Efficient Sampling Algorithm for Optimization Under Uncertainty

Uncertainty is a part of a real world optimization problem. Computational speed is critical in optimizing large scale stochastic problems. The major bottleneck in solving large scale stochastic optimization problems is the computational intensity of scenarios or samples. This research proposes a novel sampling technique which takes above mentioned problem. This thesis analyzes existing and novel sampling techniques by conducting large scale experiments with different functions. The sampling techniques which were analyzed are Monte Carlo Sampling (MCS), Latin Hypercube Sampling (LHS), Hammersley Sequence Sampling (HSS), Latin Hypercube-Hammersley Sequence Sampling (LHS-HSS), Sobol Sampling, and the proposed novel technique which is Latin Hypercube-Sobol Sampling (LHS-SOBOL). It was found that HSS performs better up to 40 uncertain variables, Sobol up to 100 variables, LHS-HSS up to 250 variables, and LHS-SOBOL for large scale uncertainties which was tested for 800 variables. Thus, by analyzing the results of this work we can conclude that LHS-HSS can be used for uncertainties from 2 to 100 variables, and LHS-SOBOL for larger than 100 variables.