Stochastic Programming Based On L-shape And Filter Algorithms

The research of stochastic programming has entered a new period,which has become an important topic in the field of operational research.The recourse stochastic programming generally assumes that the probability distribution of the random variables has complete information,but the actual situation is only part of the information could obtain.This paper will choose the two-stage recourse stochastic model with linear partial information(LPI),quadratic stochastic model and nonlinear stochastic model as study objects.Exploring more efficient algorithms based on the existing algorithms,in order to improve the operating speed and get a more accurate solution.To the two-stage stochastic programming model with discrete probability could be established under a class of linear partial information conditions and the Maximum minimum expected recourse criterion(Max EMin)evaluation,then through the quadratic method and dual decomposition method to get the feasibility cutting and optimal cutting based on the L-shaped algorithm,and prove the verification by an example.Further,to the quadratic stochastic programming problems based on linear partial information under the Max EMin evaluation,if we still use the L-shaped algorithm,it will be very complex,but we can use its main idea,exchange the precise cutting into imprecise cutting,this paper establishes a recourse stochastic programming model.By giving the fuzzy range can quickly find the optimal solution in the feasible region,the effectiveness of the proposed algorithm through an example.Finally we propose a new algorithm based on the classical SQP type filter algorithm aim at the two-stage nonlinear stochastic programming problem.In order to obtain the optimal solution of the second stage decision variables,we use quadratic program get the optimal solutions in two-stage problem,and the optimal solution is found in the filter.So the filter algorithm of stochastic nonlinear programming is obtained and proved in the end.The model and algorithm studied in this paper lay the foundation for the research of the theory and application of stochastic programming.