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.