## 2 Literature Review
### Crowd Dynamics in Tourism  
Crowd dynamics refer to the quantitative descriptions of the movement of humans in space and time, which are widely employed in urban planning and tourism to comprehend the movement of individuals [38]. Common statistical approaches to crowd dynamics include quantitative statistical analysis of flow, interaction network analysis, and the calculation of mobility indicator values [39; 40; 41].  
Crowd dynamics can enhance the tourism experience in TTDP in numerous ways, such as preventing congestion and enhancing destination awareness. Nowadays, academic interest is gradually growing in crowd-aware TTDP. Various studies have demonstratedthat large crowds within an attraction indicate the attraction's popularity and create a more enjoyable entertainment atmosphere [42; 43; 44]. However, \"over-tourism\" caused by excessive crowds poses significant safety risks, especially in the post-COVID-19 phase, when visitors become more sensitive to crowding and avoid crowded places voluntarily in the short term [45]. Some researchers have considered attraction congestion as an objective of the TTDP. [PERSON] et al. (2016) [34] constructed a multi-objective time-varying function that incorporated POI heat, user interest, and crowding data, and solved the problem by employing a variant of the ant colony optimization algorithm to provide users with a travel itinerary that avoids the most crowded time of the POI. In addition to the congestion, the interactive network of attractions constructed by tourists' mobility contains a wealth of information that can be used for destination comprehension. For instance, in the destination network, a high degree of centrality indicates higher power and status of the nodes [40; 46]. Lastly, the composition of the population structure of attractions can be used to describe the audience type of the attraction quantitatively. It can be used for substitution between attractions, which is inspired by the concept of homophily [39; 47]. However, existing studies have not explored crowds, and there is no practical method to adjust tourist routes to address sudden crowd surges.  
There are various data sources for obtaining crowd dynamics. RFID, GPS chip-embedded tickets, and pedestrian sensors can be utilized to obtain crowding data at attractions [34; 48; 49]. Information on past tour behaviors requires access to the complete travel chain of visitors in the city, which can be collected from social media data and web notes [40; 50]. However, those geo-tag data are highly biased and hardly reflect the travel activities of the vast remaining majority of those who do not post online. With the widespread penetration of smart tourism in tourism activities, big data, such as mobile tracking data, is increasingly used in the studies of tourism activities [51; 52; 53; 54]. Compared to existing data sources, mobile tracking data provides a larger volume, more comprehensive, and boarder description of travel flows [55]. However, research on using mobile tracking data to aid TTDP has not yet been proposed to the best of our knowledge.  
In this work, a novel framework for modeling and solving the Tourist Trip Design Problem with Crowd Dynamics is designed to recommend personalized, dynamic one-day tours in supercities, using broad-coverage mobile tracking data and an improved multi-objective algorithm. The two-stage strategy brings the dynamic TTDP to the front, providing the adjustment solution when faced with emergencies such as overcrowding.