Research on Cooperative Resource Management of Rural Tourism Attractions Combining Multi-objective Optimization and Data Mining

Determination of system variables

In this paper, two indicators of GDP and total population are selected as state variables, and GDP growth and population growth are selected as rate variables. In addition, auxiliary variables such as the output value of rural tourism industry and the employed population in the tourism industry are selected.

System structure division (1)

Tourism economic subsystem

The economy in the process of tourism development directly determines the industrial development of rural tourist attractions, and the improvement of economic efficiency can play a role in promoting the development of rural tourist attractions, which can be said to be the forecast table for observing the development of tourism. The tourism economic subsystem mainly includes tourism revenue, per capita ticket and service consumption, tourism development guidance funds, and various investments, as well as other factors.

Resource space subsystem

Resource spatial carrying capacity characterizes the increase in the number of tourists for the scenic area originally provided by the shortage of land area. The purpose of studying the resource space subsystem is to determine a standard of tourist density, to control the number of tourists that can be accommodated in the limited scenic area within a reasonable range, to reduce the tourist load in the scenic area by increasing the area of rural tourism scenic area, and to improve the spatial carrying capacity of scenic area resources as well as to provide comfortable spatial environment for the tourists’ viewing activities. The resource space subsystem mainly includes the total area of scenic area development, the area of scenic area under development, the number of tourists received by the scenic area, the density of scenic area tourists and the scenic area tourists’ load and other factors.

Natural environment subsystem

The carrying capacity of the natural environment characterizes the impact and environmental damage caused by garbage production and sewage discharge during the progress of tourism activities. The purpose of studying the natural environment subsystem is to strictly control the environmental pollution and resource destruction within a certain range, reduce the environmental waste load of rural tourist attractions by controlling the amount of pollution, improve the environmental carrying capacity of scenic spots, and provide a guarantee for ecological tourism. The natural environment subsystem mainly includes factors such as pollution levels, pollution emission and treatment, pollution per unit area, and environmental garbage accumulation in scenic areas.

Maximization of rural residents’ employment rate objective

Maximization of employment rate of rural residents refers to the maximum proportion of tourism employment driven by domestic tourists and overseas tourists in rural tourism environment to the total population of rural tourist attractions. It is expressed as: (2)maxz2=c3*(x1+x2)x3$$\max {z_2} = \frac{{{c_3}*\left( {{x_1} + {x_2}} \right)}}{{{x_3}}}$$

Equation (2) in z₂ for the employment rate of rural residents, c₃ per unit of tourists driven by the number of rural residents in the number of employment increases (people), x₃ for the number of residents of rural tourist attractions.

Maximize the target of the number of subjects of tourism environment capacity

The target of maximizing the number of subjects of the tourism environment capacity refers to the maximum number of subjects accommodated by the population in the tourism environment, where the population mainly includes domestic tourists, overseas tourists and residents of rural tourist attractions. Namely: (3)maxz3=x1+x2+x3$$\max {z_3} = {x_1} + {x_2} + {x_3}$$

In equation (3), z₃ represents the number of subjects of tourism environmental capacity, and x₃ is the number of residents of rural tourist attractions.

The constraints of characteristic tourism resource indicators: (6)a21λ21x1+a22λ22x2+a23λ23≤Totalurbanspace(Di)×[ei+θi(1−ei)]×hi$$\frac{{{a_{21}}}}{{{\lambda _{21}}}}{x_1} + \frac{{{a_{22}}}}{{{\lambda _{22}}}}{x_2} + \frac{{{a_{23}}}}{{{\lambda _{23}}}} \le Total{\text{ }}urban{\text{ }}space\left( {{D_i}} \right) \times \left[ {{e_i} + {\theta _i}\left( {1 - {e_i}} \right)} \right] \times {h_i}$$

Eq. (6) in a₂₁, a₂₂, a₂₃ in turn for domestic tourists, overseas tourists and rural residents in the corresponding satisfaction of the average per person total space use standards.

Constraints on water supply capacity indicators: (7)a31*t1λ31x1+a32*t2λ32x2+a33*t3λ33 ≤Annualwatersupply(Di)×[ei+θi(1−ei)]$$\begin{array}{l} \frac{{{a_{31}}*{t_1}}}{{{\lambda _{31}}}}{x_1} + \frac{{{a_{32}}*{t_2}}}{{{\lambda _{32}}}}{x_2} + \frac{{{a_{33}}*{t_3}}}{{{\lambda _{33}}}} \\ \le Annual{\text{ }}water{\text{ }}\sup ply\left( {{D_i}} \right) \times \left[ {{e_i} + {\theta _i}\left( {1 - {e_i}} \right)} \right] \\ \end{array}$$

Equation (7) in a₃₁, a₃₂, a₃₃ in turn for domestic tourists, overseas tourists and rural residents in the corresponding satisfaction of the average daily water consumption per person, t₁, t₂, t₃ in turn for domestic tourists, overseas tourists and rural residents in the average number of days of stay, the annual water supply (Di)$$\left( {{D_i}} \right)$$ does not exist in the turnover of the statement, so the constraints in the h_i also have to be adjusted.

Constraints for indicators in the waste disposal category: (8)a41*t1λ41x1+a42*t2λ42x2+a43*t3λ43 ≤Annualgarbageremoval(Di) ×[ei+θi(1−ei)]$$\begin{array}{l} \frac{{{a_{41}}*{t_1}}}{{{\lambda _{41}}}}{x_1} + \frac{{{a_{42}}*{t_2}}}{{{\lambda _{42}}}}{x_2} + \frac{{{a_{43}}*{t_3}}}{{{\lambda _{43}}}} \\ \le Annual{\text{ }}garbage{\text{ }}removal\left( {{D_i}} \right) \\ \times \left[ {{e_i} + {\theta _i}\left( {1 - {e_i}} \right)} \right] \\ \end{array}$$

Eq. (8) in a₄₁, a₄₂, a₄₃ is the average daily production of garbage per person under the corresponding satisfaction of domestic tourists, overseas tourists and rural residents in turn, and the annual garbage removal volume (Di)$$\left( {{D_i}} \right)$$ does not exist in the turnover of the statement, so the constraints in the h_i should also be adjusted.

