Optimal Incomplete-Block Designs with Low Replication: A Unified Approach Using Graphs

Optimal Incomplete Block Designs

Optimal incomplete block designs are pursued through the E-criterion of minimizing maximal variance. Methodology is developed for design choice based on graphs and an extensive catalog of downloadable designs compiled. Along with the general methodology, a near complete solution for E-optimal block designs is provided for up to 15 treatments. E-optimality is revealed as a flexible criterion tha...

Incomplete Block Designs

1. Introduction These designs were introduced by Yates in order to eliminate heterogeneity to a greater extent than is possible with randomized blocks and Latin squares when the number of treatments is large. The precision of the estimate of a treatment effect depends on the number of replications of the treatment-the larger the number of replications, the more is the precision. Similar is the ...

Finding Balanced Incomplete Block Designs with Metaheuristics

This paper deals with the generation of balanced incomplete block designs (BIBD), a hard constrained combinatorial problem with multiple applications. This problem is here formulated as a combinatorial optimization problem (COP) whose solutions are binary matrices. Two different neighborhood structures are defined, based on bit-flipping and position-swapping. These are used within three metaheu...

Splitting balanced incomplete block designs

Balanced incomplete block designs with block size~9: Part III

The necessary conditions for the existence of a balanced incomplete block design on v points, with index λ and block size k, are that: λ(v − 1) ≡ 0 mod (k − 1) λv(v − 1) ≡ 0 mod k(k − 1) Earlier work has studied k = 9 with λ ∈ {1, 2, 3, 4, 6, 8, 9, 12}. In this article we show that the necessary conditions are sufficient for λ = 9 and every other λ not previously studied.