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

Mathematics of computation, 2006-04, Vol.75 (254), p.859-878 [Peer Reviewed Journal]

Copyright 2005, American Mathematical Society ;Copyright 2006 American Mathematical Society ;2006 INIST-CNRS ;ISSN: 0025-5718 ;EISSN: 1088-6842 ;DOI: 10.1090/S0025-5718-05-01806-5 ;CODEN: MCMPAF

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Title:
Lower bounds and stochastic optimization algorithms for uniform designs with three or four levels
Author: FANG, Kai-Tai ; MARINGER, Dietmar ; YU TANG ; WINKER, Peter
Subjects: Algorithmics. Computability. Computer arithmetics ; Applied sciences ; Computational complexity ; Computer science; control theory; systems ; Design ; Design analysis ; Design engineering ; Design optimization ; Exact sciences and technology ; Experiment design ; Experimental design ; Heuristics ; Iterative solutions ; Mathematical lattices ; Mathematics ; Objective functions ; Probability and statistics ; Sciences and techniques of general use ; Statistics ; Theoretical computing
Is Part Of: Mathematics of computation, 2006-04, Vol.75 (254), p.859-878
Description: New lower bounds for three- and four-level designs under the centered L_2-discrepancy are provided. We describe necessary conditions for the existence of a uniform design meeting these lower bounds. We consider several modifications of two stochastic optimization algorithms for the problem of finding uniform or close to uniform designs under the centered L_2-discrepancy. Besides the threshold accepting algorithm, we introduce an algorithm named balance-pursuit heuristic. This algorithm uses some combinatorial properties of inner structures required for a uniform design. Using the best specifications of these algorithms we obtain many designs whose discrepancy is lower than those obtained in previous works, as well as many new low-discrepancy designs with fairly large scale. Moreover, some of these designs meet the lower bound, i.e., are uniform designs.
Publisher: Providence, RI: American Mathematical Society
Language: English
Identifier: ISSN: 0025-5718
EISSN: 1088-6842
DOI: 10.1090/S0025-5718-05-01806-5
CODEN: MCMPAF
Source: American Mathematical Society Publications

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

Copyright 2005, American Mathematical Society ;Copyright 2006 American Mathematical Society ;2006 INIST-CNRS ;ISSN: 0025-5718 ;EISSN: 1088-6842 ;DOI: 10.1090/S0025-5718-05-01806-5 ;CODEN: MCMPAF

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