A novel group tour trip recommender model for personalized travel systems

Recommendation aggregation

Aggregation of individual recommendations involves combining personalized recommendation lists into group recommendations using various approaches. Christensen & Schiaffino (2011) employed six distinct aggregation strategies for GRSs (Baltrunas, Makcinskas & Ricci, 2010). One such technique merges individual recommendations (Halder et al., 2024; Christensen & Schiaffino, 2011). This approach is based on generating recommendations for individuals and is straightforward to implement as it extends existing recommender systems. Additionally, Baltrunas, Makcinskas & Ricci (2010) describe four distinct rank aggregation approaches: (i) Spearman footrule, which minimizes the average distance among individual items, (ii) Least misery, (iii) Average, and (iv) Borda count. Regarding the most effective technique, Masthoff (2011) conducted experiments to identify the optimal strategy. The research revealed that users prioritized increasing fairness and reducing misery. However, Masthoff noted that the multiplicative strategy yielded the highest levels of user satisfaction.

Preference aggregation

In Sarkar et al. (2023), Garcia, Linaza & Arbelaitz (2012), Baskin & Krishnamurthi (2009), Garcia, Sebastia & Onaindia (2011), Garcia et al. (2009), Christensen & Schiaffino (2011), Ding et al. (2024), Yu et al. (2006), Salamó, McCarthy & Smyth (2012), Kim et al. (2010), McCarthy & Anagnost (1998), Boratto & Carta (2015), Shang et al. (2014), aggregation strategies are employed to construct a common profile by consolidating individual user preferences. Specifically, each user has particular preferences, such as parks, museums, or Indian cuisine. This methodology aggregates these individual preferences to formulate a unified preference for each group. Travelers may select more than one preference, and some preferences may overlap among users. Then, the aggregation function synthesizes the preference for the particular group.

Yu et al. (2006) propose a method for generating preferences for a particular group by evaluating users’ references for TV viewing. This method minimizes total distance to compute the dissimilarity among users’ preferences. Each preference a user likes is assigned a value of 1, dislikes are assigned −1, and unknown preferences are assigned 0. Kim et al. (2010) propose a GRS that improves group recommendation effectiveness and member satisfaction. Their system uses a collaborative filtering (CF) model to aggregate group member preferences, creating a candidate recommendation set. If a group member has interacted with an item, like reading a book, it is assigned a value of 1. The group rating for each item is then calculated, and the nearest-neighbor algorithm determines the similarity between group profiles.

Rating aggregation

In Christensen & Schiaffino (2011), Popescu (2013), Amer-Yahia et al. (2009), Berkovsky & Freyne (2010), Naamani-Dery et al. (2010), O’Hara et al. (2004), Sprague, Wu & Tory, 2008, Kim & Saddik (2015), Gartrell et al. (2010), the average and least misery are identified as the predominant aggregation functions proposed for recommendations or rating aggregations (Amer-Yahia et al., 2009). Nonetheless, Amer-Yahia et al. (2009) introduces a consensus function, composed of relevance and disagreement functions. The relevance function consolidates the ratings of all group travelers using both the average and least misery strategies, while the disagreement function assesses the extent to which the group members have collectively liked or disliked an item. Essentially, the consensus function evaluates the suitability of an item for group recommendation by determining its relevance and the level of disagreement among group members. Berkovsky & Freyne (2010) suggest a recommender model for food that seeks to identify the most appropriate data aggregation strategy for a family group. They apply four strategies: two static and two interaction-based. The first is a uniform model assigning equal weight to each user. The second is a heuristic model based on role, with weights assigned as follows: applicant = 0.5, partner = 0.3, and child = 0.1. The third strategy is a role-based model which identified a particular weight for each user based on their activity, represented by the number of observed ratings from that user. In Gartrell et al. (2010) propose a GRS model that analyzes various group characteristics. Such a model developed to anticipate group preferences through the implementation of a group-consensus function, utilizing association rules to uncover significant patterns among users within the dataset.

