A novel user-centric happiness model for personalized tour recommendations

Research background

Recently, governments, industry stakeholders, and academic researchers in tourism studies have progressively focused on happiness research to address their respective challenges (Chen & Li, 2018). Travelers often embark on vacations with the aim of enhancing their happiness levels, and recent findings highlight the positive impact of holidays on individual well-being (Nawijn, 2011). However, existing travel recommender systems (TRSs) often fail to fully capture the complexities of traveler preferences, particularly in terms of time management, activity selection, and satisfaction optimization.

Research problem

Travel-related decision-making involves consideration of multiple objectives and constraints. According to Burke & Kendall (2014), higher-quality personalized recommendations significantly persuade travelers to undertake specific trips. Essentially, aligning suggested tours with traveler preferences is found to be a key factor in fostering trust towards recommender systems. Current TRSs predominantly focus on selecting points of interest (POIs) based on static preferences, neglecting critical factors such as time constraints, waiting times, and the holistic satisfaction of travelers throughout their trips. This results in suboptimal itineraries that do not align with the dynamic needs of modern travelers. Additionally, existing models often treat waiting times and travel connections as fixed costs, failing to account for their impact on overall traveler satisfaction (Halder et al., 2024). These limitations highlight the need for a more comprehensive and time-centric approach to tour recommendations.

To further elucidate the research problem addressed in this article, an illustrative example is presented involving two distinct groups of travelers who are visiting a city, denoted as A and B. Figure 1 illustrates a city map with various POIs and designated starting and ending points. The numbers on the map represent unique identifiers for each POI. The starting point is labeled as ‘Start Point (Hotel)’, and the ending point is labeled as ‘End Point (Airport)’. POIs are categorized based on their appeal to two distinct traveler groups: Group A (preferring natural environments such as zoos, parks, and mountains) and Group B (preferring modern settings such as shopping malls, street markets, and museums). The edges between POIs represent travel routes, with associated costs or distances indicated by the numbers. This figure serves as a visual representation of the input data used to generate personalized tour recommendations. Moreover, it is not merely the type of POIs that differentiates the groups; their preferred modes of transportation between POIs also vary significantly. For instance, Group B favors walking between POIs to experience more traditional areas and street markets. In contrast, Group A prefers traveling by car, which enables them to visit a greater number of natural POIs, such as wildlife parks and rivers. This variation in travel preferences underscores the need for customized trip planning to accommodate the distinct requirements of each group.

Proposed solution

To address these challenges, this article introduces the Happiness Model (HM), a novel personalized tour recommendation model that optimizes itineraries by maximizing traveler satisfaction as a function of time. The HM integrates the Item Constraints Data Model (ICDM) to reduce data dimensionality and search space, enabling efficient and personalized recommendations. Unlike traditional POI-centric models, the HM adopts a time-centric approach, dynamically adjusting recommendations to maximize satisfaction over the entire trip duration. The model considers three key components: (1) activities at POIs, (2) connections between POIs, and (3) waiting times, ensuring a holistic and efficient travel plan.

Context and motivation

Given the growing importance of time management in travelers’ hectic schedules—wherein they frequently coordinate bookings for hotels, flights, tours, and event tickets simultaneously—there is a pressing need for a model capable of integrating these factors to provide comprehensive trip plan recommendations. Recommender systems (RSs) have emerged as a crucial tool in aiding users by providing personalized suggestions amidst extensive selections of options. This capability is anchored in decision-support mechanisms (Mao et al., 2024; Wu, Lyu & Liu, 2022; Felfernig et al., 2018; Liu, Zhong & Zhou, 2022). Specifically, travel recommender systems (TRSs) endeavor to facilitate itinerary planning by matching user preferences with the attributes of their intended journeys (Zhou et al., 2023). Nonetheless, empirical evidence indicates a bias in current TRSs towards recommending points of interest (POIs) predominantly situated in urban locales (Quijano-Sánchez et al., 2020). Effective travel planning demands the consideration of various factors, including temporal constraints, budgetary restrictions, transportation alternatives, and meteorological conditions (Sun & Wandelt, 2021).

