Pareto surfaces in the performance space determine the range of feasible performance values for a circuit topology in a given technology. We present a non-dominated sorting based global optimization algorithm to generate the nominal pareto front efficiently using a simulator-in-a-loop approach. The solutions on this pareto front combined with efficient Monte Carlo approximation ideas are then used to compute the yield-aware pareto fronts. We show experimental results for both the nominal and yield-aware pareto fronts for power and phase noise for a voltage controlled oscillator (VCO) circuit. The presented methodology computes yield-aware pareto fronts in approximately 5-6 times the time required for a single circuit synthesis run and is thus practically efficient. We also show applications of yield-aware paretos to find the optimal VCO circuit to meet the system level specifications of a phase locked loop.

Complex computer codes are often too time expensive to be directly used to perform uncertainty propagation studies, global sensitivity analysis or to solve optimization problems. A well known and widely used method to circumvent this inconvenience consists in replacing the complex computer code by a reduced model, called a metamodel, or a response surface that represents the computer code and requires acceptable calculation time. One particular class of metamodels is studied: the Gaussian process model that is characterized by its mean and covariance functions. A specific estimation procedure is developed to adjust a Gaussian process model in complex cases (non linear relations, highly dispersed or discontinuous output, high dimensional input, inadequate sampling designs,...). The efficiency of this algorithm is compared to the efficiency of other existing algorithms on an analytical test case. The proposed methodology is also illustrated for the case of a complex hydrogeological computer code, simulating radionuclide transport in groundwater.

with generalized additive models

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.

Modeling experiments with qualitative and quantitative factors is an important issue in computer modeling. A framework for building Gaussian process models that incorporate both types of factors is proposed. The key to the development of these new models is an approach for constructing correlation functions with qualitative and quantitative factors. An iterative estimation procedure is developed for the proposed models. Modern optimization techniques are used in the estimation to ensure the validity of the constructed correlation functions. The proposed method is illustrated with an example involving a known function and a real example for modeling the thermal distribution of a data center. KEY WORDS: Cokriging; Design of experiments; Kriging; Multivariate Gaussian processes; Semi-definite programming.

Kriging is a useful method for developing metamodels for product design optimization. The most popular kriging method, known as ordinary kriging, uses a constant mean in the model. In this article, a modified kriging method is proposed, which has an unknown mean model. Therefore it is called blind kriging. The unknown mean model is identified from experimental data using a Bayesian variable selection technique. Many examples are presented which show remarkable improvement in prediction using blind kriging over ordinary kriging. Moreover, blind kriging predictor is easier to interpret and seems to be more robust to misspecification in the correlation parameters.

Abstract — Condition based maintenance (CBM) is a powerful tool for improvement of system reliability and reduction of system downtime. This research considers CBM under which the system state is periodically observed with or without observational error, and maintenance is imperfect. System availability is maximized by determining the optimal maintenance threshold and the time interval between consecutive inspections of the state of the system. The optimal solution can be obtained numerically using a sequential uniform design algorithm.

Modeling experiments with qualitative and quantitative factors is an important issue in computer modeling. A framework for building Gaussian process models that incorporate both types of factors is proposed. The key to the development of these new models is an approach for constructing correlation functions with qualitative and quantitative factors. An iterative estimation procedure is developed for the proposed models. Modern optimization techniques are used in the estimation to ensure the validity of the constructed correlation functions. The proposed method is illustrated with an example involving a known function and a real example for modeling the thermal distribution of a data center. KEY WORDS: Cokriging; Design of experiments; Kriging; Multivariate Gaussian processes; Semi-definite programming.

Abstract: Nonregularfractionalfactorialdesigns such as Plackett-Burman designs and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. The traditionalanalysis focuses on main effects only. Hamada and Wu (1992) went beyond the traditional approach and proposed an analysis strategy to demonstrate that some interactions could be entertained and estimated beyond a few significant main effects. Their groundbreaking work stimulated much of the recent developmentsin optimality criteria, constructionand analysis of nonregular designs. This paper reviews important developments in nonregular designs, including projection properties, generalized resolution, generalized minimum aberration criteria, optimality results, construction methods and analysis strategies.

We propose a flexible yet computationally efficient approach for building Gaussian process models for computer experiments with both qualitative and quantitative factors. This approach uses the hypersphere parameterization to model the correlations of the qualitative factors, thus avoiding the need of directly solving optimization problems with positive definite constraints. This method is easy to compute and can be implemented straightforwardly in standard computational environments like R and Matlab. The effectiveness of the proposed method is successfully illustrated by several examples. KEY WORDS: Computer experiment; Kriging; Hypersphere decomposition 1.