347,937 research outputs found
Perspective Chapter: Cyclic Generation of Box-Behnken Designs and New Second-Order Designs
Box-Behnken designs (BBDs) are three-level second-order spherical designs with all points lying on a sphere, introduced by Box and Behnken, for fitting the second-order response surface models. They are available for 3–12 and 16 factors. Together with the central composite designs for the second-order model, BBDs are very popular response surface designs, especially for 3–7 factors. This chapter introduces an algorithm to produce cyclic generators for BBDs and similar designs, which we call cyclic BBDs (CBBDs). The new CBBDs offer more flexibility in choosing the designs for a specified number of factors. Comparisons between some BBDs and the new CBBDs indicate the superiority of the new CBBDs with respect to multiple design quality measures and graphical tools assessing prediction variance properties. A catalog of 24 new CBBDs, which includes orthogonally blocked CBBDs for 11, 13, and 14 factors, will be given
Data Driven Surrogate Based Optimization in the Problem Solving Environment WBCSim
Large scale, multidisciplinary, engineering designs are always difficult due to the complexity and dimensionality of these problems. Direct coupling between the analysis codes and the optimization routines can be prohibitively time consuming due to the complexity of the underlying simulation codes. One way of tackling this problem is by constructing computationally cheap(er) approximations of the expensive simulations, that mimic the behavior of the simulation model as closely as possible. This paper presents a data driven, surrogate based optimization algorithm that uses a trust region based sequential approximate optimization (SAO) framework and a statistical sampling approach based on design of experiment (DOE) arrays. The algorithm is implemented using techniques from two packages—SURFPACK and SHEPPACK that provide a collection of approximation algorithms to build the surrogates and three different DOE techniques—full factorial (FF), Latin hypercube sampling (LHS), and central composite design (CCD)—are used to train the surrogates. The results are compared with the optimization results obtained by directly coupling an optimizer with the simulation code. The biggest concern in using the SAO framework based on statistical sampling is the generation of the required database. As the number of design variables grows, the computational cost of generating the required database grows rapidly. A data driven approach is proposed to tackle this situation, where the trick is to run the expensive simulation if and only if a nearby data point does not exist in the cumulatively growing database. Over time the database matures and is enriched as more and more optimizations are performed. Results show that the proposed methodology dramatically reduces the total number of calls to the expensive simulation runs during the optimization process
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Optimal exact designs of experiments via Mixed Integer Nonlinear Programming
Optimal exact designs are problematic to find and study because there is no unified theory for determining them and studyingtheir properties. Each has its own challenges and when a method exists to confirm the design optimality, it is invariablyapplicable to the particular problem only.We propose a systematic approach to construct optimal exact designs by incorporatingthe Cholesky decomposition of the Fisher Information Matrix in a Mixed Integer Nonlinear Programming formulation. Asexamples, we apply the methodology to find D- and A-optimal exact designs for linear and nonlinear models using global orlocal optimizers. Our examples include design problems with constraints on the locations or the number of replicates at theoptimal design points
-SELC: Optimization by sequential elimination of level combinations using genetic algorithms and Gaussian processes
Identifying promising compounds from a vast collection of feasible compounds
is an important and yet challenging problem in the pharmaceutical industry. An
efficient solution to this problem will help reduce the expenditure at the
early stages of drug discovery. In an attempt to solve this problem, Mandal, Wu
and Johnson [Technometrics 48 (2006) 273--283] proposed the SELC algorithm.
Although powerful, it fails to extract substantial information from the data to
guide the search efficiently, as this methodology is not based on any
statistical modeling. The proposed approach uses Gaussian Process (GP) modeling
to improve upon SELC, and hence named -SELC. The performance of
the proposed methodology is illustrated using four and five dimensional test
functions. Finally, we implement the new algorithm on a real pharmaceutical
data set for finding a group of chemical compounds with optimal properties.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS199 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Design Issues for Generalized Linear Models: A Review
Generalized linear models (GLMs) have been used quite effectively in the
modeling of a mean response under nonstandard conditions, where discrete as
well as continuous data distributions can be accommodated. The choice of design
for a GLM is a very important task in the development and building of an
adequate model. However, one major problem that handicaps the construction of a
GLM design is its dependence on the unknown parameters of the fitted model.
Several approaches have been proposed in the past 25 years to solve this
problem. These approaches, however, have provided only partial solutions that
apply in only some special cases, and the problem, in general, remains largely
unresolved. The purpose of this article is to focus attention on the
aforementioned dependence problem. We provide a survey of various existing
techniques dealing with the dependence problem. This survey includes
discussions concerning locally optimal designs, sequential designs, Bayesian
designs and the quantile dispersion graph approach for comparing designs for
GLMs.Comment: Published at http://dx.doi.org/10.1214/088342306000000105 in the
Statistical Science (http://www.imstat.org/sts/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Orthogonal-Array based Design Methodology for Complex, Coupled Space Systems
The process of designing a complex system, formed by many elements and sub-elements interacting between each other, is usually completed at a system level and in the preliminary phases in two major steps: design-space exploration and optimization. In a classical approach, especially in a company environment, the two steps are usually performed together, by experts of the field inferring on major phenomena, making assumptions and doing some trial-and-error runs on the available mathematical models. To support designers and decision makers during the design phases of this kind of complex systems, and to enable early discovery of emergent behaviours arising from interactions between the various elements being designed, the authors implemented a parametric methodology for the design-space exploration and optimization. The parametric technique is based on the utilization of a particular type of matrix design of experiments, the orthogonal arrays. Through successive design iterations with orthogonal arrays, the optimal solution is reached with a reduced effort if compared to more computationally-intense techniques, providing sensitivity and robustness information. The paper describes the design methodology in detail providing an application example that is the design of a human mission to support a lunar base
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