# Optimized Travel Itineraries: Combining Mandatory Visits and Personalized Activities
## 4 Computational Study
### Real Case Instances from Tak, Thailand  
In this real case, we generated instances based on the actual geographical distances of Tak Province, Thailand. Tak Province is in western Thailand, approximately 492 km from the capital, Bangkok. The province is filled with the allure of vast forests, which serve as a source of natural diversity. Moreover, it is a destination where tourists can enjoy a variety of experiences with several types of activities including nature-based activities, Budda-based activities, leisure activities, and culture-based activities.  
To test the algorithm, 30 datasets are generated, each containing 108 locations (\(N=\{N_{0}\cup N_{c}\}\)). There are four activities considered in each location: nature-based activities, Budda-based activities, leisure activities, and culture-based activities. The mandatory locations that should be visit everyday (\(N_{d}\)) is 44 locations, \(N_{d}\in N_{c}\). The mandatory location in \(N_{m}\) and the mandatory activity in \(A_{m}\) is randomly generated for each dataset. The score or POIs (\(S_{i,a}\)) of each location is derived from the review scores displayed on Google Maps. During a visit to a location, participants may choose various activities, each of which takes a specific amount of time and yields a distinct score. However, the total score collected in each location is not more than the review score.  
The datasets were tested with two versions of ANSA. The first version sets the probability of choosing the neighborhood mechanism to remain constant throughout the running process, ANSA-1. In this case, there are five neighborhood mechanisms. Therefore, the \(R_{t}\) is set to be \(R_{t}=\frac{1}{5}\) for all neighborhood mechanism \(t\), \(  
Figures 6 and 7 display the results obtained by running the model under various testing conditions. To assess the impact of the parameters on the results, we used the analysis of variance (ANOVA) to determine the relative significance of each main factor, \(I_{iter}\), \(T_{0}\), \(T_{f}\), \(\alpha\), and \(K\). The Pareto chart in Figure 8 quantifies the size and significance of each effect. It displays the absolute values of the standardized effects in descending order, where the standardized effects represent t-statistics that test whether an effect is zero, corresponding to the null hypothesis. In this chart, the factors B, B*C, and E are represented by bars that cross the reference line at 12.71, indicating statistical significance at the 0.05 level. This means that parameters \(I_{iter}\) and \(\alpha\) have a significant effect on the objective value. Consequently, adjusting these parameters could lead to improved outcomes in the studied phenomenon. However, when we analyze in terms of the computational time in Figure 9, both \(I_{iter}\) and \(\alpha\) significant factors affect computational time as well.  
Therefore, careful consideration is needed when optimizing these parameters to balance improvements in outcomes and computational efficiency. In this study, the results of parameter settings showed that the parameter setting No.9, which are \(I_{iter}\) = 20,000, \(T_{0}\) = 5, \(T_{f}\) = 0.01, \(\alpha\) = 0.8, and \(K\) = 1, obtained the best objective value compared to other settings. However, it requires high computational time. This parameter setting is used in the subsequent experiment.  
Figure 6: Objective values of each parameter settings.  
Figure 7: Computational time (second) of each parameter settings.  
Table 5 provides a comparison between the ANSA-1 and ANSA-2 with \(p=1,2\), and 3 for 30 datasets. The ANSA-2 can obtain a better solution in terms of percentage of gap, \(Gap(\%)=\frac{(ANSA\_1-ANSA\_2)}{ANSA\_1}\times 100\). The ANSA-2 can obtain a better solution 37.88%, 6.78% and 1.5 for all \(p\).  
Figure 8: Pareto chart of the effect of objective value.  
Figure 9: Pareto chart of the effect of Computational Time.