Application of improved GA in optimizing rural tourism routes

Longjie Yin; Muzi Li

doi:10.1515/nleng-2025-0127

Article Open Access

Application of improved GA in optimizing rural tourism routes

Longjie Yin and Muzi Li

Published/Copyright: July 2, 2025

Published by

Become an author with De Gruyter Brill

Submit Manuscript Author Information

From the journal Nonlinear Engineering Volume 14 Issue 1

Abstract

With the growth of the economy, tourism has gradually become a consumer trend in people’s lives. However, the traditional optimization method of rural tourism routes cannot optimize the routes effectively and achieve the best results. The study introduces a genetic algorithm (GA), combines it with an ant colony optimization (ACO) algorithm, and proposes an improved GA to optimize rural tourism routes. The degree of adaptation is set by collecting historical rural tourism route data, initializing the data population, and performing variant crossover operations. The ACO algorithm is used to converge the route points and shift the route according to the action probability. The experimental results show that the proposed method of the study has a minimum mean absolute error of 0.784 and a maximum mean absolute error of 0.801 in optimizing rural tourism routes, which is more accurate compared to the traditional GA and ACO algorithms. Compared with the methods proposed by other scholars, the maximum error rate of solving the proposed method of the study is only 0.56%. The results show that the improved genetic method proposed by the study can effectively enhance the effect of rural tourism route optimization, providing new ideas and perspectives for the tourism industry.

Keywords: route optimization; genetic algorithm; ant colony optimization algorithm; rural tourism; mathematical modelling

1 Introduction

With the steady improvement of the social economy, people’s consumption patterns are also constantly transforming. Most people are no longer limited to shopping consumption, but are increasingly inclined toward tourism consumption in pursuit of a higher quality of life [1]. Moreover, people’s increasing demand for tourism has prompted the tourism industry to become an important pillar industry in the current society, and rural tourism has also flourished. However, the development of rural tourism also brings many challenges, the biggest of which is how to optimize the tourism routes. In traditional tourism route optimization methods, most tourism destination selection and route planning systems are built based on machine learning and deep learning techniques [2]. In traditional travel route optimization methods, most travel destination selection and route planning systems are constructed based on machine learning and deep learning techniques [3,4]. Although these traditional algorithms are capable of designing routes based on the interests and preferences of the crowd and assisting people in selecting their preferred destinations, they have many shortcomings, such as being unable to meet the personalized travel goals of the majority of the population, and the planned travel routes are not always the best solutions [5]. In addition, they are unable to provide tourists with diverse planning options based on time and economic budget, resulting in tourists not being able to make active choices based on their personal interests, but only passively accepting the attractions and routes arranged by the system [6]. Therefore, there is an urgent need for a methodology that can optimize rural tourism routes and model optimal routes. Genetic algorithm (GA) simulates natural evolution for model computation and can avoid the trap of local optimal solutions through mutation and crossover operations. It has strong search ability, and these advantages make GA widely used in path planning. However, GAs may experience premature convergence and cannot perform complex route calculations [7]. Ant colony optimization (ACO) can avoid the problem of premature convergence and has a good computational processing effect on complex routes, effectively compensating for the limitations of GA in tourism route optimization [8]. Therefore, the study introduces the ACO to improve the GA, aiming to overcome the limitations of GA, which is easy to fall into the local optimal solution and has poorer computation effect in the complex routes, to improve the optimization efficiency of the rural tourism routes, and to enhance the satisfaction of the tourism users.

The study proposes a rural tourism route optimization method based on improved GA. The optimization effect is improved by collecting historical rural tourism route data, initializing the data population, and setting the fitness by performing variant crossover operation. The method has obvious advantages in improving the optimization effect and user satisfaction. In addition, the superiority of the proposed method in different scenarios is demonstrated by analysing the effect of practical application. Whether for path planning with fewer or more attractions, the proposed algorithm can plan the optimal travel path according to the different needs of tourists, which saves tourists’ time and traveling costs. This not only enhances the effectiveness of rural tourism route optimization, but also provides new ideas and methods for the tourism industry.

The novelty of the study is to combine GA with ACO and use it in the field of rural tourism route optimization. By introducing the ACO algorithm to improve GA, it overcomes the limitations of GA, which is easy to fall into the local optimal solution and has a poor computational effect on complex routes. In addition, an ACO-GA-based rural tourism route optimization model is constructed, which not only avoids the problem of traditional GA falling into local optimums, but also combines the advantages of the classical ACO algorithm and avoids the problem of repetitive planning in the optimization process of rural tourism routes.

