# Evaluating Algorithm Efficiency for Optimizing Experimental Designs with Correlated Data
## 3 Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Condition**} & \multicolumn{2}{c}{**SP**} & \multicolumn{2}{c}{**GP4**} & \multicolumn{2}{c}{**GP14**} & \multicolumn{2}{c}{**SA**} & \multicolumn{2}{c}{**GN**} \\ \hline
**Pedigree** & \(h^{2}\) & **ODE \%** & **S.E.** & **ODE \%** & **S.E.** & **ODE \%** & **S.E.** & **ODE \%** & **S.E.** & **ODE \%** & **S.E.** \\ \hline \multirow{3}{*}{Indep} & 0.1 & 6.347 & 0.060 & 5.501 & 0.060 & 3.747 & 0.093 & 6.385 & 0.072 & - & - \\  & 0.3 & 7.398 & 0.066 & 6.194 & 0.080 & 4.371 & 0.053 & 7.403 & 0.063 & - & - \\  & 0.6 & 5.109 & 0.044 & 4.414 & 0.057 & 3.110 & 0.054 & 5.222 & 0.064 & - & - \\ \hline \multirow{3}{*}{Half-sib} & 0.1 & 5.826 & 0.026 & 5.082 & 0.055 & 3.610 & 0.065 & 5.781 & 0.045 & 1.853 & 0.042 \\  & 0.3 & 5.375 & 0.056 & 4.640 & 0.082 & 3.192 & 0.052 & 5.428 & 0.047 & 1.940 & 0.088 \\ \cline{1-1}  & 0.6 & 3.066 & 0.028 & 2.663 & 0.023 & 1.858 & 0.033 & 3.131 & 0.028 & 1.064 & 0.033 \\ \hline \multirow{3}{*}{Full-sib} & 0.1 & 4.109 & 0.030 & 3.611 & 0.026 & 2.543 & 0.038 & 4.045 & 0.027 & 1.343 & 0.034 \\ \cline{1-1}  & 0.3 & 2.656 & 0.029 & 2.265 & 0.021 & 1.601 & 0.034 & 2.667 & 0.032 & 0.920 & 0.027 \\ \cline{1-1}  & 0.6 & 1.247 & 0.006 & 1.065 & 0.009 & 0.755 & 0.012 & 1.247 & 0.013 & 0.460 & 0.011 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average ODEs from 10 replicates per condition are reported together with standard errors (S.E.) for simple pairwise (SP), greedy pairwise (GP4 and GP14), simulated annealing (SA) and genetic neighborhood (GN) procedures for \(\Omega_{A}^{(30)}\) RCB designs at a spatial correlation of 0.6. Results from the practical example that was conducted for an RCB design with \(h^{2}=0.1\) and \(\rho=0.6\) based on \(\Omega_{A}^{(30)}\) are displayed in Figure 4 which plots traces obtained from successful swaps and their overall design efficiencies. Also, Figure 5 shows the rate of convergence by plotting all the 20,000 traces obtained for each algorithm. From this illustration, the results indicate that the SP algorithm had the highest design efficiency of 6.713% with the highest number of successful swaps (192) and took about 5.8 min for the 20,000 iterations. This was closely followed by the SA algorithm that had an ODE of 6.258% with 139 successful swaps and took about 5.8 min. GP4 algorithm had an ODE of 5.552% with 104 successful swaps and also took about 5.8 min and finally, the GN algorithm recorded the lowest ODE of 2.053% with 12 successful swaps and took about 6.1 min. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \multicolumn{2}{c}{**Condition**} & \multicolumn{2}{c}{**SP**} & \multicolumn{2}{c}{**GP4**} & \multicolumn{2}{c}{**GP14**} & \multicolumn{2}{c}{**SA**} & \multicolumn{2}{c}{**GN**} \\ \hline
**Pedigree** & \(h^{2}\) & **ODE \%** & **S.E.** & **ODE \%** & **S.E.** & **ODE \%** & **S.E.** & **ODE \%** & **S.E.** & **ODE \%** & **S.E.** \\ \hline \multirow{3}{*}{Indep} & 0.1 & 1.807 & 0.014 & 1.600 & 0.014 & 1.029 & 0.014 & 0.085 & 0.019 & - & - \\  & 0.3 & 2.324 & 0.017 & 1.993 & 0.013 & 1.335 & 0.030 & 0.104 & 0.025 & - & - \\  & 0.6 & 2.247 & 0.021 & 1.930 & 0.021 & 1.265 & 0.032 & 0.178 & 0.027 & - & - \\ \hline \multirow{3}{*}{Half-sib} & 0.1 & 1.766 & 0.012 & 1.576 & 0.015 & 1.115 & 0.015 & 0.130 & 0.034 & 0.446 & 0.015 \\  & 0.3 & 2.287 & 0.023 & 2.054 & 0.024 & 1.377 & 0.022 & 0.150 & 0.041 & 0.614 & 0.013 \\  & 0.6 & 2.253 & 0.024 & 1.933 & 0.020 & 1.315 & 0.019 & 0.090 & 0.023 & 0.637 & 0.023 \\ \hline \multirow{3}{*}{Full-sib} & 0.1 & 1.666 & 0.011 & 1.514 & 0.013 & 1.037 & 0.009 & 0.097 & 0.025 & 0.431 & 0.010 \\  & 0.3 & 2.168 & 0.013 & 1.935 & 0.025 & 1.307 & 0.026 & 0.119 & 0.025 & 0.634 & 0.017 \\ \cline{1-1}  & 0.6 & 2.225 & 0.027 & 1.913 & 0.023 & 1.316 & 0.025 & 0.125 & 0.019 & 0.669 & 0.022 \\ \hline \end{tabular}
\end{table} 
Table 4: Average ODEs reported together with standard errors (S.E.)