Stochastic Optimization with Simulation Based Optimization: a Surrogate Model Framework

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.