## 4 Experimental Evaluation
### Results
\begin{tabular}{c c c c c c c c c} \hline  & \multicolumn{4}{c}{**Scenario 1**} \\ \cline{2-9}
**SA:** & i=500 & i=1000 & i=2000 & i=3000 \\ T=1 & 0.91 & 0.95 & 0.98 & **1.00** \\ T=2 & 0.90 & 0.93 & 0.97 & 0.98 \\ T=4 & 0.84 & 0.88 & 0.92 & 0.95 \\ T=8 & 0.80 & 0.85 & 0.90 & 0.91 \\ \cline{2-9}  & \multicolumn{1}{c}{**Random**} & \multicolumn{1}{c}{**SCS**} & \multicolumn{1}{c}{**ALHSO**} & \multicolumn{1}{c}{**HC**} \\ \cline{2-9}  & 0.45 & 0.82 & 0.93 & 0.94 \\ \hline \hline \multicolumn{9}{c}{Scenario 4} \\ \cline{2-9} SA: & i=500 & i=1000 & i=2000 & i=3000 \\ T=1 & 0.90 & 0.95 & 0.99 & **1.00** \\ T=2 & 0.87 & 0.95 & 0.98 & 1.00 \\ T=4 & 0.87 & 0.92 & 0.95 & 0.97 \\ T=8 & 0.82 & 0.86 & 0.91 & 0.94 \\ \cline{2-9}  & \multicolumn{1}{c}{**Random**} & \multicolumn{1}{c}{**SCS**} & \multicolumn{1}{c}{**ALHSO**} & \multicolumn{1}{c}{**HC**} \\ \cline{2-9}  & 0.43 & 0.77 & 0.95 & 0.91 \\ \hline \hline \multicolumn{9}{c}{Scenario 7} \\ \cline{2-9} SA: & i=500 & i=1000 & i=2000 & i=3000 \\ T=1 & 0.79 & 0.89 & 0.98 & **1.00** \\ T=2 & 0.80 & 0.88 & 0.95 & 0.96 \\ T=4 & 0.78 & 0.85 & 0.91 & 0.91 \\ T=8 & 0.70 & 0.77 & 0.85 & 0.86 \\ \hline \hline \end{tabular} \begin{tabular}{c c c c c c} \hline  & \multicolumn{4}{c}{**Scenario 8**} \\ \cline{2-9}
**SA:** & i=500 & i=1000 & i=2000 & i=3000 \\ T=1 & 0.88 & 0.95 & 0.98 & **1.00** \\ T=2 & 0.87 & 0.95 & 0.98 & 1.00 \\ T=4 & 0.88 & 0.91 & 0.94 \\ T=8 & 0.82 & 0.86 & 0.90 & 0.94 \\ \hline \hline \multicolumn{9}{c}{Scenario 9} \\ \cline{2-9}
**SA:** & i=500 & i=1000 & i=2000 & i=3000 \\ T=1 & 0.88 & 0.95 & 0.98 & **1.00** \\ T=2 & 0.87 & 0.95 & 0.98 & 1.00 \\ T=4 & 0.87 & 0.92 & 0.95 & 0.97 \\ T=8 & 0.82 & 0.86 & 0.91 & 0.94 \\ \hline \hline \multicolumn{9}{c}{Scenario 9} \\ \cline{2-9}
**SA:** & i=500 & i=1000 & i=2000 & i=3000 \\ T=1 & 0.79 & 0.89 & 0.98 & **1.00** \\ T=2 & 0.80 & 0.88 & 0.95 & 0.96 \\ T=4 & 0.78 & 0.85 & 0.91 & 0.91 \\ T=8 & 0.70 & 0.77 & 0.85 & 0.86 \\ \hline \hline \end{tabular} 
\begin{tabular}{c c c c c} \hline  & \multicolumn{4}{c}{**Scenario 8**} \\ \cline{2-9}
**SA:** & i=500 & i=1000 & i=2000 & i=3000 \\ T=1 & 0.88 & 0.99 & 0.98 & **1.00** \\ T=2 & 0.90 & 0.94 & 0.96 & 0.99 \\ T=8 & 0.81 & 0.86 & 0.91 & 0.91 \\ \cline{2-9}
**Random** & \multicolumn{1}{c}{**SCS**} & \multicolumn{1}{c}{**ALHSO**} & \multicolumn{1}{c}{**HC**} \\ \cline{2-9}
**SA:** & i=500 & i=1000 & i=2000 & i=3000 \\ T=1 & 0.88 & 0.95 & 0.98 & **1.00** \\ T=2 & 0.97 & 0.95 & 0.98 & 1.00 \\ T=4 & 0.88 & 0.91 & 0.94 \\ T=8 & 0.91 & 0.94 & 0.96 \\ T=4 & 0.88 & 0.91 & 0.95 & 0.97 \\ T=8 Figure 8 shows the mean value of the utility functions for the different scenarios and relative to their maximum value (in bold). To make the interpretation easier, in the table devoted to the results of the SA algorithm, we have highlighted in green those results that outperform or equal ALHSO (they also outperform SCS and random, as they are less restrictive). Moreover, we have highlighted in yellow the results where SA outperforms SCS. As a conclusion, for temperatures close to \(T=1\) and \(1000\) or more iterations, SA outperforms ALHSO. Moreover, we notice that, for almost all cases (except for very high temperatures and very few iterations), SA outperforms SCS. In the figure, we also show the results for HC (equivalent to SA with \(T=0\)) with \(3000\) iterations, and we observe that it has a worse performance than SA for the same number of iterations. As a conclusion, we can recommend the use of negotiation techniques based on SA, as it is able to obtain better results than SCS in almost all cases, and it is not difficult to find configuration parameters that make SA even better than a nonlinear optimizer like ALHSO.