Optimization of GRSs: a comparative analysis to existing studies

In recent years, the landscape of group travel recommender systems has seen a variety of approaches aimed at enhancing the experience of travelers. However, existing models, including the Multi-Constraint Multiple Team Orienteering Problem with Time Windows (MCMTOPTW), have predominantly centered around static itineraries, failing to account for the fluid dynamics of user preferences that often evolve during a trip.

To the best of the author’s knowledge and believe, only a limited number of studies (Renjith, Sreekumar & Jathavedan, 2020; Anagnostopoulos et al., 2017; Sylejmani, Dorn & Musliu, 2017) have addressed GRSs using optimization approaches. These studies have predominantly developed their models based on the orienteering problem (OP). Given that the challenges associated with individual tourist recommendations remain partially unresolved, some researchers have extended their models to accommodate groups of travelers.

Addressing GRSs as an optimization problem proves to be an effective method due to two primary reasons: (1) the GRSs for travelers encompass the challenges of TRSs, which are fundamentally data-driven issues, and (2) personalization is essential to cater to the diverse preferences of users. The OP is the most analogous model for solving the time-dependent traveling salesman problem (TTDP), as it represents a specific case of TTDP predicated on fundamental constraints.

While previous studies (Renjith, Sreekumar & Jathavedan, 2020; Anagnostopoulos et al., 2017; Sylejmani, Dorn & Musliu, 2017) have primarily focused on optimization approaches based on the OP, they fall short in addressing the complexities and variabilities inherent in group travel scenarios. Specifically, these models often overlook critical factors such as individual user constraints, multi-values for POIs, connection values, waiting times, and the aggregation of preferences. The proposed GTTRM is meticulously designed to remedy these shortcomings, providing a framework that adapts to diverse user needs and incorporates multiple relevant factors in group travel optimization.

Unlike existing models such as the MCMTOPTW and others that primarily optimize static group itineraries, the proposed GTTRM introduces a novel approach by allowing for dynamic subgroup formation. This means that during the trip, subgroups can form and dissolve based on evolving user preferences, which is not addressed in current models. The employment of the GACO algorithm within the framework of GTTRM facilitates real-time adaptations, greatly enhancing overall group satisfaction. No existing models in the current literature, to the best of our knowledge, provide such dynamic subgroup flexibility combined with GACO-based optimization.

Constraints data model

Building upon the ICDM developed in our previous work (Alatiyyah, 2024) to handle various constraints proposed by individual users, a constraints data model (CDM) is consequently developed in this article to handle the preferences and connection constraints from a particular group of travelers. The implemented constraints model contains two primary components:

• Activity constraints data model (ACDM): The ACDM focuses on aligning activity data with user constraints. It is essentially an extension of the ICDM to accommodate the needs of a group of users.

• Connection constraints data model (CCDM): The CCDM is responsible for validating connection data against user constraints. It ensures that the connections between activities or POIs adhere to the specified constraints and preferences of group members.

The key differences between the CCDM and ACDM lie in the specific data and connection constraints they handle. The ACDM primarily focuses on aligning activity data with user constraints, while the CCDM validates connection data against user constraints. This distinction is crucial for effectively managing both individual and group-level constraints within the context of group travel.

The CDM is defined as follows: $u_z\in G$ denotes a traveler within the group G where $z=1,2,\dots ,|G|$, and each traveler $u_z$ may have $n$ constraints (soft constraint (SC), hard constraint (HC)). $ActH{C}_{u_z}$ and $ConH{C}_{u_z}$ denote sets of HCs for activity and connection from user $u_z$, respectively, where $hc(Act{)}_{ptim}^{u_z}\in ActH{C}_{u_z}$ and $hc(Con{)}_{ptim}^{u_z}\in ConH{C}_{u_z};\mathrm{\forall }{u}_z\in U;\mathrm{\forall }p\in P;\mathrm{\forall }t\in p;\mathrm{\forall }i\in I$, with $m=1,2,\dots ,(|ActH{C}_{u_z}|$ or $|ConH{C}_{u_z}|)$. Similarly, $ActS{C}_{u_z}$ and $ConS{C}_{u_z}$ are sets of SCs for Activity and Connection from user $u_z$, respectively, where $sc(Act{)}_{ptim}^{u_z}\in ActS{C}_{u_z}$ and $sc(Con{)}_{ptim}^{u_z}\in ConS{C}_{u_z}$, with $v=1,2,\dots ,(|ActS{C}_{u_z}|\mathrm{a}\mathrm{n}\mathrm{d}|ConS{C}_{u_z}|)$.

