## 1 Introduction  
The tourist trip design problem (TTDP) is the core problem of the tourism recommendation system (TRS). It is used to solve the challenges of information overload and decision-making difficulties for tourists, which involves the time allocation at a point of interest (POI) and the spatial structures of the routes (including POI selection and sequencing) [1, 2, 3, 4, 5]. A solution of a TTDP aims to find optimal routes to maximize the obtained utility (e.g., score, profit) [4, 6, 7, 8] and minimize the cost (e.g., distance, expense) [9, 10], which improves the tourism experience while accounting for various constraints (e.g., time budget and personal preferences) [11]. Tourism experience is essential and necessary for tour route recommendations and is complex due to its multi-faceted nature, tourists' mobile nature, and uncertainty in tourism destinations [12]. In addition to facilities and services, attractions' crowding situation significantly impacts the tourist experience, as \"over-tourism\" can negatively affect visitors' perceptions of crowding, resulting in lower customer satisfaction and revisit rates [5, 13, 14]. For instance, the current crowding-related TTDP is limited to the interiors of specific attractions and lacks the co-analysis of the crowding of multiple attractions. In addition, few studies have focused on coping with the sudden increase in crowds, and a dynamic adjustment mechanism and attraction replacement strategy are urgently required in route recommendation [11, 15, 16]. In addition, the tourism value is essential for determining whether an attraction is worth visiting and is ordinarily measured and rated objectively with the ranking of facilities and services. However, the recommendations made often ignore the current trending and tourists' selection behaviors. Notably, supervities (cities with a permanent population of 5 to 10 million) are rich in tourism resources, representing a vast number of attractions and a wider geographical spread, making them popular destinations for many tourists. Apparently, it is quite difficult for those tourists with limited knowledge about the destinations and current trends to choose attractions and plan routes in the supercity. Furthermore, the expansion of the city scale poses a significant challenge to the data source's applicability, the model's practicality, and the algorithm's capability in TTDP. To cope with these gaps, crowd dynamics derived from broad-coverage mobile tracking data, which refer to the quantitative descriptions of the movement of humans in space and time, are feasibly capable of evaluating the value of attractions in the supercity and managing crowding. Mapping tourist movements gives an understanding of tourism destinations and the interconnections between destinations [17; 18]. For example, capturing tourists' mobility (e.g., distribution of the duration of stay per attraction and which attractions are frequently visited together) and social connections (e.g., identifying similar users with spatial co-occurrences) are helpful in ranking and composing the itinerary [19]. With crowd dynamics information, the tourism experience quality of the TTDP could be further improved. The contribution of this paper can be summarized as follows. First, this paper defines a tourist trip design problem with crowd dynamics (TTDP-CD) for the first time in literature and proposes an effective two-stage route strategy of \"global optimization first, local update later\" to generate dynamic, personalized tour routes with less crowded situations, including initial pre-tour itineraries and dynamically adjusted in-tour itineraries for avoiding sudden overcrowding. Second, the crowd dynamics indicators (i.e., crowd flow, crowd interaction, and crowd structure) are derived from mobile tracking data to support the construction of two-stage multi-objective model in terms of three conflicting objectives (i.e., crowding, value, and distance) and dynamic adjustment strategy.