Challenges in existing systems

Driven by the economic importance of the tourism industry, computer scientists have been at the forefront of developing innovative tools to enhance the sector. Such tools provide personalized recommendations that cater to users’ unique constraints and preferences, potentially enhancing tourist satisfaction and industry growth. This research area has garnered significant attention from various disciplines, including computer science, information systems, and marketing (Sarkar et al., 2023). Travel recommender systems (TRSs) have become a cornerstone of the tourism industry, offering personalized itinerary suggestions (Sarkar et al., 2023). These systems leverage various models that consider user preferences and constraints to design optimal tour plans (Beed et al., 2020). While relevant studies from literature acknowledge the limitations of solely focusing on POIs, they still face challenges in comprehensively addressing both travel preferences and time management (Beed et al., 2020). Subramaniyaswamy et al. (2018) propose a multi-modal itinerary recommendation system that considers user preferences for transportation and activity duration. However, their model treats waiting times as a fixed cost between POIs, neglecting the impact of unplanned delays or activity overruns. Renjith, Sreekumar & Jathavedan (2020) introduce a context-aware recommendation system that incorporates real-time information like weather and traffic conditions. This approach offers dynamic recommendations but may struggle with limited user data on travel preferences for connection types and their impact on enjoyment. On the other hand, some studies delve deeper into specific aspects beyond POI selection, but lack a holistic approach. Chen et al. (2017) present a framework for optimizing travel routes considering user preferences for scenic beauty along the way. While this caters to a specific travel desire, it does not integrate preferences for transportation type or waiting times. Su et al. (2020) propose an emotion-based model for personalized travel recommendation systems. This addresses the emotional aspect of travel but does not explicitly consider the impact of connection preferences and waiting times on user emotions.

Key contributions

In light of the preceding discussion, this article presents a novel personalized tour recommendation model, the HM, that offers the following key contributions:

• Time-centric approach: Unlike traditional models that focus on points of interest (POIs), the proposed HM focuses on maximizing user satisfaction over time, dynamically adjusting to traveler preferences during the trip.

• Integration of the Item Constraints Data Model (ICDM): By incorporating ICDM, the HM reduces data dimensionality, thereby improving computational efficiency while maintaining personalization.

• Consideration of various activities: The proposed HM incorporates activities such as visiting POIs, traveling between POIs, and minimizing wasted time to create more comprehensive itineraries while ensuring a holistic and efficient travel plan.

• Overcoming limitations of existing methods: The proposed HM addresses the shortcomings of current models by considering a wider range of factors that influence traveler satisfaction, such as time management, connection preferences, and waiting times.

The article is organized as follows: “Related Works” provides a review of related work. “Item Constraints Data Model” introduces the Item Constraints Data Model (ICDM). “The Proposed Happiness Model” presents the proposed Happiness Model (HM), including its mathematical formulation and integration with the ICDM. “Experiments” and “Discussion” details the experimental setup and results. Finally, “Conclusion” concludes the article, summarizing the key findings and discussing future research directions.

Comparison with previous work

To the best of our knowledge, all preceding models concentrate exclusively on the cumulative scores of visited POIs, which constitutes a significant limitation. Table 1 provides a detailed comparison between the proposed Happiness Model (HM) and existing approaches, highlighting the unique advantages of the HM. Firstly, the Happiness Model (HM) and the Multi-Objective Orienteering Problem (MOOP) assign multiple values (MVs) to each node. The HM is specifically developed to attribute multiple values to various aspects of a trip, including points of interest, travel options, and time constraints. Moreover, the Multi-Constraint Team Orienteering Problem with Multiple Time Windows (MCTOPMTW) incorporates multi-attributes to enforce multi-constraints (MC), ensuring that the trip remains within the bounds of these limitations. Furthermore, the MOOP deals with distinct categories, each offering unique benefits, with the goal of maximizing overall benefits across these categories. Additionally, the MCTOPMTW accommodates tags, allowing each point of interest to have multiple attributes.

In contrast, the proposed HM has the ability to manage both categories and attributes by leveraging the strengths of both types of models. Such innovative approach introduces the consideration of multi-values (MVs) between each node, while other models traditionally focus solely on distance. Specifically, the transition between points of interest involves various values, such as time, journey length, and cost. Additionally, the HM combines these values into a single metric that represents the traveler’s satisfaction level. Moreover, travelers with reservations (e.g., flights, hotels, or trains) typically prefer using the entire allocated time for a given trip. Therefore, the proposed HM is designed to consider time inefficiency as a crucial factor that likely impacts the traveler’s satisfaction level.

