Evaluating Transition Probabilities for a Stochastic Dynamic Programming Model Used in Water System Optimization

Abstract

Stochastic dynamic programming is one of the most widely used optimization techniques for water system optimization. In this study, four methods for estimating transition probabilities have been evaluated to determine how they influence water system performance for short-term operating policies. The methods are counting, ordinary least-squares regression, robust linear model regression and multivariate conditional distribution. Two discretization schemes—equal-width interval and equal-frequency and data transformation—have also been included in the study as sources of uncertainty. The study was carried out for three water systems: the Outardes River, Manicouagan River, and Lac Saint-Jean, located in Quebec, Canada. The results show that the water system configuration played a significant role in the performance of the transition probabilities. The discretization scheme and data transformation had a considerable influence on the counting and regression methods, whereas they had less of an impact on the multivariate conditional distribution. The robust linear models with equal-frequency discretization without data transformation gave satisfactory results for all the water systems.