Abstract
In structural design, nonsmooth and noisy responses are frequently encountered, e.g. for dynamic problems. It is well known, that for optimization of systems with nonsmooth and noisy responses, conventional derivative-based methods might not converge. On the contrary, the directional Direct Search Method (DSM), which is a derivative-free method, is a promising candidate providing global convergence even in nonsmooth optimization. DSM combines so-called poll steps, ensuring convergence, and search steps, improving efficiency. However, some derivatives may be smooth and easily available, i.e. inexpensive to calculate. Clearly, derivative-free methods ignore this valuable information, rendering them inefficient. To remedy this, we attempt a practical compromise between derivative-based and derivative-free methods by enhancing the DSM. The main ingredients of the proposed augmented DSM are: (i) a tangent cone which is identified efficiently by using derivatives of some, but not all, response functions, (ii) randomly generated poll directions in a tangent cone, (iii) Search steps facilitating a large flexibility, particularly for Kriging model with subset selection. The efficiency and robustness of the method is studied on a seismic design problem of a 10-story building model. The studied problem confirms the efficiency and robustness of the proposed method.
