Interchange Algorithms for Constructing Designs with Complex Blocking Structures

The different types of designs, involving one or more blocking factors, which have evolved since the 1930’s are briefly reviewed. Lately, with the widespread availability of powerful computers, a number of interchange algorithms to construct efficient block and row-column designs have been developed. The features of an interchange algorithm are identified, and the alternative strategies used in existing programs examined and compared. An algorithm is then described which incorporates many of these features, and which can be used to construct designs with a variety of treatment and blocking structures, such as resolvability, adjusted orthogonality, latinization, factorial and residual treatment effects. Such an algorithm goes a long way in realising the eventual aim of providing a comprehensive expert system for the design and analysis of experiments with alternative treatment and blocking requirements.

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