1. Introduction

With the rapid development of the tourism industry, the optimization of tourist routes has gradually become a prominent research topic in both academia and practice. Optimizing tourist routes not only enhances the experience for tourists but also effectively reduces transportation costs and saves time resources. With the continuous advancement of information technology, tourism methods have undergone significant transformations. People’s travel demands are continuously evolving in both form and content, increasingly inclined toward tourism experiences that emphasize service quality and personalization ¹.

Compared to conventional product recommendation systems, tourist route recommendation systems present a higher level of decision-making complexity. This process not only requires the integration of user preferences but also needs to simultaneously optimize multiple constraints such as time restrictions, spatial distribution of attractions, economic costs, trip length, and environmental variables ². Only by optimizing the design of tourist routes can tourists visit multiple points of interest (POIs) during their journey, which means maximizing the number of POIs visited by tourists ³. In the current field of tourism recommendation research, multi-objective optimization algorithms and hypergraph learning techniques have been widely applied, covering areas such as POI prediction, historical travel sequence mining, and route planning.

Derya et al. introduced the problem related to personalized tourist route construction, known as the tourist trip design problem (TTDP) ⁴. TTDP involves planning a travel itinerary to visit various POIs without exceeding the constraints related to time, transportation, budget, and tourist preferences. The core of TTDP lies in optimizing the access sequence for multiple POIs while strictly satisfying multi-dimensional constraints such as time windows, transportation methods, budget limits, and tourist preferences ^5,6,7.

A large number of studies have been conducted on tourist route planning. Niu ¹ proposed a multi-objective optimization method based on an improved ant colony algorithm and topological optimization for personalized tourist route recommendations. A multi-objective optimization model was developed, considering factors such as time, cost, and service quality, to optimize the tourist service combination. The planning efficiency of tourist routes was improved through the enhanced ant colony algorithm and topological structure optimization. Zheng et al. ⁸ proposed a route optimization method based on the improved ant colony optimization (ACO) algorithm and tourism big data for route planning in intelligent tourism. The study combined the MAX–MIN ant system, principal component analysis, and clustering analysis to construct a flexible optimization model capable of optimizing tourist routes according to different demands.

Lin et al. ⁹ proposed a greedy-algorithm-based tourist route planning method that integrates hotel and attraction evaluation recommendations into an intelligent management system, enabling efficient and personalized route suggestions by minimizing travel time and cost while maximizing attraction coverage. Wang ¹⁰ developed a tourist route optimization approach based on the teaching-learning-based optimization algorithm, generating personalized travel plans by incorporating tourists’ historical data and preferences while optimizing both time and distance. Hua ¹¹ addressed the multi-day tourism problem using an improved Monte Carlo simulated annealing algorithm to optimize route-related objectives such as time and cost, aiming to obtain short and low-cost itineraries. Lu et al. ¹² constructed multiple tourism route models using Nanjing as a case study, optimizing different path structures (e.g., single-node and linear paths) to support multi-node, circular, and radial tourism and enhance tourist satisfaction. Zhang and Sun ¹³ proposed an improved ACO-based model that enhances path selection and pheromone updating to efficiently identify optimal routes while considering tourist preferences, travel time, and attraction quality.

Early tourist route planning studies often relied on the traveling salesman problem (TSP); however, TSP fails to incorporate activity selection, accommodation, multi-objective requirements, and tourist preferences ¹⁴. To address these limitations, several extended models have been proposed, such as the trip planning problem ¹⁵, the one-period bus touring problem ¹⁶, the city bus tour problem ¹⁷, and the optimal tourist problem, including the reward maximization tourist and budget minimization tourist variants ¹⁸. Among these, the orienteering problem is widely regarded as a fundamental modeling framework for TTDP, as it determines both the set and visiting sequence of nodes to maximize rewards under budget and time constraints ^4,19.

There are various methods for solving tourist route planning problems. Exact methods are typically used for solving small-scale cases. For example, Zhao and Alfandari ²⁰ applied the Branch and Price and Branch-and-Cut-and-Price algorithms to solve instances of the TOP-DC problem with 21 to 66 nodes. Heuristic methods are commonly used to solve large-scale problems in a shorter time frame. For instance, Jia et al. ²¹ presents a multi-objective optimization model to address the sightseeing bus problem, aiming to balance tourist benefits and operational costs. A two-stage adaptive large neighborhood search (MO-ALNS) algorithm is designed to solve the decisions related to bus fleet scheduling, route planning, and tourist assignment. Additionally, meta-heuristics are the primary methods for solving such models, including improved large neighborhood search ²², improved iterated local search ²³, improved particle swarm optimization (PSO) ²⁴, and improved Genetic Algorithms ²⁵.