(1) $$ActH{C}_{pti}^{u_z}=\prod _{m=1}^{|ActH{C}_{u_z}|}hc(Act{)}_{ptim}^{u_z}$$

(2) $$ActH{C}_{pti}^G=\prod _{z=1}^{|G|}ActH{C}_{pti}^{u_z}.$$

Equation (1) consolidates all the HCs for the individual user $u_z$, while Eq. (2) aggregates all the HCs for the entire user group. Specifically, Eq. (2) denotes the process of group aggregation (GA).

(3) $$ConH{C}_{ptij}^{u_z}=\prod _{m=1}^{|ConH{C}_{u_z}|}hc(Con{)}_{ptijm}^{u_z}$$

(4) $$ConH{C}_{ptij}^G=\prod _{z=1}^{|G|}ConH{C}_{ptij}^{u_z}.$$

Equations (3) and (4) are utilized to compute the HC for both individual users and groups.

(5) $$ActS{C}_{pti}^{u_z}\mathrm{a}\mathrm{n}\mathrm{d}{\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{S}\mathrm{C}}_{\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{j}}^{{\mathrm{u}}_{\mathrm{z}}}=\mathrm{A}\mathrm{g}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{g}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{d}\mathrm{s}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{u}\mathrm{s}\mathrm{e}\mathrm{r}(u_z)$$

(6) $$ActS{C}_{pti}^G\mathrm{a}\mathrm{n}\mathrm{d}{\mathrm{C}\mathrm{o}\mathrm{n}\mathrm{S}\mathrm{C}}_{\mathrm{p}\mathrm{t}\mathrm{i}\mathrm{j}}^{\mathrm{G}}=\mathrm{A}\mathrm{g}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{g}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{d}\mathrm{s}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{p}(G).$$

Equations (5) and (6) denote the aggregations of all soft constraints for group G and traveler $u_z$.

(7) $$\sum _{v=1}^{|ActS{C}_{u_z}|}{W}_v=1\mathrm{a}\mathrm{n}\mathrm{d}\sum _{v=1}^{|ConS{C}_{u_z}|}{W}_v=1$$

(8) $$\sum _{u_z=1}^{|G|}{W}_{u_z}^G=1\mathrm{a}\mathrm{n}\mathrm{d}\sum _{{\mathrm{u}}_{\mathrm{z}}=1}^{|\mathrm{G}|}{\mathrm{W}}_{{\mathrm{u}}_{\mathrm{z}}}^{\mathrm{G}}=1.$$

Equation (7) illustrates that each SC may possess a distinct weight, signifying the relative importance of one SC in comparison to another. Equation (8) demonstrates the capacity to adjust for the varying expertise levels among group travelers, whereby a traveler with a higher expertise is accorded a greater weight.

(9) $$A_{pti}^{u_z}=ActH{C}_{pti}^{u_z}\times ActS{C}_{pti}^{u_z}$$

(10) $$A_{pti}=ActS{C}_{pti}^G\times ActS{C}_{pti}^G$$

(11) $$C_{ptij}^{u_z}=ConH{C}_{ptij}^{u_z}\times ConS{C}_{ptij}^{u_z}$$

(12) $$C_{ptij}=ConH{C}_{ptij}^G\times ConS{C}_{ptij}^G.$$

Equation (9) highlights the aggregation among Eqs. (1) and (5) to determine the weight that implies the satisfaction level for traveler $u_z$ in each item $i$ on day $p$ at time $t$ based on the traveler’s constraints. Equation (10) collects the soft and hard constraints of the group.

