Accelerated Adaptive Surrogate-Based Optimization Through Reduced-Order Modeling
Résumé
The efficient global optimization approach was often used to reduce the computational cost in the optimization of complex engineering systems. This algorithm can, however, remain expensive for large-scale problems because each simulation uses the full numerical model. A novel optimization approach for such problems is proposed in this paper, in which the numerical model solves partial differential equations involving the resolution of a large system of equations, such as by finite element. This method is based on the combination of the efficient global optimization approach and reduced-basis modeling. The novel idea is to use inexpensive, sufficiently accurate reduced-basis solutions to significantly reduce the number of full system resolutions. Two applications of the proposed surrogate-based optimization approach are presented: an application to the problem of stiffness maximization of laminated plates and an application to the problem of identification of orthotropic elastic constants from full-field displacement measurements based on a tensile test on a plate with a hole. Compared with the crude efficient global optimization algorithm, a significant reduction in computational cost was achieved using the proposed efficient reduced-basis global optimization.