An improved version of DYNAMIC-Q for simulation-based optimization using response surface gradients and an adaptive trust region

Abstract

This paper proposes an improvement on the DYNAMIC-Q method for optimization of applications requiring expensive and (often) noisy numerical stimulations for function evaluations. The original DYNAMIC-Q method requires the selection of a step size and a move limit by the user. For noisy responses, the success of the original method depends on the correct choice of step size and move limit. The improved version uses the adaptive trust region features of an existing successive response surface method (SRSM) algorithm to replace the selection of the step size and move limit with one parameter, the initial trust region size. For the testing of the new method, DYNAMIC-Q(RSG), an arbitrary selection from the well-known Hock and Schittkowski problems as well as a non-linear structural engineering problem are used. It is shown that for problems where the gradient information is reliable, the original DYNAMIC-Q method is superior as expected. However, where noisy responses cause inaccurate and unreliable gradient information, the SRSM and DYNAMIC-Q(RSG) methods are proven to be more robust with SRSM superior in its ability to coverage more stably. The performance of DYNAMIC-Q(RSG) is encouraging as it maintains the robustness and minimum user input of SRSM, but has faster convergence for analytical problems. © 2003 John Wiley and Sons, Ltd.