Abstract
This research study aims to enhance the optimization accuracy of the two recently emerged metaheuristics of whale and sine–cosine optimizers by means of the balanced improvements in intensification and diversification phases of the algorithms provided by cellular automata (CA). Stagnation at the early phases of the iterations, which leads to entrapment in local optimum points in the search space, is one of the inherent drawbacks of the metaheuristic algorithms. As a favorable solution alternative to this problem, different types of cellular topologies are implemented into these two algorithms with a view to ameliorating their search mechanisms. Exploitation of the fertile areas in the search domain is maintained by the interaction between the topological neighbors, whereas the improved exploration is resulted from the smooth diffusion of the available population information among the structured neighbors. Numerical experiments have been carried out to assess the optimization performance of the proposed cellular-based algorithms. Optimization benchmark problems comprised of unimodal and multimodal test functions have been applied and numerical results have been compared with those found by some of the state-of-the-art literature optimizers including particle swarm optimization, differential evolution, artificial cooperative search and differential search. Cellular variants have been outperformed by the base algorithms for multimodal benchmark problems of Levy and Penalized1 functions. Then, the proposed cellular algorithms have been applied to two different parameter identification cases in order to test their efficiencies on real-world optimization problems. Extensive performance evaluations on different parameter optimization cases reveal that incorporating the CA concepts on these algorithms not only improves the optimization accuracy but also provides considerable robustness to acquired solutions.
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References
Abd-Elaziz ME, Ewees AA, Oliva D, Duan P, Xiong S (2017a) A hybrid method of sine cosine algorithm and differential evolution for feature selection. In: Liu D, Xie S, Li Y, Zhao D, El-Alfy ES (eds) Neural information processing, ICONIP 2017. Lecture notes in computer science, vol 10638. Springer
Abd-Elaziz M, Oliva D, Xiong S (2017b) An improved opposition-based sine cosine algorithm for global optimization. Expert Syst Appl 90:484–500
Ahmadi M, Mojallali H (2012) Chaotic invasive weed optimization algorithm with application to parameter estimation of chaotic systems. Chaos Soliton Fract 45:1108–1120
Al-Assaf Y, El-Khazali R, Ahmad W (2004) Identification of fractional chaotic system parameters. Chaos Soliton Fract 22:897–905
Al-Betar MA, Awadallah MA (2018) Island bat algorithm for optimization. Expert Syst Appl 107:126–145
Al-Betar MA, Kader AT, Awadallah MA, Alawan MH, Zaqaibeh B (2013) Cellular harmony search for optimization problems. J Appl Math 20:139464
Al-Betar MA, Awadallah MA, Khader AT, Abdalkareem ZA (2015) Island-based harmony search for optimization problems. Expert Syst Appl 42:2026–2035
Alkan H, Balkaya C (2018) Parameter estimation by differential search algorithm from horizontal loop electromagnetic (HLEM) data. J Appl Geophys 149:77–94
Al-Shaikh A, Mahafzah BA, Alshraideh M (2019) Metaheuristic approach using grey wolf optimizer for finding strongly connected components in digraphs. J Theor Appl Inf Technol 97:4439–4452
Askerzadeh A (2016) A novel metaheuristic method for solving constrained engineering optimization problems: crow search algorithm. Comput Struct 169:1–12
Biswas PP, Suganthan PN, Wu G, Amaratunga GAJ (2019) Parameter estimation of solar cells using datasheet information with the application of an adaptive differential evolution algorithm. Renew Energy 132:425–438
Chang JF, Yang YS, Liao TH, Yan JJ (2008) Parameter identification of chaotic systems using evolutionary programming approach. Expert Syst Appl 35:2074–2079
