Approximate method for solving two-stage stochastic programming and its application to the groundwater management

Abstract

Stochastic two-stage programming, a main branch of stochastic programming, offers models and methods to find the optimal objective function and decision variables under uncertainty. This dissertation is concerned with developing an approximate procedure to solve the stochastic two-stage programming problem and applying it in relative field. Five methods used in evaluating the expected value of function for distribution problem are discussed and their basic characteristics and performances are compared to choose the most effective approach for use in a two-stage program. Then the stochastic two-stage programming solving method has been established with the combination of a genetic algorithm (GA) and point estimation (PE) procedure. This approach avoids the inherent limitations of other methods by using PE to estimate the expected value of recourse function and the GA to search optimal solution of the problem. To extend the advantage of GA the modified genetic algorithm (MGA) is built to improve the performance of GA. Finally, the whole procedure is used in several examples with different kinds of variable and linear or nonlinear style objective functions. A stochastic two-stage programming model for an aquifer management problem is set up with considering conductivity and local random recharge as the source of uncertainty in the system. The designed procedure includes the response matrix process that replaces the partial differential flow equation, Girinski potential process and a pre-setup process that makes the response matrix process application in general aquifer random field possible. Other chosen problems are solved with designed approach to illustrate the effects of uncertainty source in the stochastic programming model and compared with results with ones given in literatures.