几类神经网络的分析与优化及其应用研究
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摘要
人工神经网络是人工智能研究领域的重要分支之一，在控制、预测、优化、系统辨识、信号处理和模式识别等方面有广泛的应用。本文分析和研究了几类主要的神经网络模型：进化神经网络、Integrate-and-Fire神经网络以及细胞神经网络，并将其应用于函数逼近、模式识别、数据分类和图像处理。论文的主要研究工作可概括为以下几个方面：
1．对无约束全局优化问题，分别将高斯变异和正交杂交用于差分进化算法的变异算子和杂交算子中，给出了一种插值局部搜索算子，提出了嵌入正交杂交和局部搜索的差分进化算法。对20个标准测试函数作了数值实验。与文献中其它差分进化算法的比较结果表明了算法的有效性。
由预估-校正法确定前馈神经网络结构的情况下，将改进的差分进化算法和Levenberg-Marquardt （LM）算法相结合，提出了一种混合训练算法，优化前馈神经网络的权值和阈值。将该进化神经网络应用于函数逼近、模式分类和识别问题。
2．对同时含有二进制变量和实数变量的非线性优化问题，采用二进制和实数混合编码，在差分进化变异算子中引入异或逻辑运算处理二进制变量，将正交杂交引入到杂交算子中，提出了一种协同二进制—实数差分进化算法。对该算法作了大量的数值测试，并与文献中已有的进化算法作了比较，结果表明了该算法性能优良。
将改进的协同二进制—实数差分进化算法和尺度化共轭梯度反向传播算法相结合，构成两阶段训练算法，同时优化前馈神经网络的结构和权值。将该进化神经网络应用于函数逼近和模式分类问题。
3．对含有二进制变量和整数变量的非线性离散优化问题，采用二进制和整数混合编码，分别将异或逻辑运算和正交杂交引入到离散差分进化算法的变异算子和杂交算子中，提出了一种协同二进制—整数差分进化算法，对该算法作了大量的数值测试，并与文献中已有算法作了比较，结果表明了该算法的有效性。
采用协同二进制—整数差分进化算法，同时进化前馈神经网络的结构和整数权值。将该进化神经网络应用于函数逼近和模式分类问题。
4．针对Lapicque提出的Integrate-and-Fire（IF）模型，给出了一种新的侧抑制连接的IF网络模型，并讨论了其输入—输出关系。与以往的IF模型相比，此模型的活动方程被大大简化了。其运行结果很好地拟合了神经细胞的生理特性，尤其是该模型较好地匹配了突触连接的非线性特性。对其点火机制进行了改进，采用异步点火法，这使得网络的适应性有了很大的提高。
讨论了指数衰减阈值对高斯白噪声刺激下的IF神经元的影响，主要研究了对点火脉冲时间间隔的均值和标准差的影响。结果显示当阈值衰减缓慢时，不论神经元的点火频率何时与衰减频率相当，脉冲时间间隔的变化系数都能达到最小值。通过改变噪声强度或者输入电流而改变点火频率也可以产生同样的影响。分析了在神经元点火后重新设置膜电位所引起的误差。
5．提出了一种具有经典条件反射行为的认知模型，该模型以IF神经元为基本元素，互联形成具有反射弧结构的神经网络，能充分表现经典条件反射对时间的依赖性。计算机仿真显示IF模型能成功地模拟习得、遗忘、刺激间隔效应、阻止和二阶条件反射等现象。
6.提出了一种具有暂态混沌的细胞神经网络，该网络是利用欧拉算法将模型的状态方程转化为离散形式，并引入一项负的自反馈而形成的。对单个神经元的仿真发现该模型具有分叉和混沌的特性。在函数优化中，该网络首先经过一个倍周期倒分叉过程进行混沌搜索，然后进行类似Hopfield网络的梯度搜索。由于它利用了混沌搜索固有的随机性和轨道遍历性，因而具有较强的全局寻优的能力。用两个函数优化的例子验证了这种网络的有效性。
Artificial neural networks (ANNs) are one of the important branches in the artificialintelligence fields. ANNs are the nature-based computing techniques which have beenapplied widely in tasks such as controls, prediction, optimization, system identification,signal processing and pattern recognition, etc. This dissertation is focused on analysisand optimization of some important ANNs including evolutionary ANNs,Integrate-and-Fire ANNs and cellular ANNs, as well as their applications in functionapproximation, pattern recognition, data classification and image processing. The mainworks on these subjects can be summarized as follows:
1. For solving unconstrained global optimization problems, a differential evolution(DE) with orthogonal crossover and local search is proposed. In the proposed algorithm,the Gaussian mutation and orthogonal crossover are combined with the DE mutationand DE crossover operators, respectively. The simplified quadratic interpolation is thentaken as the local search operator of the proposed algorithm. The simulationexperiments on20benchmark functions are carried out. The comparisons with otherDEs show its effectiveness and superiority.
