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  This study is concerned with the estimation of constant  and time-varying parameters in non-linear ordinary differential equations, which do not have analytical solutions. The estimation is done in a multi-stage method where constant and time-varying parameters are estimated in a straight sequential way from several stages. In the first stage, the model of the differential equations is converted to a regression model that includes the state variables with their derivatives and then the estimation of the state variables and their derivatives in a penalized splines method and compensating the estimations in the regression model. In the second stage, the pseudo- least squares method was used to es

Background Due to the intermittent, nonlinear, and uncertain behavior of renewable energy sources (res) such as solar and wind, grid stability and reliability require very high forecasting and optimization skills as widely reported in the literature. Traditional optimization methods work very well in small or static systems but are suffer difficulty on large-scale, dynamic and stochastic renewable environment due to their NP-hard nature. Methods The framework introduces the concept of a Machine Learning-Assisted Hybrid Cuckoo Search (ML-HCS) that combines CS with a hybrid metaheuristic and integrates Long Short-Term Memory (LSTM) networks for forecasting based on both regression models of LSTMs and hybrid optimization algorithm

Optimization is essentially the art, science and mathematics of choosing the best among a given set of finite or infinite alternatives. Though currently optimization is an interdisciplinary subject cutting through the boundaries of mathematics, economics, engineering, natural sciences, and many other fields of human Endeavour it had its root in antiquity. In modern day language the problem mathematically is as follows - Among all closed curves of a given length find the one that closes maximum area. This is called the Isoperimetric problem. This problem is now mentioned in a regular fashion in any course in the Calculus of Variations. However, most problems of antiquity came from geometry and since there were no general methods to solve suc