The comparative analysis is further expanded to include additional models, such as the Genetic Algorithm-based Tour Recommendation System (GATRS) and the particle swarm optimization-based approach (PSO). Table 1 demonstrates the superiority of the HM in terms of personalization and the consideration of multiple factors such as time and waiting times, which are not addressed by other models like GATRS and PSO.

In light of the preceding discussion, it is evident that the proposed HM addresses the deficiencies inherent in extant models documented in the literature. In alignment with prior research, the proposed model is structured to assess each discrete moment of a trip by taking into account various trip-related actions. Moreover, the HM employs a temporal framework, utilizing an algorithm to optimize activities at each individual moment rather than relying on a cumulative aggregation of events.

Advantages of the proposed solutions

The HM offers several advantages over existing models:

• Time-centric optimization: By focusing on maximizing satisfaction over time, the HM provides more dynamic and personalized itineraries.

• Comprehensive consideration of factors: The model accounts for activities, connections, and waiting times, addressing limitations of traditional POI-centric approaches.

• Improved efficiency: The integration of the ICDM reduces computational complexity, enabling faster and more scalable recommendations.

• Enhanced personalization: Experimental results demonstrate that the HM outperforms existing models in terms of satisfaction scores, waiting time reduction, and the number of recommended POIs.

Mathematical model

The proposed happiness model is formulated as follows:

• Directed weighted graph: A directed weighted graph $G=(V,E)$ represents a city with nodes $i\in I$; $i=1,\dots ,|I|$ (Points of Interest) and attributes $k\in K$; $k=1,\dots ,|K|$. The edges in E connect these nodes and have values in $r\in R$; $r=1,\dots ,|R|$.

• Travel time and time spent: The travel time between nodes $i,j\in I$ is denoted by $T{T}_{ij}$, and the time spent at node $i$ denoted by $S{T}_i$.

• Starting and ending points: Let $s$ and $t$ be a starting and terminal nodes, respectively, where $s=1$ and $t=|I|$, in which the trip duration can span multiple days. Hence, $p\in P$; $p=\{1,\dots ,|P|\}$ denotes the trip days. Furthermore, each trip encompasses a start and end time within the day $p$, where $t\in p$; $t=1,\dots ,|p|$ represents the set of moments in day $p$.

• Time constraints: The daily time constraint is represented by $T_{max}$, and $S_{max}$ denotes the maximum value for all actions, scaled from $0$ to $1$.

• Decision variables: $X_{pti}$ represents whether the user remains at node $i$ on day $p$ at time $t$, $Y_{ptij}$ represents whether the user moves from node $i$ to node $j$ on day $p$ at time $t$, and $Z_{pt}$ represents whether the user is waiting on day $p$ at time $t$.

• Score values: $S_{pti}$ denotes the score value of activities at node $i$ on day $p$ at time $t$. The value of a connection from node $i$ to node $j$ based on attribute $r$ on day $p$ at time $t$ is denoted by $C_{ptijr}$, and the value of the waiting time on day $p$ at time $t$ is denoted by $W_{pt}$.

Objective function

The proposed happiness model is formulated as a multi-objective optimization problem aimed at maximizing traveler satisfaction over time. The objective function of the model is to maximize the total score derived from three actions: activity, connection, and waiting. This is represented by Eq. (5), which includes three functions: $f_1(a)$, $f_2(c)$, and $f_3(w)$. The HM is quantified on a scale from $0$ to $1$, with $1$ indicating optimal user satisfaction during the tour.

(5) $$Max\left(\frac{f_1(a)+f_2(c)+f_3(w)}{T_{max}\times S_{max}\times |P|}\right)$$where $f_1(a)$, $f_2(c)$, and $f_3(w)$ are defined in Eqs. (6)–(8), respectively. The function $f_1(a)$ represents the level of happiness associated with a given activity. It is normalized to a range between $0$ and $1$ by dividing the raw value by $\left(T_{max}\times S_{max}\times |P|\right)$.

