1 Introduction

With the improvement of people’s living standards and the upgrading of consumption ideas, travel has become the first choice for many adults and children to relax and relieve pressure (Chen and Guo 2012). Tourist attraction screening and scientific planning of travel routes can reduce travel costs and improve tourists’ satisfaction during traveling. Planning the minimum distance of travel routes and reducing travel costs is of great significance to promote the development of local travel and economic growth (Lee et al. 2009).

The travel route planning problem is also called the traveling salesman problem (TSP), which is also a typical NP-Hard problem (Theys et al. 2010). Taking Taiwan, China as an example, Lee et al. (2009) proposed a multi-agent travel model, which can draw a travel route map on Google maps. Wang et al. (2012) believed that with the increase of TSP scale, the calculation difficulty would increase significantly and put forward the artificial fish algorithm to solve this problem. Cheng et al. (2012) proposed a neural network algorithm based on time complexity to solve the TSP of cities. Wang et al. (2015) took the uncertainty theory into account in the TSP problem and put forward the uncertain multi-objective TSP, which enriched the research content in the field of TSP. Malik and Kim (2019) proposed a travel route recommendation mechanism to predict the next tourist attraction, and considered the travel route planning according to many factors such as distance and weather. The solution of TSP problem often involves optimization algorithms. Many scholars have applied different kinds of optimization algorithms to TSP problem, such as particle swarm optimization-ant colony optimization (PSO-ACO) algorithm (Chen et al. 2017), intelligent water drops (IWD) algorithm (Capali and Ceylan 2020), simulated annealing (SA) algorithm (Kurtulus et al. 2020), discrete greedy flower pollination algorithm (Chen et al. 2017), ant colony optimization (ACO) algorithm (Yang et al. 2015) and so on. Genetic algorithm is a population-based search algorithm and utilizes the concept of survival of the fittest, which is an optimization algorithm inspired by natural selection (Katoch et al. 2021). By simulating the inheritance, crossover and mutation of chromosomes in biological evolution, the best genes were screened out and the inferior genes were discarded. Genetic algorithm has been widely used in optimization problems in many fields. Liang et al. (2020) proposed an improved genetic algorithm to optimize the fuzzy controller and the experimental results showed that the controller has great advantages in speed, stability and other aspects, which significantly improved the performance of wellhead backpressure control system. Lu et al. (2020) analyzed and summarized the optimization effects of genetic algorithm in various energy management strategies, contributing to the research on improving the energy utilization efficiency of hybrid power systems and prolonging the life of fuel cells. Genetic algorithm is also one of the most widely used in the field of TSP (Hacizade and Kaya 2018). Sun (2020) studied the influence of different parameters in the genetic algorithm on the results and proposed a method to solve TSP based on the improved genetic algorithm, and proved the effectiveness of the improved genetic algorithm through practice. Abbasi et al. (2020) proposed a genetic algorithm parallelization method to solve the TSP, which realized the parallelization of the genetic algorithm by designing three parallel cores, and the effectiveness of the method was verified by the parallelization experiment of the TSP solution based on genetic algorithm on a multi-core system.

Tourist attraction screening is the premise of travel route planning. Multi-criteria decision-making method can solve the problem of tourist attraction screening (Kaliszewski and Podkopaev 2016). The multi-criteria decision-making method can be used to rank the alternative, so that tourist attractions can screen out the scenic spots with travel value (Qin et al. 2021). Analytic hierarchy process (AHP) is one of the most widely used methods in the field of multi-criteria decision-making methods (Mahase et al. 2016). The practicability and applicability of AHP method have been proved in many research fields (Haseli et al. 2016; Vafadarnikjoo et al. 2020). In order to deal with complex practical decision-making problems, best-worst method (BWM) is proposed as an improved method of AHP (Liu et al. 2021). Compared with AHP method, BWM reduces the number of paired comparisons (Haseli et al. 2016). Liu et al. (2022) used BWM to prioritize suppliers to select appropriate suppliers and assign orders. Majumder et al. (2021) combined trapezoidal fuzzy number with BWM and proposed a trapezoidal fuzzy BWM to determine the most important alternative responsible for the performance and efficiency of hydropower plants under climate scenarios.

In this paper, BWM will be used to rank the alternative tourist cities and attractions in order to screen out the competitive tourist attractions, and genetic algorithm will be used to solve the travel route planning. Then, taking Hubei Province of China as an example, the practical application of the proposed method is carried out.

2 Key problem statement

This section details the key problem of core scenic spots travel route planning and the selection of indicators.