Chegini SN, Bagheri A, Najafi F (2018) PSOSCALF: a new hybrid PSO based on sine cosine algorithm and levy flight for solving optimization problems. Appl Soft Comput 73:697–726
Chen G, Ueta T (1999) Yet another chaotic attractor. Int J Bifurc Chaos 9:1465–1466
Chen H, Xu Y, Wang M, Zhao X (2019) A balanced whale optimization algorithm for constrained engineering design problems. Appl Math Model 71:45–59
Chen H, Heidari AA, Zhao X, Zhang L, Chen H (2020a) Advanced orthogonal learning-driven multi-swarm sine cosine optimization: framework and case studies. Expert Syst Appl 144:113113
Chen H, Wang M, Zhao X (2020b) A multi-strategy enhanced sine cosine algorithm for global optimization and constrained practical engineering problems. Appl Math Comput 369:124872
Civicioglu P (2012) Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm. Comput Geosci 46:229–247
Civicioglu P (2013) Artificial cooperative search algorithm for numerical optimization problems. Inf Sci 229:58–76
Das B, Mukherjee V, Das D (2020) Student psychology based optimization algorithm: a new population based optimization algorithm for solving optimization problems. Adv Eng Softw 146:102804
Dhiman G, Kumar V (2017) Spotted hyena optimizer: a novel bio-inspired based metaheuristic technique for engineering applications. Adv Eng Softw 114:48–70
Dhiman G, Kumar V (2019) Seagull optimization algorithm: theory and its applications for large-scale industrial engineering problems. Knowl-Based Syst 165:169–196
Du KL, Swamy MNS (2016) Search and optimization by metaheuristics. Springer, Cham
Eberhart RC, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science, pp 39–43
Elaziz M, Oliva D (2018) Parameter estimation of solar cells diode models by an improved opposition-based whale optimization algorithm. Energy Convers Manag 171:1843–1859
Elhosseini MA, Haikal AY, Badawy M, Khashan N (2019) Biped robot stability based on an A–C parametric whale optimization algorithm. J Comput Sci Neth 31:17–32
Fan Y, Wang P, Heidari AA, Wang M, Zhao X, Chen H, Li C (2020) Rationalized fruit fly optimization with sine cosine algorithm: a comprehensive analysis. Expert Syst Appl 157:113486
Ferhat-Hamida A, Ouennoughi Z, Hoffmann A, Weiss R (2002) Extraction of Schottky diode parameters including parallel conductance using a vertical optimization method. Solid-State Electron 46:615–619
Gao L, Huang JD, Li XY (2012) An effective cellular particle swarm optimization for parameters optimization of a multi-pass milling process. Appl Soft Comput 12:3490–3499
Ghasemi M, Davoudkhani IF, Akbari E, Rahimnejad A, Ghavidel S, Li L (2020) A novel and effective optimization algorithm for global optimization and its engineering applications: turbulent flow of water-based optimization (TFWO). Eng Appl Artif Intell 92:103666
Goldbogen JA, Friedlaender AS, Calambokidis J, Mckenna MF, Simon M, Nowacek DP (2013) Integrative approaches to the study of baleen whale diving behaviour, feeding performance, and foraging ecology. Bioscience 63:90–100
Gong YJ, Chen WN, Zhan ZH, Zhang J, Li Y, Zhang Q, Li JJ (2015) Distributed evolutionary algorithms and their models: a survey of the state-of-the-art. Appl Soft Comput 34:286–300
Gupta S, Deep K (2019) A hybrid self-adaptive opposition based learning. Expert Syst Appl 119:210–230
Hayyolalam V, Kazem AAP (2020) Black widow optimization algorithm: a novel meta-heuristic approach for solving engineering optimization problems. Eng Appl Artif Intell 87:103249
He Q, Wang L, Liu B (2007) Parameter estimation for chaotic systems by particle swarm optimization. Chaos Soliton Fract 34:654–661
Heidar AA, Mirjalili S, Farrris H, Aljarah I, Mafarja M, Chen H (2019) Harris hawks optimization: algorithm and applications. Futur Gener Comput Syst 97:849–872
Issa M, Hassanien AE, Oliva D, Helmi A, Ziedan I, Alzohairy A (2018) ASCA-PSO: adaptive sine–cosine optimization integrated with particle swarm for pairwise local sequence alignment. Expert Syst Appl 99:56–70