Existing research on tourist route optimization often focuses on a single objective or simplifies constraints, neglecting the comprehensive consideration of personalized tourist needs and multi-dimensional constraints. Moreover, the algorithms used to solve these models tend to get trapped in local optima when processing large-scale data, lacking efficiency. Therefore, this paper establishes a tourist route optimization model that comprehensively considers multiple constraints, including tourist preferences, travel time, budget, and attraction opening hours. Based on the characteristics of the model, the ant colony algorithm is improved by introducing a heuristic information mechanism and an adaptive adjustment factor, enhancing the algorithm’s global search capability and convergence speed, ultimately achieving a more personalized and efficient tourist route optimization. ACO is chosen for this study due to its ability to solve complex combinatorial optimization problems in dynamic and constrained environments. While reinforcement learning, particularly deep reinforcement learning, has gained popularity in combinatorial optimization, it often requires large datasets and significant training time. In contrast, ACO relies on simple agents (ants) and uses a pheromone-based heuristic that is less data-intensive and more suited for real-time applications with predefined constraints, such as travel time, budget, and tourist preferences.

Although reinforcement learning offers greater flexibility, its application in highly constrained environments like tourism route optimization can be computationally expensive and slow to converge. ACO’s balance of exploration and exploitation, along with its adaptive nature, makes it a more efficient and practical choice for personalized tourist route planning in such scenarios.

2. Problem Description and Mathematical Model

2.2. Notations

The sets, parameters, and notation used in this paper are summarized in Table 1.

3. Hybrid Multi-Strategy Improved ACO (HMIACO) Algorithm

3.2. Improved ACO Algorithm

3.2.1. A Heuristic Information Mechanism with Directional Guidance

To enhance the global performance of the algorithm, the Euclidean distance from the current node to the next node and from the next node to the target node is integrated into the heuristic information. A weight factor is used to optimize the trade-off between the distance from the current node to the next node and the distance from the next node to the target node. Additionally, an angle-guided factor is introduced to strengthen the directionality toward the target node, and an adaptive adjustment factor based on the current iteration number is designed to dynamically regulate the algorithm’s convergence rate. The expression for the improved heuristic information function is shown in Eq. 26 ²⁷:

\begin{equation} \eta_{ij} = \delta_{1} \times \delta_{2} \left(\dfrac{1}{\sigma_{1}d_{ij} + \sigma_{2}d_{jg}}\right), \label{eq:26} \end{equation}

where \(\eta_{ij}\) represents the heuristic information value between the current node \(i\) and the next reachable node \(j\) at the current time; \(d_{ij}\) represents the distance between the current node and the next node; \(d_{jg}\) represents the distance between the next node and the target point; \(\sigma_{1}\) and \(\sigma_{2}\) are weight factors; \(\delta_{1}\) is the adaptive adjustment factor associated with the iteration number, and \(\delta_{2}\) is the angle-guided factor calculated by Eq. 28. The calculation of \(\delta_{1}\) is shown in Eq. 27:

\begin{equation} \delta_{1} = \exp \left(-2\left(\dfrac{N}{N_{\textit{max}}}^{2}\right)\right), \label{eq:27} \end{equation}

where \(N\) represents the current iteration number, and \(N_{\textit{max}}\) represents the maximum number of iterations. In the initial phase of the algorithm, the adaptive adjustment factor \(\delta_{1}\) takes a relatively large value to accelerate the convergence process. As the iteration number increases, \(\delta_{1}\) decreases monotonically, which suppresses the influence of the heuristic information in the later stages of the algorithm, thus enhancing global convergence performance. The calculation of \(\delta_{2}\) is shown in Eq. 28:

\begin{equation} \delta_{2} = \exp \left(-0.5\left(\dfrac{\theta}{\pi}\right)^{2}\right). \label{eq:28} \end{equation}

Equation 28 explicitly defines the angle-guided factor \(\delta_{2}\), which is used to penalize turning angles and encourage smoother route transitions.

