Exhaustive Search Algorithms to Find α(0,1) Designs with High Harmonic Mean Canonical Efficiency Factors

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2019-01-01
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Chen, Zihao
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Dan Nettleton
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Statistics
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Resolvable incomplete block designs have been of interest in many fields for decades. Considerable research has been done on how to construct highly efficient resolvable incomplete block designs with respect to various efficiency criteria. Introduced by E.R Williams in 1975, α designs with zeros or ones in the off-diagonal of the concurrence matrix (denoted as α(0, 1) designs) comprise one class of resolvable incomplete block designs with v varieties, b blocks, r replicates and block size of k. It can be challenging to find an α(0, 1) design with high efficiency, and when v and b become large, an exhaustive search is required. This paper proposes algorithms for constructing α(0, 1) designs for r = 2, r = 3 and r = 4 with highest possible harmonic mean canonical efficiency factors. The algorithms are based on the ideas of the combinatorial and factorial number systems. The performance of the algorithms for large v (v ≥ 100) is evaluated, and harmonic mean canonical efficiency factors are compared to theoretical upper bounds. A simulation study was carried out to compare randomized complete block designs and α(0, 1) designs with different efficiency factors.

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Tue Jan 01 00:00:00 UTC 2019