2.1 Key problem of core scenic spots travel route planning

With the continuous improvement of people’s living standards, travel has gradually become the main way of people’s leisure (Chen and Guo 2012). People’s demand for travel is increasing day by day and travel industry has developed rapidly (Wang 2022). The level of scenic spots, traffic conditions and scenery will affect tourists’ sense of travel experience. For example, during the peak period of travel, some scenic spots often have problems such as traffic jams, difficult parking, and inadequate public health, which have a serious negative impact on the tourist experience for tourists. In addition, tourists choose usually scenic spots according to their own preferences and generally learn travel information through the Internet. However, faced with the massive information on the Internet and numerous tourist attractions, it is difficult for tourists to choose which scenic spots to visit. When traveling to multiple scenic spots, how to plan the travel route can minimize the travel distance, which is very important to reduce the fatigue of tourists on the travel road. Therefore, the selection of tourist attractions and the planning of travel routes are the main issues in travel planning and are of great significance. Many scholars have done a lot of research on TSP. They optimized the routes for multiple tourist attractions according to the factors of travel route, time, cost, and tourist satisfaction. This paper will solve the problem of the selection of tourist attractions and the planning of travel routes. This paper first selects travel cities, choosing a city with multiple attractions to travel can reduce travel distance and travel costs to a certain extent. The number of scenic spots in a city, the level of scenic spots, etc., are all considerations of whether to visit the city. The tourist attractions are selected by multi-criteria decision-making method—BWM. In the next section, this paper will constructe the evaluation indicator system of travel city selection and scenic spot selection and BWM will be used to evaluate and rank all cities according to the indicator system of city selection. The cities with more high travel value among all cities will be selected as main travel cities. After main travel cities are selected, BWM is used to evaluate and rank each scenic spot in the selected city according to the evaluation indicator system of scenic spots. Then the top scenic spots are selected as core scenic spots and the shortest travel routes of core scenic spots are obtained by genetic algorithm. The selection process of core scenic spots is shown in Fig. 1.

2.2 Evaluation indicator system for main travel cities and core scenic spots

By reading a large number of literatures and inviting several experts in related fields, this paper constructs indicator systems for selecting main travel cities and core scenic spots on the basis of following the construction principles of the indicator system. The construction of the indicator system follows the following principles:

  • The principle of systematicness: the selection of indicators should take into account the overall systematicness of the indicators. Each indicators should be quite different and representative, and the same dimensional information should not appear as much as possible.

  • The principle of operability: when selecting an indicator, it is necessary to consider the difficulty of obtaining the indicator data and whether excessive economic input is needed. The indicators that are easy to obtain, simple to calculate and representative should be selected as much as possible.

  • The principle of dynamic: evaluation indicators are dynamic and will change with social and economic development.

  • The principle of comparability: indicator names and the unification of measurement must conform to relevant international or domestic standards, so as to satisfy the comparison of the same indicators in different periods, or the comparison of different indicators at the same time.

In order to select the main travel cities better, this paper chooses the proportion of tertiary industry (denoted as \(C_1\)), the number of 5A-level scenic spots (denoted as \(C_2\)), the number of 4A-level scenic spots (denoted as \(C_3\)), the number of tourists (denoted as \(C_4\)), and travel revenue (denoted as \(C_5\)) as the evaluation indicators of main travel cities. After the main travel cities are selected, the core scenic spots are selected from each main travel cities. The core scenic spots are selected from the 5A-level scenic spots and 4A-level scenic spots in the selected cities according to the evaluation indicator system of tourist attractions.

The evaluation of tourist attractions is considered from three aspects: environmental factors, service factors and facility factors. The environmental factors include the ecological environment of the scenic spot (denoted as \(I_1\)), the sanitation condition of the scenic spot (denoted as \(I_2\)), and the culture of the scenic spot (denoted as \(I_3\)). The service factors include the maintenance of tourists’ rights and interests (denoted as \(I_4\)), the travel order (denoted as \(I_5\)), and the service attitude of the scenic area staff (denoted as \(I_6\)). Facility factors include scenic traffic conditions (denoted as \(I_7\)), leisure venues (denoted as \(I_8\)), and tour routes (denoted as \(I_9\)). The evaluation indicator system of core scenic spots can be seen in Fig. 1.

Fig. 1
figure 1

Selection process of core scenic spots

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3 Methodology

In this study, BWM is used to determine the indicator weights of main travel cities and core scenic spots. The comprehensive score of each city is obtained by weighting the indicator performance of each city, and the cities with high comprehensive score are selected as the main travel cities of travel route planning. After selecting the main travel cities, BWM is also used to select the core scenic spots in the main travel cities, and then genetic algorithm is used to solve the optimal solution of the travel route planning problem, namely, the shortest distance of the travel route. The steps of BWM and genetic algorithm will be briefly introduced below.

