# Evaluating Algorithm Efficiency for Optimizing Experimental Designs with Correlated Data
## 4 Discussion  
Optimization algorithms are commonly used in agriculture and forestry research for several planning and management problems [23; 24]. In the current study, an array of these algorithms was implemented and evaluated to assess how well the efficiency of experimental designs can be improved once spatial and genetical correlation is considered. In particular, the evaluation of algorithm efficiency to improve experimental designs focused on the use of RCB designs in field trials with application in plant breeding. Family structure such as half-sib or full-sib families requires appropriate modelling of their genetic relationships (i.e., correlations) and similarly, their phyisical proximity within rows and/or columns needs to be accounted for as genotypes in close range will share microsite and thus will be correlated. Here, accounting for spatial correlations within rows and columns was necessary to minimize this experimental bias. Incorporation of these correlations not only on the design stage but also in the analysis stage has been shown by [PERSON] et al. [5], for RCB designs, to produce designs that are nearly as efficient as those generated using more complex models such as row-column designs that were analyzed assuming uncorrelated residual errors. From the detailed practical example that examined a specific condition, results indicated that the SP algorithm is the best as it managed to improve the initial experiment by reducing the average variance of treatment effects by 6.713%. This was followed closely by the SA algorithm with an ODE of 6.258%. The more aggressive algorithm GP4, under the evaluated experimental conditions, was underperoming but it might do better in other design conditions. Also, the algorithm GN had only 12 successful swaps, which was much less than SP and SA algorithms which recorded 192 and 139 swaps, respectively. Results from Tables 2 and 3 have shown that SP and SA algorithms achieved the highest relative design efficiencies under all experimental conditions for \(\Omega_{A}^{(30)}\) and \(\Omega_{A}^{(196)}\) scenarios with the next best algorithm appearing to be the GP4 algorithm followed by GP14 for \(\Omega_{A}^{(30)}\) scenario or GP98 for \(\Omega_{A}^{(196)}\) scenario, and last by the GN algorithm. These results could be attributable to the fact that SP swaps a single pair of treatments per iteration, thus taking small steps in the search for an optimal design which makes it more likely to find an optimal condition than GP algorithms that take larger random steps. SA algorithm performed well under \(A\)-optimality criterion since it has the ability not to be trapped in a local minima by accepting a proportion of bad solutions using an exponential distribution and a cooling schedule. It is expected that this algorithm will have better performance in tha case of hundreds or thousand entries, where the likelihood of being trapped in local minima is higher. SA algorithm achieved the lowest relative design efficiencies for the same number of iterations of 5,000 under \(\Omega_{D}^{(30)}\) scenario as shown in Table 4. It is not very clear why this occurs, but it was observed that it accepted too many bad (or random) solutions as it tried not to be trapped in a local minima, hence, making its progress difficult to maximize the objective function. This study demonstrated that the incorporation of genetic relationships can affect the optimality of a given design. However, large design improvements have been observed among genetically unrelated individuals, which agrees with findings from [PERSON] and [PERSON] [25] although they did not analyse varied levels of spatial correlations. Optimization based on \(A\)-criterion has revealed, from the present study, that a substantial decrease in average variance of treatment effects (i.e., trace) among full-sib families can be achieved for treatments with small levels of narrow-sense heritabilities (\(h^{2}=0.1\)).