Efficient sampling algorithm for large-scale optimization under uncertainty problems

Abstract

Uncertainty is part of the real-world optimization problems. The major bottleneck in solving large-scale stochastic optimization problems is the computational intensity of scenarios or samples. To this end, this research presents a novel sampling approach. This sampling called LHS-SOBOL combines one-dimensional uniformity of LHS and d-dimensional uniformity of Sobol. This paper analyzes existing and novel sampling techniques by conducting large-scale experiments with different functions. The sampling techniques which are 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 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 for larger than 100 variables.