基于吸引域的总体极小化问题的神经网络求解

Neural networks based on the attractive region for solving global minimization

中文关键词  总体极值  神经网络  全局吸引性  吸引域

英文关键词  global optimization  neural network  global attractability  attractive region

中文摘要

      神经网络求解优化问题具有非常强大的实时计算功用,因此近年来受到了密切的关注.这里考察了求解无约束总体极小化问题的神经网络方法,提出了一种新的网络求解模型.从基于吸引域分析方法为出发点证明了所给网络平稳点集合的全局吸引性.分析了网络的电路实现,并估计了各个平稳点的吸引域.这些理论分析与估计是构造所提神经网络模型的依据,同时也是网络可靠运行的基础.此外,数值模拟试验也充分揭示了这个网络模型在实际运行中都能够很好地求解总体极小化问题,是一个十分有效的神经网络系统.这里的结果表明:这里提出的网络模型无论从理论上还是实际运行中都能够可靠且稳定地求解总体极值问题,基于吸引域构造神经网络的方法是一种很有潜力的神经网络求解优化问题的研究方向.

英文摘要

      Neural networks for solving optimisation problems own very robust real time computation ability and much attention had paid for it in recent years. Neural network method for solving global unconstrained minimized problems was investigated and a new neural network model was then proposed. Starting from method on analysis of attractive region, the global attraction of equilibrium point set was demonstrated for the proposed model. The circuit realization of the given model was analysed and the attraction region for individual equilibrium was estimated also. All these theoretical analyses and estimation results were the foundations for constructing the proposed neural network model. At the same time, they also provide the basic supports for the network's reliable running. In addition, numerical experimental results revealed enough evidence to show that the proposed neural network model could work well in practice on finding solutions for the global minimized problems, which means the model was a very efficient neural network system. The results showed that the proposed neural network model could conduct reliably and stably, whether in theory or in practice, to solve the global minimized problems and hence methods based on the attractive region of neural network construction is a promising research direction for solving optimisation problems.