After the structures of feedforward ANNs are determined by trial and error, a hybridtraining algorithm, in which the modified DE algorithm is combined with theLevenberg-Marquardt method, is proposed to optimize the network weights and bias.The evolutionary ANNs are used in function approximation, pattern classification andrecognition.
2. For solving the nonlinear optimization problems involving binary and realvariables, a cooperative binary-real differential evolution is proposed. In this algorithm,a binary-real mixed encoding is used, and the XOR logic operation is introduced in DEmutation to deal with binary variables, as well as the orthogonal crossover is combinedwith DE crossover. Some well-known benchmark problems are used to validate itsefficiency. The proposed algorithm performs well, and the results obtained are verycompetitive when comparing the proposed algorithm against other existing algorithms.
To optimize simultaneously structure and weights of feedforward ANNs, a two-stagetraining algorithm is formed by combining the modified cooperative binary-real DEwith the scaled conjugate gradient method. The evolutionary ANNs are used in functionapproximation and pattern classification.
3. For solving the nonlinear discrete optimization problems with binary and (or)integer variables, a cooperative binary-integer differential evolution is proposed. In theproposed algorithm, a binary-integer mixed encoding is used, and the XOR logicoperation is introduced in the DE mutation to deal with binary variable, as well as theorthogonal crossover is combined with the DE crossover. Some numerical examples areused to validate its effectiveness. The results obtained are also compared against those of other existing algorithms.
To optimize simultaneously structure and integer weights of feedforward ANNs, thecooperative binary-integer DE training algorithm is proposed. The evolutionary ANNsare used in function approximation and pattern classification.
4. To study the Integrate-and-Fire (IF) model, a new IF model is presented, and therelation between input and output is given, in which each of the nerve cells restrains theothers nearby them. Although this model has been simplified greatly, it characterizesmany aspects of real neurons. Especially, it is comparatively good that the modelmatches the nonlinear performance of the synaptic connection. We develop the previousmechanism and use the asynchronous firing mechanism, which makes the network moreflexible.
The effect of an exponentially decaying threshold on a white-noise driven IF neuronis studied, especially on the mean and standard variance of the interspike interval. It isshown that for slow threshold decay the IF model shows a minimum in the coefficientof variation whenever the firing rate of the neuron matches the decay rate of thethreshold. This novel effect can be seen if the firing rate is changed by varying the noiseintensity or the input current. The errors are analyzed, which is associated with resettingthe potential following a spike in simulations of IF neural networks.
5. A cognitive model is presented with classical conditioning behaviors. The modelcomprises a number of IF neurons connecting to form a neural network with reflex arcstructure, which made it fully exhibit the dependency of classical conditioning ontiming. The simulation results show that the model can successfully simulate manytypical experiments such as acquire, extinction, inter-stimulus effects, block andsecondary conditioning.
6. A new model of cellular neural network with transient chaos is proposed, in whicha negative self-feedback is introduced into a cellular neural network after transformingthe dynamic equation to discrete time via Euler’s method. The simulation of singleneuron model shows their characteristics of bifurcation and chaos. In the optimizationproblem, the model gradually approaches, through a chaos search by the course ofreversed period-doubling bifurcations, to a dynamical structure similar to the Hopfieldneural network which converges to a stable equilibrium point. As the model has richdynamics such as randomicity, it can be expected to have robust search ability for globaloptimal solutions. The simulation results on two examples of function optimizationshow that the neural networks are efficient.
