Robust SA Algorithm For Two Stage Stochastic Linear Programming

In all fields,the optimization problem is an eternal theme.Due to the influence of many uncertain factors in the actual production and life,the introduction of random variables makes the random programming problem more suitable for the solution of the actual problems.This paper mainly studies a special form of the two stage stochastic programming ??two stage linear stochastic programming with fixed compensation.The two stage stochastic linear programming plays an important role in many fields,such as traffic,inventory,agriculture,finance and power systems.There are many studies on the solving algorithms of this problem,but the convergence rate of most of the algorithms is slow when the random variables are much more.On the basis of previous studies,this paper makes an in-depth study of the nature of the problem and uses the robust SA algorithm to solve this problem.In the large scale of random variables,the Latin hypercube sampling method is used to solve the problem.The experiment is carried out to compare robust SA algorithm with the SAA algorithm.This article is mainly studied in the following aspects:The first chapter mainly introduces the generation and development of random programming,the model of the two stage stochastic linear programming problem,and the current research methods: the origin and development of the SA algorithm and the SAA algorithm,as well as the thinking of the solution.The second chapter mainly introduces some preparatory knowledge used in this paper: the properties of the objective function of the two stage stochastic linear programming problem and the properties of the feasible domain,which is the theoretical support for the solution of the two stage stochastic linear programming problem by the robust SA algorithm.The third chapter proves the convergence of the robust SA algorithm for solving the two stage stochastic linear programming problem with fixed compensation,and analyzes its convergence speed.The fourth chapter mainly introduces the common algorithm for solving the two stage stochastic linear programming problem??the SAA algorithm and the decomposition algorithm.In the fifth chapter,the numerical experiment is carried out to prove the feasibility of the robust SA algorithm to solve the two stage stochastic linear programming problem.Compared with the SAA algorithm,it is proved that the convergence speed of the robust SA algorithm is fast.