Adaptive surrogate-based design optimization with expected improvement used as infill criterion

• Published in: Optimization 2012-06, Vol.61 (6), p.661-684
• Main Authors: Xu, Q., Wehrle, E., Baier, H.
• Format: Article
• Language: English
• Subjects: Accuracy; adaptive surrogate based design optimization; Design optimization; expected improvement; Finite element analysis; Mathematical models; Optimization techniques; Studies; surrogate modelling
• ISSN: 0233-1934; 1029-4945
• DOI: 10.1080/02331934.2011.644286

A prominent advantage of using surrogate models in structural design optimization is that computational effort can be greatly reduced without significantly compromising model accuracy. The essential goal is to perform the design optimization with fewer evaluations of the typically finite element analysis and ensuring accuracy of the optimization results. An adaptive surrogate based design optimization framework is proposed, in which Latin hypercube sampling and Kriging are used to build surrogate models. Accuracy of the models is improved adaptively using an infill criterion called expected improvement (EI). It is the anticipated improvement that an interpolation point will lead to the current surrogate models. The point that will lead to the maximum EI is searched and used as infill points at each iteration. For constrained optimization problems, the surrogate of constraint is also utilized to form a constrained EI as the corresponding infill criterion. Computational trials on mathematical test functions and on a three-dimensional aircraft wing model are carried out to test the feasibility of this method. Compared with the traditional surrogate base design optimization and direct optimization methods, this method can find the optimum design with fewer evaluations of the original system model and maintain good accuracy.