带扰动的变频正弦混沌神经网络研究

为了研究变频正弦混沌神经网络(FCSCNN)的抗扰动能力,在该混沌神经元的内部状态中分别引入三角函数和小波函数扰动项,提出了带扰动的变频正弦混沌神经元模型。给出了该混沌神经元的倒分岔图及Lyapunov指数的时间演化图,分析了其动力学特性。利用该模型构建了新型暂态混沌神经网络,通过选择不同的扰动系数,将其应用于函数优化和组合优化问题上。仿真实验表明,在适当的扰动系数下,变频正弦混沌神经网络能够有效地解决函数优化和组合优化问题,体现了该模型具有较强的鲁棒性和抗扰动能力。     

一种用于函数优化的小波混沌神经网络

混沌神经网络能有效地解决函数优化问题。通过把sigmoid函数转化为墨西哥帽小波函数,而单一化退火因子函数被分段指数模拟退火函数所取代,提出了一种新型的混沌神经网络。与传统的混沌神经网络相比,该网络具有更强的全局寻优能力。仿真结果表明,小波混沌神经网络在搜索全局最优解的速度和精确度上都明显优于传统的混沌神经网络。     

墨西哥帽小波混沌神经网络及其应用

此文用墨西哥帽小波函数和Sigmoid函数相加组成一个新函数,利用此函数作为激励函数,提出一种新型的暂态混沌神经元模型,通过实验给出该神经元的倒分叉图以及最大Lyapunov指数时间演化图,并且分析此神经元的动力学特性。基于该神经元模型,构造一种暂态神经网络,并将其应用于组合优化和预测方面,通过对经典的10城市TSP,验证墨西哥帽小波混沌神经网络在克服陷入极小点的有效性。     

Shannond小波混沌神经网络及其TSP（城市旅行商）问题的求解

混沌神经网络已经被证明是解决组合优化问题的有效工具．针对混沌神经网络的单调的激励函数。通过引入Shannond小波和Sigmoid函数加和组成的非单调激励函数,提出了一种新型的暂态混沌神经元模型．给出了该混沌神经元的倒分岔图和最大Lyapunov指数时间演化图,分析了其动力学特性．基于该模型,构造了一种暂态混沌神经网络,并将其应用于函数优化和组合优化问题．通过经典的10城市TSP验证了该暂态混沌神经网络的有效性．     

Shannon小波混沌神经网络及其TSP(城市旅行商)问题的求解

混沌神经网络已经被证明是解决组合优化问题的有效工具.针对混沌神经网络的单调的激励函数,通过引入Shannon小波和Sigmoid函数加和组成的非单调激励函数,提出了一种新型的暂态混沌神经元模型.给出了该混沌神经元的倒分岔图和最大Lyapunov指数时间演化图,分析了其动力学特性.基于该模型,构造了一种暂态混沌神经网络,并将其应用于函数优化和组合优化问题.通过经典的10城市TSP验证了该暂态混沌神经网络的有效性.     

SLF混沌神经网络及其应用

针对混沌神经网络的单调激励函数,引入Legendre函数和Sigmoid函数组合作为非单调激励函数,构造了一种新的暂态混沌神经元模型（SLF模型）,并给出了此混沌神经元的倒分岔图和最大Lyapunov指数时间演化图,利用该模型构建了一种暂态混沌神经网络,通过对非线性函数优化和TSP问题的求解验证了该模型的有效性。     

小波混沌神经网络的研究与应用

混沌神经网络已被证明是解决组合优化问题的有效工具,但单一化的退火因子无法同时满足准确性和速度性两方面要求,因此改变传统的混沌方式以提高搜索速度和精度就变得尤为重要.文中将Sigmoid函数转化为小波函数可以有效地解决该问题,通过将Sigmoid函数转化为Mexican hat小波函数,以及引入Shannon小波和Sigmoid函数加和组成的非单调激励函数这两种方式,提高了搜索效率和准确度,并用这两种新的模型对两种优化问题进行仿真.仿真结果表明小波混沌神经网络无论在全局最优解的搜索效率还是精确度上都明显优于传统的混沌神经网络.可知将小波函数引入混沌神经网络是极具研究潜力的.     

一种求解优化问题的新型小波混沌神经网络

基于神经元的自反馈项可产生混沌的现象,将Gauss小波函数作为混沌神经元的自反馈项。分析了Gauss小波的尺度和平移参数对神经元动力学的影响,提出了自反馈连接权和Gauss小波尺度双重模拟退火的混沌神经元。构建了混沌神经网络模型,分析了由Gauss小波函数产生的附加能量函数对网络优化能力的影响。优化问题的仿真结果表明,该网络能够以较快的速度找到优化问题的全局最优解。     

带扰动的混沌神经网络的研究

为了研究混沌神经网络的抗扰动能力,在Chen’s混沌神经网络中引入了三角函数扰动项,研究了带扰动的Chen’s混沌神经元模型,给出了该混沌神经元的倒分岔图和Lyapunov指数图,分析了其动力学特性。基于该混沌神经元模型,构造了带扰动的Chen’s混沌神经网络,并将其应用于函数优化和旅行商问题（TSP）。仿真结果表明：Chen’s混沌神经网络有一定的抗扰动能力。     