(6) $$f_1(a)=\sum _{p=1}^{|P|}\sum _{t=1}^{|p|}\sum _{i=1}^{|I|}{X}_{pti}\times S_{pti}$$

$f_2(c)$ denotes the satisfaction metric for the connectivity activity. This metric ranges from $0$ to $1$, achieved by normalizing the value through division by $\left(T_{max}\times S_{max}\times |P|\right)$.

(7) $$f_2(c)=\sum _{p=1}^{|P|}\sum _{t=1}^{|p|}\sum _{i=1}^{|I|}\sum _{j=1}^{|I|}\left(Y_{ptij}\times \sum _{r=1}^{|R|}{C}_{ptijr}\right).$$

The function $f_3(w)$ denotes the level of satisfaction associated with waiting time, which is computed by normalizing the value through division by $\left(T_{max}\times S_{max}\times |P|\right)$.

(8) $$f_3(w)=\sum _{p=1}^{|P|}\sum _{t=1}^{|p|}\left(Z_{pt}\times W_{pt}\right).$$

Constraint functions

The following constraints ensure the feasibility of the solution. Equation (9) imposes a restriction that permits only a single activity at any given moment. Furthermore, Eq. (10) mandates that the journey on each day $p$ commences from $s$, designated as the starting point. Additionally, Eq. (11) guarantees that on each day $p$, the journey concludes at $e$, which represents the terminal point.

(9) $$\sum _{i=1}^{|I|}{X}_{pti}+\left(\sum _{i=1}^{|I|}\sum _{j=1}^{|I|}{Y}_{ptij}\right)+Z_{pt}=1;\mathrm{\forall }t=1,\dots ,|p|;\mathrm{\forall }p=1,\dots ,|P|$$

(10) $$\sum _{j=1}^{|I|}{Y}_{p11j}=1;\mathrm{\forall }p=1,\dots ,|P|$$

(11) $$\sum _{i=1}^{|I|-1}\left(\frac{\sum _{t=1}^{|p|}{Y}_{pti|I|}}{T{T}_{i|I|}}\right)=1;\mathrm{\forall }p=1,\dots ,|P|.$$

Equation (12) serves as a constraint to ensure the connectivity of the tour trip, guaranteeing that the travel time and visiting times correspond accurately to the given data, denoted by $T{T}_{i,j}$ and $S{T}_i$, respectively. Furthermore, Eq. (12) aligns with the corresponding equations in the OP model.

(12) $$\begin{array}{rl}& \frac{{\sum }_{t=n}^{t_1=n+T{T}_{s,r}}{Y}_{p,s,r}^t\times {\sum }_{t=t_1+1}^{t_2=t1+S{T}_r}{X}_{p,r}^t}{T{T}_{s,r}+S{T}_r}=\frac{{\sum }_{t=t_2+1}^{t_3=t_2+T{T}_{r,m}}{Y}_{p,r,m}^t}{T{T}_{r,m}}\le 1\\ & \mathrm{\forall }n\in \{1,\dots ,|p-3|\};\mathrm{\forall }p=1,\dots ,|P|;m\in I;\mathrm{\forall }s,m=1,\dots ,|I|;\mathrm{\forall }r=2,\dots ,|I-1|.\end{array}$$

Algorithm

The proposed HM can be solved using a variety of optimization algorithms, such as genetic algorithms, ant colony optimization, or mixed-integer programming. In this article, an ant colony optimization (ACO) algorithm is proposed to solve the HM.

An ant colony optimization

The ACO algorithm is employed to solve an NP-hard problem. The algorithm iteratively constructs solutions by simulating the behavior of ants searching for optimal paths. At each iteration, ants probabilistically select the next node (POI) based on pheromone levels and heuristic information.

In ACO algorithm, two sequential pheromone update steps are employed to enhance its efficacy. The initial update, termed as the local pheromone update, occurs during the second step (refer to Fig. 2); after an ant is deployed, it evaluates whether it can identify an improved score for the discovered path (refer to Eq. (15)). The subsequent update transpires after all ants have been deployed (refer to Eq. (17)).

Equation (13) computes the connection value (C_ij) relative to distance (TT_ij) and rate of activity value (S_i) relative to distance (TT_ij). The parameter Eta signifies the user’s preference for the POI. Furthermore, Equation 14 delineates the probability computation for transitioning from POI i to j. Equation 15 illustrates the function that determines the maximum total score achieved by Ant_x, while Equation 16 represents the local update (the initial update). Additionally, Equation 17 depicts the global update (the subsequent update).

