Genetic Algorithm in Uncertain Environments for Solving Stochastic Programming Problem

Many real problems with uncertainties may often be formulated as Stochastic Programming Problem. In this study, Genetic Algorithm (GA) which has been recently used for solving mathematical programming problem is expanded for use in uncertain environments. The modified GA is referred as GA in uncertain environments (GAUCE). In the method, the objective function and/or the constraint are fluctuated according to the distribution functions of their stochastic variables. Firstly, the individual with highest frequency through all generations is nominated as the individual associated with the solution presenting the best expected value of objective function. The individual with highest frequency is associated with the solution by GAUCE. The proposed method is applied to Stochastic Optimal Assignment Problem, Stochastic Knapsack Problem and newly formulated Stochastic Image Compression Problem. Then, it has been proved that the solution by GAUCE has excellent agreement with the solution presenting the best expected value of objective function, in cases of both Stochastic Optimal Assignment Problem and Stochastic Knapsack Problem. GAUCE is also successfully applied to Stochastic Image Compression Problem where the coefficients of discrete cosine transformation are treated as stochastic variables.