Equation (9) aggregates Eqs. (1) and (5) to determine the weight representing the satisfaction level for traveler $u_z$ in each item $i$ on day $p$ at time $t$. This weight is determined based on the user’s individual HCs and SCs. Equation (10) subsequently combines the SCs and HCs of all group members to calculate the overall group weight for each item. This group weight reflects the collective satisfaction level of the group members regarding the item.

(13) $$ActH{C}_{pti}^{u_z},ActH{C}_{pti}^G,ConH{C}_{pti}^G,ConH{C}_{pti}^{u_z}\in \{0,1\}$$

(14) $$ActS{C}_{pti}^{u_z},ActS{C}_{pti}^G,ConS{C}_{pti}^G,ConS{C}_{pti}^{u_z}\in \mathbb{Q};$$

$$\mathrm{W}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{i}\mathrm{s}0\le {ActSC}_{pti}^{u_z},{ActSC}_{pti}^G\le 1;$$

$$\mathrm{W}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}\mathrm{i}\mathrm{s}0\le {ConSC}_{pti}^G,{ConSC}_{pti}^{u_z}\le 1.$$

The principal functionality of partitioning the group into subgroups is facilitated by our proposed algorithm. The details of the algorithm are delineated in “The Proposed Algorithm” (Tables 3 and 4).

Mathematical model

The proposed model can be formally identified as follows. Let $G=(I,TT)$ represent a directed weighted graph, where $i\in I$ and $i=1,\dots ,|I|$ denote the nodes corresponding to POIs within a particular city. The travel time among two nodes $i$ and $j$ is represented by $T{T}_{ij}$, while $S{T}_i$ indicates the time allocated at node $i$. Given an initial node $s$ and an ending node $t$, we define $s=1$ and $t=|I|$. The duration of the tour may span one or more days, hence let $p\in P$; $p=\{1,\dots ,|P|\}$ denote the set of tour days. Additionally, each tour day includes a set of time instances $t\in p$; $t=1,\dots ,|p|$, representing specific moments within day $p$. The daily time constraint for the trip is denoted by $T_{max}$.

The subsequent equations delineate the GTTRM along with its constraints. Equation (15) specifies the objective function, which aims to maximize the overall score derived from three distinct actions: (i) Activity, (ii) Connection, and (iii) Waiting. This equation encompasses three principal functions: $f_1(a)$, $f_2(c)$, and $f_3(w)$, each one is corresponded to the aforementioned actions, respectively.

(15) $$Max\left(f_1(a)+f_2(c)+f_3(w)\right).$$

The three functions $f_1(a)$, $f_2(c)$, and $f_3(w)$ are shown in Eqs. (16), (18), and (20).

(16) $$f_1(a)=\sum _{p=1}^{|P|}\sum _{t=1}^{|p|}\sum _{i=1}^{|I|}\sum _{z=1}^{|G|}{X}_{pti}^{u_z}\times A_{pti}^{u_z}+\sum _{o=1}^{|G|}Act{G}_{pti}^{u_z{u}_o}\times V_{u_o}^{u_z}.$$

Equation (16) denotes the satisfaction of a particular group G by traveling to some POIs. Additionally, if $u_z$ travels to POIs with a particular froup member, the level of their satisfaction levels may enhance.

(17) $$Act{G}_{pti}^{u_z{u}_o}=X_{pti}^{u_z}=X_{pti}^{u_o}$$

$$\mathrm{\forall }t=1,\dots ,|p|;\mathrm{\forall }p=1,\dots ,|P|;\mathrm{\forall }z=1,\dots ,|G|;\mathrm{\forall }o=1,\dots ,|G|;\mathrm{\forall }i=1,\dots ,|I|.$$

Equation (17) guarantees that if traveler $u_z$ visits a particular POI at least one member of the group would also visit the same POI.

