Optimal test-control block designs with unequal block sizes and correlated errors

Abstract

The purpose of the present article is to introduce theoretical and algorithmic approaches to address the problem of finding optimal test-control incomplete block designs with unequal block sizes where intra-block observations are correlated. Theoretical approach is used to find Etc -optimal designs analytically. In addition, due to the computational complexity of theoretical methods, in this article a two-phase optimization algorithm is proposed to construct -optimal or nearly -optimal designs. The effectiveness of the proposed algorithm is validated by comparing our results with optimal designs presented in several prior studies. Our algorithm has the advantages of being independent from the sizes of blocks, structure of correlation, and the optimality criteria. Moreover, it takes only a few minutes to obtain the optimal designs.