3.1 Selection of main travel cities and core scenic sites by BWM

The best-worst method (BWM) is a new multi-criteria decision-making method which is evolved from AHP method. This method selects the best criterion and the worst criterion from all criteria according to the preference of the decision-maker and compares them with other criteria to get two sets of comparison vectors, then optimizes the modeling to make a decision (Rezaei 2014). Since BWM requires less comparative data and can be combined with other multi-criteria decision-making methods, it has been increasingly applied in the study of practical problems. The specific steps of BWM are as follows:

Step 1. Determine the best criterion and the worst criterion. The best criterion (the most important criterion) and the worst criterion (the least important criterion) are identified in the decision criteria system. The best criterion is denoted as \(C_B\) and the worst criterion is denoted as \(C_W\). In order to reduce the impact of different criterion data dimensions on the evaluation results, Eq. (1) is used to normalize the criterion data.

$$\begin{aligned} r_{ij}=\frac{X_{ij}-X_{\min }}{X_{\max }-X_{\min }}, \end{aligned}$$
(1)

where \(r_{ij}\) the standardized data of criterion i about alternative j; \(X_{ij}\) represents the data of criterion i about alternative j; \(X_{\min }\) represents the minimum value of criterion i and \(X_{\max }\) represents the maximum value of criterion i among all alternatives.

Step 2. Determine the vector (BO, best-to-others) of the best criterion compared to other criteria and the vector (OW,Others-to-Worst) of other criteria compared to the worst criterion. Vector \(\overrightarrow{A_{B}}\) is obtained by pairwise comparison of the best criterion with the others, and vector \(\overrightarrow{A_{W}}\) is obtained by pairwise comparison of the others with the worst criterion.

$$\begin{aligned} \overrightarrow{A_{B}}= & {} (a_{B1},a_{B2},\cdots ,a_{Bn}), \\ \overrightarrow{A_{W}}= & {} (a_{1W},a_{2W},\cdots ,a_{nW}). \end{aligned}$$

Step 3. Evaluate the importance of priority criteria for each cities. A solution model of priority criteria for travel cities is established. The nonlinear model (2) can be used to solve the weights to minimize the maximum absolute deviation between the weight ratio and its corresponding comparison preference value.

$$\begin{aligned} \begin{array}{l} \min \max \{\Vert \frac{w_{B}}{w_{i}}-a_{Bi}\Vert ,\Vert \frac{w_{i}}{w_{W}}-a_{iW}\Vert \} \\ \ s.t.\left\{ \begin{array}{l} \sum \limits _{i=1}^{l} w_{i}=1, \\ w_{i}\ge 0,~\text{ for } \text{ all }~i, \end{array}\right. \end{array} \end{aligned}$$
(2)

where, \(w_{i}\) is the weight of criterion \(C_i\), \(w_{B}\) and \(w_{W}\) are the weight of the most important criterion \(C_B\) and the least important criterion \(C_W\) respectively. And \(a_{Bi}\) is the relative importance of the most important criterion \(C_B\) to other criteria \(C_i\), \(a_{iW}\) is the relative importance of other criteria \(C_i\) to the least important criterion \(C_W\). Let \(\xi\) represents the maximum absolute deviation, then model (2) is equivalent to model (3):

$$\begin{aligned} \begin{array}{l} \min \xi \\ \ s.t.\left\{ \begin{array}{l} \Vert \frac{w_{B}}{w_{i}}-a_{Bi}\Vert \le \xi ,~\text{ for } \text{ all }~i, \\ \Vert \frac{w_{i}}{w_{W}}-a_{iW}\Vert \le \xi ,~\text{ for } \text{ all }~i, \\ {\mathop {\sum }\limits _{i=1}^{n}}{w_{i}=1}, \\ w_{i}\ge 0,~\text{ for } \text{ all }~i. \end{array}\right. \end{array} \end{aligned}$$
(3)

By solving model (3), the optimal weights \((w_1,w_2,\cdots ,w_n)\) and the maximum absolute deviation value \(\xi\) were obtained. The consistency ratio can be calculate by Eq. (4):

$$\begin{aligned} \text{ Consistency } \text{ ratio }~CR=\frac{\xi }{\text{ Consistency } \text{ indicator }~CI}. \end{aligned}$$
(4)

Table 1 lists the corresponding values of consistency indicators.

