Illustrative Computational Experiments

Abstract

Throughout this book, we have presented the Stochastic Decomposition algorithm and a number of features that have been designed to enhance its computational effectiveness. In this chapter we illustrate SD’s computational viability through the results of various computational experiments that have been conducted. As one might expect, the SD computer programs have evolved over time, and the results reported in this chapter were obtained from various generations of the program. To facilitate comparisons, we have attempted to report in a manner that is not dependent upon the particular implementation used. We note that the tasks in each iteration are well defined (i.e., solve a subproblem, execute the argmax procedure, update the cut coefficients, etc.), and the time required to implement each task depends critically upon the care with which they are implemented, as well as the machine on which the program is run. In this chapter, we are primarily focussed on measures related to the number of iterations required. Additionally, because SD uses sampled data in its quest for an optimal solution, it is important to review the quality of the solutions produced. For this reason, we report the extent to which the objective value associated with the SD solution deviates from the optimal objective value whenever possible. Finally, we explore run time characteristics, such as solution times and memory requirements for our large scale implementation as well.