Applying of Zhang neural network in time-varying nonlinear function optimization

Subject Areas : Intelligent Multimedia Processing and Communication Systems (IMPCS)

zeinab  Mousavi ¹ (Azad University Abhar)
elaahe  Karami ² (M.Sc. in applied Mathematics in Bushehr Azad university)
Kobra  Gholami ³ (Mathematic faculty of Boshehr Azad university)

Received: 2023-04-20 Accepted : 2023-05-31 Published : 2023-06-22

Keywords: Neural network, Zhang neural network, Nonlinear optimization, , Optimization, Time-varying nonlinear optimization,

Abstract :

Abstract: Optimization of nonlinear time-varying functions, as a subset of nonlinear programming, has been widely observed in various economic and engineering models. In energy management, one example of optimizing nonlinear functions with time-variable components is the efficient allocation of energy resources and managing changes in demand and supply, leading to increased efficiency and reduced energy waste. In this article, we intend to use Zhang neural networks for optimizing nonlinear functions with time-varying components. By harnessing the parallel processing power of neural networks, Zhang networks search the solution space faster than traditional methods, significantly reducing the required computational time. In this research, the proposed neural network receives data using MATLAB software. The data is first standardized using standard normalization methods. The data is then divided into four stages: training, testing, experimenting and validation which are further evaluated in five phases. The training data is based on the Luenberger-Madala algorithm for the first layer and a linear function for the second layer. Subsequently, the best network structure is considered with the transformation function and the proposed neural network model is tested in five stages. In this paper, we are going to use Zhang's neural networks to optimize time-varying nonlinear functions. In this direction, a general Zhang discretization model with truncation error O (τ^5) has been used and an attempt has been made to study two general five-stage discrete time models of the Zhang neural network and survey about parameter a_1 and expand the optimal step size h. In this research, using MATLAB software, in order to enter the data into the proposed neural network, they are first normalized with the standard normalization method. The desired data in the research were examined and evaluated in four stages, training, testing, second step of testing and validation and in five phases. The training of the data is based on the Lunberg-Maud algorithm model for the first layer and linear function for the second layer. In the following, the best network structure with transformation function is considered and based on the proposed neural network model, it has been tested in five stages. On the other hand, during the past decades, neural network has attracted the attention of researchers due to its good features, including distributed storage, high-speed parallel processing, hardware applications, and superior performance in large-scale online applications. has attracted Some neural networks have been developed to solve nonlinear optimization during recent decades