Table 1 The consistency indicator value
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Obviously, the consistency ratio \(CR\in [0,1]\). The closer the consistency ratio is to 0, the higher the consistency is; the closer it is to 1, the lower the consistency is. Since the original model is a non-linear model that may lead to multiple optimal solutions, the following linear model is proposed. The nonlinear BWM model (2) can be transformed into a linear model (5) in the following ways:

$$\begin{aligned} \begin{array}{l} \min \max \{\Vert w_{B}-a_{Bi}{w_{i}}\Vert ,\Vert {w_{i}}-a_{iW}{w_{W}}\Vert \} \\ \ s.t.\left\{ \begin{array}{l} \sum \limits _{i=1}^{n}{w_{i}=1,} \\ w_{i}\ge 0,~\text{ for } \text{ all }~i. \end{array}\right. \end{array} \end{aligned}$$
(5)

Model (3) can be further transformed into the following model (6):

$$\begin{aligned} \begin{array}{l} \min \xi ^{*} \\ \ s.t.\left\{ \begin{array}{l} \Vert {w_{B}}-a_{Bi}{w_{i}}\Vert \le \xi ^{*},~\text{ for } \text{ all }~i, \\ \Vert {w_{i}}-a_{iW}{w_{W}}\Vert \le \xi ^{*},~\text{ for } \text{ all }~i, \\ {\mathop {\sum }\limits _{i=1}^{n}w_{i}=1}, \\ w_{i}\ge 0,~\text{ for } \text{ all }~i. \end{array}\right. \end{array} \end{aligned}$$
(6)

After solving the model (6), the optimal weights \(\overrightarrow{w}=(w_1,w_2,\cdots ,w_n)^{T}\) and \(\xi ^{*}\) can be obtained. For this linear model, it can be directly regarded as an indicator to measure and judge the consistency relationship. The closer the value of is to 0, the higher the consistency degree is. From this, the weight of each criterion (i.e. indicator weight) can be obtained. By aggregating the weighted indicator performance of each city and scenic spot, the comprehensive score of the city and scenic spot can be obtained. This paper plans travel routes for cities and scenic spots with high comprehensive scores.

3.2 Genetic algorithm for travel route planning

In this section, genetic algorithm is introduced briefly. Genetic algorithm was first proposed by John Holland in 1970s (Katoch et al. 2021). The essence of genetic algorithm is the rule of “survival of the fittest” in the biological world (Scrucca 2013). By simulating the inheritance, crossover, and mutation of chromosomes in biological evolution, the best genes are screened and inferior genes are discarded. Corresponding to mathematical problems, it is the process of finding the optimal solution. The basic idea of genetic algorithm to solve the problem is: to encode genes through certain rules, express the optimization target in the form of fitness function, then use the selection operator, crossover operator, and mutation operator in the genetic algorithm to simulate the biological genetic evolution rules to seek the most optimal solution. Firstly, a certain number of solutions that meet the requirements of the problem are randomly generated, and individuals are compiled through coding operations to form the initial population. Individuals in the population have their own fitness, and the individuals with higher fitness value are selected to be retained. Then, the new population is formed by crossing and mutating simulated by different preset rules. The above process is repeated until it converges to the one with the highest fitness, and then the solution of the problem is decoded. The process of solving the shortest route by genetic algorithm is shown in Fig. 2. The specific steps of the genetic algorithm in solving the travel route planning problem are as follows:

Fig. 2
figure 2

The process of solving the shortest route by genetic algorithm

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Step 1. Define the objective function. In the optimization of travel routes, the shortest path of the travel route is the main consideration. Therefore, this paper takes the shortest distance sum as the objective function to carry out the travel route planning, and the distance between scenic spots is represented by straight-line distance. The distance between two scenic spots can be obtained according to the relative coordinate value of each scenic spot and Eq. (7).

$$\begin{aligned} D=\sum ^{n}_{p=1}D_{pq}=\sqrt{(x_{p}-x_{q})^{2}+(y_{p}-y_{q})^{2}}, \end{aligned}$$
(7)

where D represents the total distance of all core scenic spots. \(D_{pq}\) represents the distance between two scenic spots p and q and \((x_{p},y_{p}),(x_{q},y_{q})\) represents the relative coordinates of scenic spots p and q.

Step 2. Gene coding. The common coding types of genetic algorithm include binary coding, decimal coding, symbol coding, etc. This paper chooses the symbol coding method. Symbol coding is to assign a label to each scenic spot. The label has no sequential meaning only the function of marking. When these labels representing core travel scenic spots are randomly arranged, it represents the generation of a complete travel route. And a complete travel route randomly arranged is called a chromosome. Chromosomes containing 10 scenic spots and the process of chromosomes exchange and mutation is shown in Fig. 3.

Fig. 3
figure 3

The process of chromosomes exchange and mutation in genetic algorithm

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Step 3. Construct the fitness function. Generally, the fitness function is considered to be larger, the better. The shortest distance sum is chose as the objective function, which is seeking the minimum total distance of travel routes. Therefore, the reciprocal of the total distance of the travel route is taken as fitness function, and the chromosome with higher fitness is closer to the final optimal solution. The objective function and fitness function are constructed from the shortest distance variable. The fitness function can be is constructed as follows:

$$\begin{aligned} F=\frac{1}{\sum \limits ^{n}_{p=1}D_{pq}}. \end{aligned}$$
(8)

Step 4. Initialize population. A certain number of individuals are randomly generated to form the initial population, with one chromosome as one individual. Generally, the initial population size should not be too large or too small. An initial population of 30–100 individuals is reasonable.