2 Related work

As the economy rapidly develops, tourism has become increasingly popular among people. Therefore, the optimization of tourism routes has received widespread attention from scholars all over the world. Pei et al. proposed a geographic information system-based tourism route optimization method for optimal planning of tourism routes. They evaluated route models and analysed tourism resources through geographic information systems, optimized vehicle routes and tourism routes through network analysis, and constructed an intelligent framework for route optimization to integrate tourism resources [9]. Li et al. developed a tourism route optimization method grounded on improved knowledge ant colony to address the problems of uneven allocation of tourism resources and poor route planning. By establishing a mathematical model with tourism satisfaction as the objective function, tourism constraints were determined, and hierarchical clustering and random sampling methods were used to process the obtained data [10]. Xu et al. developed a personalized route planning method grounded on urgency to address the problem that traditional route planning methods cannot meet user needs. By constructing a planning model, historical tourism data were collected to extract user feature preferences, routes were determined based on urgency values, and GAs were used for numerical calculations on the dataset [11]. Zheng et al. developed a multi-objective tourism route optimization method to address the issue of uneven distribution in traditional evolutionary algorithms. The multi-objective problem was divided into multiple subproblems, and a two-stage approach was used to improve the distribution of solutions, and finally, Pareto stratification was utilized for population diversification [12]. Zhu developed a multi-objective tourism route optimization method to address the problem of limited bicycle tourism route planning. By establishing a multi-objective mixed linear programming model, generating non-dominant solutions to balance multiple objectives, and utilizing the utility of bicycle tourists’ access to interest peaks, tourism route planning is carried out [13]. Wozniak addressed the problem of urban centre pedestrian traffic fluctuating throughout the day due to a variety of factors and proposed an agent-based model that is specifically designed to examine pedestrian traffic fluctuations at the meso-level. The model’s ability to capture the actual dynamics of pedestrian movement in urban centres was enhanced by accurate calibration using popular time period data from Google Location Services and demographic data from GIS [14]. Li et al. proposed a pedestrian trajectory prediction method combining the Gaussian mixture model and artificial potential field for the pedestrian trajectory prediction problem faced by self-driving cars operating safely and efficiently in urban environments, thus improving the accuracy and safety of the prediction [15].

GA simulates natural evolution and searches for optimal solutions through selection, crossover, and mutation operations, which has strong global search capability but is prone to premature convergence, while the ACO algorithm simulates the behaviour of ants releasing pheromone and guides the search through pheromone update, which has good convergence performance and strong robustness. Combining GA and ACO can synthesize the advantages of both and solve complex optimization problems more effectively. Raj et al. developed a data-driven path optimization method grounded on GA to solve the problem of fair allocation of data-driven paths. By dynamically allocating and managing network resources, a particle swarm optimization algorithm was used to process network data [16]. Cui et al. developed a distribution route optimization method grounded on adaptive GA to address the problem of high delivery costs caused by routes during logistics distribution. By establishing a constrained soft time window urban logistics distribution model, with cost as the optimization objective function and customer satisfaction as the influencing factor, the fitness value was calculated [17]. Shi et al. developed a path-planning method grounded on an improved GA to solve the issue of uneven path planning in four-wheel intelligent vehicles. By constructing a physical model of intelligent vehicles, the fitness function and mutation crossover operation of GAs were improved, and missing operators were added [18]. Luan and Thinh members developed a smooth path planning method grounded on hybrid GA to generate the optimal safe path planning for robots relative to the map. By providing dynamic mutation rates to GA mutation operators, search methods were transformed, and finally, population replacement was utilized to handle chromosome length [19]. Hao et al. designed a global path planning method grounded on adaptive GA to solve the issue of low quality and poor performance in three-dimensional AUV path planning. By adopting a conflict detection mechanism as an optimization strategy to optimize the global path, the spatial vector method was used to raise the calculation method of the resultant force direction, and local obstacle avoidance was performed using critical path points [20].

From the current research status at home and abroad, in the optimization methods for rural tourism routes, the allocation of rural tourism resources is uneven, and the selection of the best tourism route cannot be carried out. Therefore, the study introduces GA and combines the ACO algorithm to establish a route optimization model for rural tourism route optimization selection, with the aim of improving the effectiveness of route optimization and evenly distributing tourism route resources.

3 Optimization of tourist route design based on improved GA

3.1 Design of improved GA based on the ACO algorithm

When traveling, travellers will comprehensively consider various factors during the journey to achieve the desired travel effect, and the issue of tourism route planning is to plan the path of the tourism route [21,22]. GAs that simulate natural evolution processes can effectively plan rural tourism routes. The basic process of solving GA is shown in Figure 1.

Figure 1

GA solution process (the author’s own collation).