改进暂态混沌神经网络在信道分配中的应用

研究信道分配优化问题,由于传统迭代过程中存在收敛率低,易于陷入局部最优解等缺点。为改善算法收敛速率和信道分配效果,采用改进的暂态混沌神经网络(MTCNN)。在混沌神经网络的动态特性中采用时变增益,在退火过程中采取分段的退火机制,使得混沌搜索阶段保持较长时间的混沌态,利于进行全局搜索,稳定收敛阶段能够迅速收敛于最优解,提高收敛率。仿真结果表明,改进后的算法能很好地解决信道分配问题。和暂态混沌神经网络及仅分段的暂态神经网络相比,最优解率得到很大的提高,网络收敛速度提高了12%以上。最后,给出了模型参数对网络性能影响的一些结论。     

A noisy chaotic neural network for solving combinatorial optimization problems: stochastic chaotic simulated annealing

Recently Chen and Aihara have demonstrated both experimentally and mathematically that their chaotic simulated annealing (CSA) has better search ability for solving combinatorial optimization problems compared to both the Hopfield-Tank approach and stochastic simulated annealing (SSA). However, CSA may not find a globally optimal solution no matter how slowly annealing is carried out, because the chaotic dynamics are completely deterministic. In contrast, SSA tends to settle down to a global optimum if the temperature is reduced sufficiently slowly. Here we combine the best features of both SSA and CSA, thereby proposing a new approach for solving optimization problems, i.e., stochastic chaotic simulated annealing, by using a noisy chaotic neural network. We show the effectiveness of this new approach with two difficult combinatorial optimization problems, i.e., a traveling salesman problem and a channel assignment problem for cellular mobile communications.     

Dynamic characteristic of a multiple chaotic neural network and its application

Based on chaotic neural network, a multiple chaotic neural network algorithm combining two different chaotic dynamics sources in each neuron is proposed. With the effect of self-feedback connection and non-linear delay connection weight, the new algorithm can contain more powerful chaotic dynamics to search the solution domain globally in the beginning searching period. By analyzing the dynamic characteristic and the influence of cooling schedule in simulated annealing, a flexible parameter tuning strategy being able to promote chaotic dynamics convergence quickly is introduced into our algorithm. We show the effectiveness of the new algorithm in two difficult combinatorial optimization problems, i.e., a traveling salesman problem and a maximum clique problem.     

Paralleled hardware annealing for optimal solutions on electronicneural networks

Three basic neural network schemes have been extensively studied by researchers: the iterative networks, the backpropagation networks, and the self-organizing networks. Simulated annealing is a probabilistic hill-climbing technique that accepts, with a nonzero but gradually decreasing probability, deterioration in the cost function of the optimization problems. Hardware annealing, which combines the simulated annealing technique with continuous-time electronic neural networks by changing the voltage gain of neurons, is discussed. The initial and final voltage gains for applying hardware annealing to Hopfield data-conversion networks are presented. In hardware annealing, the voltage gain of output neurons is increased from an initial low value to a final high value in a continuous fashion which helps to achieve the optimal solution for an optimization problem in one annealing cycle. Experimental results on the transfer function and transient response of electronic neural networks achieving the global minimum are also presented.     

随机神经网络发展现状综述

随机神经网络 (RNN)在人工神经网络中是一类比较独特、出现较晚的神经网络 ,它的网络结构、学习算法、状态更新规则以及应用等方面都因此具有自身的特点 .作为仿生神经元数学模型 ,随机神经网络在联想记忆、图像处理、组合优化问题上都显示出较强的优势 .在阐述随机神经网络发展现状、网络特性以及广泛应用的同时 ,专门将RNN分别与Hopfield网络、模拟退火算法和Boltzmann机在组合优化问题上的应用进行了分析对比 ,指出RNN是解决旅行商 (TSP)等问题的有效途径     

Optimal solutions for cellular neural networks by paralleledhardware annealing

An engineering annealing method for optimal solutions of cellular neural networks is presented. Cellular neural networks are very promising in solving many scientific problems in image processing, pattern recognition, and optimization by the use of stored program with predetermined templates. Hardware annealing, which is a paralleled version of mean-field annealing in analog networks, is a highly efficient method of finding optimal solutions of cellular neural networks. It does not require any stochastic procedure and henceforth can be very fast. The generalized energy function of the network is first increased by reducing the voltage gain of each neuron. Then, the hardware annealing searches for the globally minimum energy state by continuously increasing the gain of neurons. The process of global optimization by the proposed annealing can be described by the eigenvalue problems in the time-varying dynamic system. In typical nonoptimization problems, it also provides enough stimulation to frozen neurons caused by ill-conditioned initial states.     

用随机神经网络优化求解改进算法的研究

随机神经网络是一种仿照实际的生物神经网络的生理机制而定义的网络，其网络结构及应用具有自身的特点。在详细讨论了动态随机神经网络求解典型NP优化问题TSP的算法的同时，特别提出了一种有效改进算法，使得参数在简单选取的情况下保证能量函数的下降，在组合优化问题上具有普遍意义，并且在10城市TSP对改进算法进行验证，指出RNN是解决TSP问题的有效途径。     

A unified framework for chaotic neural-network approaches to combinatorial optimization.

As an attempt to provide an organized way to study the chaotic structures and their effects in solving combinatorial optimization with chaotic neural networks (CNN), a unifying framework is proposed to serve as a basis where the existing CNN models ran be placed and compared. The key of this proposed framework is the introduction of an extra energy term into the computational energy of the Hopfield model, which takes on different forms for different CNN models, and modifies the original Hopfield energy landscape in various manners. Three CNN models, namely the Chen and Aihara model with self-feedback chaotic simulated annealing [CSA] (1995, 1997), the Wang and Smith model with timestep CSA (1998), and the chaotic noise model, are chosen as examples to show how they can be classified and compared within the proposed framework.