A complex-valued encoding satin bowerbird optimization algorithm for global optimization

  • Sen Zhang
  • Yongquan ZhouEmail author
  • Qifang Luo
Original Paper


The real-valued satin bowerbird optimization (SBO) is a novel metaheuristic bio-inspired algorithm which imitates the ‘male-attracts-the-female for breeding’ principle of the specialized stick structure mechanism of satin birds. SBO has achieved success in congestion management, accurate software development effort estimation. In this paper, to enhance the SBO algorithm global exploration ability, a complex-valued encoding satin bowerbird optimization algorithm (CSBO) is proposed. We use complex-valued encoding enhance the diversity of the population, and the global exploration ability of the SBO algorithm. The proposed CSBO optimization algorithm is compared to SBO and other state-of-art optimization algorithms using ten benchmark functions. Simulation results show that the proposed CSBO can significantly improve the convergence accuracy and convergence speed of the original algorithm.


Complex-valued encoding Satin bowerbird optimization Benchmark functions Metaheuristic algorithm 



This work is supported by National Science Foundation of China under Grants No. 61563008, and by Project of Guangxi Natural Science Foundation under Grant No. 2018GXNSFAA138146.


  1. Abdel-Baset M, Wu H, Zhou Y (2017) A complex encoding flower pollination algorithm for constrained engineering optimisation problems. Int J Math Model Numer Optim 8(2):108–126Google Scholar
  2. Angelov P (1994) A generalized approach to fuzzy optimization. Int J Intell Syst 9(3):261–268zbMATHCrossRefGoogle Scholar
  3. de Vasconcelos Segundo EH, Mariani VC, dos SantosCoelho L (2019) Design of heat exchangers using Falcon Optimization Algorithm. Appl Thermal Eng 156:119–144CrossRefGoogle Scholar
  4. Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28–39CrossRefGoogle Scholar
  5. Du J-X, Huang DS, Wang X-F, Gu X (2007) Shape recognition based on neural networks trained by differential evolution algorithm. Neurocomputing 70(4–6):896–903CrossRefGoogle Scholar
  6. El-Hay EA, El-Hameed MA, El-Fergany AA (2018) Steady-state and dynamic models of solid oxide fuel cells based on Satin Bowerbird Optimizer. Int J Hydrogen Energy 43(31):14751–14761CrossRefGoogle Scholar
  7. Fister I Jr, Yang X-S, Fister I, Brest J, Fister D (2013) A brief review of nature-inspired algorithms for optimization. Elektrotehniski Vestnik 80(3):1–7zbMATHGoogle Scholar
  8. Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning. Mach Learn 3(2):95–99CrossRefGoogle Scholar
  9. Han F, Huang DS (2008) A new constrained learning algorithm for function approximation by encoding a priori information into feedforward neural networks. Neural Comput Appl 17(5–6):433–439CrossRefGoogle Scholar
  10. Han F, Ling Q-H, Huang DS (2008) Modified constrained learning algorithms incorporating additional functional constraints into neural networks. Inf Sci 178(3):907–919zbMATHCrossRefGoogle Scholar
  11. Huang DS (1996) Systematic theory of neural networks for pattern recognition (in Chinese). Publishing House of Electronic Industry of China, BeijingGoogle Scholar
  12. Huang DS (1999) Radial basis probabilistic neural networks: model and application. Int J Pattern Recognit Artif Intell 13(7):1083–1101CrossRefGoogle Scholar
  13. Huang DS (2004) A constructive approach for finding arbitrary roots of polynomials by neural networks. IEEE Trans Neural Networks 15(2):477–491CrossRefGoogle Scholar
  14. Huang DS, Du J-X (2008) A constructive hybrid structure optimization methodology for radial basis probabilistic neural networks. IEEE Trans Neural Netw 19(12):2099–2115CrossRefGoogle Scholar
  15. Huang DS, Ma SD (1999) Linear and nonlinear feedforward neural network classifiers: a comprehensive understanding. J Intell Syst 9(1):1–38CrossRefGoogle Scholar
  16. Huang DS, Zhao WB (2005) Determining the centers of radial basis probabilistic neural networks by recursive orthogonal least square algorithms. Appl Math Comput 162(1):461–473MathSciNetzbMATHGoogle Scholar