In Figure 1, when solving, the GA first initializes the population parameters and determines the encoding scheme based on the problem being solved. Then, by generating an initialization cluster, setting its fitness function, and selecting a population operator, cross-mutation operations are performed on the population operator according to the encoding scheme. Finally, it outputs the results when the iteration requirements are met. When the iteration requirement is not met, the population operator is re-selected, and the operation is repeated until the iteration requirement is met. When GA is used for encoding, the length calculation of binary encoding for variables in the problem can be expressed mathematically, as shown in Eq. (1), when the variables are continuous variables

(1) L = ceil log 2 U bound − L bound h min + 1 + 1 ,

where U bound represents the maximum search range of binary encoding length and L bound represents the minimum search range of binary encoding length. The commonly used operator selection method in GAs for selection operations is the roulette wheel selection method. This method selects operators through random sampling, and its mathematical expression is shown as follows:

(2) p i = f i ∑ i = 1 m f i ,

where p i denotes the probability of selecting a particular individual, m represents the population size, and f i denotes the fitness value of individuals in the population. The fitness value calculation of GA can be grounded on the mini and max values, as follows:

(3) Fit = c max + a ∑ i = 1 n s min ,

where c max represents the complexity of the environment in which the GA operates, a represents the penalty coefficient, and s min represents the shortest path length of the GA during route planning. The GA has strong applicability and simple operation in route planning [23]. However, in the process of convergence, premature convergence may occur, and the calculation effect for complex routes is poor, requiring multiple calculations. Accordingly, the study proposes the integration of the ACO algorithm as a means of enhancing the GA. The ACO algorithm is an optimization algorithm that emulates the foraging behaviour observed in natural ant colonies. The basic implementation process of the ACO algorithm is shown in Figure 2 [24].

Figure 2

Implementation process of the ACO algorithm (the author’s own collation).

In Figure 2, when optimizing the ACO, the parameters are first initialized, and the number of ants and iteration times are set. By storing the set ants in feature nodes and using the ant’s action probability formula for policy transition feature selection, the pheromone is updated when all individual ants complete their respective tasks, and the output of the optimal feature subset is selected based on whether the max amount of iterations has been reached. When the ACO algorithm takes action, its action probability is expressed as followed:

(4) P i j k ( t ) = [ τ i j ( t ) ] ∂ [ η i j ( t ) ] β ∑ j ∈ allowed [ τ i j ( t ) ] ∂ [ η i j ( t ) ] β , j ∈ allowed 0 , j ∉ allowed .

In Eq. (4), ∂ means the information heuristic factor of ACO, and β means the expected heuristic factor of ACO. τ i j represents the concentration of pheromones moving from path node i to path node j , and η i j represents the heuristic information moving from path node i to path node j . After the ACO completes an action, the path information of its action will be updated, and the mathematical expression of the path update is shown as follows:

(5) τ i j ( t + 1 ) = ( 1 − ρ ) τ i j ( t ) + Δ τ i j ( t ) ,

where ρ means the volatility coefficient, where ( 1 − ρ ) and 1 are coefficients and ( 1 − ρ ) + 1 = 1 . This suggests that the pheromone updating process can be viewed as a convex linear combination where the new pheromone concentration is a weighted sum of the old pheromone concentration and the added pheromone. The calculation expression for the variation of pheromone concentration with the amount of iterations is indicated as

(6) Δ τ i j ( t ) = ∑ k = 1 K Δ τ i j k ( t ) .

In Eq. (6), Δ τ i j k ( t ) represents the increment of pheromones left by ants during iteration from the previous feature node to the next feature node. The ACO iteratively calculates the path points to make the optimal decision and passes the decision to the GA for fitness value calculation and mutation crossover operation. The ACO-GA process is shown in Figure 3.

Figure 3

ACO-GA flowchart (the author’s own collation).

In Figure 3, the parameters of GA and ACO are initialized, and the path is selected for encoding. The population is initialized through the ACO strategy, paths are transferred according to action probability, and pheromones are updated. The ACO outputs the optimal solution that satisfies the termination condition and uses the output optimal solution as the initial solution of the GA to evaluate the fitness of individuals in the population, completing crossover and mutation operations. The mathematical expression for calculating the crossover probability in the ACO-GA during operator crossover operation is shown as follows:

(7) Pc = k 1 ( f max − f ) f max − f avg , f ≥ f avg k 2 , f < f avg ,

In Eq. (7), f max refers to the max fitness value of individuals in the population, f avg refers to the average fitness value among individuals in the algorithm population, f refers to the fitness value of the operator performing the crossover operation. k 1 and k 2 represent parameters with a value range of [0, 1].

