A Class Of Stochastic Programming Algorithms And The Convergence Analysis

In production and living, in order to build more in line with the actual conditions ofthe programming model, usually want to consider some of the practical problemsuncertain factors, such contain random variables is planning for stochastic programmingproblems. In order to be transformed into a deterministic programming problem, oftenwith random variables mathematical expectation to replace in the planning of randomvariables and the solution. But often the optimal solution because they do not meet theconstraints and failure. Thus must use other ways to deal with stochastic programmingproblems. Random planning of this science theory and calculation method is not perfect,not mature, but it has set up a file in the management science, economics, electric powersystem scheduling, engineering structure design, the optimal control, and otherdisciplines and fields showed strong vitality!In stochastic programming problems, how to select the sample size is related to theaccuracy of the solution. This makes the study a random sample capacity is of greatsignificance. This issue is in the home and abroad on the basis of existing researchresults, focusing on Monte Carlo sampling sample size iteration method and iterativetermination conditions, and considering the error accuracy through statisticalmethods.on the basic of previous results to get new algorithm, and to expand theresearch.This paper is divided into five chapters, each chapters is organized as follows:Chapter1, stochastic programming problems generally states. A brief introductionto the generation,development and classification of stochastic programming,andintroduced the present situation of the study at home and abroad.Chapter2, this paper introduces the basic idea of the Monte Carlo andconvergence.Given in the application of the Monte Carlo method in the expectations of the thestochastic programming model, and gives the numerical experiments.Chapter3, presents a kind of the Genetic Algorithm based on dynamic of MonteCarlo simulation, the Monte Carlo to reduce the blindness of random simulation. Toreduce the blindness of the Monte Carlo random simulation.Given the optimal solutionof the expression of form and the iteration algorithm termination conditions.,andconvergence analysis and numerical experiments. Chapter4, combined with the steepest descend method, this paper puts forward adynamic Particle Swarm Algorithm. Given the dynamic iteration method of sample sizeand iterative algorithm termination conditions. And in the assumptions, to prove theconvergence of the algorithm, the numerical result shows the feasibility of thealgorithm.Chapter5, summary and outlook.Summarized in this paper, and points out that thefurther research direction.