(18) $$f_2(c)=\sum _{p=1}^{|P|}\sum _{t=1}^{|p|}\sum _{i=1}^{|I|}\sum _{j=1}^{|I|}\sum _{z=1}^{|G|}{Y}_{ptij}^{u_z}\times C_{ptijr}^{u_z}+\sum _{o=1}^{|G|}Con{G}_{ptij}^{u_z{u}_o}\times T_{u_o}^{u_z}.$$

Equation (18) calculates the overall group satisfaction level by considering the most preferred connections among POIs $i$ and $j$. This equation considers the individual satisfaction levels of group members for traveling together and the overall preference for specific connections. Additionally, if traveler $u_z$ moves from one POI to another with a group member, their satisfaction may also enhance.

(19) $$Con{G}_{ptij}^{u_z{u}_o}=Y_{ptij}^{u_z}=Y_{ptij}^{u_o}$$

$$\mathrm{\forall }t=1,\dots ,|p|;\mathrm{\forall }p=1,\dots ,|P|;\mathrm{\forall }z=1,\dots ,|G|;$$

$$\mathrm{\forall }o=1,\dots ,|G|;\mathrm{\forall }i=1,\dots ,|I|;\mathrm{\forall }j=1,\dots ,|I|.$$

Equation (19) guarantees that if traveler $u_z$ visits a POI, at least one member of the group would also visit this particular POI.

(20) $$f_3(w)=\sum _{p=1}^{|P|}\sum _{t=1}^{|p|}\sum _{z=1}^{|G|}{Z}_{pt}^{u_z}\times W_{pt}^{u_z}.$$

Equation (20) find the overall waiting time for all members in the group to identify the overall satisfaction of the group members.

(21) $$\sum _{i=1}^{|I|}{X}_{pti}^{u_z}+\left(\sum _{i=1}^{|I|}\sum _{j=1}^{|I|}{Y}_{ptij}^{u_z}\right)+Z_{pt}^{u_z}=1$$

$$\mathrm{\forall }t=1,\dots ,|p|;\mathrm{\forall }p=1,\dots ,|P|;\mathrm{\forall }z=1,\dots ,|G|$$

(22) $$\sum _{j=1}^{|I|}{Y}_{p11j}^{u_z}=1$$

$$\mathrm{\forall }p=1,\dots ,|P|;\mathrm{\forall }z=1,\dots ,|G|$$

(23) $$\sum _{i=1}^{|I|-1}\left(\frac{\sum _{t=1}^{|p|}{Y}_{pti|I|}^{u_z}}{T{T}_{i|I|}}\right)=1$$

$$\mathrm{\forall }p=1,\dots ,|P|;\mathrm{\forall }z=1,\dots ,|G|.$$

Equation (21) is a crucial constraint that ensures that each user can only perform one activity at a time. This constraint prevents conflicts and ensures efficient itinerary planning. Furthermore, Eqs. (22) and (23) enforce the starting and ending points of the trip for each day $p$. Equation (22) guarantees that the trip begins at the designated starting point $s$, while Eq. (23) ensures that the trip concludes at the designated end point $e$. These constraints are essential for maintaining the overall structure and feasibility of the itinerary.

(24) $$\frac{\sum _{t=n}^{t_1=n+T{T}_{sr}}{Y}_{ptsr}^{u_z}+\sum _{t=t_1+1}^{t_2=t1+S{T}_r}{X}_{ptr}^{u_z}}{T{T}_{sr}+S{T}_r}=\frac{\sum _{t=t_2+1}^{t_3=t_2+T{T}_{rm}}{Y}_{ptrm}^{u_z}}{T{T}_{rm}}\le 1$$

$$\mathrm{\forall }n\in \{1,\dots ,|p-3|\};\mathrm{\forall }p=1,\dots ,|P|;\mathrm{\forall }s,m=1,\dots ,|I|;\mathrm{\forall }r=2,\dots ,|I-1|;$$

$$\mathrm{\forall }z=1,\dots ,|G|.$$

Equation (24) is a constraint that guarantees the tour is connected, and guarantees the connection and visiting times are equivalent to $T{T}_{i,j}$ and $S{T}_i$, respectively.