3.2 Optimization design of rural tourism routes based on ACO-GA

The ACO-GA solves the problem of classic GA algorithms easily getting stuck in local optima and combines the advantages of the classic ACO algorithm to avoid duplicate route planning in rural tourism route optimization. In the planning of tourist routes, to explore the optimal path, the first step is to process the path planning problem. When processing the planning problem, the collected problem data is mainly processed. In the process of processing the problem data, a function is first constructed to initialize the problem parameters. The function expression is shown as follows:

(8) η i j ( t ) = 1 t i j ,

where η represents the function value and i and j represent scenic spots. The number of cycles N c is computed and updated according to the constructed function, and for each update, N c is increased by 1. Second, the probability of selection of paths p is computed by means of N c . After processing the path planning problem through the above steps, the specific solution process of the path planning problem is obtained, as shown in Figure 4.

Figure 4

Process of optimizing tourist routes (the author’s own collation).

In Figure 4, in the problem of tourism route planning, a mathematical model is first built and solved. The findings obtained from solving the mathematical model are used to solve the specific route planning. Finally, the planned route is verified to ensure that it can meet the required optimized route. At present, tourism route planning is mainly solved based on mathematical models and user interests. When using mathematical models for tourism route optimization, there are multi-objective and single-objective modeling methods for the mathematical models. In the establishment of multi-objective solving mathematical models, multi-objective optimization of tourism routes is particularly important, and the mathematical expression for multi-objective optimization is shown as follows:

(9) min y = F ( x ) = [ f 1 ( x ) , f 2 ( x ) , … , f m ( x ) ] T ,

where x represents the decision vector for multi-objective optimization of rural tourism routes. However, these methods cannot effectively plan rural tourism routes, and there may be issues of duplicate planning during the route optimization process. Therefore, the study introduces an improved GA for optimizing rural tourism routes. Using the ACO-GA to construct a mathematical model for optimizing rural tourism routes, the model structure is shown in Figure 5.

Figure 5

ACO-GA tourism route optimization model (the author’s own collation).

In Figure 5, f i j , p i j , h i j , q i j , c i j , and r i j represent the factors related to the tourist routes. s i j k represents whether to choose the k -th route from the attractions i to the attractions j . v i j and w i j represent the attributes related to the destinations j , respectively. K represents the total number of routes. max F represents the maximization of the efficiency. The ACO-GA algorithm carries out the construction of the mathematical model for optimization of the countryside tourist routes. First, the objective function is built according to the routes of rural tourist attractions, and then the constraints are set. The constraints are established by setting conditions through the objective function, and then the number of attractions in the scenic area and the playing time are calculated, and finally, the establishment of the mathematical model is completed. The model optimizes the rural tourism routes by minimizing the total cost M and maximizing the efficiency F . The model is designed to optimize the rural tourism routes. Each summation and sum variable represents different aspects of route planning such as cost, value, time, and resource use. The process of solving the mathematical model for optimizing rural tourism routes using the ACO-GA is denoted in Figure 6.

Figure 6

Solution process of ACO-GA route optimization model (the author’s own collation).

In Figure 6, the ACO-GA first initializes the parameters of the GA and ACO algorithm when solving the mathematical model, uses the GA for data crossover and mutation operations, and uses the action probability of the ACO algorithm for data transfer. Then, the pheromones of rural tourism routes are updated, and their fitness values are calculated. Finally, the rural tourism route is output and concluded. In rural tourism route optimization, population initialization is equivalent to generating an initial set of tourism routes. These initial routes can be seen as random choices made by tourists without the guidance of the optimization algorithm. By randomly generating the initial routes, the model is able to cover a wide range of possible tourist routes, providing diverse starting points for subsequent optimization. The fitness function is used to evaluate the advantages and disadvantages of each tourism route. In rural tourism route optimization, the fitness function usually considers factors such as path length, attraction of attractions, and tourism cost. Ultimately, by combining the ability of global search and local search, the model is able to avoid the local optimal solution, find the global optimal tourism route, and improve the satisfaction of tourists.

4 Empirical analysis of rural tourism routes optimization using improved GA

4.1 Validity verification of ACO-GA

To validate the effectiveness of the proposed ACO-GA of the study, the study was experimented with MATLAB R2010b software. The operating system was Windows 11, Graphics card Intel(R) Core(TM) i5-12450H, CPU AMD Ryzen 7 4800H, and 8 GB of RAM. To analyse the changes in the optimal fitness value of the ACO-GA, one-dimensional, two-dimensional, and multi-dimensional functions were used as test functions to conduct experiments on the optimal fitness value changes of the ACO-GA. The population sizes of one-dimensional f ₁, two-dimensional f ₂, and multi-dimensional f ₃ functions were 50, 100, and 300, respectively, with iteration times of 200, 200, and 500, respectively. The experiment findings are denoted in Figure 7.

