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-the-art optimization algorithms.
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Funding
This research was funded by the Shaanxi Natural Science Basic Research Project (Grant No.2020JM-565), the fund of National Laboratory of Network and Detection Control (Grant No. GSYSJ2016007), the research project on teaching reform of Xi’an Technological University (Grant No. 18JGZ03), and the national innovation and entrepreneurship training program for college students (Grant No. 1070214030).
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Zijian Cao has received research grants from Xi’an Technological University, and declares that he has no conflict of interest.
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Cao, Z. Evolutionary optimization of artificial neural network using an interactive phase-based optimization algorithm for chaotic time series prediction. Soft Comput 24, 17093–17109 (2020). https://doi.org/10.1007/s00500-020-05002-7
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DOI: https://doi.org/10.1007/s00500-020-05002-7