Scenario generation in stochastic programming using principal component analysis based on moment-matching approach

Abstract

In optimization models based on stochastic programming, we often face the problem of representing expectations in proper form known as scenario generation. With advances in computational power, a number of methods starting from simple Monte-Carlo to dedicated approaches such as method of moment-matching and scenario reduction are being used for multistage scenario generation. Recently, various variations of moment-matching approach have been proposed with the aim to reduce computational time for better outputs. In this paper, we describe a methodology to speed up moment-matching based multistage scenario generation by using principal component analysis. Our proposal is to pre-process the data using dimensionality reduction approaches instead of using returns as variables for moment-matching problem directly. We also propose a hybrid multistage extension of heuristic based moment-matching algorithm and compare it with other variants of moment-matching algorithm. Computational results using non-normal and correlated returns show that the proposed approach provides better approximation of returns distribution in lesser time.