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Evaluating Algorithm Efficiency for Optimizing Experimental Designs with Correlated Data

The search for efficient methods and procedures to optimize experimental designs is a vital process in field trials that is often challenged by computational bottlenecks. Most existing methods ignore the presence of some form of correlations in the data to simplify the optimization process at the design stage. This study explores several algorithms for improving field experimental designs using a linear mixed models statistical framework adjusting for both spatial and genetic correlations based on A- and D-optimality criteria. Relative design efficiencies are estimated for an array of algorithms including pairwise swap, genetic neighborhood, and simulated annealing and evaluated with varying levels of heritabilities, spatial and genetic correlations. Initial randomized complete block designs were generated using a stochastic procedure and can also be imported directly from other design software. Results showed that at a spatial correlation of 0.6 and a heritability of 0.3, under the A-optimality criterion, both simulated annealing and simple pairwise algorithms achieved the highest design efficiencies of 7.4 % among genetically unrelated individuals, implying a reduction in average variance of the random treatment effects by 7.4 % when the algorithm was iterated 5000 times. In contrast, results under D-optimality criterion indicated that simulated annealing had the lowest design efficiency. The simple pairwise algorithm consistently maintained highest design efficiencies in all evaluated conditions. Design efficiencies for experiments with full-sib families decreased with increasing heritability. The number of successful swaps appeared to decrease with increasing heritability and were highest for both simulated annealing and simple pairwise algorithms, and lowest for genetic neighborhood algorithm.