## 5 Experiments
### Algorithms Comparison
For a deeper analysis of the results, it may be helpful to compare a gap between initial approximations and optimal solutions presented in Tables 8 and 9 for algorithms using total energy performance index and maximal energy performance index, respectively. Data in the tables are values of the relaxed (continuous) solution and the initial integer upper bound found in the root node of the branch and bound procedure. It must be noted that the algorithm could not find an integer solution in the root node for some cases. The distance between two approximated solutions and optimal solution gives some idea of the general complexity of the task. Specifically, there are some favorable cases when the number of branch and bound iterations may be low or even zero, like nine nodes scenarios. In general, the algorithm using the total energy consumption performance index needs more branch and bound iterations than that using maximal energy consumption, and the number of iterations grows rapidly with the problem size. For the algorithm using a maximal energy consumption performance index, this growth is not so apparent. In this case, the influence of a gap between the initial upper bound on the number of branch and bound iterations is more visible. When the upper bound cannot be found in the root node--as in some cases marked with (*) and (**) in the Tables 8 and 9--the branch and bound procedure becomes more difficult as the possibility to skip some branches early is limited. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \multirow{2}{*}{**Number of Nodes**} & \multicolumn{3}{c}{**Computation Time [s]**} & \multicolumn{3}{c}{**Performance Index**} \\ \cline{2-7}  & **Average** & **Min.** & **Max.** & **Average** & **Min.** & **Max.** \\ \hline
9 & 0.062 & 0.024 & 0.1 & 996.3 & 874.3 & 1118.2 \\ \hline
16 & 67.2 & 0.064 & 266 & 1276.5 & 655.5 & 1774.5 \\ \hline
25 & 1476.9 & 0.26 & 8162 & 1485 & 597.7 & 2264.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results for algorithm using total energy consumption index. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \multirow{2}{*}{**Number of Nodes**} & \multicolumn{3}{c}{**Computation Time [s]**} & \multicolumn{3}{c}{**Performance Index**} \\ \cline{2-7}  & **Average** & **Min.** & **Max.** & **Average** & **Min.** & **Max.** \\ \hline
9 & 0.42 & 0.26 & 0.57 & 112 & 112 & 112 \\ \hline
16 & 7.45 & 0.23 & 12.4 & 108.5 & 98 & 112 \\ \hline
25 & 17 & 3.67 & 41.2 & 112 & 112 & 112 \\ \hline
36 & 12.9 & 1.77 & 36.2 & 110.4 & 98 & 112 \\ \hline
49 & 16.9 & 4.1 & 64 & 112 & 112 & 112 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results for algorithm using maximal energy consumption index. \begin{table}
\begin{tabular}{c l l l l l} \hline \hline \multirow{2}{*}{**Number of Nodes**} & \multicolumn{3}{c}{**Average Solution**} & \multicolumn{3}{c}{**Average Branch**} \\ \cline{2-5}  & **Root: Relaxed** & **Root: Upper Bound** & **Optimal** & **and Bound Iterations** \\ \hline
9 & 914.8 & 996.3 & 996.3 & 0 \\ \hline
16 & 914 & 1441.2 & 1276.5 & 288,759 \\ \hline
25 & 994.2 & 1771.5 * & 1485 & 2,592,057.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of average relaxed solution and upper bounds in the root node for algorithm using total energy consumption index. The optimal solution is found after the number of branch and bound iterations presented in the last column. Value marked with (*) is the mean of 4 of 6 cases as CPLEX did not provide an initial approximation in the root node for all tasks. Another important observation is that computation time may vary significantly within a scenario. This suggests that coordinating data transmission in some frames may be more difficult than in others. An example of such a situation may be seen in Table 6 for the 25 nodes scenario. The solution for one of the frames may be found in about a quarter of a second, while the other needs over 2 hours to be solved. Furthermore, the solution of the first case requires no branch and bound iterations, while the second needs nearly 400 million iterations.