Optimal factorizations for the construction of alpha_n-designs
by
Katya Ruggiero
Massey University
Coauthors: Lutz Gross (CSIRO, Mathematical and Information Sciences, Melbourne)

Consider the design of an experiment involving r replicates of v treatments arranged in resolvable blocks of size k (k < v). Such a design is available from the family of alpha_n-designs if v can be factorized as v=v₁v₂ ... v_n and k as k=k₁k₂ ... k_n, such that the integer k_i divides the integer v_i (John et. al, in press). Usually more than one such set of factorizations is possible. Empirically, it can be shown that finding the best available alpha_n-design is dependent on the factorization that is chosen.

In order to find the factorization that yields the best an-design, all possible factorizations sets must first be found. An algorithm based on the prime number factorization of v and k was developed for this purpose. Since for large experiments, say v=1000, the number of possible factorizations is very large, the search algorithm was implemented on a parallel computer. A master-slave programming model was applied to optimize the objective function for each factorization in parallel. The algorithm and its implementation will be discussed. A summary of the findings from the investigation of many different sized an-designs will be presented.

John, J.A., Ruggiero, K. and Williams, E.R. (in press) alpha_n-Designs. To appear in Austral. NZ J. Statist.

Date received: April 29, 2002