The use of surrogate models or metamodeling has lead to new areas of research in simulation-based design optimization. Metamodeling approaches have advantages over traditional techniques when dealing with the noisy responses and=or high computational cost characteristic of many computer simulations. This paper focuses on a particular algorithm, Efficient Global Optimization (EGO) that uses kriging metamodels. Several infill sampling criteria are reviewed, namely criteria for selecting design points at which the true functions are evaluated. The infill sampling criterion has a strong influence on how efficiently and accurately EGO locates the optimum. Variance-reducing criteria substantially reduce the RMS error of the resulting metamodels, while other criteria influence how locally or globally EGO searches. Criteria that place more emphasis on global searching require more iterations to locate optima and do so less accurately than criteria emphasizing local search.

Abstract

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With the advent of fast methods to significantly speed up numerical computation of large-scale realistic electromagnetic (EM) structures, EM design and optimization is becoming increasingly attractive. In recent years, genetic algorithms, neural network and evolutionary optimization methods have become increasingly popular for EM optimization. However, these methods are usually associated with a slow convergence bound and, furthermore, may not yield a deterministic optimal solution. In this paper, a new hybrid method using Kriging metamodeling in conjunction with the divided rectangles (DIRECT) global-optimization algorithm is used to yield a globally optimal solution efficiently. The latter yields a deterministic answer with fast convergence bounds and inherits both local and global-optimization properties. Three examples are given to illustrate the applicability of the method, i.e., shape optimization for a slot-array frequency-selective surface, antenna location optimization to minimize EM coupling from the antenna to RF devices in automobile structures, and multisensor optimization to satisfy RF coupling constraints on a vehicular chassisin the presence of a wire harness. In the first example, DIRECT with Kriging surrogate modeling was employed. In the latter two examples, the adaptive hybrid optimizer, superEGO, was used. In all three examples, emphasis is placed on the speed of convergence, as well as on the flexibility of the optimization algorithms. Index Terms-Coupling, DIRECT optimization algorithm, electromagnetic compatibility (EMC), electromagnetic interference (EMI), finite element boundary integral (FE-BI), frequency-selective surface (FSS), Kriging metamodeling, Kriging surrogate modeling, multilevel fast multipole moment method (MLFMM), superEGO. Manuscript

Nonlinear constrained optimization algorithms are widely utilized in artifact design. Certain algorithms also lend themselves well to design of experiments (DOE). Adaptive design refers to experimental design where determining where to sample next is influenced by information from previous experiments. We present a constrained optimization algorithm known as superEGO (a variant of the EGO algorithm of Schonlau, Welch and Jones) that is able to create adaptive designs effectively. Its ability to allow easily for a variety of sampling criteria and to incorporate constraint information accurately makes it well suited to the needs of adaptive design. The approach is demonstrated on a human reach experiment where the selection of sampling points adapts successfully to the stature and perception of the individual test subject. Results from the initial study indicate that superEGO is able to create experimental designs that yield more accurate models using fewer points than the original testing procedure.