Jaddi NS, Abdullah S (2017) A cooperative-competitive master-slave global-best harmony search for ANN optimization and water-quality prediction. Appl Soft Comput 51:209–224
Jadhav AN, Gomathi N (2018) WGC: hybridization of exponential grey wolf optimizer with whale optimization for data clustering. Alex Eng J 57:1569–1584
Jiang Q, Wang L, Hei X (2015) Parameter identification of chaotic systems using artifical raindrop algorithm. J Comput Sci 8:20–31
Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical report-TR06, Erciyes University, Engineering Faculty, Computer Engineering Department
Karaboga N, Kockanat S, Dogan H (2011) Parameter determination of the Schottky barrier diode using by artificial bee colony algorithm. In: International symposium on innovations in intelligent systems and applications (INISTA), pp 6–10
Karaboga N, Kockanat S, Dogan H (2013) The parameter extraction of the thermally annealed Schottky barrier diode using the modified artifical bee colony. Appl Intell 38:279–288
Kaur S, Awasthi LK, Sangal AL, Dhiman G (2020) Tunicate swarm algorithm: a new bio-inspired based metaheuristic paradigm for global optimization. Eng Appl Artif Intell 90:103541
Khattab H, Sharieh A, Mahafzah BA (2019) Most valuable player algorithm for solving minimum vertex cover problem. Int J Adv Comput Sci Appl 10:159–167
Li H, Wu H (2016) An oppositional wolf pack algorithm for parameter identification of the chaotic systems. Optik 127:9853–9864
Li C, Zhou J, Xiao J, Xiao H (2012) Parameters identification of chaotic system by choatic gravitational search algorithm. Chaos Soliton Fract 45:539–547
Liu M, Yao X, Li Y (2020) Hybrid whale optimization algorithm enhanced with Levy flight and differential evolution for job shop scheduling problems. Appl Soft Comput 87:105954
Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20:130–141
Lu C, Gao L, Yi J (2018) Grey wolf optimizer with cellular topological structure. Expert Syst Appl 107:89–114
Mafarja MM, Mirjalili S (2017) Hybrid whale optimization algorithm with simulated annealing for feature selection. Neurocomputing 260:302–312
Masadeh R, Mahafzah BA, Sharieh A (2019a) Sea lion optimization algorithm. Int J Adv Sci Technol 10:388–395
Masadeh R, Sharieh A, Mahafzah BA (2019b) Humpback whale optimization algorithm based on vocal behaviour for task scheduling in cloud computing. Int J Adv Sci Technol 13:121–140
Mirjalili S (2016) A sine cosine algorithm for solving optimization problems. Knowl Based Syst 96:120–133
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Soft 95:51–67
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61
Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature -inspired algorithm for global optimization. Neural Comput Appl 27:495–513
Mohanty DK (2016) Gravitational search algorithm for economic optimization design of a shell and tube heat exchanger. Appl Therm Eng 107:184–193
Mousavi Y, Alfi A (2018) Fractional calculus-based firefly algorithm applied to parameter estimation of chaotic systems. Chaos Soliton Fract 114:202–215
Murad O, Jabri R, Mahafzah BA (2019) A metaheuristic approach for static scheduling based on chemical reaction optimizer. J Theor Appl Inf Technol 97:3144–3165
Nenavath H, Jatoth RK (2018) Hybridizing sine cosine algorithm with differential evolution for global optimization and object tracking. Appl Soft Comput 62:1019–1043
Neumann JV (1966) Theory of self-reproducing automata. University of Illinois Press, Champaign
Norde H (1979) A modified forward I–V plot for Schottky diodes with high series resistance. J Appl Phys 50:5052–5053
Nunes HGG, Pombo JAN, Bento PMR, Mariano SJPS, Calado MRA (2019) Collaborative swarm intelligence to estimate PV parameters. Energy Convers Manag 185:866–890
Peng B, Liu B, Zhang FY, Wang L (2009) Differential evolution algorithm-based parameters estimation for chaotic systems. Chaos Soliton Fract 5:2110–2118
Reinhardt KA, Kern W (2008) Handbook of silicon wafer cleaning technology, 2nd edn. William Andrew Publishing, New York
Rhoderick EH, Williams RH (1988) Metal-semiconductor contacts. Clarendon Press, Oxford