1．对无约束全局优化问题，分别将高斯变异和正交杂交用于差分进化算法的变异算子和杂交算子中，给出了一种插值局部搜索算子，提出了嵌入正交杂交和局部搜索的差分进化算法。对20个标准测试函数作了数值实验。与文献中其它差分进化算法的比较结果表明了算法的有效性。
由预估-校正法确定前馈神经网络结构的情况下，将改进的差分进化算法和Levenberg-Marquardt （LM）算法相结合，提出了一种混合训练算法，优化前馈神经网络的权值和阈值。将该进化神经网络应用于函数逼近、模式分类和识别问题。
2．对同时含有二进制变量和实数变量的非线性优化问题，采用二进制和实数混合编码，在差分进化变异算子中引入异或逻辑运算处理二进制变量，将正交杂交引入到杂交算子中，提出了一种协同二进制—实数差分进化算法。对该算法作了大量的数值测试，并与文献中已有的进化算法作了比较，结果表明了该算法性能优良。
将改进的协同二进制—实数差分进化算法和尺度化共轭梯度反向传播算法相结合，构成两阶段训练算法，同时优化前馈神经网络的结构和权值。将该进化神经网络应用于函数逼近和模式分类问题。
3．对含有二进制变量和整数变量的非线性离散优化问题，采用二进制和整数混合编码，分别将异或逻辑运算和正交杂交引入到离散差分进化算法的变异算子和杂交算子中，提出了一种协同二进制—整数差分进化算法，对该算法作了大量的数值测试，并与文献中已有算法作了比较，结果表明了该算法的有效性。
采用协同二进制—整数差分进化算法，同时进化前馈神经网络的结构和整数权值。将该进化神经网络应用于函数逼近和模式分类问题。
4．针对Lapicque提出的Integrate-and-Fire（IF）模型，给出了一种新的侧抑制连接的IF网络模型，并讨论了其输入—输出关系。与以往的IF模型相比，此模型的活动方程被大大简化了。其运行结果很好地拟合了神经细胞的生理特性，尤其是该模型较好地匹配了突触连接的非线性特性。对其点火机制进行了改进，采用异步点火法，这使得网络的适应性有了很大的提高。
讨论了指数衰减阈值对高斯白噪声刺激下的IF神经元的影响，主要研究了对点火脉冲时间间隔的均值和标准差的影响。结果显示当阈值衰减缓慢时，不论神经元的点火频率何时与衰减频率相当，脉冲时间间隔的变化系数都能达到最小值。通过改变噪声强度或者输入电流而改变点火频率也可以产生同样的影响。分析了在神经元点火后重新设置膜电位所引起的误差。
5．提出了一种具有经典条件反射行为的认知模型，该模型以IF神经元为基本元素，互联形成具有反射弧结构的神经网络，能充分表现经典条件反射对时间的依赖性。计算机仿真显示IF模型能成功地模拟习得、遗忘、刺激间隔效应、阻止和二阶条件反射等现象。
6.提出了一种具有暂态混沌的细胞神经网络，该网络是利用欧拉算法将模型的状态方程转化为离散形式，并引入一项负的自反馈而形成的。对单个神经元的仿真发现该模型具有分叉和混沌的特性。在函数优化中，该网络首先经过一个倍周期倒分叉过程进行混沌搜索，然后进行类似Hopfield网络的梯度搜索。由于它利用了混沌搜索固有的随机性和轨道遍历性，因而具有较强的全局寻优的能力。用两个函数优化的例子验证了这种网络的有效性。
Artificial neural networks (ANNs) are one of the important branches in the artificialintelligence fields. ANNs are the nature-based computing techniques which have beenapplied widely in tasks such as controls, prediction, optimization, system identification,signal processing and pattern recognition, etc. This dissertation is focused on analysisand optimization of some important ANNs including evolutionary ANNs,Integrate-and-Fire ANNs and cellular ANNs, as well as their applications in functionapproximation, pattern recognition, data classification and image processing. The mainworks on these subjects can be summarized as follows:
1. For solving unconstrained global optimization problems, a differential evolution(DE) with orthogonal crossover and local search is proposed. In the proposed algorithm,the Gaussian mutation and orthogonal crossover are combined with the DE mutationand DE crossover operators, respectively. The simplified quadratic interpolation is thentaken as the local search operator of the proposed algorithm. The simulationexperiments on20benchmark functions are carried out. The comparisons with otherDEs show its effectiveness and superiority.