Figure 7

Optimal fitness value and mean variation of ACO-GA (the author’s own collation). (a) f ₁ optimal value and mean change. (b) f ₂ optimal value and mean change. (c) f ₃ optimal value and mean change.

From Figure 7(a), the ACO-GA could find the optimal solution at the beginning of the iteration when solving the one-dimensional f ₁ function, and the fitness curve of the algorithm showed a small fluctuation when optimizing the function, with an average fitness value of 358.49, indicating that the algorithm could quickly find the optimal solution when solving the one-dimensional f ₁ function. From Figure 7(b), when the ACO-GA solved the two-dimensional f ₂ function, its fitness value showed an upward trend with the increase of iteration times, and the fitness value curve fluctuated significantly. The algorithm explored the optimal solution in the middle of the iteration. From Figure 7(c), the fitness value of the ACO-GA decreased with the increase of iteration times when solving multi-dimensional f ₃ functions, and the algorithm could quickly converge to the optimal solution in the early stage of iteration. From this, the ACO-GA could quickly find the optimal solution in one-dimensional f ₁, two-dimensional f ₂, and multi-dimensional f ₃ functions, indicating that the algorithm has strong search ability and verifying its effectiveness in solving functions of different dimensions. To verify the accuracy of the algorithm, the MAE values and precision of ACO-GA, ACO, and GA were compared. The comparative experiment outcomes are denoted in Figure 8.

Figure 8

Comparison of MAE values and precision of different algorithms (the author’s own collation). (a) MAE values of different algorithms. (b) Accuracy of different algorithms.

According to Figure 8(a), the ACO, GA, and ACO-GA maintained the MAE value in the range of 0.784–0.801 when planning rural tourism paths, which was significantly lower than the MAE values of the other two algorithms. Moreover, the MAE value of this algorithm showed a downward trend with a relatively gentle change, while the MAE values of the other two algorithms were significantly higher than those of the ACO-GA. The MAE value of the ACO algorithm increased by 0.014 compared to the ACO-GA, and the MAE value of the GA increased by 0.009 compared to the ACO-GA. This indicated that the ACO-GA could plan the optimal route for rural tourism routes using the three algorithms, and the MAE value was minimized during route planning. From Figure 8(b), the precision of the ACO-GA reached 0.968 when planning rural tourism paths, greatly higher than the accuracy of the other two algorithms. However, the precision of the ACO algorithm remained consistently in the range of 0.157–0.536, significantly lower than the other two algorithms, with the highest precision being 0.536. The precision of GA was slightly higher than that of the ACO algorithm, with a maximum precision of 0.765, but significantly lower than that of ACO-GA. This indicated that the ACO-GA showed significant advantages in planning rural tourism routes among the three algorithms, and the performance advantage of this algorithm was verified. To further validate the efficacy of the ACO-GA algorithm proposed by the research for optimizing rural tourism routes, a total of 100 data points including the amount of scenic spots, travel routes, and travel modes in Pinghua Township were used as the test set for experiments. The ACO-GA was compared with the ACO algorithm and GA for optimal solutions, and the experimental findings are denoted in Table 1.

Table 1

Comparison of optimal solutions findings three different algorithms (the author’s own collation)

Data	Optimal solution	ACO-GA		ACO		GA
Data	Optimal solution	Best	Error rate (%)	Best	Error rate (%)	Best	Error rate (%)
u24	625	625	0	614	1.76	621	1.64
u27	781	781	0	767	1.79	764	1.53
u35	795	795	0	786	1.13	789	0.75
u41	812	812	0	812	0	804	0.98
u43	841	835	0.71	831	1.18	841	0
u51	861	861	0	859	0.03	860	0.01
u55	924	921	0.32	924	0	912	0
u67	983	983	0	912	7.22	951	3.25
u70	1,067	1,067	0	1,037	2.81	1,055	1.12
u86	1,128	1,128	0	1,093	3.11	1,098	2.65
u94	1,384	1,384	0	1,186	14.31	1,206	12.86

From Table 1, when using the ACO-GA, GA, and ACO to solve the selected data, the ACO-GA failed to obtain the optimal solution when the data nodes were less than 50 and only when the data nodes were 43, with an error rate of 0.71%, while the other nodes obtained the optimal solution. However, the ACO and GA obtained the optimal solution when the data nodes were 41 and 43, respectively, while the other nodes did not obtain the optimal solution. When the data nodes were greater than 50, the ACO-GA only failed to obtain the optimal solution when the data nodes were 55, with an error rate of 0.32%. The ACO and GA could only obtain the optimal solution when the data node was 55, while the other nodes did not obtain the optimal solution.

