抄録
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.
