Using the HSS technique for improving the efficiency of the stochastic decomposition algorithm

Abstract

Abstract This work focuses on the Stochastic Decomposition (SD) algorithm of Higle and Sen (1996) for two-stage stochastic linear programming problems with complete recourse. Such an algorithm uses sampling when the random variables are represented by continuous distribution functions. Traditionally, this method has been applied by using the Monte Carlo sampling technique to generate the samples of the stochastic variables. However, Monte Carlo methods can result in large error bounds and variance. Hence, some other approaches use importance sampling to reduce variance and achieving convergence faster that the method based on the Monte Carlo sampling technique. This work proposes to replace the use of the Monte Carlo Sampling Technique in the SD algorithm by the use of the Hammersley Sequence Sampling (HSS) technique. Recently, such a technique has proved to provide better uniformity properties than other sampling techniques and, as a consequence, the variance and the number of samples required for the convergence of the SD algorithm are reduced. The approach has been implemented as a computational framework that integrates the GAMS modeling environment ( Brooke et al., 1998 ), the HSS sampling code and a C++ program. The algorithm is tested with a chemical engineering case-study and the results are discussed.