(13) $${\eta }_{ij}=\frac{S_i}{T{T}_{ij}}+\frac{C_{ij}}{T{T}_{ij}}$$ (14) $$P_{i,j}=\frac{{\left({\tau }_{i,j}\right)}^{\alpha }{\left({\eta }_{ij}\right)}^{\beta }}{\mathrm{\Sigma }\left({\left({\tau }_{i,j}\right)}^{\alpha }{\left({\eta }_{ij}\right)}^{\beta }\right)}$$ (15) $${\delta }_{i,j}=Max({\delta }_{i,j},An{t}_x(i,j))$$ (16) $${\tau }_{i,j}=\left(1-\rho \right)\times {\tau }_{i,j}+{\delta }_{i,j}$$ (17) $${\tau }_{i,j}=\rho \times {\tau }_{i,j}+\left(1-\rho \right)\times {\delta }_{i,j}$$

Overview of HM

A comprehensive overview of the HM is presented in this section by illustrating its design to address certain limitations inherent in existing methodologies. Primarily, in classifying the diverse actions associated with trips (such as activities, connections, and waiting periods), time emerges as a critical component within the HM framework. The HM aims to optimize the aggregate scores accrued from these three trip-related actions. assesses if users are involved in an activity, moving between activities, or waiting. Subsequently, the HM calculates the combined scores based on these different actions.

Figure 3 exemplifies the HM’s management of the distinct actions involved in a trip. In this illustration, POIs #13 and #25 are associated with multi-scores. The chosen route from the start point to #13, from #13 to #25, and from #25 to the end point is also attributed with multiple scores. Waiting time is depicted as a yellow diamond, indicating periods where travelers have additional time for extra activities, even though the recommendation systems propose an itinerary shorter than the maximum available time ( $T_{max}$). Furthermore, the value of each action is scaled by the duration required for its completion (for instance, the transfer from POI#13 to POI#25 spans 19 min, thus calculated as 19 min × $Scor{e}_{13,25}$).

Overview of HM with ICDM

This section elucidates the integration of the ICDM with the HM. In essence, the ICDM is engineered to address multi-item constraints, whereas the HM is tailored to manage multiple values for POIs and connections. Figure 4 provides an overview of the HM and illustrates the collaborative functioning of the HM and ICDM. This figure are segmented into three main components: (1) data, (2) the HM, and (3) the ICDM.

Primarily, the ICDM addresses POIs data, connections data, and user constraints. Essentially, the user constraints are conditions applied to some or all POIs, considering factors like location, entrance fee, or weather conditions. These constraints are presented as a three-dimensional table (labeled as A in Fig. 4). The primary aspects of user constraints are: (1) each constraint assigns a value to an item at a specific moment; (2) at each moment, each constraint assigns a value to some items; and (3) each item is associated with some constraints at every moment. The POIs data contains information about the POIs, including their opening/closing times, locations, and categories, and is displayed in a three-dimensional table (labeled as B in Fig. 4). Moreover, connections data refers to travelers’ movements from one POI to another (labeled as C in Fig. 4). The ICDM takes into account congestion levels, which are represented as layers of $p$ tables, where each table indicates the time consumed in traveling from one POI to another at time $T_p$.

Secondly, the core of the ICDM lies in its constraints, categorized into hard constraints (HC) and soft constraints (SC): (1) HC (denoted as D in Fig. 4) and (2) SC (denoted as E in Fig. 4). Equation (4) (denoted as G in Fig. 4) aggregates all constraints values into a single value ( $S_{pti}$). The primary output of the model is a matrix that narrows down the search space (denoted as H in Fig. 4).

Thirdly, the HM is designed to address user constraints utilizing the ICDM while taking into account various connection values (represented as F in Fig. 4). The subsequent graph demonstrates the intricate nature of connection data when multiple values are included. Fig. 5 displays |R| tables based on the quantity of multi-values in the connections at a specific moment, such as $t_1$. It requires a set of aggregated tables, denoted as $p$, to comprehensively address the entire multi-value issue. Finally, an algorithm, denoted as I in Fig. 4, is devised to solve the HM problem.