Rizk-Allah RM (2018) Hybridizing sine cosine algorithm with multi-orthogonal search strategy for engineering design problems. J Comput Des Eng 5:249–273
Rodriguez-Fernandez M, Egea JA, Banga JR (2006) Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems. BMC Bioinform 7:483
Rossler OE (1976) An equation for continuous chaos. Phys Lett A 57:397–398
Roy G, Lee H, Welch JL, Zhao Y, Pandey D, Thurston D (2009) A distributed pool architecture for genetic algorithms. In: IEEE congress on evolutionary computation (CEC), pp 1177–1184
Sellai A, Ouennoughi Z (2005) Extraction of Illuminated solar cell and Schottky diode parameters using a genetic algorithm. Int J Mod Phys C 7:1043–1050
Shi Y, Liu HC, Gao L, Zhang GH (2011) Cellular particle swarm optimization. Inf Sci 181:4460–4493
Singh N, Hachimi H (2018) A new hybrid whale optimizer algorithm with mean strategy of grey wolf optimizer for global optimization. Math Comput Appl 23:14
Storn R, Price K (1997) Differential evolution: a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359
Suarez-Castanon MS, Aguilar-Ibanez C, Flores-Ando F (2003) Reconstructing the states and parameters of Chua’s system based on successive integrations of the output. Phys Lett A 317:265–274
Subbu R, Sanderson AC (2004) Modeling and convergence analysis of distributed coevolutionary algorithms. IEEE Trans Syst Man Cybern B Cybern 34:806–822
Sulaiman MH, Mustaffa Z, Saari MM, Daniyal H (2020) Barnacles mating optimizer: a new bio-inspired algorithm for solving engineering optimization problems. Eng Appl Artif Intell 87:103330
Sun J, Zhao J, Wu X, Fang W, Cai Y, Xu W (2010) Parameter estimation of chaotic systems with a drift particle swarm optimization method. Phys Lett A 374:2816–2822
Turgut OE (2019) Multi-agent metaheuristic framework for thermal design optimization of a shell and tube evaporator operated with R134a-Al2O3. Arab J Sci Eng 44:777–801
Wang L, Xu Y (2011) An effective hybrid biogeography-based optimization algorithm for parameter estimation of chaotic systems. Expert Syst Appl 38:15103–15109
Wang K, Ye M (2009) Parameter determination of the Schottky barried diode model using differential evolution. Solid State Electron 53:234–240
Wang L, Xu Y, Li L (2011) Parameter identificaition of chaotic systems by hybrid Nelder–Mead simplex search and differential evolution algorithm. Expert Syst Appl 38:3238–3245
Xiong G, Zhang J, Shi D, He Y (2018) Parameter extraction of solar photovoltaic models using an improved whale optimization algorithm. Energy Convers Manag 174:388–405
Yang K, Maginu K, Nomura H (2009) Parameters identification of chaotic systems by quantum-behaved particle swarm optimization. Int J Comput Math 86:2225–2235
Yi J, Gao L, Li XY, Gao J (2016) An efficient modified harmony search algorithm with intersect mutation operator and cellular local search for continuous function optimization problems. Appl Intell 44:725–753
Yong LIU, Liang MA (2017) Sine cosine algorithm with nonlinear decreasing conversion parameter. Comput Eng Appl 53:1–5
Yousri D, Allam D, Eteiba MB (2019) Chaotic whale optimizer variants for parameters estimation of the chaotic behavior in permanent magnet synchronous motor. Appl Soft Comput 74:479–503
Zhao W, Wang L, Zhang Z (2019) Atom search optimziation and its application to solve a hyrdogeologic parameter estimation problem. Knowl Based Syst 163:283–304
Zhao W, Zhang Z, Wang L (2020) Manta ray foraging optimization: an effective bio-inspired optimizer for engineering applications. Eng Appl Artif Intell 87:103300
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Turgut, M.S., Sağban, H.M., Turgut, O.E. et al. Whale optimization and sine–cosine optimization algorithms with cellular topology for parameter identification of chaotic systems and Schottky barrier diode models. Soft Comput 25, 1365–1409 (2021). https://doi.org/10.1007/s00500-020-05227-6
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DOI: https://doi.org/10.1007/s00500-020-05227-6