Quantum mechanics

Slice sampling

Algorithm

Scale (ratio)

Discrete mathematics

Optimization algorithm

Statistics

Sobol sequence

Importance sampling

Computer science

Mathematical optimization

Filter (signal processing)

Physics

Mathematics

Sampling (signal processing)

Monte Carlo method

Hypercube

Latin hypercube sampling

Computer vision

Computers & Chemical Engineering

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.

Efficient sampling algorithm for large-scale optimization under uncertainty problems