Research On Unconstrained Optimization Method Based On Equilibrium Point And Its Application

Nonlinear unconstrained optimization is widely used in the fields of financial economy,industrial production,cyber security,artificial intelligence and other fields.It is characterized by discrete,nonlinear,unknown and high dimensional.The traditional numerical optimization solution methods are sensitive to initial values,and when the gradient information is difficult to obtain,these methods are difficult to solve the high-dimensional and complex optimization model.Therefore,many scholars have devoted themselves to the study of unconstrained optimization methods that possess both theoretical properties and strong numerical performance.Control system optimization algorithms are widely used in the solution of practical optimization problems because of their wide applicability,scalability and flexibility in the design of control strategies.In this thesis,the control system optimization algorithms are studied in depth to solve noninear unconstrained optimization problems,the specific research contents and innovations are as follows:1.An unconstrained optimization method based on equilibrium pointst: First,we constructed an equilibrium point optimization control mode based on the principle of feedback control,then proposed the existence theory of equilibrium points,and proved that the equilibrium points obtained from the model are stable.Further,a nonlinear unconstrained optimization solution method based on the equilibrium point is proposed.The method automatically adjusts the controlled quantities to reduce the deviation according to the control strategy,thus achieving the approximation of the equilibrium point to the optimal point.The method is compared with other optimization algorithms by conducting numerical experiments with univariate and multivariate test functions on a common test set.The experiments demonstrate that this algorithm can initially mitigate the effect of initial values on the optimal solution and have some advantages in terms of solution time.2.Filled function based on equilibrium unconstrained optimization method: In order to further reduce the sensitivity of the algorithm to the initial point,we introduced a filled function to increase the likelihood of obtaining a globally optimal solution.The basic principle of the algorithm is to use the fill function to jump out of the region where the current local minima are located.Then we use the point that makes the model solution result better as the initial point.Futhermore,we use the equilibrium point optimization algorithm for global search.During the solution process,the system has two feasible solutions.When the result of the fill function solution is less than another feasible solution,we believe that a new disturbance has arisen.Then it used to make controllers,actuators operate based on feedback biases.This algorithm is able to increase the chance of jumping out of the range of locally optimal solutions,and it can obtain more accurate results.Finally,we validate on a generic test set,the experimental results show the advantages of the proposed algorithm in terms of solution accuracy.3.Application research: The main application is to solve the power load scheduling problem in power plants and the cutting data fitting problem.For the power load scheduling problem,an unconstrained optimization method based on equilibrium points is used to solve the problem under existing power optimization scheduling schemes and real data conditions.Compared with other optimization methods,the results show that the method can alleviate the initial value sensitivity problem and reduce the cost of power generation to a certain extent.For the data fitting experiments,we have analysed actual cutting temperature data and modelled the relationship between them in order to measure the extent to which the cutting dosage affects the cutting temperature.Then,an equilibrium point unconstrained optimization method based on a filled function was used to solve the model.Meanwhile,we use the residual standard deviation of the model as an evaluation indicator of the data fitting results.The experimental results show that the data fit is promising and the validity of the algorithm is verified.