Step 5. Selection operator. The first step of genetic algorithm evolution is selection, which represents the selection of high-quality chromosomes from the initial population. There are many selection operators methods in gene algorithms, among which Roulette wheel Selection is the simplest and most commonly used selection method. The essence of this method is to determine the probability of selecting the chromosome according to the fitness of each chromosome in the population. The larger the fitness value, the more likely the chromosome will be selected. In addition, the selection method of roulette algorithm is widely used in the travel salesman problem, so this paper adopts roulette wheel selection algorithm to select chromosomes. The calculation formula of probability is as follows:

$$\begin{aligned} P=\frac{F(p)}{\sum \limits ^{m}_{i=1}F(p)}, \end{aligned}$$
(9)

where P represents the probability of chromosome selection and m represents the number of initial populations.

Step 6. Crossover operator. Genetic algorithm maintains the diversity of the population through crossover operators. The chromosomes selected in Step 5 are crossed to generate offspring chromosomes. Crossover operators include single point crossover, multi-point crossover, sequential crossover, etc. An improved sequential crossover method is chose in this paper, whose crossover principle is as follows. Suppose that there are two parental chromosomes \(A= 8,3,5,1,4,9,2,10,7,6\) and \(B = 5,7,3,9,2,6,1,4,8,10\). Two positions a and b are randomly selected, such as \(a=3\) and \(b=6\). The genes at positions \(3-6\) on chromosome A are copied to the front of chromosome B and the gene at position \(3-6\) on chromosome B is copied to the front of chromosome A. At this time, chromosome A becomes chromosome \(A^*= 3,9,2,6,8,3,5,1,4,9,2,10,7,6\) after crossing; chromosome B becomes chromosome \(B^* = 5,1,4,9,5,7,3,9,2,6,1,4,8,10\). Each scenic spot can only pass through once in the travel route planning problem, therefore the chromosomes after crossing need to go through conflict detection to delete the duplicate genes. When deleting the duplicate genes, the former should be retained and the latter deleted. Finally, the sequence of offspring chromosome gene after cross and conflict detection are \(A=3,9,2,6,8,5,1,4,10,7\) and \(B = 5,1,4,9,7,3,2,6,8,10\).

Step 7. Mutation operator. Genetic mutation can occur during the evolution of a population, and genetic mutations are possible but usually occur at a low rate. Mutation operator refers to the replacement of the gene value at some loci in the coding string of individual chromosome with other alleles of that loci to form a new individual, mutation operator is applied to the offspring produced by selection and crossover operation. The common mutation operator has a reversal mutation, exchange mutation, inversion mutation. Exchange mutation is selected to carry out mutation operation on chromosomes in this paper. Exchange mutation works by exchanging genes from two randomly selected locations on a chromosome. For example, if two locations \(a=4\) and \(b=8\) are randomly selected in the chromosome \(A=8,3,5,1,4,9,2,10,7,6\), the exchange mutation is carried out and then the new chromosome is \(A^*=8,3,5,10,4,9,2,1,7,6\).

Step 8. Iteration and end. After selection, crossover and mutation, the initial population will generate new offspring population. In order to ensure that the population will not always expand, the individuals with lower fitness in the initial population and offspring species group will be eliminated after each iteration to keep the population size constant. After completion of the elimination work, the new population will become the parent population again through selection, exchange, mutation operation, again to produce the offspring population, and so on. The number of iterations of the genetic algorithm is generally set to \(200-2000\). The final result is printed when the iteration is complete.

4 Case study

4.1 Case description

This paper takes Hubei Province, China as the study area, which is shown in Fig. 4. Firstly, the main travel cities and the core scenic spots in Hubei Province are selected by BWM. After selecting the core scenic spots, genetic algorithm is used to carry out travel route planning for the selected scenic spots to obtain the minimum distance route.

Fig. 4
figure 4

The map of the geographical location of the study area

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Hubei Province is located in the middle reaches of the Yangtze River, bordering Anhui and Jiangxi in the east, Henan and Shanxi in the north, Chongqing in the west, and Hunan in the south, which provide a unique geographical advantage for the development of travel in Hubei Province. Hubei Province consists of 13 prefecture-level administrative regions and 4 county-level administrative regions under the direct jurisdiction of the province, including Wuhan (WH), Huangshi (HS), Shiyan (SY), Yichang (YC), Xiangyang (XY), Ezhou (EZ), Jingmen (JM), Xiaogan (XG), Jingzhou (JZ), Huanggang (HG), Xianning (XN), Suizhou (SZ), Enshi (ES), Xiantao (XT), Qianjiang (QJ), Tianmen (TM) and Shennongjia (SNJ). Hubei Province has 16 5A-level scenic spots and 157 4A-level scenic spots. According to statistics, the total travel revenue of Hubei Province in 2020 is 437.949 billion CNY, receiving 437.296 million domestic and foreign tourists. From the perspective of travel resources, Hubei Province has virgin forests, natural rock caves, ground crevices and canyons, as well as Wudang Taiji, historical buildings, and culture. The good natural resources and abundant human resources have laid a solid foundation for the development of travel in Hubei’s travel industry.

