Evolutionary optimization of artificial neural network using an interactive phase-based optimization algorithm for chaot
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METHODOLOGIES AND APPLICATION
Evolutionary optimization of artificial neural network using an interactive phase-based optimization algorithm for chaotic time series prediction Zijian Cao1
Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The prediction of chaotic time series is an important issue in nonlinear information procession. Due to the multi-modal, high-dimensional and non-differentiable or discontinuous characteristics of chaotic systems, global optimization techniques are required to avoid from falling into local optima for the prediction of chaotic time series. Phase-based optimization is recently proposed as a global search algorithm inspired by natural phenomena. In this paper, an improved phase-based optimization algorithm integrating stochastic interaction strategy and global optimal interaction strategy, termed interactive phase-based optimization (IPBO), is proposed to train feed-forward neural networks (FNNs) for chaotic time series prediction. The combination of stochastic interaction strategy and global optimal interaction strategy can balance the capability of exploration and exploitation in the global optimization process. To demonstrate the searching capability, sixteen widely used benchmark functions are firstly used to investigate its optimization performance. Then, the prediction effectiveness of FNNs trained by IPBO has been illustrated using classical chaotic time series of Lorenz, Box– Jenkins and Mackey–Glass. The training and testing performances of IPBO and other state-of-the-art optimization algorithms have been compared for predicting these time series. Conducted numerical experiments indicate that IPBO is not only competitive in functions optimization and has also a better learning ability in training FNNs among other state-of-theart optimization algorithms. Keywords Time series prediction Feed-forward neural network Phase based optimization Evolutionary optimization
1 Introduction Prediction of chaotic time series is an important branch of nonlinear information procession and has already received increasing interests and applications in the fields of science, engineering, medicine and econometrics, among others (Samantha 2011). Prediction of time series involves utilizing an information sequence of the current and the past status of a chaotic system to develop a prediction model to estimate the system behavior in future (Casdagli 1989). Due to the characteristic of unstable dynamic behavior of chaotic systems, the prediction of a chaotic system can be Communicated by V. Loia. & Zijian Cao [email protected] 1
School of Computer Science and Engineering, Xi’an Technological University, Xi’an 710021, China
seen as a multi-dimensional nonlinear optimization problem (Wang et al. 2014). Consequently, some methods based on statistical models for the prediction of chaotic time series, such as Recursive Least Squares (RLS) (Stark 1993), Auto Regressive (AR) (Akaike 1969), Auto Regressive Moving Average (ARMA) (Nava
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