## 2 Literature Review  
### Tourist Trip Design Problem  
Personalized tour itineraries have replaced standard tour packages as the norm in travel planning [20; 21]. TRSs are committed to meeting individual travel requirements and helping to organize leisure and travel plans. The emphasis of TRS research is now shifting to recommendations for complete travel itineraries, which can be addressed by solvingthe TTDP [19]. The existing research has led to tremendous advances in the model and algorithm design of TTDP. TTDP variants can be categorized as either single-tour or multiple-tour variants [22]. The orienteering problem (OP) is the basis for modeling the single-tour TTDP, aiming to maximize the overall profit obtained while adhering to time and budget constraints [23]. Several extensions of OP, such as the orienteering problem with time windows (OPTW) [24] and the time-dependent orienteering problem (TDOP) [25], have been successfully applied to model complex versions of single-tour TTDP. Multiple-tour TTDP can be modeled as a vehicle routing problem with profits (VRPP) in which profits are distributed across multiple vehicles with a limited capacity [26]. The objectives in TTDP can be summarized as maximizing profit, minimizing cost, and customized objectives. Profit gained from visiting POIs, such as the total score and utility of attractions, should be maximized [7; 27; 28]. Minimizing costs can be reflected in minimizing the distance [29] and expenses [30]. Moreover, customized objectives are designed to solve specific application-related problems. For instance, [PERSON] et al. (2022) [30] included minimizing total emissions from travel as one of the TTDP's green travel goals. Concerning the algorithms for solving TTDP, exact and meta-heuristic methods are typically employed. In the exact algorithm field, methods such as the weighted-sum method and mixed-integer linear programming are generally applied, which can transform multi-objective problems into single-objective problems. In relation to meta-heuristic algorithms, single-solution-based and population-based metaheuristics are commonly-used approaches [31]. Single-solution-based metaheuristics include local search, tabu search, and simulated annealing [21; 27; 30; 32]. Evolutionary algorithms (e.g., genetic algorithms, evolutionary strategies) and swarm intelligence-based methods (e.g., ant colony, particle swarm optimization) [6; 33; 34] are examples of population-based metaheuristics. Typically, a multi-objective problem is resolved by augmenting the metaheuristic algorithm with specific search components, such as fitness assignment, diversity preservation, and elitism. As research in TTDP flourishes, the theories and methods applied to TTDP are used in various intelligent tools, such as digital applications and e-guides [35]. Specifically, several mobile and web-based decision support applications that facilitate tourism have been introduced. [PERSON] et al. [36] employed a metaheuristic based on a local search, namely the SlackRoutes, to solve the TTDP and developed a web and mobile client application, eCOMPASS, to help users to plan their multi-day tours by providing them with the specific route, time schedule, and transportation mode. [PERSON] et al. [37] introduced a user-friendly web-based tour planning application, CT-Planner4 ([[https://ctplanner.jp/ctp5/](https://ctplanner.jp/ctp5/)]([https://ctplanner.jp/ctp5/](https://ctplanner.jp/ctp5/)), accessed on 5 December 2022), where the user can select the target area, mode of transport, starting point, end point, and travel style on the web page and then acquire the planned route visualized on an online map. The above TTDP-related works focus more on the profit and utility tourists attained from attractions and give less attention to how the crowd movements of tourists influence the attraction characteristics dynamically. These crowd dynamics contain a wealth of information that can help to understand the attractions better and enhance the tourism experience.