4.2 Practical effect analysis of optimizing tourism routes based on ACO-GA

To verify the practical application effect of ACO-GA in rural route optimization, different tourist attractions in Pinghua Township were collected from the network. ACO-GA was used to optimize destination tourism routes and compared with traditional GA for destination route optimization. Graph theory is the branch of mathematics that studies graphs, and it has a wide range of applications in path optimization problems. In graph theory, a graph consists of nodes (vertices) and edges (lines connecting nodes), and a path is a sequence of nodes in a graph, where each pair of consecutive nodes has an edge between them. The study used graph theory for the comparison of the validation results, considering the rural tourism routes as a graph, where the attractions serve as nodes and the paths serve as edges. By applying the shortest path algorithm in graph theory, the shortest path from one attraction to another could be calculated more efficiently. The experimental results are shown in Figure 9.

Figure 9

Comparison of rural tourism route optimization (the author’s own collation). (a) Less scenic area route optimization. (b) More scenic area route optimization.

From Figure 9(a), when ACO, GA, and ACO-GA were used to optimize the routes of fewer scenic spots in Pinghua Township, the ACO-GA could plan the optimal tourist route based on the requirements of tourists for the destination, and its route not only saved time and costs for tourists, but also allowed them to enjoy the scenery of other scenic spots on the way to the destination. However, the other two algorithms could not plan the optimal tourist route based on the actual requirements of tourists when optimizing traditional tourist routes. From Figure 9(b), the ACO, GA, and ACO-GA showed significant advantages in optimizing the routes of many scenic spots in Pinghua Township. The ACO-GA not only saved tourists’ time but also optimized traditional rural tourism routes. Moreover, the tourism route planned by this algorithm was the optimal route, while the other two algorithms not only consumed tourists’ time but also did not plan the optimal tourism route when planning rural tourism routes. The above results indicated that the ACO-GA could plan the optimal travel path based on the requirements of tourists, whether it is for path planning with fewer or more attractions. In addition, the practical application effect evaluation of the proposed algorithm model for optimizing rural tourism routes without a destination in the same dataset is shown in Figure 10.

Figure 10

Three algorithm models for optimizing purposeless routes (the author’s own collation). (a) ACO-GA Route optimization. (b) GA route optimization. (c) ACO route optimization.

From Figure 10(a), the ACO-GA could plan the optimal rural tourism route based on the time and cost of tourists when they did not require a destination. Moreover, tourists could visit more tourist attractions according to the tourism route. From Figure 10(b), the GA could not provide the optimal route for traditional rural tourism routes while meeting the time and cost requirements of tourists. Moreover, the route planned by this algorithm not only consumed the time and cost of tourism users, but also was not the optimal tourism route. From Figure 10(c), when the ACO algorithm was used for planning rural tourism routes, the routes planned by this algorithm consumed more time and cost for tourists compared to the other two algorithms, and the planned routes were suboptimal routes. The results showed that the three algorithms could optimize traditional rural tourism routes while planning the best rural tourism routes for tourists when they did not require a destination.

4.3 Performance comparison of different methods

To further illustrate the superiority of the proposed method, the study introduced the methods proposed by Shi et al. [18], Luan and Thinh [19], and Hao et al. [20] to compare their performance with ACO-GA. The study defined small rural scenarios (including 30 nodes, shorter paths, and more concentrated distribution of attractions), large rural scenarios (including 50 nodes, longer paths, and more uniform distribution of attractions), and super-large rural scenarios (including 70 nodes, very long paths, and wide distribution of attractions, and complex traffic conditions) for the experimental scenarios to verify the path planning. The specific results are shown in Table 2.

Table 2

Performance comparison of different methods (the author’s own collation)

Number of data nodes	Optimal solution				Error rate (%)
Number of data nodes	This paper	Reference [18]	Reference [19]	Reference [20]	This paper	Reference [18]	Reference [19]	Reference [20]
30	520.12	522.34	521.56	523.01	0.56	0.82	0.64	0.93
50	830.78	833.54	832.34	834.56	0.25	0.61	0.42	0.71
70	1090.12	1092.78	1091.67	1093.34	0.12	0.45	0.29	0.54

From Table 2, with the increase of the number of data nodes (the expansion of the scale of the rural scenic area), the optimal solutions obtained by the four methods gradually increased, while the error rate decreased accordingly. Compared with the other three methods, the optimal solution obtained by ACO-GA was obviously more advantageous, and its solution error was only 0.12–0.56%. This indicated that the model had good adaptability and consistency and was able to maintain a high optimization effect on datasets of different sizes. The ACO algorithm was able to dynamically adjust the search direction through the pheromone updating mechanism to avoid falling into the local optimum. The GA was able to maintain the diversity of the population through mutation and crossover operations to further improve the search efficiency. This combination makes ACO-GA maintain a high optimization effect on different datasets.