4.2 Data collection and processing

In this case study, the data of travel city indicator is from the statistical yearbook of Hubei Province (Hubei Statistical Yearbook 2021), Hubei Provincial Department of Culture and travel (Hubei Provincial Department of Culture and Tourism (2021) and statistical yearbook of various cities. The indicator data of 5A-level and 4A-level scenic spots of selected cities can be obtained through network questionnaire survey and expert scoring method. The comprehensive score of each scenic spot is obtained by BWM, and the scenic spots with high comprehensive score are selected. Then, the latitude and longitude coordinates of scenic spots are obtained through Baidu map picking coordinate system, and the latitude and longitude coordinate system is transformed into a coordinate system in kilometers in ArcGIS (Table 2).

Table 2 The standardized indicator data of each region
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4.3 Interpretation of results

After obtaining the travel indicator data of each city, the comprehensive evaluation of each city is carried out by BWM. The indicator data and comprehensive score in travel city selection is shown in Table 2, which shows the comprehensive score and ranking of each city. The top six cities are selected as main travel cities in this paper, WH, YC, ES, SY, HG, and XN namely. The core scenic spots of each tourist city are selected by the same way. The selected core scenic spots include Wuchang Shouyi Cultural Tourist Area (\(A_1\)), Yellow Crane Tower (\(A_2\)), East Lake Scenic Area of Wuhan (\(A_3\)), Mulan Ecological Cultural Travel Zone (\(A_4\)), Three Gorges Dam (\(A_5\)), Qu Yuan’s hometown (\(A_6\)), People scenic Three Gorges (\(A_7\)), Qingjiang Gallery Scenic Area (\(A_8\)), Xiling Gorge Scenic Area (\(A_9\)), Three Gorges Bamboo Sea Scenic Area (\(A_{10}\)), Mingfeng Mountain Scenic Spot (\(A_{11}\)), Chaotianhou Rafting Scenic Spot (\(A_{12}\)), Wudang Mountains (\(A_{13}\)), Chibi Ancient Battlefield Scenic Spot (\(A_{14}\)), Shennongxi Scenic Area (\(A_{15}\)), Enshi Grand Canyon (\(A_{16}\)), Tenglong Cave Scenic Spot (\(A_{17}\)), Sanjiang Forest Travel Area (\(A_{18}\)), Jiugong Mountain (\(A_{19}\)), Wuyun Mountain Ecological Travel Scenic Spot (\(A_{20}\)), Triangle Mountain Scenic Area (\(A_{21}\)), Saiwudang Scenic Area (\(A_{22}\)), Wulong River Scenic Area (\(A_{23}\)), Nuwa Mountain Scenic Area (\(A_{24}\)). The grade information and location information of core scenic spots are shown in Table 3.

Table 3 The location coordinates of the core scenic spots
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After this case study runs genetic algorithm for 30 times, the shortest route obtained is as follows: \(A_{20}\) Wuyun Mountain Ecological Travel Scenic Spot—\(A_{21}\) Triangle Mountain Scenic Area—\(A_{4}\) Mulan Ecological Cultural Travel Zone—\(A_{2}\) Yellow Crane Tower—\(A_{1}\) Wuchang Shouyi Cultural Tourist Area—\(A_{3}\) East Lake Scenic Area of Wuhan—\(A_{19}\) Jiugong Mountain—\(A_{18}\) Sanjiang Forest Travel Area—\(A_{14}\) Chibi Ancient Battlefield Scenic Spot—\(A_{11}\) Mingfeng Mountain Scenic Spot—\(A_{9}\) Xiling Gorge Scenic Area—\(A_{8}\) Qingjiang Gallery Scenic Area—\(A_{7}\) People scenic Three Gorges—\(A_{5}\) Three Gorges Dam—\(A_{6}\) Qu Yuan’s hometown—\(A_{10}\) Three Gorges Bamboo Sea Scenic Area—\(A_{12}\) Chaotianhou Rafting Scenic Spot—\(A_{13}\) Wudang Mountains—\(A_{22}\) Saiwudang Scenic Area—\(A_{23}\) Wulong River Scenic Area—\(A_{24}\) Nuwa Mountain Scenic Area—\(A_{15}\) Shennongxi Scenic Area—\(A_{16}\) Enshi Grand Canyon—\(A_{17}\) Tenglong Cave Scenic Spot. The minimum total distance is 1355.72 km. According to the operation results, the travel route map of the minimum total distance of core scenic spots in Hubei Province is drew as shown in Fig. 5.

