Stochastic Optimization with Simulation Based Optimization

Stochastic optimization is vital to making sound
engineering and business decisions under uncertainty.
While the limited capability of handling complex
domain structures and random variables renders
analytic methods helpless in many circumstances,
stochastic optimization based on simulation is widely
applicable. This work extends the traditional
response surface methodology into a surrogate model
framework to address high dimensional stochastic
problems. The framework integrates Latin hypercube
sampling (LHS), domain reduction techniques, least
square support vector machine (LSSVM) and design &
analysis of computer experiment (DACE) to build
surrogate models that effectively captures domain
structures. In comparison with existing simulation
based optimization methods, the proposed framework
leads to better solutions especially for problems
with high dimensions and high uncertainty. The
surrogate model framework also demonstrates the
capability of addressing the curse-of-dimensionality
in stochastic dynamic risk optimization problems,
where several important modification of the classical
Bellman equation for stochastic dynamic problems
(SDP) is also proposed.