# Evaluating Algorithm Efficiency for Optimizing Experimental Designs with Correlated Data
## 3 Results  
Averages and standard errors (S.E.) of overall design efficiency (ODE %) for the three scenarios, that is, \(\Omega_{A}^{(30)}\), \(\Omega_{A}^{(196)}\) and \(\Omega_{D}^{(30)}\) for all algorithms are presented in Tables 2-4, respectively. Figure 2 displays visible trends of ODEs by genetic relatedness and heritability levels whereas Figure 3 shows the average number of successful swaps out of 5000 (that is, swaps that were accepted due to the resulting design having a smaller criterion value than the previous layout) for each algorithm. These results indicate that, for all experiments conducted based on \(\Omega_{A}^{(30)}\) and \(\Omega_{A}^{(196)}\) scenarios, simulated annealing (SA) and simple pairwise (SP) algorithms achieved the highest ODE averages in all evaluated conditions followed by GP4 (for \(\Omega_{A}^{(30)}\)) or GP98 (for \(\Omega_{A}^{(196)}\)) and lowest for genetic neighbourhood (GN). Also, the overall highest ODEs were achieved when \(h^{2}=0.3\) among genetically unrelated individuals for all algorithms. Among full-sib families, highest ODEs were achieved when \(h^{2}=0.1\) and decreased with increasing heritability for all algorithms evaluated under \(\Omega_{A}^{(30)}\) and \(\Omega_{A}^{(196)}\) scenarios. SA recorded the highest average ODE of 7.403% (S.E. = 0.063) followed by SP with average ODE of 7.398% (S.E. = 0.066) all obtained when \(h^{2}=0.3\) among genetically unrelated individuals. Algorithms SA, SP, GP4 and GP14 evaluated with half-sib families under \(\Omega_{A}^{(30)}\) had highest ODEs obtained for treatments with the lowest heritability of 0.1, whereas GN achieved its highest ODE when \(h^{2}=0.3\) for the same genetic structure. Based on a \(\Omega_{D}^{(30)}\) scenario, the best performing algorithm with highest average ODE among all conditions was SP, closely followed by GP4, GP14, GN and SA which recorded the lowest average ODE. Under this scenario, the overall highest ODEs were observed among genetically unrelated individuals for SP, GP4, and GP14 when \(h^{2}=0.3\). Among half-sib families, highest ODEs occurred when \(h^{2}=0.3\) but no clear trends among full-sib families were observed. Both \(\Omega_{A}^{(30)}\) and \(\Omega_{D}^{(30)}\) took, on average, about 2 min to improve a given initial experimental design for \(p=5000\) iterations, whereas \(\Omega_{A}^{(196)}\) required about 25 min for the same number of iterations. Figure 3 shows that the number of successful swaps decrease with increasing heritability especially for \(\Omega_{A}^{(30)}\) and \(\Omega_{A}^{(196)}\) scenarios with small difference in numbers between SA and SP algorithms but larger differences are noted under \(\Omega_{D}^{(30)}\) scenario. The number of successful swaps out of 5000 appeared to be highest for SA and SP under \(A\)-optimality criterion. From \(\Omega_{D}^{(30)}\) scenario, the number of successful swaps were highest for SA which recorded above 2500 out of the 5000 swaps but this was not refelcted in terms of improving the overall design efficiency under this criterion in contrast with other algorithms.