  17. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39(3):459–471MathSciNetzbMATHCrossRefGoogle Scholar
  18. Kennedy J (2011) Particle swarm optimization. Encyclopedia of machine learning. Springer, New York, pp 760–766Google Scholar
  19. Klein CE, dos Santos Coelho L (2018) Meerkats-inspired algorithm for global optimization problems. ESANN 2018 proceedings, European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning. Bruges (Belgium), 25–27 April 2018Google Scholar
  20. Klein CE, Mariani VC, dos Santos Coelho L (2018) Cheetah based optimization algorithm: a novel swarm intelligence paradigm. ESANN 2018 proceedings, European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning. Bruges (Belgium), 25–27 April 2018Google Scholar
  21. Li B, Wang C, Huang DS (2009) Supe rvised feature extraction based on orthogonal discriminant projection. Neurocomputing 73(1–3):191–196CrossRefGoogle Scholar
  22. Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 27(4):1053–1073CrossRefGoogle Scholar
  23. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67CrossRefGoogle Scholar
  24. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61CrossRefGoogle Scholar
  25. Moosavi SHS, Bardsiri VK (2017) Satin bowerbird optimizer: a new optimization algorithm to optimize ANFIS for software development effort estimation. Eng Appl Artif Intell 60:1–15CrossRefGoogle Scholar
  26. Mortazavia Ali, Toğanb Vedat, Nuhoğluc Ayhan (2018) Interactive search algorithm: a new hybrid metaheuristic optimization algorithm. Eng Appl Artif Intell 71:275–292CrossRefGoogle Scholar
  27. Pierezan J, Dos Santos Coelho L (2018) Coyote optimization algorithm: a new metaheuristic for global optimization problems. IEEE Congress on Evolutionary Computation (CEC), Rio de Janeiro, Brazil, 8–13 July 2018Google Scholar
  28. Rainer S, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359MathSciNetzbMATHCrossRefGoogle Scholar
  29. Rashid S, Saraswathi S, Kloczkowski A et al (2016) Protein secondary structure prediction using a small training set (compact model) combined with a complex-valued neural network approach. BMC Bioinform 17(1):362CrossRefGoogle Scholar
  30. Sakthivel VP, Bhuvaneswari R, Subramanian S (2010) Multi-objective parameter estimation of induction motor using particle swarm optimization. Eng Appl Artif Intell 23(3):302–312CrossRefGoogle Scholar
  31. Shadravan S, Naji HR, Bardsiri VK (2019) The Sailfish Optimizer: a novel nature-inspired metaheuristic algorithm for solving constrained engineering optimization problems. Eng Appl Artif Intell 80:20–34CrossRefGoogle Scholar
  32. Shang L, Huang DS, Du J-X, Zheng C-H (2006) Palmprint recognition using FastICA algorithm and radial basis probabilistic neural network. Neurocomputing 69(13–15):1782–1786CrossRefGoogle Scholar
  33. Shayanfar H, Gharehchopogh FS (2018) Farmland fertility: a new metaheuristic algorithm for solving continuous optimization problems. Appl Soft Comput 71:728–746CrossRefGoogle Scholar
  34. Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713CrossRefGoogle Scholar
  35. Xiong T, Bao Y, Hu Z et al (2015) Forecasting interval time series using a fully complex-valued RBF neural network with DPSO and PSO algorithms. Inf Sci 305:77–92CrossRefGoogle Scholar
  36. Yang X-S (2010) A new metaheuristic bat-inspired algorithm. Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, Berlin, pp 65–74CrossRefGoogle Scholar
  37. Yang X-S (2012) Flower pollination algorithm for global optimization. UCNC, BarasatzbMATHCrossRefGoogle Scholar
  38. Yang X-S, Deb S (2009) Cuckoo search via Lévy flights. Nature & biologically inspired computing, 2009. NaBIC 2009. World Congress on. IEEEGoogle Scholar
  39. Zhao WB, Huang DS, Du J-Y, Wang L-M (2004) Genetic optimization of radial basis probabilistic neural networks. Int J Pattern Recognit Artif Intell 18(8):1473–1500CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Information Science and EngineeringGuangxi University for NationalitiesNanningChina
  2. 2.Key Laboratory of Guangxi High Schools Complex System and Computational IntelligenceNanningChina

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