The proposed algorithm

Based on the individual traveler preferences and associated constraints, the proposed GTTR model is capable of strategically dividing the group into subgroups. The proposed algorithm employs ant colony optimization (ACO) to facilitate this subgrouping process for travelers with potentially conflicting preferences and constraints. This algorithm effectively addresses intra-group conflicts by generating tailored sub-routes for specific group members, ultimately enhancing the satisfaction level of each individual.

Comparison with existing models

While many existing models, such as multiobjective optimization problem (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 GTTRM 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. Existing models are often limited by their ability to effectively handle the diverse constraints of group members. However, the proposed GTTRM addresses these limitations by incorporating a comprehensive set of features. Thus, comparing these models directly might be misleading as they address different aspects of travel planning.

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

• Dynamic subgroups formation: Unlike existing models such as MCMTOPTW and others that primarily optimize static group itineraries, the proposed GTTRM introduces a novel approach by allowing for dynamic subgroup formation. This means that during the trip, subgroups can form and dissolve based on evolving user preferences, which is not addressed in current models.

• Multi-value (MV) consideration for nodes and connections: Unlike models like MOOP, which evaluate POIs based solely on scores or distances, GTTRM 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, GTTRM 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). GTTRM 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, GTTRM 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 GTTRM uniquely equipped to handle the complexities of modern travel planning, unlike MOOP, which considers only multi-value POIs without addressing connections or waiting time.

The comparison between the proposed GTTRM model and previous works is summarized in Table 7. It can be observed that the proposed model 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:

• GTTRM 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 GTTRM’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. Our 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.

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 7 demonstrates the superiority of the GTTRM 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.

Complexity analysis

The time complexity of the proposed GTTRM is derived from the complexity of the ACO algorithm. Given that the ACO iteratively optimizes the path selection based on pheromone updates, the time complexity of ACO is $O(n\log n)$, where $n$ is the number of POIs to be visited. This makes the proposed GTTRM more efficient than traditional models, such as the MCMTOPTW, which has a time complexity of $O(n^3)$ due to its reliance on exhaustive search algorithms. To further clarify the computational efficiency of GTTRM, we compared the complexity of our model with other relevant schemes. As shown in Table 8, GTTRM achieves a balance between computational efficiency and flexibility, making it a more practical solution for large-scale group travel recommendations.

Benchmark instances

Due to the absence of an existing dataset for GRSs in travel domains, a real-world dataset is compiled. Such dataset, designated as Durham, UK, indicates the geographical location of data collection.

Table 9 provides a detailed overview of the different group scenarios and sizes used in the experiments. Additionally, Tables 10–14 present the social relationship values among group members, which were randomly assigned within a range of $1$ to $2$. A value of $1$ indicates the weakest relationship, while a value of two signifies the strongest relationship.

To ensure the robustness of our findings, we have tested the model extensively across a range of initial values and parameter settings. The GTTRM model was evaluated over multiple scenarios with varying relationship values, preferences, and subgroup configurations. Each test scenario consistently produced satisfactory results, indicating that the GTTRM is stable and effective under different initial conditions. Moreover, the ACO algorithm used in GTTRM inherently contributes to the model’s robustness. ACO’s iterative optimization process, which includes pheromone updating and path selection based on cumulative runs, ensures convergence to an optimal solution regardless of initial conditions. This multi-scenario approach has confirmed that the results are reliable, and no significant variations were observed across different runs, underscoring the stability and reliability of GTTRM’s performance in real-world applications.

Comparative analysis

This section provides a comparative analysis of two aggregation methods, revealing that the GACO algorithm surpasses other methods in terms of maximizing the satisfaction levels of group members.

Group aggregation

The outcomes of the experiments on group aggregation is presented in this section, wherein group travelers are consolidated into a single profile. The satisfaction level for each traveler within the groups has been illustrated. Figures 3–7 depict the satisfaction levels for each traveler from the commencement to the conclusion of the tour, demonstrating the variability in satisfaction among group members.

