Simulation based optimization with surrogate models.

摘要

This thesis presents surrogate model based algorithms to solve static and dynamic stochastic optimization problems under the Simulation Based Optimization (Sim-Opt) framework.; For static problems, a surrogate framework comprising domain reduction, DACE (design and analysis computer experiment) and LSSVM (least square support vector machine) is proposed. Domain reduction directs the attention of the optimization to sub-regions containing good solutions and avoids spending effort equally across the whole space, DACE intelligently explores the decision space with adaptive experimental design, while LSSVM generalizes observed simulation results by extracting the embedded input vs. output relations, upon which optimization is performed to locate good decisions. Essentially, the framework builds a series of surrogate models with a gradually reduced domain and accumulated information from experimental design until good decisions are found. Applying the framework to testing functions and a supply chain optimization problem demonstrated its superiority over existing Sim-Opt algorithms.; Surrogate model based Sim-Opt algorithms are also proposed to conduct risk optimization in dynamic systems with SDP (stochastic dynamic programming), a subject not addressed by any existing algorithm. The one-step back-propagation based on the Bellman equation is extended to multi-step back-propagation to enable the calculation of desired risks; the optimal decision for any state is obtained through maximizing its pseudo-utility which combines the average return with the risk to balance their trade-of. The curse-of-dimensionality associated with the pseudo-utility function is addressed with a surrogate model by generalizing the results of a sample to the whole space with LSSVM; a second level surrogate model is also devised to directly approximate the optimal policy of SDP, which replaces the online optimization in simulation sample paths with simple function evaluations and substantially reduces the computational overhead. The effectiveness of the proposed algorithms were manifested through constructing the NPV (net present value) vs. risk efficient frontiers for a pharmaceutical company making capacity decisions under various uncertainties.