Two-Stage Stochastic and Deterministic Optimization

The purpose of this paper is to explore some interesting aspects of stochastic opti- mization and to propose a two-stage optimization process for highly nonlinear automotive crash problems. In the first stage of this process, a preliminary stochastic optimization is conducted with a large number of design variables. The stochastic optimization serves the dual purpose of obtaining a (nearly) optimal solution, which need not be close to the initial design, and of identifying a small set of design variables relevant to the optimization problem. In the second stage, a deterministic optimization using only the set of relevant design variables is conducted. The result of the preceding stochastic optimization is used as the starting point for the deterministic optimization. This procedure is demonstrated with a van-component model (previously introduced in [1]) used for crash calculations. LS-OPT [4] is used due to its ability to perform both stochastic (Latin Hypercube) and deterministic optimization.