Abstract
This benchmark study investigates the robustness and efficiency of LS-OPT through a response surface and sensitivity-based optimization methodology, emphasizing its applicability to parametric modeling and shape optimization problems. The approach constructs linear response surfaces within adaptive subregions of the design space using a D-optimal experimental design or available gradient information, thereby creating local approximations of both objective and constraint functions. A domain reduction scheme—requiring only one user-defined parameter, the initial subregion size—is employed to iteratively contract the design space and converge to an optimum. The methodology is evaluated against standard sequential quadratic programming (SQP) methods using a suite of analytical test problems from the Hock and Schittkowski benchmarks. Despite slower convergence to very tight tolerances when compared to SQP, LS-OPT demonstrates robust performance even on challenging and pathological problems. This study illustrates how response surface methods can effectively filter noise and handle non-linear behaviors, making them valuable tools in the context of parametric modeling and shape optimization for complex engineering applications such as automotive crashworthiness and structural design.
