Soft Computing

, Volume 22, Issue 8, pp 2667–2681 | Cite as

Optimization of neural network for nonlinear discrete time system using modified quaternion firefly algorithm: case study of Indian currency exchange rate prediction

  • Uday Pratap Singh
  • Sanjeev Jain
Methodologies and Application


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.


Firefly algorithm (FA) MQFA BPNN Nonlinear Box–Jenkins data 



We would like to thank the editors and anonymous reviewers for their valuable suggestions and constructive comments which will really help us improve presentation and quality of paper.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Madhav Institute of Technology and ScienceGwaliorIndia

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