After the structures of feedforward ANNs are determined by trial and error, a hybridtraining algorithm, in which the modified DE algorithm is combined with theLevenberg-Marquardt method, is proposed to optimize the network weights and bias.The evolutionary ANNs are used in function approximation, pattern classification andrecognition.
2. For solving the nonlinear optimization problems involving binary and realvariables, a cooperative binary-real differential evolution is proposed. In this algorithm,a binary-real mixed encoding is used, and the XOR logic operation is introduced in DEmutation to deal with binary variables, as well as the orthogonal crossover is combinedwith DE crossover. Some well-known benchmark problems are used to validate itsefficiency. The proposed algorithm performs well, and the results obtained are verycompetitive when comparing the proposed algorithm against other existing algorithms.
To optimize simultaneously structure and weights of feedforward ANNs, a two-stagetraining algorithm is formed by combining the modified cooperative binary-real DEwith the scaled conjugate gradient method. The evolutionary ANNs are used in functionapproximation and pattern classification.
3. For solving the nonlinear discrete optimization problems with binary and (or)integer variables, a cooperative binary-integer differential evolution is proposed. In theproposed algorithm, a binary-integer mixed encoding is used, and the XOR logicoperation is introduced in the DE mutation to deal with binary variable, as well as theorthogonal crossover is combined with the DE crossover. Some numerical examples areused to validate its effectiveness. The results obtained are also compared against those of other existing algorithms.
To optimize simultaneously structure and integer weights of feedforward ANNs, thecooperative binary-integer DE training algorithm is proposed. The evolutionary ANNsare used in function approximation and pattern classification.
4. To study the Integrate-and-Fire (IF) model, a new IF model is presented, and therelation between input and output is given, in which each of the nerve cells restrains theothers nearby them. Although this model has been simplified greatly, it characterizesmany aspects of real neurons. Especially, it is comparatively good that the modelmatches the nonlinear performance of the synaptic connection. We develop the previousmechanism and use the asynchronous firing mechanism, which makes the network moreflexible.
The effect of an exponentially decaying threshold on a white-noise driven IF neuronis studied, especially on the mean and standard variance of the interspike interval. It isshown that for slow threshold decay the IF model shows a minimum in the coefficientof variation whenever the firing rate of the neuron matches the decay rate of thethreshold. This novel effect can be seen if the firing rate is changed by varying the noiseintensity or the input current. The errors are analyzed, which is associated with resettingthe potential following a spike in simulations of IF neural networks.
5. A cognitive model is presented with classical conditioning behaviors. The modelcomprises a number of IF neurons connecting to form a neural network with reflex arcstructure, which made it fully exhibit the dependency of classical conditioning ontiming. The simulation results show that the model can successfully simulate manytypical experiments such as acquire, extinction, inter-stimulus effects, block andsecondary conditioning.
6. A new model of cellular neural network with transient chaos is proposed, in whicha negative self-feedback is introduced into a cellular neural network after transformingthe dynamic equation to discrete time via Euler’s method. The simulation of singleneuron model shows their characteristics of bifurcation and chaos. In the optimizationproblem, the model gradually approaches, through a chaos search by the course ofreversed period-doubling bifurcations, to a dynamical structure similar to the Hopfieldneural network which converges to a stable equilibrium point. As the model has richdynamics such as randomicity, it can be expected to have robust search ability for globaloptimal solutions. The simulation results on two examples of function optimizationshow that the neural networks are efficient.
引文
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