The calculation of \(\theta\) is shown in Eq. 29:

\begin{equation} \theta = \arccos \left(\dfrac{v_{sg} \cdot \omega_{jg}}{v_{sg} \times \omega_{jg}}\right). \label{eq:29} \end{equation}

3.2.2. Pseudorandom Transition Strategy

To regulate the ant path selection mechanism, a node selection strategy combining determinism and randomness is adopted to determine the next visited node for the decision-making ants at their current position. Specifically, the transition rule for an ant moving from the current node \(j\) to a node \(i\) in the candidate set L\(_\textit{1}\) is defined as Eq. 30 ²⁸:

\begin{equation} p_{ji} = \left\{ \begin{aligned} &\dfrac{\lambda_{ji}}{\displaystyle \sum_{i \in I_{1}} \lambda_{ji}},{\ }i \in L_{1} \backslash \{j\}, &&r \le r_{0}, \\ &\max_{i \in I_{1}} \bigl\{\lambda_{ji}\bigr\}, &&r > r_{0}, \end{aligned} \right. \label{eq:30} \end{equation}

where \(p_{ji}\) is the probability that the transportation mode moves from attraction \(j\) to the required point \(i\).

3.2.3. Elite Ant Strategy

In ACO, all ants release pheromones along the paths during each iteration to guide the selection of subsequent ants. However, this approach may lead to an overly uniform pheromone distribution, which can slow down the convergence speed of the algorithm. The core idea of the elite ant strategy is that, in each iteration, only the best-performing ant (i.e., the ant that finds the shortest path) or a few high-performing ants are allowed to release pheromones. This approach enhances the pheromone concentration on high-quality solutions, thereby accelerating the convergence of the algorithm. In the standard ACO, the pheromone update formula is typically expressed as

\begin{equation} \tau_{ij}(t+1) = (1 - \rho) \cdot \tau_{ij}(t) + \Delta \tau_{ij}, \label{eq:31} \end{equation}

where \(\tau_{ij}(t)\) is the pheromone concentration on the path from node \(i\) to node \(j\) at time \(t\); \(\rho\) is the pheromone evaporation rate, representing the degree of pheromone decay; and \(\Delta\tau_{ij}\) is the total amount of pheromone released by all ants on the path \((i,j)\) during the current iteration.

In the elite ant strategy, the pheromone update formula can be adjusted as follows:

\begin{equation} \tau_{ij}(t+1) = (1 - \rho) \cdot \tau_{ij}(t) + \Delta\tau_{ij}^{\textit{best}}, \label{eq:32} \end{equation}

where \(\Delta\tau_{ij}^{\textit{best}}\) is the amount of pheromone released by the elite ant on the path \((i,j)\).

4. Simulation Experiments and Analysis

4.2. Case Study

Taking the tourism case of Yunnan Province, China, as an example, this paper references the tourist attraction information of Kunming City, Yunnan Province, provided in the study by Wang et al. ²⁹, to validate the effectiveness of the proposed approach. There are two tourists, A and B, in the study. Tourist A prefers to explore natural landscapes and has strict round-trip time constraints, while Tourist B prefers shopping in commercial streets and has a more relaxed schedule.

Based on the preferences of Tourists A and B, the improved HMIACO algorithm proposed in this paper is used to solve the models established according to the preference parameters of the two tourists. The parameters of the ant colony algorithm used in this experiment are shown in Table 2.

Referring to the tourist attraction information of Kunming City, Yunnan Province, in reference ²⁹, the attractions are numbered from 1 to 14, starting from Daguan Park to the World Horticultural Expo Garden. The HMIACO algorithm and the other nine optimization algorithms were compared and used to solve the problem. The average objective function values for Tourists A and B obtained from running the algorithm 30 times are shown in Fig. 7.

To validate the effectiveness of the model and algorithm proposed in this paper, a comparison is made between the proposed solution (Tourists A and B) and several state-of-the-art methods, including (1) deep graph convolutional networks and (2) reinforcement learning as well as traditional approaches such as (3) the minimum travel budget plan and (4) the random plan. The comparison focuses on key metrics such as tourist satisfaction and the number of attractions visited. The results are shown in Table 3.

As shown in Table 3, the solution proposed in this paper results in higher customer satisfaction compared to both the random plan and the minimum travel cost plan. Additionally, the travel time required is lower than that of the other four plans.

The route planning solutions for Tourists A and B obtained from the proposed tourist route planning scheme are shown in Table 4.

5. Conclusion

This study proposed an HMIACO algorithm for personalized tourist route planning under practical constraints. A multi-objective optimization model was developed to maximize tourist satisfaction while considering travel time and cost, attraction opening hours, transportation mode, rest time, weather conditions, transfer limits, and inter-city travel constraints. The proposed enhancements strengthen global search ability and accelerate convergence compared with conventional ACO and representative meta-heuristics.

Experiments on 15 benchmark functions and a real-world case study in Kunming verify that HMIACO produces higher-quality and feasible personalized itineraries, improving tourist satisfaction by 22.37% and 13.41% over budget-minimum and random strategies, respectively, with competitive time and cost performance. Future work will extend the framework to support dynamic preference updates and real-time re-optimization under uncertain travel conditions.