Background of the experiment

The experiments were designed to evaluate the effectiveness of the proposed HM in generating personalized tour recommendations. The primary goal was to demonstrate how the HM optimizes traveler satisfaction by considering activities, connections, and waiting times, addressing the limitations of existing models. The experiments were conducted using publicly available datasets, including the OPTW and TOPTW datasets, which provide features such as time windows, visiting times, and POI attributes.

Method of the experiment

The experiments were conducted in two phases:

• Dataset preparation: The OPTW and TOPTW datasets were preprocessed to align with the HM’s requirements. This included extracting POI attributes, travel times, and user constraints.

• Model evaluation: The HM was implemented using the ACO algorithm to solve the optimization problem. The performance of the HM was evaluated based on satisfaction scores, waiting times, and the number of recommended POIs.

The eight experiments E1, E2,…, E8

To comprehensively evaluate the HM, eight experiments (E1 to E8) were conducted, each with different configurations of connection and waiting time preferences. These experiments were designed to test the HM’s ability to adapt to varying user preferences and constraints. The details of each experiment are as follows:

• E1: Connection score = 1, Waiting time score = 0.

• E2: Connection score = 1, Waiting time score = 0.5.

• E3: Connection score = Random, Waiting time score = 0.

• E4: Connection score = Random/2, Waiting time score = 0.

• E5: Connection score = 1, Waiting time score = 0 (applied to Dataset 2).

• E6: Connection score = 1, Waiting time score = 0.5 (applied to Dataset 2).

• E7: Connection score = Random, Waiting time score = 0 (applied to Dataset 2).

• E8: Connection score = Random/2, Waiting time score = 0 (applied to Dataset 2).

These experiments allowed us to analyze how different configurations of connection and waiting time preferences impact the HM’s performance.

Features of the original dataset

The experiments were conducted using two datasets:

• Dataset 1: Derived from the OPTW dataset, this dataset includes 48 to 288 POIs across 10 scenarios. Each POI has attributes such as visiting time, time windows, and satisfaction scores.

• Dataset 2: Derived from the TOPTW dataset, this dataset also includes 48 to 288 POIs across 10 scenarios, with additional features such as travel times between POIs and user constraints.

In our investigation, multiple experiments are conducted to evaluate the capabilities of the HM model. At the outset, the HM model is applied to various pre-existing datasets (refer to Table 2) to assess its effectiveness in constructing tour itineraries. Additionally, an ACO algorithm is devised to generate results that are comparable to those produced by existing models.

The datasets were selected based on the availability of public data, with a specific emphasis on the OPTW and TOPTW datasets (KU Leuven, 2024). These datasets were chosen for the HM experiment due to their provision of several pertinent features, such as time windows and visiting times.

Multiple experiments are carried out to find the optimal ACO parameters. The initial parameters for ACO are detailed in Table 3, and the variations in values based on different parameter settings are illustrated in Figs. 6 and 7.

A series of experiments are conducted to determine the best iteration number for the algorithm. It is critical to recognize that the running time is a pivotal factor, particularly when dealing with NP-hard problems. Figure 8 illustrates the average running time of the ACO algorithm for different numbers of iterations. The results demonstrate that the running time increases linearly with the number of iterations, ranging from 2.9 s for 10 iterations to 26.7 s for 100 iterations. This linear relationship highlights the scalability of the ACO algorithm, making it suitable for solving the Happiness Model’s optimization problem efficiently. For experimentation, ten different values are selected for the iteration parameter.

Alpha and Beta denote the significance of the score and the rate of score relative to the distance (refer to Equation (14)). Selecting the best values for such parameters is crucial as the performance of the algorithm hinges on these parameters. Thus, a tuning method is employed that iteratively adjusts these parameters from zero to the point of maximum gain. Multiple experiments were conducted (each scenario within each dataset was executed over 200 times for different values of the parameters) to identify the optimal performance of the algorithm across all datasets. Figures 6 and 7 illustrate the normalized total scores (where 1 represents the highest total scores across all datasets) for various Alpha and Beta values in all scenarios.

