Locally weighted regression combines the advantages of polynomial regression and kernel smoothing. We present three ideas for appropriate and effective use of LOcally WEighted Scatterplot Smoothing (LOWESS) models for surrogate optimization. First, a method is proposed to reduce the computational cost of LOWESS models. Second, a local scaling coefficient is introduced to adapt LOWESS models to the density of neighboring points while retaining smoothness. Finally, an appropriate order error metric is used to select the optimal shape coefficient of the LOWESS model. Our surrogate-assisted optimization method relies on the the Mesh Adaptive Direct Search (MADS) algorithm in which LOWESS models are used to generate and rank promising candidates. The blackbox functions governing the optimization problem are then evaluated at these ranked candidates with an opportunistic strategy, thus minimizing CPU time. Extensive computational results are reported for three engineering design problems. These results demonstrate the effectiveness of the LOWESS models as well as the order error metric for surrogate-assisted optimization.
B. Talgorn, C. Audet, M. Kokkolaras, and S. Le Digabel, Locally weighted regression models for surrogate-assisted design optimization. Optimization and Engineering, 19(1), p. 213-238, 2018.