Optimization of neural network for nonlinear discrete time system using modified quaternion firefly algorithm: case study of Indian currency exchange rate prediction
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Success of neural networks depends on an important parameter, initialization of weights and bias connections. This paper proposes modified quaternion firefly algorithm (MQFA) for initial optimal weight and bias connection to neural networks. The proposed modified quaternion firefly method is based on updating population, moving fireflies and best solution in quaternion space. The combination of modified quaternion firefly and neural network is developed with the scope of creating an improved balance between premature convergence and stagnation. The performance of the proposed method is tested on two nonlinear discrete time systems, Box–Jenkins time series data and exchange rate prediction of Indian currency. Results of the MQFA with back-propagation neural network (MQFA-BPNN) compared with existing differential evolution-based neural network and opposite differential evolution-based neural network. Results obtain using MQFA-BPNN envisage that this method is effective and provides better identification accuracy. Computational complexity of MQFA-BPNN is deliberated, and validation of proposed method is tested by statistical methods.
KeywordsFirefly algorithm (FA) MQFA BPNN Nonlinear Box–Jenkins data
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The authors declare that they have no conflict of interest.
- Eberly D (2002) Quaternion algebra and calculus. Magic Software Inc. http://www.magic-software.com
- Schetzmen M (1980) The voltera and winner theories on nonlinear systems. Wiley, New YorkGoogle Scholar
- Simon Haykin S (2009) Neural networks and learning machines, vol 3. Pearson Education, Upper Saddle River. http://www.mif.vu.lt/~valdas/DNT/Literatura/Haykin09/Haykin09.pdf
- Ticknor JL (2013) A Bayesian regularized artificial network for stock market forecasting. Expert Syst Appl 40(14):5501–5506Google Scholar
- Tong SC, Li YM, Zhang HG (2011) Adaptive neural network decentralized backstepping output-feedback control for nonlinear large scale systems with time delays. IEEE Trans Neural Netw 22(7):1073–1086Google Scholar
- Yang XS (2014) Nature-inspired optimization algorithms, Elsevier Insights Series, 1st edn. pp 111–123Google Scholar