A Kind Of Stochastic Programming Algorithm And Application Research Under Uncertain Probability Distribution

Stochastic programming is a model widely used in modern engineering and economic fields to solve optimization problems in uncertain systems.The design of traditional stochastic programming algorithms usually assumes that the probability distribution of the compensation function in the second stage has complete information,that is,the expected value of the compensation function is completely determined.However,this assumption is often not easy to realize in real problems.This paper discusses a type of two-stage stochastic convex programming problem under the condition that the probability distribution has linear partial information.Two algorithms are given,and the method in this paper is applied to the power market bidding problem with the participation of virtual power plants.First of all,for random variables whose probability distribution has linear partial information conditions,based on the maximization minimum expectation criterion,a two-stage stochastic convex programming model based on robust decision-making is given.Aiming at the non-differentiable feature of the second stage compensation function of this model,the paper studies two solving algorithms.The first algorithm is a variable polyhedron optimization method based on direct optimization.It is a complex algorithm based on the traditional complex method and combined with the characteristics of the stochastic programming model in this paper,which can be used to solve the stochastic programming problem under uncertain probability distribution information.And the effectiveness of the proposed method is verified by the examples of three probability distributions with varying degrees of linear partial information constraints.In the second algorithm,based on the subdifferentiability of the model and the idea of conjugate gradient method,a subgradient optimization algorithm is studied.On this basis,an improved projection subgradient algorithm is proposed to solve the stochastic convex programming model with linear partial information.The convergence of the algorithm is proved,and the effectiveness and stability of the algorithm are verified by an example,And it has fast convergence speed.Based on the above theories and methods,this paper finally considers a power market bidding problem with the participation of virtual power plants.Considering the instability of wind power output,a stochastic programming model for optimal bidding of virtual power plants is established with the objective of maximizing bidding revenue.The improved projection subgradient algorithm is used to model and solve the practical problem.Comparing three examples of probability distribution information with different levels of completeness in a single time period,the results show that the bidding revenue with linear partial information of probability distribution in a single period is32.18% higher than that without effective probability distribution information.The example analysis shows that the model can effectively increase the bidding revenue and reduce the decision-making risk,and the proposed algorithm is feasible and effective.