Fig. 5
figure 5

The map of minimum total distance of core scenic spots in Hubei Province

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4.4 Rationality analysis

In this travel route planning case, it is verified whether the required route is the shortest route by planning the scenic spots in YC. If the scenic spot route in YC is \(A_{11}\) Mingfeng Mountain Scenic Spot—\(A_9\) Xiling Gorge Scenic Area—\(A_8\) Qingjiang Gallery Scenic Area—\(A_7\) People scenic Three Gorges—\(A_5\) Three Gorges Dam—\(A_6\) Qu Yuan’s hometown—\(A_{10}\) Three Gorges Bamboo Sea Scenic Area—\(A_{12}\) Chaotianhou Rafting Scenic Spot, then the distance of this route is 193.38 km. If the scenic spot route in YC is \(A_{11}\) Mingfeng Mountain Scenic Spot—\(A_9\) Xiling Gorge Scenic Area—\(A_7\) People scenic Three Gorges—\(A_8\) Qingjiang Gallery Scenic Area—\(A_5\) Three Gorges Dam—\(A_{10}\) Three Gorges Bamboo Sea Scenic Area—\(A_6\) Qu Yuan’s hometown—\(A_{12}\) Chaotianhou Rafting Scenic Spot, then the distance of this route is 197.12 km. The former is the shortest route sought by the genetic algorithm. In addition, different starting points will also cause different distances. When the travel route is \(A_{23}\) Wulong River Scenic Area—\(A_{22}\) Saiwudang Scenic Area—\(A_{13}\) Wudang Mountains—\(A_{24}\) Nuwa Mountain Scenic Area—\(A_{17}\) Tenglong Cave Scenic Spot—\(A_{16}\) Enshi Grand Canyon—\(A_{15}\) Shennongxi Scenic Area—\(A_{12}\) Chaotianhou Rafting Scenic Spot—\(A_{6}\) Qu Yuan’s hometown—\(A_{5}\) Three Gorges Dam—\(A_{10}\) Three Gorges Bamboo Sea Scenic Area—\(A_{8}\) Qingjiang Gallery Scenic Area—\(A_{7}\) People scenic Three Gorges—\(A_{9}\) Xiling Gorge Scenic Area—\(A_{11}\) Mingfeng Mountain Scenic Spot—\(A_{14}\) Chibi Ancient Battlefield Scenic—\(A_{19}\) Jiugong Mountain—\(A_{18}\) Sanjiang Forest Travel Area Spot—\(A_{2}\) Yellow Crane Tower—\(A_{1}\) Wuchang Shouyi Cultural Travel Area—\(A_{3}\) East Lake Scenic Area of Wuhan—\(A_{20}\) Wuyun Mountain Ecological Travel Scenic Spot—\(A_{21}\) Triangle Mountain Scenic Area—\(A_{4}\) Mulan Ecological Cultural Travel Zone, the total distance is 1476.99 km, which is greater than the shortest distance. Therefore, this comparison verifies the rationality of the route sought by the genetic algorithm.

4.5 Comparison analysis

In the previous study of travel route planning, most studies selected directly travel attractions and then used algorithms for route planning, without evaluating the travel value of cities to select several cities as the main travel cities and evaluating core attractions. Therefore, this paper will select directly tourist attractions and then use genetic algorithm to carry out travel route planning for the study case to set up a control experiment. In order to reduce the influence of subjective factors, this paper randomly selects 24 scenic spots from 5A-level scenic spots and 4A-level scenic spots in Hubei Province as the scenic spots of the control group: Happy Valley Of Wuhan \((A_{1}^{'})\), Jiuzhen Mountain Scenic Area \((A_{2}^{'})\), Wudaoxia Scenic Area \((A_{3}^{'})\), Zaoyang Hancheng Scenic Spot \((A_{4}^{'})\), Shipai Fortress Tourist Area \((A_{5}^{'})\), Chaotianhou Rafting Scenic Spot \((A_{6}^{'})\), Wuling Gorge Ecological Tourism Zone \((A_{7}^{'})\), Shiyan City Museum \((A_{8}^{'})\), Shangjin Cultural Tourism Zone \((A_{9}^{'})\), Songzi Gushui Tourist Area \((A_{10}^{'})\), Pengdun Rural World Tourist Attraction \((A_{11}^{'})\), Guanyin Lake Tourist Resort \((A_{12}^{'})\), Jinhui Manor Scenic Spot \((A_{13}^{'})\), Eighteen Pools Scenic Spot \((A_{14}^{'})\), Jute Uprising Memorial hall \((A_{15}^{'})\), Dabie Mountain South Wudang Tourist Area \((A_{16}^{'})\), Huanggang Wuyun Mountain Ecological Tourism Scenic Spot \((A_{17}^{'})\), Wuzu Temple Scenic Spot \((A_{18}^{'})\), Mountain Lake Hot Spring Scenic Spot \((A_{19}^{'})\), Dahongshan Scenic Spot in Suizhou City \((A_{20}^{'})\), Tenglong Cave Scenic Spot \((A_{21}^{'})\), Xuanen Wujiatai Country Leisure Resort \((A_{22}^{'})\), Xiantao Mengli Water Town Cultural Tourism Zone \((A_{23}^{'})\), Shennongjia Tianyan Scenic Spot \((A_{24}^{'})\).

