Analysis And Design Of Frequency Conversion Sinusoidal Chaotic Neural Network

Transiently chaotic neural network(TCNN)is a special chaotic neural network(CNN)for solving the optimization problem.TCNN can overcome the deficiency of local minimum in HNN based on the random-like behavior and ergodicity of chaos by introducing decaying self-feedback item.However,the global optimization performance of TCNN is limited by various factors such as intensity of chaotic characteristic,annealing function,model parameters,and problem complexity,etc.In order to solve the mentioned problem,the optimization mechanism and chaotic dynamics characteristic of TCNN are researched and analyzed.A novel frequency conversion sinusoidal chaotic neural network(FCSCNN)with the non-monotonous activation function is proposed based on the relationship between the frequencyamplitude feature of brain waves and degree of activity.FCSCNN has richer chaotic dynamic characteristic than TCNN.The chaotic characteristic of FCSCNN are analyzed detailedly.Meanwhile,the simulated annealing strategy and robustness of FCSCNN are researched and improved.Besides,a multi-objective optimization algorithm based on FCSCNN is designed for filling in the gap that CNN cannot solve the multi-objective optimization problems(MOP).In this paper,the main research work and innovation points are shown as follows:(1)Design for frequency conversion sinusoidal chaotic neural networkAs to the limitation of global optimization for TCNN,a novel chaotic neuron model is proposed with the non-monotonous activation function which is composed by the frequency conversion sinusoidal(FCS)function and sigmoid function based on the neurobiological mechanisms that the electroencephalogram is overlapped with different frequencies sinusoidal waves.The reversed bifurcation and the Lyapunov exponent of the chaotic neuron are given and the dynamic system is analyzed.Based on the neuron model,a novel FCSCNN is proposed and applied to nonlinear function optimization and combinational optimization problems.The simulation results show that TCNN can avoid local minimum than HNN,FCSCNN has better optimization accuracy than TCNN,improved-TCNN due to its rich dynamic characteristic.(2)Design for FCSCNN with self-adaptive simulated annealingFCSCNN cannot consider search accuracy and convergence speed simultaneously.In order to solve the mentioned problem,a novel self-adaptive simulated annealing(SSA)strategy is proposed by analyzing the optimization mechanism of the TCNN and the existing annealing strategy.It can give appropriate self-feedback connection weights based on the characteristics of Lyapunov exponent.The reversed bifurcation,Lyapunov exponent and annealing function evolution diagram of the chaotic neuron are given and the dynamic characteristic is analyzed.It shows that the SSA strategy can choose appropriate annealing speed in different stages,which can not only make full use of chaotic global searching ability but also accelerate convergence speed.Based on the neuron model,a novel FCSCNN with SSA strategy(FCSCNN-SSA)is proposed and applied to nonlinear function optimization and combinational optimization problems.The simulation results show that: 1)The SSA strategy can targeted choose the appropriate annealing speed.It is superior to other several existing simulated annealing methods for pertinence and adaptability and can be expanded to other similar models with same optimization mechanism;2)FCSCNN-SSA can converge with a fast speed and search accuracy simultaneously than TCNN,TCNN-SEA,I-TCNN,NCNN,BFS-TCNN,FCSCNN.(3)Research on the anti-disturbance ability of FCSCNNA novel FCS chaotic neuron model with disturbance is proposed to study the antidisturbance ability of the FCSCNN with the trigonometric function and wavelet function disturbance introduced into the internal state of the chaotic neuron model respectively.The reversed bifurcation and the Lyapunov exponent of the chaotic neuron are given and the dynamic system is analyzed.A TCNN which is constructed with the novel chaotic neuron model is applied to function optimization and combinational optimization problems with different disturbance coefficient.The simulation results demonstrate that the FCSCNN can solve the function optimization and combinational optimization problems effectively with the appropriate disturbance coefficient.It reflects FCSCNN has a strong robustness and anti-disturbance ability.(4)Design for hysteretic noisy FCSCNNFor the purpose of solving the problem that the optimal performance degradation due to higher noise and limited precision due to premature convergence,the hysteretic dynamics and stochastic noise are introduced into the internal state equation of FCSCNN's chaotic neuron.A novel hysteretic noisy FCSCNN(HNFCSCNN)is proposed to improve the solution quality at higher noise.HNFCSCNN combines chaotic searching,stochastic wandering with hysteretic dynamics for better global searching ability.A specific activation function with anticlockwise and clockwise hysteretic-loops is adopted to relieve the adverse impact caused by higher noise and maintain stochastic wandering ability for FCSCNN.At the same time,FCSCNN with two hysteretic loops have jumping power to get away from the local minima in saturate stage.The simulation results show that the proposed HNFCSCNN can increase the optimization accuracy and speed of FCSCNN at higher noises,and that the proposed energy function can decrease the runtime of optimal computation.It has better optimization performance than the other several algorithms.(5)Design for multi-objective FCSCNNIn order to make up the deficiency that FCSCNN cannot solve the MOP,the design principle and process of multi-objective optimization algorithms are researched and analyzed.A multi-objective FCSCNN(MOFCSCNN)is designed based on its optimization mechanism and characteristic.Nondominated solutions are extracted from all process solutions of dynamical evolution,then are stored into archives.The three key points(i.e.the selection of nondominated solutions and optimal solution,bank archive management)are analyzed,designed and realized when transform single object optimization problems into multi-objective optimization problems.Multi-objective benchmark test functions are adopted to test MOFCSCNN and other algorithms.The simulation results show the validity and feasibility of the proposed MOFCSCNN.