Keywords: expected improvement, surrogate model, metamodel, optimization, sequential design, adaptive sampling, application, electro-magnetics.

For many problems from science, and engineering it is impractical to perform experiments on the physical world directly (e.g. airfoil design, earthquake propagation). Instead, complex, physics-based simulation codes are used to run experiments on computer hardware. While allowing scientists more flexibility to study phenomena under controlled conditions, computer experiments require a substantial investment in computation time. This is especially evident for routine tasks such as optimization, sensitivity analysis and design space exploration [4].

As a result researchers have turned to various approximation methods that mimic the behavior of the simulation model as closely as possible while being computationally less expensive to evaluate. This work concentrates on the use of data-driven approximations using compact surrogate models (also known as metamodels, or response surface models (RSM)). Examples of surrogate models include: rational functions, Gaussian process (GP) models, and support vector machines (SVM).

In particular, this work describes a popular surrogate modelling technique for optimization of expensive blackbox simulators, i.e., expected improvement [2]. The results of this research have been incorporated in a flexible and integrated research platform, the surrogate modelling (SUMO) toolbox [1]. Consequently the toolbox is afterwards applied to an optimization problem from electro-magnetics (EM) to design an inter-digital filter [3].

Results show that designs obtained through surrogate modelling techniques, which require no domain specific knowledge of the application at hand, are competitive to a reference design constructed by a domain expert, using a combination of analytic methods, circuit simulation and finite element methods.

1

D. Gorissen, L. De Tommasi, K. Crombecq, T. Dhaene, "Sequential Modeling of a Low Noise Amplifier with Neural Networks and Active Learning", Neural Computing and Applications, accepted, 2008.

2

D.R. Jones, M. Schonlau, W.J. Welch, "Efficient Global Optimization of Expensive Black-Box Functions", J. of Global Optimization, 13(4):455-492, 1998. doi:10.1023/A:1008306431147

3

D.G. Swanson, "Microwave Filter Design", IEEE Microwave magazine, 8:105-114, 2007. doi:10.1109/MMM.2007.904724

4

G.G. Wang, S. Shan, "Review of Metamodeling Techniques in Support of Engineering Design Optimization", Journal of Mechanical Design, 129(4):370-380, 2007. doi:10.1115/1.2429697

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