5 Conclusion

In today’s rapidly developing economy, rural tourism has become a popular way of life and entertainment for the general public, and optimizing rural tourism routes has become an urgent need for the rural tourism industry. A rural tourism route optimization method based on the ACO-GA algorithm was proposed to address the issue of traditional route optimization methods not being effective in making optimal travel route decisions. This method first processed historical tourism data using GA and then used ACO-GA to mathematically model rural tourism routes. The findings denoted that the MAE of the ACO-GA proposed by the research was 0.784, which was 0.014 lower than the ACO algorithm and 0.009 lower than the GA. When the ACO-GA was used for route optimization, the precision reached 0.968, while the highest precision of the traditional ACO algorithm was 0.536, and the highest precision of the GA was 0.765. In the practical application effect of ACO-GA route optimization, ACO-GA could maintain good performance in destination-free route optimization and could plan routes according to the different needs of users. The error rate of ACO-GA was reduced by an average of 29.71% at 30 number of nodes as compared to other models. At 70 number of data nodes, the optimal solution obtained by ACO-GA optimization was still superior. Overall, the ACO-GA proposed by the research can greatly improve the optimization effect of rural tourism routes and enhance the satisfaction of tourism users. However, the ACO-GA proposed by the research only focuses on optimizing the routes of rural tourist attractions and cannot effectively optimize the internal routes of rural tourist attractions. Therefore, in future work, the proposed algorithm will be further improved to enable optimization of the internal routes of tourist attractions.

Acknowledgments

The authors would like to acknowledge the anonymous reviewers for their contribution to this manuscript.

Funding information: Authors state no funding involved.
Author contributions: Longjie Yin: study design, data collection, statistical analysis, visualization, writing, and revision of the original draft, led and supervised this study. Muzi Li: data collection, statistical analysis, and revised the manuscript. The final draft was verified by all authors before submission. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
Conflict of interest: Authors state no conflict of interest.
Data availability statement: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

References

[1] Uva D, Rolando A. A method to select and optimize slow tourism routes using a quality index procedure based on image segmentation and DTM modelling based on NURBS: The case study of multimodal access to inner places from the nodes of the Adriatic coastline’s infrastructure bundle. Sustainability. 2022;15(1):373–86.10.3390/su15010373Search in Google Scholar

[2] Divsalar G, Divsalar A, Jabbarzadeh A, Sahebi H. An optimization approach for green tourist trip design. Soft Comput. 2022;26(9):4303–32.10.1007/s00500-022-06834-1Search in Google Scholar

[3] Pitakaso R, Nanthasamroeng N, Gonwirat S, Khonjun S, Kaewta C, Srichok T, et al. Designing safety-oriented tourist routes for heterogeneous tourist groups using an artificial multi-intelligence system. J Ind Prod Eng. 2023;40(7):589–609.10.1080/21681015.2023.2248144Search in Google Scholar

[4] Zhang S, Lin J, Feng Z, Wu Y, Zhao Q, Liu S, et al. Construction of cultural heritage evaluation system and personalized cultural tourism path decision model: An international historical and cultural city. J Urban Manag. 2023;12(2):96–111.10.1016/j.jum.2022.10.001Search in Google Scholar

[5] Lavín-Delgado JE, Gómez-Aguilar JF, Urueta-Hinojosa DE, Zamudio-Beltrán Z, Alanís-Navarro JA. An efficient technique for object recognition using fractional Harris–Stephens corner detection algorithm. Multimed Tools Appl. 2024;83(8):23173–99.10.1007/s11042-023-16428-0Search in Google Scholar

[6] Lavín-Delgado JE, Solís-Pérez JE, Gómez-Aguilar JF, Razo-Hernández JR, Etemad S, Rezapour S. An improved object detection algorithm based on the Hessian matrix and conformable derivative. Circuits Syst Signal Process. 2024;43:4991–5047.10.1007/s00034-024-02669-3Search in Google Scholar

[7] Sohail A. Genetic algorithms in the fields of artificial intelligence and data sciences. Ann Data Sci. 2023;10(4):1007–18.10.1007/s40745-021-00354-9Search in Google Scholar

[8] Sushma MB, Roy S, Maji A. Exploring and exploiting ant colony optimization algorithm for vertical highway alignment development. Comput-Aided Civ Infrastruct Eng. 2022;37(12):1582–601.10.1111/mice.12814Search in Google Scholar