As depicted in Figs. 6 and 7, only a subset of the results attained top scores, while the others varied; no single pair of Alpha and Beta values consistently yielded uniform algorithm performance (each distinct value for Alpha and Beta produced variant outcomes). The best values for these parameters are found to be Alpha = 1 and Beta = 13, Alpha = 15 and Beta = 8, and others, that consistently delivered excellent performance across all datasets. You can see these values highlighted in dark red in Figs. 6 and 7 which achieved the best results. Essentially, any values in dark red will consistently produce good results across all datasets.

The HM benchmark instances

The outcomes of the proposed HM with those derived from the TOPTW on Dataset 1 and Dataset 2 are presented in this section (additional details are provided in Table 2). Broadly, the findings elucidate the influence of the HM in structuring a tour trip by tailoring the itinerary according to user preferences. Specifically, the HM results indicate that a higher degree of personalization in the trips is attainable, as the model integrates and optimizes additional elements of trip itineraries like idle time and connectivity. Furthermore, the metrics for activities score, waiting times and connections have been standardized to a scale ranging from zero to one, with one denoting the maximal value.

Table 4 enumerates the 8 distinct experiments carried on the model. Initially, the values for activities were based on the public dataset, following which various values for connections and waiting times were generated in these experiments. Such experiments encompass diverse scenarios to underscore the advantages conferred by the model.

Experiments $E_1$ to $E_4$ were conducted on Dataset 1, and the outcomes of these experiments are detailed in Tables 5–8. Each experiment provides the code for the scenario along with the number of POIs included in the recommended trip. Additionally, the primary three activities of the trip are identified, with the corresponding durations for each activity and the total scores assigned to each specific activity presented.

Table 5 presents the outcomes of $E_1$, as specified by the parameters outlined in Table 4. Each entry in the table corresponds to a distinct scenario in which the cumulative scores for each action vary across scenarios, with the exception of the total waiting-time scores, which are consistently zero (refer to Table 4). Furthermore, all action scores are normalized to a range between 0 and 1, ensuring that the total score represents the sum of individual moments, and the total score for any action is never greater than the total number of moments in the activity.

The results of this table demonstrate the HM’s ability to generate itineraries with high activity scores and efficient connections. For example, in scenario Pr02, the HM recommends 19 POIs with a total activity score of 125 and a connection score of 384. The absence of waiting time scores indicates that the HM prioritizes minimizing idle time, aligning with the goal of maximizing traveler satisfaction.

Table 6 shows the outcomes of Experiment 2 ( $E_2$), where the connection score remains 1, but the waiting time score is set to 0.5. The results are similar to E1, with the addition of waiting time scores. For instance, in scenario Pr02, the waiting time score is 194, indicating that the HM can incorporate waiting times when necessary. This flexibility allows the HM to adapt to varying user preferences, addressing the limitations of traditional models that treat waiting times as fixed costs.

Table 7 presents the outcomes of Experiment 3 ( $E_3$), where the connection score is randomly assigned, and the waiting time score is set to 0. The results highlight the HM’s ability to handle varying connection preferences. For example, in scenario Pr02, the connection score drops to 214, but the HM still recommends 19 POIs, demonstrating its robustness in optimizing itineraries under different conditions.

Table 8 shows the outcomes of Experiment 4 ( $E_4$), where the connection score is halved, and the waiting time score is set to 0. The results indicate that the HM can generate efficient itineraries even with reduced connection scores. For instance, in scenario Pr02, the connection score is 110, but the HM still recommends 21 POIs, showcasing its ability to balance multiple factors effectively.

Table 9 presents the outcomes of Experiment 5 ( $E_5$), applied to Dataset 2. The results demonstrate the HM’s scalability and effectiveness across different datasets. For example, in scenario Pr11, the HM recommends 19 POIs with a total activity score of 87 and a connection score of 394, highlighting its ability to handle larger and more complex datasets.

Table 10 shows the outcomes of Experiment 6 ( $E_6$), applied to Dataset 2. The results are similar to E5, with the addition of waiting time scores. For instance, in scenario Pr11, the waiting time score is 200, indicating that the HM can incorporate waiting times even in larger datasets.

Table 11 presents the outcomes of Experiment 7 ( $E_7$), applied to Dataset 2. The results highlight the HM’s ability to adapt to random connection scores. For example, in scenario Pr12, the HM recommends 5 POIs with a total activity score of 26 and a connection score of 169, demonstrating its flexibility in handling diverse user preferences.