Figure 3 visually represents the changes in satisfaction levels for all members of the first group over time. Each line corresponds to an individual user’s satisfaction level, normalized to a maximum of 1. The varying satisfaction levels among users highlight the diverse preferences and constraints within the group, demonstrating the challenges of achieving optimal satisfaction for all members.

Figure 4 visually represents the overall satisfaction levels for all members of the second group. The y-axis represents the satisfaction level, while the x-axis indicates the group members. The data points and error bars illustrate the distribution of satisfaction levels within the group. The figure suggests that the majority of travelers do not achieve the highest satisfaction level under the group aggregation approach, as this approach consolidates all users’ values into a single value, potentially leading to dissatisfaction for some members.

Figure 5 visually illustrates the satisfaction levels of traveler 1 and traveler 2 within the third group. The variation in satisfaction among the travelers is depicted from the commencement of the tour up to 150 min (with the tour duration segmented into minutes). It is evident that the satisfaction levels for both users in the final two-thirds of the trip duration are significantly higher compared to the initial third.

Figure 6 illustrates the diverse preferences of travelers within group 4, highlighting a scenario in which the group aggregation approach yields a trip which does not meet the satisfaction of all members.

Figure 7 illustrates the significant disparity in users’ preferences due to the necessity of remaining together throughout the trip, as their distinct preferences are not taken into account.

User aggregation

The outcomes of implementing the proposed GACO optimization algorithm within the proposed GTTRM are presented in this section.

First group: A comprehensive evaluation and comparison of satisfaction levels for each user is conducted under both user aggregation and group aggregation. The results consistently demonstrate that user aggregation, as determined by the GACO algorithm, generally outperforms group aggregation in terms of maximizing overall satisfaction. Figures 8–12 provide a detailed visualization of the satisfaction levels for members of the first group.

Figure 8 illustrates the satisfaction level of traveler 1 within the first group across different methodologies. It is evident that the user aggregation approach yields a higher level of satisfaction in comparison to the group aggregation method. Furthermore, the figure indicates the differential performance of these models; the group aggregation method bases its decisions on the group profile, whereas the user aggregation method derives its decisions from individual user profiles.

Figure 9 illustrates the satisfaction level of traveler 2 in the first group, where the traveler’s satisfaction surpasses that of the group aggregation method. Although user aggregation demonstrates superior performance overall, there are instances where the group aggregation method yields better results over short periods. This occasional advantage of the group aggregation method can be attributed to the GACO algorithm’s design, which sequentially selects individual POIs without considering the entire route collectively.

Figure 10 illustrates the satisfaction level of user 3 in the initial group, in which both methods yield comparable results. It also demonstrates that, at certain instances, the group aggregation method outperforms the user aggregation method. This occurs because the user aggregation algorithms may select a POI that subsequently limits the availability of other suitable POIs, resulting in the selection of a POI with lower satisfaction.

Figure 11 illustrates a comparison of the two methods concerning traveler 4’s satisfaction levels, indicating similar outcomes for both methods. Initially, the group method outperforms the user method, primarily because traveler 4 has a strong relationship with a group member selected by the proposed GACO algorithm.

Figure 12 illustrates the satisfaction level for traveler 5 within group 1, demonstrating that the user aggregation approach sometimes yields superior results, while at other times, the group aggregation method proves more effective. As previously discussed in the context of User 3, the GACO algorithm may select a POI in an area of the city where surrounding POIs offer low satisfaction.

Second group: In the second instance, we evaluated the satisfaction levels for the members of group 2 using group aggregation method. Figures 13–18 provide a comparative analysis between user aggregation and group aggregation based on satisfaction levels.

Figure 13 illustrates the distinctions between group aggregation and user aggregation. The latter yields superior results, whereas the former results in an extended tour. It is evident that user aggregation concludes the tour sooner than group aggregation method. Overall, user aggregation generally provides a higher level of satisfaction for the trip.

