# A Novel Application Based on a Heuristic Approach for Planning Itineraries of One-Day Tourist
## 1 Introduction
### Related Works: Methodology-Based Classification  
This section groups and analyses research works that provide rigorous description of heuristic and metaheuristic approaches to solve the Tourist Trip Design Problem (TTDP). These approaches result the only viable methods to efficiently optimize the travel itinerary, by analyzing the problem from different perspectives, with different problem variables and constraints. The objective in TTDP modeling is to identify a set of near-optimal itineraries to maximize tourist satisfaction. The baseline combinatorial optimization problem for TTDP is the orienteering problem (OP). The OP can be used to model the TTDP where the PoIs are associated with a profit and the goal is to find a single tour that maximizes the profit collected within a given time budget. In the OP, given a starting node \(s\), a terminal node \(t\) and a positive time limit (budget), the goal is to find a path from \(s\) to \(t\) such that the total profit of the visited nodes is maximized. In the related literature, [PERSON] et al. [10] propose an intelligent routing system that defines an optimization problem including multiple paths to move from one location to another. Such a system, by exploiting an iterated local search metaheuristic method, suggests a personalized tour combining information about the local attractions, weather forecasting and public transportation. [PERSON] analyzes the models, algorithmic approaches and methodologies about tourist trip design problems [11]. Recent approaches are reported aiming at taking into account a multitude of realistic PoIs attributes and user constraints. In this context, [PERSON] et al. focus on the most recent works about the Orienteering Problem (OP) and its variants [12]. The authors focus on a comprehensive and thorough survey of recent variants of the OP, including the proposed solution approaches. The work reports the new variants of the OP, such as the Stochastic OP, the Generalized OP, the Arc OP, the Multi-agent OP, the Clustered OP and others. The authors summarize several interesting applications which are related to the mobile crowdsourcing problem, the Tourist Trip Design Problem, the theme park navigation problem and others. The authors in [13] provide a detailed explanation about operation on tour routes only qualitatively. An optimizer is proposed in [14], where a multiobjective evolutionary algorithm is used to identify the near-optimal solutions to the planning of multiple-day routes in a reasonable computational time. In the contribution [15], the authors present a heuristic procedure for the generalization of a optimization problem to plan personalized recommendations for daily sightseeing itineraries for mobile tourist guides. Extensions of the OP have been applied to model more complex versions of TTDP: the OP with time windows (OPTW) considers visits to locations within a predefined time window; this allows modeling opening days/hours of PoIs. The time-dependent OP (TDOP) considers time dependency in the estimation of time required to move from one location to another; therefore, it is suitable for modeling multimodal transports among Pols. In particular, [PERSON] considers a more complex variant of the tourist trip design problem i.e., the time-dependent in the estimation of the time required to move from one location to another for planning daily tours according to tourist's preferences [16]. The team orienteering problem (TOP) is the extension of the OP to multiple tours. The TOP with time windows (TOPTW) has been mostly commonly studied among the aforementioned OP variants since it is useful for modeling several real-life optimization problems. [PERSON] et al. propose a metaheuristic algorithm to tackle a more effective extension of the optimization problem [17]. The proposed algorithm performs a planning of a multipleday tour by considering a set of PoIs, a visiting duration, and a set of multiple opening and closing times per day combined with the trip constraints of the tourist.