Table 12 shows the outcomes of Experiment 8 ( $E_8$), applied to Dataset 2. The results indicate that the HM can generate efficient itineraries even with reduced connection scores. For instance, in scenario Pr12, the connection score is 70, but the HM still recommends 5 POIs, showcasing its ability to balance multiple factors effectively.

In this study, several simulated user scenarios have been conducted with diverse travel preferences and experiences. The personalized itineraries generated by the HM for these scenarios are checked based on the following aspects: How well did the itinerary align with the provided preferences and interests? How well did the itinerary optimize the time and resources and satisfy the overall travel experience? In fact, the obtained results were overwhelmingly positive. The proposed HM generated highly relevant and personalized itineraries that met the expectations. In addition, the proposed model has the ability to optimize the time and resources, leading to a more efficient and enjoyable travel experience. While the simulated user feedback provides valuable insights, it is important to note that it does not replace real-world user studies. Further research is needed to gather feedback from a larger and more diverse group of users to fully validate the HM’s effectiveness in enhancing user satisfaction.

Summary of key findings

The results of experiments, presented in Tables 5–12, demonstrate that the proposed Happiness Model effectively addresses the limitations of existing travel recommendation systems by:

• Maximizing traveler satisfaction: The HM generates itineraries with high activity and connection scores, ensuring a satisfying travel experience.

• Minimizing waiting times: The HM incorporates waiting times as a key factor, reducing idle time and improving efficiency.

• Adapting to user preferences: The HM can handle varying connection and waiting time preferences, showcasing its flexibility and robustness.

• Scaling to larger datasets: The HM performs well on both Dataset 1 and Dataset 2, demonstrating its scalability and applicability to real-world scenarios.

While many existing models, such as MOOP and MCTOPMTW, focus primarily on optimizing the selection of POIs based on specific dimensions (e.g., total scores, distance), the proposed model takes a broader approach. The proposed HM considers a wider range of factors—such as multi-value (MV) connections, waiting times, and personalized travel constraints—that are often overlooked in existing techniques. Thus, comparing these models directly might be misleading as they address different aspects of travel planning.

Despite the differences in factors studied, the proposed HM model offers several distinct advantages over existing approaches:

• Multi-value (MV) consideration for nodes and connections: Unlike models like MOOP, which evaluate POIs based solely on scores or distances, HM incorporates multiple attributes for each POI and the transitions between them (e.g., time, cost, journey length). This multi-dimensional evaluation provides a more comprehensive understanding of traveler satisfaction.

• Aggregation for traveler satisfaction: While MOOP focuses on maximizing benefits within POI categories, HM aggregates multiple values into a single metric representing the traveler’s overall satisfaction, factoring in elements such as time spent at POIs, journey length, and costs.

• Personalization and waiting time consideration: One key limitation of models like MOOP is the lack of support for personalization, such as waiting time, which is crucial for travelers with reservations (e.g., flights, hotels). HM addresses this by including waiting time as an essential factor, enhancing its suitability for real-world travel scenarios.

• Handling multiple decision-making parameters: Unlike the more limited scope of MOOP and MCTOPMTW, HM covers a comprehensive range of tourist decision-making parameters by categorizing them into: Activities, Connections, and Waiting Time.

This broader set of factors makes the proposed HM uniquely equipped to handle the complexities of modern travel planning, unlike MOOP, which considers only multi-value POIs without addressing connections or waiting time.

It is worth mentioning that the proposed HM differs from the existing models not only in its handling of multiple values for POIs but also in its inclusion of transitions between POIs and waiting time considerations. In contrast:

• HM provides a comprehensive approach by integrating multi-value POIs, multi-value connections, and waiting time, offering a more comprehensive solution for travel planning.

• MOOP lacks personalization and does not consider waiting time or multi-value transitions, focusing only on maximizing benefits within POI categories.

• MCTOPMTW supports multiple constraints but lacks an effective aggregation mechanism like HM’s traveler satisfaction metric, making it more complex and less intuitive.

Although existing models such as MOOP and MCTOPMTW have certain strengths, they are limited in scope. The proposed model provides a more comprehensive and personalized approach by incorporating multi-value POIs, connections, and waiting time, making it better suited to meet the needs of travelers in practical, real-world scenarios.