Introduction Deterministic computer simulations of physical phenomena are becoming widely used in science and engineering. Computers are used to describe the flow of air over an airplane wing, combustion of gasses in a flame, behavior of a metal structure under stress, safety of a nuclear reactor, and so on. Some of the most widely used computer models, and the ones that lead us to work in this area, arise in the design of the semiconductors used in the computers themselves. A process simulator starts with a data structure representing an unprocessed piece of silicon and simulates the steps such as oxidation, etching and ion injection that produce a semiconductor device such as a transistor. A device simulator takes a description of such a device and simulates the flow of current through it under varying conditions to determine properties of the device such as its switching speed and the critical voltage at which it switches. A circuit simulator takes a list of devices and the

We present an overview of evolutionary algorithms that use empirical models of the fitness function to accelerate convergence, distinguishing between Evolution Control and the Surrogate Approach. We describe the Gaussian process model and propose using it as an inexpensive fitness function surrogate. Implementation issues such as efficient and numerically stable computation, exploration vs. exploitation, local modeling, multiple objectives and constraints, and failed evaluations are addressed. Our resulting Gaussian Process Optimization Procedure (GPOP) clearly outperforms other evolutionary strategies on standard test functions as well as on a real-world problem: the optimization of stationary gas turbine compressor profiles.

this paper is a recent article on model-based geostatistics by Diggle, Tawn and Moyeed (1998) where pure kriging (i.e. no covariates) is the focus. Our paper inherits some of its aspects: model-based and with mixed model connections. In particular the comment by Bowman (1998) in the ensuing discussion suggested that additive modelling would be a worthwhile extension. This paper essentially follows this suggestion. However, this paper is not the first to combine the notions of geostatistics and additive modelling. References known to us are Kelsall and Diggle (1998), Durban Reguera (1998) and Durban, Hackett, Currie and Newton (2000). Nevertheless, we believe that our approach has a number of attractive features (see (1)-(4) above), not all shared by these references. Section 2 describes the motivating application and data in detail. Section 3 shows how one can express additive models as a mixed model, while Section 4 does the same for kriging and merges the two into the geoadditive model. Issues concerning the amount of smoothing are discussed in Section 5 and inferential aspects are treated in Section 6. Our analysis of the Upper Cape Cod reproductive data is presented in Section 7. Section 8 discusses extension to the generalised context.We close the paper with some disussion in Section 9. 2 Description of the application and data

Computer-based simulation and analysis is used extensively in engineering for a variety of tasks. Despite the steady and continuing growth of computing power and speed, the computational cost of complex high-fidelity engineering analyses and simulations limit their use in important areas like design optimization and reliability analysis. Statistical approximation techniques such as design of experiments and response surface methodology are becoming widely used in engineering to minimize the computational expense of running such computer analyses and circumvent many of these limitations. In this paper, we compare and contrast five experimental design types and four approximation model types in terms of their capability to generate accurate approximations for two engineering applications with typical engineering behaviors and a wide range of nonlinearity. The first example involves the analysis of a two-member frame that has three input variables and three responses of interest. The second example simulates the roll-over potential of a semi-tractor-trailer for different combinations of input variables and braking and steering levels. Detailed error analysis reveals that uniform designs provide good sampling for generating accurate approximations using different sample sizes while kriging models provide accurate approximations that are robust for use with a variety of experimental designs and sample sizes.

This paper describes a state space discretization scheme based on statistical experimental designs generated from orthogonal arrays of strength three with index unity. Chen et al. (1999) employed this efficient discretization scheme in a numerical solution method for high-dimensional continuous-state stochastic dynamic programming (SDP). These OAs are instrumental in reducing the dimensionality of continuous-state SDP. In particular, computationally efficient space-filling measures for these OAs are derived for evaluating how well a specific OA discretization fills the state space. Comparisons were made with two types of common measures: ones which maximize the average (or minimum) distance between discretization points within the OA and ones which minimize the average (or maximum) distance between discretization points and nondiscretization points lying on a full grid (i.e., points lying on the full grid that are not contained in the OA discretization). OAs of strength three were test...

Space-filling "coverage" designs are spatial sampling plans which optimize a distance-based criterion. Because they do not depend on the covariance structure of the process to be sampled, coverage designs are more efficiently computed than designs which are optimal for mean squared error criteria. This paper presents an efficient algorithm for the construction of coverage designs and evaluates it's performance in terms of computation time and effectiveness at finding "good" designs. Results suggest that near-optimal designs for reasonably large problems can be computed very efficiently. The algorithm is implemented in the statistical programming language SPLUS, and examples of the construction of coverage designs are given involving an existing network of ozone monitoring sites. Keywords: Spatial design, space-filling designs, spatial statistics, spatial sampling, network design. Address: Box 3000, Boulder, Colorado 80307. (303) 497-1704. 1 Introduction A practical problem in spat...

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A novel concept for estimating smooth functions by selection techniques based on boosting is developed. It is suggested to put radial basis functions with different spreads at each knot and to do selection and estimation simultaneously by a componentwise boosting algorithm. The methodology of various other smoothing and knot selection procedures (e.g. stepwise selection) is summarized. They are compared to the proposed approach by extensive simulations for various unidimensional settings, including varying spatial variation and heteroskedasticity, as well as on a real world data example. Finally, an extension of the proposed method to surface fitting is evaluated numerically on both, simulation and real data. The proposed knot selection technique is shown to be a strong competitor to existing methods for knot selection.

This paper appeared in the proceedings of the ECML 2006,

A randomly generated Latin hypercube design (LHD) can be quite structured: the variables may be highly correlated or the design may not have good space-filling properties. There are procedures to find good LHDs by minimizing the pairwise correlations or maximizing the inter-site distances. In this article we have shown that these two criteria need not agree with each other. In fact, maximization of inter-site distances can result in LHDs where the variables are highly correlated and vice versa. Therefore, we propose a multi-objective optimization approach to find good LHDs by combining correlation and distance performance measures. We also propose a new exchange algorithm for efficiently generating such designs. Several examples are presented to show that the new algorithm is fast and that the optimal designs are good in terms of both the correlation and distance criteria.