Improvements in Sparse Response Surfaces for Engineering Optimization: A Reweighting Approach

Engineering product optimization requires many times of simulation which is often time-consuming. The High Sparse Response Surface (HSRS) is an efficient method. However, the efficiency of coefficient solving and the stability of the results need to be improved. An improved HSRS method is proposed, which employs an iteratively reweighted technique to efficiently resolve sparse coefficients. This method prioritizes the selection of sub-dictionaries by assigning lesser weights to those with smaller ℓ1-norms, and facilitates the selection of base functions within these sub-dictionaries by assigning lower weights to those with larger coefficients. Through a constrained number of iterations, this refined approach yields a sparse solution that more closely approximates the ℓ0-norm minimal solution, thereby elevating the accuracy of the HSRS approximation. The efficacy and robustness of the proposed HSRS method were evaluated using five benchmark functions.