# Efficient Metaheuristics for the Mixed Team Orienteering Problem with Time Windows
## 7 Experimental Results
### Results
With regard to the SA algorithm, the profit for one million iterations is higher than that of half a million iterations by at most 0.5% for any number of walks. As for the parameters coolItFactor and schemelFactor, the results indicate that the parameter coolItFactor does not significantly influence the output of SA algorithm. For example, for half a million iterations and schemelItFactor equal to 10, the difference of SA_0.5M_0.8_10's profit and SA_0.5M_0.25_10's profit is less than 0.27% and this is the largest difference, given that the other parameters are the same. The parameter schemeItFactor seems to influence the results slightly more, however, the difference in profit is always less than 0.5%. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{2}{c}{**1 Walk**} & \multicolumn{2}{c}{**2 Walks**} & \multicolumn{2}{c}{**3 Walks**} & \multicolumn{2}{c}{**4 Walks**} \\ \cline{2-9}  & **Profit** & **Time (ms)** & **Profit** & **Time (ms)** & **Profit** & **Time (ms)** & **Profit** & **Time (ms)** \\ \hline ILS\_100 & 816.698 & 295.728 & 1359.972 & 340.59 & 1865.546 & 387.194 & 2286.534 & 402.608 \\ ILS\_200 & 821.578 & 590.264 & 1365.354 & 678.658 & 1872.24 & 771.2  
The experimental results demonstrate that ILS outperforms SA with respect to solution quality, yet, at the expense of longer execution time. For one walk, the solutions obtained by both ILS and SA are of similar profit, _i.e._, the ILS_100 produces slightly inferior solutions than those of SA overall, while ILS_200, ILS_400, ILS_800 produce marginally better solutions, however, with higher running time. For more than one walks, ILS prevails over SA even with 100 iterations. For example, ILS_100's profit for two walks is higher than that of SA by at least 1.7%, regardless of the particular parameters of SA. For three or four walks, the profit is at least 2.47% and 2.19% respectively, higher than the profit obtained from any execution of SA. However, ILS requires more execution time than SA. For constant number of iterations, the running time of ILS increases with the number of walks, since in the perturbation step, ILS removes a chain of included TAs from each walk. This increases the running time when the number of walks is large, since reaching a local optimum requires inserting TAs to all the walks. On the other hand, the execution time of the SA algorithm does not depend on the number of the constructed walks, but only on the number of iterations. This is because at each step of SA, only one walk is modified, hence, the execution time is independent of the number of walks. In the sequel we examine the behavior of ILS and SA in the case that the same running time is allowed to both algorithms, whatever the number of iterations. Tables 3-5 present the results obtained when the running time is fixed to one second, five and ten seconds respectively. Again, the experimental results show that ILS outperforms SA in solution quality. For one walk, the solutions obtained by both ILS and SA are of similar profit while the difference in solution quality increases as the number of walks increases. A reasonable explanation for the observed differences is that in the case of multiple walks, SA does not explicitly allow an exchange between walks, so it may move around less efficiently within the feasible region. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & **1 Walk** & **2 Walks** & **3 Walks** & **4 Walks** \\ \cline{2-5}  & **Profit** & **Profit** & **Profit** & **Profit** \\ \hline ILS & 832.48 & 1381.05 & 1886.10 & 2303.01 \\ SA\_0\_8 & 823.34 & 1332.36 & 1816.23 & 2233.94 \\ SA\_0\_5\_8 & 824.15 & 1332.59 & 1815.91 & 2234.28 \\ SA\_0\_25\_8 & 824.05 & 1333.06 & 1816.29 & 2234.76 \\ SA\_0\_8\_10 & 824.70 & 1335.58 & 1819.55 & 2236.04 \\ SA\_0\_5\_10 & 824.80 & 1336.19 & 1818.93 & 2236.74 \\ SA\_0\_25\_10 & 825.53 & 1335.78 & 1819.42 & 2235.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental Results—Same Execution Time (5 s).