物理学报2017，Vol.66Issue(9)：12-23,12.DOI:10.7498/aps.66.090502
变频正弦混沌神经网络及其应用
Frequency conversion sinusoidal chaotic neural networkand its application
摘要
Abstract
The optimization performance of transiently chaotic neural network (TCNN) is affected by various factors such as chaotic characteristic, model parameters, and annealing function, and its capacity of global optimization is limited. It is demonstrated that the non-monotonic activation function can generate richer chaotic characteristic than the monotonic activation function in the TCNN model. Besides, the activation function involving neurobiological mechanism can not only reflect the rich brain activity in brain waves, but also enhance the non-linear dynamic characteristic, which may further improve the global optimization ability. Hence, a novel chaotic neuron model is proposed with the non-monotonic activation function based on the neurobiological mechanisms from the electroencephalogram.The electroencephalogram consists of five brain waves(i.e.,α,β,δ,γ,and θ waves)which are defined by the quality and intensity of brain waves with different frequency bands ranging from 0.5 Hz to 100 Hz. The brain wave with a higher frequency and a lower amplitude represents a more active brain. Researches demonstrate that the five brain waves can be simplified into sinusoidal waves with different frequencies. Hence, a frequency conversion sinusoidal (FCS) function which has the consistent frequency range and features with brain waves is designed based on the above neurobiological mechanisms. Then a novel chaotic neuron model with non-monotonic activation function which is composed of the FCS function and sigmoid function, is proposed for richer chaotic dynamic characteristic. The reversed bifurcation and the Lyapunov exponent of the chaotic neuron are given and the dynamic system is analyzed, indicating that the proposed FCS neuron model owns richer chaotic dynamic characteristic than transiently chaotic neuron model due to its specialnon-monotonic activation function.Based on the neuron model, a novel transiently-chaotic neural network—frequency conversion sinusoidal chaoticneural network (FCSCNN) is constructed and the basis of model parameter selection is provided as well. To validate the effectiveness of the proposed model, the FCSCNN is applied to nonlinear function optimization and 10-city, 30-city,75-city traveling salesman problem. The experimental results show that 1) the FCSCNN has a good performance under the condition of moderate a, smaller c·A(0) and ε2(0);2) on the basis of the appropriate model parameters, the FCSCNN has better global optimization ability and optimization accuracy than Hopfield neural network, TCNN, improved-TCNN due to its richer chaotic characteristic in complicated combinational optimization problem, especially in middle and large scale problem.关键词
混沌神经网络/脑电图/变频正弦混沌神经网络/组合优化Key words
chaotic neural network/electroencephalogram/frequency conversion sinusoidal chaotic neural network/combination optimization引用本文复制引用
胡志强,李文静,乔俊飞..变频正弦混沌神经网络及其应用[J].物理学报,2017,66(9):12-23,12.基金项目
国家自然科学基金重点项目(批准号: 61533002)、国家杰出青年科学基金(批准号: 61225016)、国家自然科学基金青年科学基金(批准号: 61603009)、中国博士后科学基金(批准号: 2015M570910)、朝阳区博士后研究基金(批准号: 2015ZZ-6) 和北京工业大学基础研究基金(批准号:002000514315501) 资助的课题.Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 61533002), the National Science Fund for Distinguished Young Scholars of China (Grant No. 61225016), the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 61603009), the China Postdoctoral Science Foundation (Grant No. 2015M570910), the ChaoYang District Postdoctoral Research Foundation, China (Grant No. 2015ZZ-6), and the Basic Research Foundation Project of Beijing University of Technology, China (Grant No. 002000514315501). （批准号: 61533002）
