Constrained Maximin Designs for Computer Experiments

Finding a design scheme for expensive computer experiments in arbitrary design regions is often a difficult task. A well-known criterion that is often used for computer experiments is the minimal (Euclidean) distance between any pair of design sites, which should be maximal. In this article we describe methods to create such a constrained maximin simulation scheme. We give some numerical results for both theoretical and practical examples.

[1]  Marco Locatelli,et al.  Packing equal circles in a square: a deterministic global optimization approach , 2002, Discret. Appl. Math..

[2]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[3]  M. E. Johnson,et al.  Minimax and maximin distance designs , 1990 .

[4]  Raymond H. Myers,et al.  Response Surface Methodology--Current Status and Future Directions , 1999 .

[5]  Arne Stolbjerg Drud,et al.  CONOPT - A Large-Scale GRG Code , 1994, INFORMS J. Comput..

[6]  Rex K. Kincaid,et al.  Approximate Solutions of Continuous Dispersion Problems , 2005, Ann. Oper. Res..

[7]  Dick den Hertog,et al.  Optimizing color picture tubes by high-cost nonlinear programming , 2002, Eur. J. Oper. Res..

[8]  A. J. Booker,et al.  A rigorous framework for optimization of expensive functions by surrogates , 1998 .

[9]  Raimund Seidel,et al.  Exact Upper Bounds for the Number of Faces in d-Dimensional Voronoi Diagrams , 1990, Applied Geometry And Discrete Mathematics.

[10]  D. Dennis,et al.  SDO : A Statistical Method for Global Optimization , 1997 .

[11]  T. J. Mitchell,et al.  Exploratory designs for computational experiments , 1995 .

[12]  Said Salhi,et al.  Facility Location: A Survey of Applications and Methods , 1996 .

[13]  Zvi Drezner,et al.  Solving the Continuous p-Dispersion Problem Using Non-linear Programming , 1995 .

[14]  W. Welch.  Branch-and-Bound Search for Experimental Designs Based on D Optimality and Other Criteria , 1982 .

[15]  Thomas J. Santner,et al.  Design and analysis of computer experiments , 1998 .

[16]  Jerome Sacks,et al.  Designs for Computer Experiments , 1989 .

[17]  J. Sacks,et al.  A system for quality improvement via computer experiments , 1991 .

[18]  J. -F. M. Barthelemy,et al.  Approximation concepts for optimum structural design — a review , 1993 .

[19]  W. Welch.  ACED: Algorithms for the Construction of Experimental Designs , 1985 .