[9] Pei Q, Wang L, Du P, Wang Z. Optimization of tourism routes in Lushunkou District based on ArcGIS. PLoS One. 2022;17(3):526–41.10.1371/journal.pone.0264526Search in Google Scholar PubMed PubMed Central

[10] Li S, Luo T, Wang L, Xing L, Ren T. Tourism route optimization based on improved knowledge ant colony algorithm. Complex Intell Syst. 2022;8(5):3973–88.10.1007/s40747-021-00635-zSearch in Google Scholar

[11] Xu X, Wang L, Zhang S, Li W, Jiang Q. Modelling and optimization of personalized scenic tourism routes based on urgency. Appl Sci. 2023;13(4):2017–31.10.3390/app13042030Search in Google Scholar

[12] Zheng X, Han B, Ni Z. Tourism route recommendation based on a multi-objective evolutionary algorithm using two-stage decomposition and Pareto layering. IEEE/CAA J Autom Sinica. 2023;10(2):486–500.10.1109/JAS.2023.123219Search in Google Scholar

[13] Zhu S. Multi-objective route planning problem for cycle-tourists. Transp Lett. 2022;14(3):298–306.10.1080/19427867.2020.1860355Search in Google Scholar

[14] Wozniak M. From dawn to dusk: Daily fluctuations in pedestrian traffic in the city center. Simulation. 2024;100(3):245–63.10.1177/00375497231212543Search in Google Scholar

[15] Li H, Wang X, Su X, Wang Y. Improved gaussian mixture probabilistic model for pedestrian trajectory prediction of autonomous vehicle. Recent Pat Mech Eng. 2024;17(1):65–75.10.2174/0122127976268211231110055647Search in Google Scholar

[16] Raj A, Punia P, Kumar P. A novel hybrid pelican-particle swarm optimization algorithm (HPPSO) for global optimization problem. Int J Syst Assur Eng Manag. 2024;15(8):3878–93.10.1007/s13198-024-02386-9Search in Google Scholar

[17] Cui H, Qiu J, Cao J, Guo M, Chen X, Gorbachev S. Route optimization in township logistics distribution considering customer satisfaction based on adaptive genetic algorithm. Math Comput Simul. 2023;204(5):28–42.10.1016/j.matcom.2022.05.020Search in Google Scholar

[18] Shi K, Huang L, Jiang D, Sun Y, Tong X, Xie Y, et al. Path planning optimization of intelligent vehicle based on improved genetic and ant colony hybrid algorithm. Front Bioeng Biotechnol. 2022;10(2):956–71.10.3389/fbioe.2022.905983Search in Google Scholar PubMed PubMed Central

[19] Luan PG, Thinh NT. Hybrid genetic algorithm based smooth global-path planning for a mobile robot. Mech Based Des Struct Mach. 2023;51(3):1758–74.10.1080/15397734.2021.1876569Search in Google Scholar

[20] Hao K, Zhao J, Li Z, Liu Y, Zhao L. Dynamic path planning of a three-dimensional underwater AUV based on an adaptive genetic algorithm. Ocean Eng. 2022;263(2):112–31.10.1016/j.oceaneng.2022.112421Search in Google Scholar

[21] Thantawi AM, Indriyati SA. Conceptual design impacts in new normal era: The use of artificial intelligence (AI) and internet of things (IoT) (case studies: Class room and restaurant). Acta Inform Malaysia. 2022;6(2):39–42.10.26480/aim.02.2022.39.42Search in Google Scholar

[22] Chen Q, Hu X. Design of intelligent control system for agricultural greenhouses based on adaptive improved genetic algorithm for multi-energy supply system. Energy Rep. 2022;8(3):12126–38.10.1016/j.egyr.2022.09.018Search in Google Scholar

[23] De R, Nanda I. Network/security threats and countermeasures for cloud computing. Acta Electron Malaysia. 2022;6(1):1–3.10.26480/aem.01.2022.01.03Search in Google Scholar

[24] Mou N, Jiang Q, Zhang L, Niu J, Zheng Y, Wang Y, et al. Personalized tourist route recommendation model with a trajectory understanding via neural networks. Int J Digit Earth 2022;15(1):1738–59.10.1080/17538947.2022.2130456Search in Google Scholar

Received: 2024-12-13

Revised: 2025-03-11

Accepted: 2025-03-19

Published Online: 2025-07-02

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/nleng-2025-0127

Keywords for this article

route optimization; genetic algorithm; ant colony optimization algorithm; rural tourism; mathematical modelling

Creative Commons

BY 4.0