On the robustness of a simple domain reduction scheme for simulation-based optimization

This paper evaluates a Successive Response Surface Method (SRSM) specifically developed for simulation-based design optimization, e.g. that of explicit nonlinear dynamics in crashworthiness design. Linear response surfaces are constructed in a subregion of the design space using a design of experiments approach with a D-optimal experimental design. To converge to an optimum, a domain reduction scheme is utilized. The scheme requires only one user-defined parameter, namely the size of the initial subregion. During optimization, the size of this region is adapted using a move reversal criterion to counter oscillation and a move distance criterion to gauge accuracy. To test its robustness, the results using the method are compared to SQP results of a selection of the well-known Hock and Schittkowski problems. Although Convergence to a small tolerance is slow when compared to SQP, the SRSM method does remarkably well for these sometimes pathological analytical problems. The second test concerns three engineering problems sampled from the nonlinear structural dynamics field to investigate the method's handling of numerical noise and non-linearity. It is shown that, despite its simplicity, the SRSM method converges stably and is relatively insensitive to its only user-required input parameter.