Figure 14 illustrates a comparison of the outcomes generated by the different aggregation approaches. The user aggregation approach yields superior overall results, whereas the group aggregation method results in an extended tour. The GACO algorithm is constrained to select sequences of POIs that are visited simultaneously, thereby ensuring a consistent level of satisfaction. The primary reason for this outcome is that GACO selects POIs on an individual basis.

Figure 15 illustrates that the user aggregation approach yields a recommended trip of shorter duration compared to the tour derived from group aggregation. As depicted in the figure, group aggregation offers a more favorable outcome for User 3. The primary reason for this is that the GACO algorithm selected User 3 to pair with another user based on their high relationship value, disregarding User 3’s individual preferences.

Figure 16 illustrates that the user and group aggregation approaches yield comparable tours in view of overall satisfaction. The GACO algorithm selected traveler 4 to accompany another traveler in the group for a segment of the tour, resulting in a slightly lower satisfaction level compared to the overall group aggregation.

Moreover, Fig. 17 demonstrates that both group and user aggregation approaches result in a high satisfaction for traveler 5 within the second group. When the proposed algorithm selects a POI in a particular direction, the subsequent point may not meet traveler’s satisfaction due to the limited number of options available in that direction. It is observed that the initial segment of the trip, as determined by user aggregation, exhibits a high satisfaction level; however, GACO struggles to identify another suitable POI to maintain this level of satisfaction consistently.

Figure 18 reveals that the group aggregation method initially outperforms the user aggregation approach at the beginning of the tour. However, as the trip progresses, the user aggregation approach demonstrates superior performance, particularly at the midpoint. This can be attributed to the fact that user 6 is paired with another user within the same group, leading to potential conflicts or misalignments in preferences that can impact satisfaction levels under the user aggregation approach.

Discussion

In this article, multiple experiments are conducted on the two aggregation methods. The results from the user aggregation method surpass those from the group aggregation method. For instance, Fig. 8 illustrates the comparative performance of these aggregation methods, highlighting that the user aggregation method excels in maximizing the traveler’s satisfaction level. Additionally, the first and second traveler within the groups consistently exhibited higher level of satisfaction as compared to other group members. The proposed GTTRM was validated under diverse test conditions to ensure that it performs consistently. Through repeated scenario testing with various initial values, we confirmed that GTTRM reliably maximizes group satisfaction and dynamically adapts to subgroup configurations. These results are not subject to random variation due to single-run dependencies; rather, the consistent results observed across scenarios demonstrate the robustness of our model. Future work may involve further statistical testing, but the current approach provides a stable and effective foundation for group travel recommendations. In summary, our findings demonstrate that the GACO algorithm achieves superior outcomes (i.e., higher level of satisfaction for travelers) relative to the group aggregation approach, particularly for the first and second traveler in the group. This enhanced performance can be attributed to the social relationship values integrated within the algorithm. These values drive the algorithm to prioritize the satisfaction of the first traveler who is accompanied by a second traveler, who may not derive full satisfaction from visiting the POIs preferred by the first user.

Limitations of the GTTRM

While the proposed GTTRM offers significant improvements in handling group travel recommendations and dynamic subgroup formation, there are certain limitations that should be considered. One limitation is the dependency on accurate preference data for effective subgroup formation. If group members do not provide sufficient or accurate preference data prior to the trip, the model may struggle to form meaningful subgroups, leading to suboptimal satisfaction outcomes. Another potential limitation is the frequency of preference changes. The model assumes that subgroup formation can adapt to evolving preferences throughout the trip. However, if preferences change too frequently, the algorithm may require excessive recalculations, leading to increased computational overhead and potentially reducing the system’s real-time performance. In addition, the model may not perform as effectively in groups where interpersonal relationships heavily influence decisions. The current implementation of ACO focuses on optimizing satisfaction based on preferences, but does not explicitly account for social dynamics or group decision-making hierarchies, which could affect the outcome in real-world group travel scenarios.