Lower bounds and stochastic optimization algorithms for uniform designs with three or four levels

DOI10.1090/S0025-5718-05-01806-5zbMath1093.90031OpenAlexW2011805480MaRDI QIDQ3376999

Peter Winker, Kai-Tai Fang, Dietmar G. Maringer, Yu. Tang

Publication date: 27 March 2006

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-05-01806-5

zbMATH Keywords

balance-pursuit heuristic

Mathematics Subject Classification ID

Design of statistical experiments (62K99) Stochastic programming (90C15) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17) Complexity classes (hierarchies, relations among complexity classes, etc.) (68Q15)

Related Items (28)

Search for minimum aberration designs with uniformity ⋮ A catalog of optimal foldover plans for constructing U-uniform minimum aberration four-level combined designs ⋮ A closer look at de-aliasing effects using an efficient foldover technique ⋮ Construction of uniform mixed-level designs through level permutations ⋮ Construction of uniform \(U\)-designs ⋮ Lower bound of average centeredL2-discrepancy forU-type designs ⋮ An effective construction method for multi-level uniform designs ⋮ New lower bound for centered \(L_2\)-discrepancy of four-level \(U\)-type designs ⋮ Construction of main effects plans orthogonal through the block factor based on level permutation ⋮ Optimum addition of information to computer experiments in view of uniformity and orthogonality ⋮ Some new lower bounds to centered and wrap-round \(L_2\)-discrepancies ⋮ A new look on optimal foldover plans in terms of uniformity criteria ⋮ Optimized \(U\)-type designs on flexible regions ⋮ The stochastics of threshold accepting: analysis of an application to the uniform design problem ⋮ Two- and three-level lower bounds for mixture \(L_2\)-discrepancy and construction of uniform designs by threshold accepting ⋮ New results on quaternary codes and their Gray map images for constructing uniform designs ⋮ Optimal space-filling design for symmetrical global sensitivity analysis of complex black-box models ⋮ Lower bounds of various criteria in experimental designs ⋮ Level permutation method for constructing uniform designs under the wrap-around \(L_2\)-discrepancy ⋮ Construction of uniform designs without replications ⋮ The convergence of estimators based on heuristics: theory and application to a GARCH model ⋮ An efficient method for constructing uniform designs with large size ⋮ Augmented uniform designs ⋮ Measures of uniformity in experimental designs: A selective overview ⋮ Space-Filling Fractional Factorial Designs ⋮ Sharp lower bounds of various uniformity criteria for constructing uniform designs ⋮ Ta algorithms for D-optimal OofA mixture designs ⋮ Lower bound of centered \(L_2\)-discrepancy for mixed two and three levels \(U\)-type designs

Cites Work

• Construction of minimum generalized aberration designs
• A systematical procedure in the construction of multi-level supersaturated design.
• Constructions of uniform designs by using resolvable packings and coverings.
• Lower bounds for centered and wrap-around \(L_2\)-discrepancies and construction of uniform designs by threshold accepting.
• Construction of \(E(s^2)\) optimal supersaturated designs using cyclic BIBDs
• Centered $L_2$-discrepancy of random sampling and Latin hypercube design, and construction of uniform designs
• A generalized discrepancy and quadrature error bound
• Uniform Design: Theory and Application
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