Stochastic Optimization with Simulation Based Optimization

Stochastic optimization is vital to making soundengineering and business decisions under uncertainty.While the limited capability of handling complexdomain structures and random variables rendersanalytic methods helpless in many circumstances,stochastic optimization based on simulation is widelyapplicable. This work extends the traditionalresponse surface methodology into a surrogate modelframework to address high dimensional stochasticproblems. The framework integrates Latin hypercubesampling (LHS), domain reduction techniques, leastsquare support vector machine (LSSVM) and design &analysis of computer experiment (DACE) to buildsurrogate models that effectively captures domainstructures. In comparison with existing simulationbased optimization methods, the proposed frameworkleads to better solutions especially for problemswith high dimensions and high uncertainty. Thesurrogate model framework also demonstrates thecapability of addressing the curse-of-dimensionalityin stochastic dynamic risk optimization problems,where several important modification of the classicalBellman equation for stochastic dynamic problems(SDP) is also proposed.