Mahmoud M., Eman M. El-Gendy IWOSSA: An Improved Whale Optimization Salp Swarm Algorithm for Solving Optimization Problems. Expert Systems with Applications, vol. 176, 2021.
4. Gao, X. et al. Advances in Computational Intelligence and Communication Technology: Proceedings of CICT 2019. Singapore, Springer Singapore, Imprint Springer, 2021.
© Li Jiawei, 2022
