Computationally efficient solution algorithm for a large scale stochastic dynamic program

Abstract

Stochastic dynamic programs suffer from the so called curse of dimensionality whereby the number of evaluations grows exponentially as the number of stages increases. This curse is further magnified when the stochastic variable is discretized as this adds another dimension to the number of evaluations required. As a result, it is computationally infeasible (in some cases outright impractical) to try solving these problems using an exhaustive search over all the parameters. Computational algorithms that combine decomposition techniques and simulation with reasonable assumptions on the stochastic variables can render very efficient solutions with a high degree of accuracy. This paper develops and tests such an algorithm to solve a large scale stochastic dynamic program. The algorithm's performance is tested through a simulation study of a system with the prescribed parameters determined by the algorithm. The results analyzed show that the algorithm generates very good solutions as validated by the performance indicators of the system. The solutions provide the managers of the system with insights into the complex relationships that characterize the system.

Amostragem de Séries Sintéticas Hidrológicas

“…Os resultados apresentados foram extremamente positivos, mostrando ser possível a utilização de um número menor de séries sintéticas sem prejudicar a estrutura de correlações espaciais ou a distribuição de probabilidades empíricas obtidas com o modelo estocástico. Desta maneira, o método encontra aplicabilidade em estudos diversos como, por exemplo, trabalhos focados na otimização estocástica da operação de múltiplos reservatórios, reconhecidamente onerosos do ponto de vista computacional (KELMAN et al, 1990;PEREIRA & PINTO, 1985;SRIFI & HIPEL, 2001;SAADOULI, 2010;FA-BER & STEDINGER, 2001).…”