2019/02/09 by Felipe Carraro, Rafael Holdorf Lopez, Leandro Fleck Fadel Miguel +1 · 9 citations
Computer Science · Decision Sciences · Mathematics · #Advanced Multi-Objective Optimization Algorithms #Benchmark (surveying) #Computer science #Global optimization #Hybrid Monte Carlo #Kriging #Machine learning #Mathematical optimization #Mathematics #Monte Carlo integration #Monte Carlo method #Optimal Experimental Design Methods #Optimization problem #Probabilistic and Robust Engineering Design #Robustness (evolution) #Statistics #Stochastic optimization #Variance (accounting) #Variance reduction #cs.NA #math.NA #msc:62J02 #stat.AP
paper · pdf · doi:10.1007/s00158-019-02212-y
published in Structural and Multidisciplinary Optimization 60(1), 245-268 (Springer Science+Business Media) · 24 pages
openalex publication_date 2019/02/09 · arxiv created 2019/06/26 · arxiv updated 2019/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, the minimization of computational cost on evaluating multi-dimensional integrals is explored. More specifically, a method based on an adaptive scheme for error variance selection in Monte Carlo integration (MCI) is presented. It uses a stochastic Efficient Global Optimization (sEGO) framework to guide the optimization search. The MCI is employed to approximate the integrals, because it provides the variance of the error in the integration. In the proposed approach, the variance of the integration error is included into a Stochastic Kriging framework by setting a target variance in the MCI. We show that the variance of the error of the MCI may be controlled by the designer and that its value strongly influences the computational cost and the exploration ability of the optimization process. Hence, we propose an adaptive scheme for automatic selection of the target variance during the sEGO search. The robustness and efficiency of the proposed adaptive approach were evaluated on global optimization stochastic benchmark functions as well as on a tuned mass damper design problem. The results showed that the proposed adaptive approach consistently outperformed the constant approach and a multi-start optimization method. Moreover, the use of MCI enabled the method application in problems with high number of stochastic dimensions. On the other hand, the main limitation of the method is inherited from sEGO coupled with the Kriging metamodel: the efficiency of the approach is reduced when the number of design variables increases.