The Interval Estimate Of Chance Constrained Programming Based On Genetic Algorithm

Stochastic programming is an important branch of mathematical programming. However, it is very different from ordinary mathematical programming. How to solve it is much more complex than that of ordinary mathematical programming because of its random coefficients. This paper tries to study stochastic programming, especially chance constrained programming on the theory of probability and statistics.At present there are two main methods to solving stochastic programming. The first is transforming it into equivalent deterministic programming and then solving it by using the theory of deterministic programming that has been developed successfully. Another is getting the approximate optimum value and optimum solution of chance-constrained programming through some certain genetic algorithm based on random simulated technology.This paper summarizes two methods of chance constrained programming. According to the first method, this article generalizes the coefficient type of those that can be transformed into deterministic programming to exponential family. For more general chance constrained programming, we have obtained its estimated interval and have discussed the factors that affect the precision of estimated optimum value and pointed out the method that raises estimated precision. This estimated interval contained an estimated value of goal function. In view of the fact that the genetic algorithm of stochastic programming based on random simulated technology has succeed greatly, this paper points out that changing parameters of genetic algorithm can obtain a sequence of optimum values of goal function. Taking these genetic algorithm values as sampling data, we can get fitting optimum function by using multivariate spline regression and get the Lipschitzs constant of the fitting optimum function. So for any chance constrained programming problem, we can get its interval estimate.