Abstract
To solve the problems of premature convergence and easily falling into local optimum, a whale optimization algorithm based on dynamic pinhole imaging and adaptive strategy is proposed in this paper. In the exploitation phase, the dynamic pinhole imaging strategy allows the whale population to approach the optimal solution faster, thereby accelerating the convergence speed of the algorithm. In the exploration phase, adaptive inertial weights based on dynamic boundaries and dimensions can enrich the diversity of the population and balance the algorithm’s exploitation and exploration capabilities. The local mutation mechanism can adjust the search range of the algorithm dynamically. The improved algorithm has been extensively tested in 20 well-known benchmark functions and four complex constrained engineering optimization problems, and compared with the ones of other improved algorithms presented in literatures. The test results show that the improved algorithm has faster convergence speed and higher convergence accuracy and can effectively jump out of the local optimum.
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References
Holland JH (1973) Genetic algorithms and the optimal allocation of trials. SIAM J Comput 2(2):88–105
Koza JR (1992) Genetic programming
Rechenberg I (1978) Evolutions strategien. Springer, Berlin, Heidelberg, pp 83–114
Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680
Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248
Seyedali M (2015) Moth-flame optimization algorithm: a novel nature-inspired heuristic paradigm. Knowl-Based Syst 89:228–249
Du H, Wu X, Zhuang J (2006) Small-world optimization algorithm for function optimization. In: Jiao L Wang L, Gao X, Liu J, Wu F (eds.), Advances in natural computation. ICNC (2006) Lecture Notes in Computer Science, vol 4222. Springer, Berlin, Heidelberg
Richard F (2007) Central force optimization: a new metaheuristic with applications in applied electromagnetics. Prog Electromag Res 77:425–491
Eskandar H, Sadollah A, Bahreininejad A et al (2012) Water cycle algorithm: a novel metaheuristic optimization method for solving constrained engineering optimization problems. Comput Struct 110:151–166
Kennedy J, Eberhart RC (2002) Particle swarm optimization. In: Proceedings of the 1995 IEEE International Conference on Neural Networks 4:1942–1948
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61
Xue J, Shen B (2020) A novel swarm intelligence optimization approach: sparrow search algorithm. Syst Sci Control Eng 8(1):22–34
Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp swarm algorithm. Adv Eng Softw 114:163–191
Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28–39
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67
Saha N, Panda S (2020) Cosine adapted modified whale optimization algorithm for control of switched reluctance motor. Comput Intell. https://doi.org/10.1111/coin.12310
Kong Z, Zhao J, Yang Q, Ai J, Wang L (2020) Parameter reduction in fuzzy soft set based on whale optimization algorithm. IEEE Access 8:217268–217281
Sulaiman M, Samiullah I, Hamdi A, Hussain Z (2019) An improved whale optimization algorithm for solving multi-objective design optimization problem of PFHE. J Intell Fuzzy Syst 37:3815–3828
Gaganpreet K, Sankalap A (2018) Chaotic whale optimization algorithm. J Comput Des Eng 5(3):275–284
Li Y, Han M, Guo Q (2020) Modified whale optimization algorithm based on tent chaotic mapping and its application in structural optimization. KSCE J Civ Eng 24:3703–3713
Hemasian-Etefagh F, Safi-Esfahani F (2020) Group-based whale optimization algorithm. Soft Comput 24:3647–3673
Kaveh A, Ilchi Ghazaan M (2017) Enhanced whale optimization algorithm for sizing optimization of skeletal structures. Mech Based Des Struct Mach 45(3):345–362
Ma L, Wang C, Xie NG et al (2021) Moth-flame optimization algorithm based on diversity and mutation strategy. Appl Intell 51:5836–5872
Xingguo Q, Ruizhi W, Weiguo Z, Zhaozhao Z, Jing Z (2021) Improved whale optimization algorithm based on hybrid strategy. Comput Eng Appl 1-12
Shuang X, Jingmin Z (2021) Hybrid WOAMFO algorithm based on Lévy flight and adaptive weights. Math Pract Understanding: 1-11[2021-05-15]
Luo J, Shi B (2019) A hybrid whale optimization algorithm based on modified differential evolution for global optimization problems. Appl Intell 49:1982–2000
Zhang J, Wang JS (2020) Improved whale optimization algorithm based on nonlinear adaptive weight and golden sine operator. IEEE Access 8:77013–77048
Tanyildizi E, Demir G (2017) Golden sine algorithm: a novel math inspired algorithm. Adv Electr Comput Eng 17(2):71–78
Tizhoosh HR (2015) Opposition-based learning: a new scheme for machine intelligence. In: International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCA-IAWTIC‘06). Austria, Vienna, pp 695–701
Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3:82–102
Digalakis J, Margaritis K (2001) On benchmarking functions for genetic algorithms. Int J Comput Math 77:481–506
Molga M, Smutnicki C (2005) Test functions for optimization needs
Yang X-S (2010) Firefly algorithm, stochastic test functions and design optimisation. Int J Bio-Inspired Comput 2(2):78–84
Wentao F, Kekang S (2020) An enhanced whale optimization algorithm. Comput Simul 37(11):275–279
Zhang Damin X, Yirou HW, Song T, Wang L (2021) Whale optimization algorithm for embedded circle mapping and one-dimensional learning based small hole imaging. Control Decis 36(05):1173–1180
Seyedali M (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133
Gandomi AH, Yang X-S, Alavi AH (2013) Cuckoo search algorithm: a meta- heuristic approach to solve structural optimization problems. Eng Comput 29:17–35
Song Y, Wang F, Chen X (2019) An improved genetic algorithm for numerical function optimization. Springer, US
Yan Z et al (2021) Nature-inspired approach: an enhanced whale optimization algorithm for global optimization. Math Comput Simul 185:17–46
Bayraktar Z, Komurcu M, Bossard JA et al (2013) The wind driven optimization technique and its application in electromagnetics. IEEE Trans Antennas Propagation 6(5):2745–2755
Ray T, Saini P (2001) Engineering design optimization using a swarm with an intelligent information sharing among individuals. Eng Optim 33(6):735–748
Acknowledgements
This work was supported by the National Natural Science Foundation of China (No. 61603127). The authors would like to thank all the anonymous referees for their valuable comments and suggestions to further improve the quality of this work.
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Li, M., Xu, G., Fu, B. et al. Whale optimization algorithm based on dynamic pinhole imaging and adaptive strategy. J Supercomput 78, 6090–6120 (2022). https://doi.org/10.1007/s11227-021-04116-5
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DOI: https://doi.org/10.1007/s11227-021-04116-5