# Optimized Travel Itineraries: Combining Mandatory Visits and Personalized Activities
## 4 Computational Study
### TOPTW-PS Instances  
The TOPTW-PS instances, designed by [PERSON] et al. [28], are derived from [PERSON] (1987) datasets, which include six different classes: R1, R2, C1, C2, RC1, and RC2. These datasets feature instances with varying numbers of vertices (100, 50, and 25) and no depot, with each class containing a total of 56 instances. In this experiment, ANSA is applied to a set of 100 instances from these datasets. The goal is to evaluate the performance of ANSA in terms of computational time and compare the results with those obtained using the Selective D-PSO (Discrete Particle Swarm Optimization) algorithm. This comparison helps assess the efficiency and effectiveness of ANSA in solving the TOPTW-PS instances. According to the results in Tables 2 and 3, The Average CPU shown that ANSA achieves its objectives more quickly than S-DPSO. This implies that ANSA converges to a satisfactory or optimal solution quicker than S-DPSO under the given experimental conditions. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Name**} & **Objective** & **CPU** & & **Objective** & **CPU** \\  & **Value** & **(Seconds)** & & **Value** & **(Seconds)** \\ \cline{2-6}  & & **S-DPSO** & **ANSA** & & & **S-DPSO** & **ANSA** \\ \hline c101\_ACS & 334 & 140 & 91 & c201\_ACS & 845 & 90 & 61 \\ c102\_ACS & 369 & 86 & 56 & c202\_ACS & 892 & 121 & 90 \\ c103\_ACS & 399 & 154 & 161 & c203\_ACS & 886 & 98 & 130 \\ c104\_ACS & 409 & 186 & 150 & c204\_ACS & 920 & 125 & 91 \\ c105\_ACS & 348 & 254 & 245 & c205\_ACS & 885 & 114 & 165 \\ c106\_ACS & 355 & 101 & 90 & c206\_ACS & 906 & 174 & 156 \\ c107\_ACS & 370 & 132 & 120 & c207\_ACS & 914 & 126 & 120 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results for 100-TOPTW-PS instances (\(p=1\)). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Objective**} & \multicolumn{2}{c}{**CPU**} & \multicolumn{2}{c}{**Objective**} & \multicolumn{2}{c}{**CPU**} \\ \cline{2-7}
**Name** & \multicolumn{2}{c}{**Value**} & \multicolumn{2}{c}{**(Seconds)**} & \multicolumn{2}{c}{**Name**} & \multicolumn{2}{c}{**Value**} & \multicolumn{2}{c}{**(Seconds)**} \\ \cline{2-7}
**c108\_ACS** & 374 & 180 & 153 & c208\_ACS & 923 & 125 & 96 \\ c109\_ACS & 383 & 135 & 100 & r201\_ACS & 743 & 99 & 90 \\ r101\_ACS & 199 & 95 & 101 & r202\_ACS & 826 & 158 & 146 \\ r102\_ACS & 271 & 250 & 182 & r203\_ACS & 884 & 157 & 123 \\ r103\_ACS & 282 & 96 & 108 & r204\_ACS & 999 & 190 & 156 \\ r104\_ACS & 297 & 88 & 115 & r205\_ACS & 848 & 115 & 100 \\ r105\_ACS & 237 & 154 & 111 & r206\_ACS & 901 & 211 & 169 \\ r106\_ACS & 280 & 130 & 106 & r207\_ACS & 946 & 102 & 99 \\ r107\_ACS & 282 & 157 & 166 & r208\_ACS & 996 & 199 & 180 \\ r108\_ACS & 301 & 98 & 80 & r209\_ACS & 865 & 179 & 166 \\ r109\_ACS & 270 & 87 & 65 & r210\_ACS & 880 & 166 & 145 \\ r110\_ACS & 275 & 150 & 142 & r211\_ACS & 931 & 148 & 169 \\ r111\_ACS & 288 & 256 & 161 & r201\_ACS & 753 & 132 & 163 \\ r112\_ACS & 286 & 89 & 152 & r202\_ACS & 863 & 158 & 98 \\ r101\_ACS & 219 & 86 & 90 & r203\_ACS & 917 & 101 & 120 \\ r102\_ACS & 258 & 131 & 152 & r204\_ACS & 1008 & 129 & 95 \\ r103\_ACS & 254 & 209 & 226 & r205\_ACS & 802 & 158 & 120 \\ r104\_ACS & 284 & 90 & 121 & r206\_ACS & 793 & 155 & 85 \\ r105\_ACS & 235 & 150 & 121 & r207\_ACS & 869 & 93 & 79 \\ r106\_ACS & 248 & 122 & 129 & r208\_ACS & 950 & 153 & 114 \\ r107\_ACS & 268 & 85 & 90 & Average CPU & & 140 & 123 \\ rc108\_ACS & 283 & 270 & 156 & & & & \\ \hline Average CPU & 299 & 144 & 129 & & & & \\ \hline \hline \end{tabular}
\end{table}