One-Dimensional Nested Maximin Designs

The design of computer experiments is an important step in black box evaluation and optimization processes.When dealing with multiple black box functions the need often arises to construct designs for all black boxes jointly, instead of individually.These so-called nested designs are used to deal with linking parameters and sequential evaluations.In this paper we discuss one-dimensional nested maximin designs.We show how to nest two designs optimally and develop a heuristic to nest three and four designs.Furthermore, it is proven that the loss in space-fillingness, with respect to traditional maximin designs, is at most 14:64 percent and 19:21 percent, when nesting two and three designs, respectively.simulation;computers;integer programming

Multidimensional Constrained Global Optimization in Domains with Computable Boundaries

Multidimensional constrained global optimization problem with objective function under Lipschitz condition and constraints generating a feasible domain with computable boundaries is considered. For solving this problem the dimensionality reduction approach on the base of the nested optimization scheme is used. This scheme reduces initial multidimensional problem to a family of one-dimensional subproblems and allows applying univariate methods for the execution of multidimensional optimization. Sequential and parallel modifications of well-known information-statistical methods of Lipschitz optimization are proposed for solving the univariate subproblems arising inside the nested scheme in the case of domains with computable boundaries. A comparison with classical penalty function method being traditional means of taking into account the constraints is carried out. The results of experiments demonstrate a significant advantage of the methods proposed over the penalty function method

Nested Maximin Latin Hypercube Designs in Two Dimensions

In black box evaluation and optimization Latin hypercube designs play an important role.When dealing with multiple black box functions the need often arises to construct designs for all black boxes jointly, instead of individually.These so-called nested designs consist of two separate designs, one being a subset of the other, and are used to deal with linking parameters and sequential evaluations.In this paper we construct nested maximin designs in two dimensions.We show that different types of grids should be considered when constructing nested designs and discuss how to determine which grid to use best for a specifc computer experiment.In the appendix to this paper maximin distances for different numbers of points are provided; the corresponding nested maximin designs can be found on the website http://www.spacefillingdesigns.nl.

Nested Maximin Latin Hypercube Designs

In the field of design of computer experiments (DoCE), Latin hypercube designs are frequently used for the approximation and optimization of black-boxes. In certain situations, we need a special type of designs consisting of two separate designs, one being a subset of the other. These nested designs can be used to deal with training and test sets, models with different levels of accuracy, linking parameters, and sequential evaluations. In this paper, we construct nested maximin Latin hypercube designs for up to ten dimensions. We show that different types of grids should be considered when constructing nested designs and discuss how to determine which grid to use for a specific application. To determine nested maximin designs for dimensions higher than two, four different variants of the ESE-algorithm of Jin et al. (2005) are introduced and compared. In the appendix, maximin distances for different numbers of points are provided; the corresponding nested maximin designs can be found on the website http://www.spacefillingdesigns.nl.Design of computer experiments;Latin hypercube design;linking parameter;nested designs;sequential simulation;space-filling;training and test set

Maximin Designs for Computer Experiments.

Decision processes are nowadays often facilitated by simulation tools. In the field of engineering, for example, such tools are used to simulate the behavior of products and processes. Simulation runs, however, are often very time-consuming, and, hence, the number of simulation runs allowed is limited in practice. The problem then is to determine which simulation runs to perform such that the maximal amount of information about the product or process is obtained. This problem is addressed in the first part of the thesis. It is proposed to use so-called maximin Latin hypercube designs and many new results for this class of designs are obtained. In the second part, the case of multiple interrelated simulation tools is considered and a framework to deal with such tools is introduced. Important steps in this framework are the construction and the use of coordination methods and of nested designs in order to control the dependencies present between the various simulation tools

Nested Maximin Latin Hypercube Designs

In the field of design of computer experiments (DoCE), Latin hypercube designs are frequently used for the approximation and optimization of black-boxes. In certain situations, we need a special type of designs consisting of two separate designs, one being a subset of the other. These nested designs can be used to deal with training and test sets, models with different levels of accuracy, linking parameters, and sequential evaluations. In this paper, we construct nested maximin Latin hypercube designs for up to ten dimensions. We show that different types of grids should be considered when constructing nested designs and discuss how to determine which grid to use for a specific application. To determine nested maximin designs for dimensions higher than two, four different variants of the ESE-algorithm of Jin et al. (2005) are introduced and compared. In the appendix, maximin distances for different numbers of points are provided; the corresponding nested maximin designs can be found on the website http://www.spacefillingdesigns.nl.