After 30 runs of the genetic algorithm, the shortest path of the tourist route can be obtained as follows: \((A_{18}^{'})\) Wuzu Temple Scenic Spot—\((A_{17}^{'})\) Huanggang Wuyun Mountain Ecological Tourism Scenic Spot—\((A_{16}^{'})\) Dabie Mountain South Wudang Tourist Area—\((A_{15}^{'})\) Jute Uprising Memorial hall—\((A_{14}^{'})\) Eighteen Pools Scenic Spot—\((A_{13}^{'})\) Jinhui Manor Scenic Spot—\((A_{12}^{'})\) Guanyin Lake Tourist Resort—\((A_{1}^{'})\) Happy Valley Of Wuhan—\((A_{2}^{'})\) Jiuzhen Mountain Scenic Area—\((A_{19}^{'})\) Mountain Lake Hot Spring Scenic Spot—\((A_{23}^{'})\) Xiantao Mengli Water Town Cultural Tourism Zone—\((A_{11}^{'})\) Pengdun Rural World Tourist Attraction—\((A_{20}^{'})\) Dahongshan Scenic Spot in Suizhou City—\((A_{4}^{'})\) Zaoyang Hancheng Scenic Spot—\((A_{7}^{'})\) Wuling Gorge Ecological Tourism Zone—\((A_{8}^{'})\) Shiyan City Museum—\((A_{3}^{'})\) Wudaoxia Scenic Area—\((A_{24}^{'})\) Shennongjia Tianyan Scenic Spot—\((A_{9}^{'})\) Shangjin Cultural Tourism Zone—\((A_{6}^{'})\) Chaotianhou Rafting Scenic Spot—\((A_{5}^{'})\) Shipai Fortress Tourist Area—\((A_{22}^{'})\) Xuanen Wujiatai Country Leisure Resort—\((A_{21}^{'})\) Tenglong Cave Scenic Spot—\((A_{10}^{'})\) Songzi Gushui Tourist Area. The total length of the shortest path of the travel route is 1650.69 km, which is 294.97 km longer than the total distance of the shortest route obtained by the method proposed in this paper. It can be seen that the selection of major travel cities and core scenic spots before travel routes planning can reduce the travel distance and obtain greater travel value.

5 Conclusions

Traveling is one of the most popular ways of leisure for adults and children nowadays. This paper mainly solved two problems that people will encounter in the actual travel process:

  1. (1)

    How to screen out main cities and core scenic spots with high travel value among many alternatives.

  2. (2)

    How to plan travel routes to reduce travel costs and improve travel efficiency during the journey.

For these two problems, the solutions given in this paper are as follows:

  1. (1)

    Based on the core scenic spots travel routes distance optimization problem the indicator system of choosing the main travel cities and the core scenic spots was constructed and BWM was used to rank the travel priorities of the candidate cities and scenic spots, and the cities and scenic spots with the highest travel priority would be selected.

  2. (2)

    Genetic algorithm was used to plan the travel route for core scenic spots selected by the BWM and obtain the shortest travel route.

Subsequently, this paper applies the proposed solution to a travel case in Hubei Province, China. A total of 6 main cities and 24 core scenic spots were selected from many cities and scenic spots in Hubei Province. And the total distance of the optimal travel route was 1355.72 km by genetic algorithm. The research in this paper can promote the theoretical research of BWM and genetic algorithm, and can also provide reference for people to make actual travel plans.

The case study shows that BWM can select the most tourist-worthy cities and scenic spots among many cities and scenic spots and can plan the shortest route of the selected scenic spots in combination with the genetic algorithm. For cities ranking lower in the evaluation results, some scenic spots in the lower ranking cities cannot be selected eventually that may have very high travel value. Therefore, local optimization exists in the evaluation results, which will be further studied in the future.