Constraints of social environment sustainable carrying indicators (1)

The constraints of the indicator of the degree of tourism staffing in place: (9)a61λ61x1+a62λ62x2+a63λ63 ≤Numberofpeopleworkingintourism (Di)×Numberofdaysperyear[ei+θi(1−ei)]×hi$$\begin{array}{l} \frac{{{a_{61}}}}{{{\lambda _{61}}}}{x_1} + \frac{{{a_{62}}}}{{{\lambda _{62}}}}{x_2} + \frac{{{a_{63}}}}{{{\lambda _{63}}}} \\ \le Number{\text{ }}of{\text{ }}people{\text{ }}working{\text{ }}in{\text{ }}tourism \\ \left( {{D_i}} \right) \times Number{\text{ }}of{\text{ }}days{\text{ }}per{\text{ }}year\left[ {{e_i} + {\theta _i}\left( {1 - {e_i}} \right)} \right] \times {h_i} \\ \end{array}$$

In equation (9), a₅₁, a₅₂ and a₅₃ are the number of times that domestic tourists, overseas tourists and rural residents demand the services of tourism employees per person under the corresponding satisfaction level.

The constraints of the tourism residence ratio indicator: (10)Hi*95%≤x1+x2x3≤Hj*105%$${H_i}*95\% \le \frac{{{x_1} + {x_2}}}{{{x_3}}} \le {H_j}*105\%$$

In Eq. (10), H_i represents the minimum value of the roaming ratio within the statistical years, and H_j represents the maximum value of the roaming ratio within the statistical years.

Constraints of economic and environmental sustainability indicators (1)

Constraints of road area indicators: (11)a71λ71x1+a72λ72x2+a73λ73 ≤Totalareaofurbanroads(Di) ×[ei+θi(1−ei)]×hi$$\begin{array}{l} \frac{{{a_{71}}}}{{{\lambda _{71}}}}{x_1} + \frac{{{a_{72}}}}{{{\lambda _{72}}}}{x_2} + \frac{{{a_{73}}}}{{{\lambda _{73}}}} \\ \le Total{\text{ }}area{\text{ }}of{\text{ }}urban{\text{ }}roads\left( {{D_i}} \right) \\ \times \left[ {{e_i} + {\theta _i}\left( {1 - {e_i}} \right)} \right] \times {h_i} \\ \end{array}$$

In equation (11), a₇₁, a₇₂ and a₇₃ are the road area occupied by domestic tourists, overseas tourists and rural residents per person under the corresponding satisfaction level.

The constraints of catering supply capacity indicators: (12)a81λ81x1+a82λ82x2+a83λ83x3 ≤Numberofmealsservedperyearincities (Di)×[ei+θi(1−ei)]×hi(5.12)$$\begin{array}{l} \frac{{{a_{81}}}}{{{\lambda _{81}}}}{x_1} + \frac{{{a_{82}}}}{{{\lambda _{82}}}}{x_2} + \frac{{{a_{83}}}}{{{\lambda _{83}}}}{x_3} \\ \le Number{\text{ }}of{\text{ }}meals{\text{ }}served{\text{ }}per{\text{ }}year{\text{ }}in{\text{ }}cities \\ \left( {{D_i}} \right) \times \left[ {{e_i} + {\theta _i}\left( {1 - {e_i}} \right)} \right] \times {h_i}(5.12) \\ \end{array}$$

In equation (12), a₈₁, a₈₂ and a₈₃ are the number of meals per person for domestic tourists, overseas tourists and rural residents under the corresponding satisfaction level.

Constraints on accommodation supply capacity indicators: (13)a91λ91x1+a92λ92x2+a93λ93x3 ≤Numberofbedsinurbanaccommodation (D11)[ei+θ11×(1−ei)]×hi$$\begin{array}{l} \frac{{{a_{91}}}}{{{\lambda _{91}}}}{x_1} + \frac{{{a_{92}}}}{{{\lambda _{92}}}}{x_2} + \frac{{{a_{93}}}}{{{\lambda _{93}}}}{x_3} \\ \le Number{\text{ }}of{\text{ }}beds{\text{ }}in{\text{ }}urban{\text{ }}accom\bmod ation \\ \left( {{D_{11}}} \right)\left[ {{e_i} + {\theta _{11}} \times \left( {1 - {e_i}} \right)} \right] \times {h_i} \\ \end{array}$$

In equation (13), a₉₁, a₉₂ and a₉₃ are the average number of times that domestic tourists, overseas tourists and rural residents use the accommodation facilities of rural tourist attractions under the corresponding satisfaction.

Constraints on transportation supply capacity indicators: (14)a101λ101x1*K1+a102λ102x2*K2+a103λ103x3*K3 ≤Numberofmeansoftransportation(D12) ×[ei+θ12(1−ei)]×hi$$\begin{array}{l} \frac{{{a_{101}}}}{{{\lambda _{101}}}}{x_1}*{K_1} + \frac{{{a_{102}}}}{{{\lambda _{102}}}}{x_2}*{K_2} + \frac{{{a_{103}}}}{{{\lambda _{103}}}}{x_3}*{K_3} \\ \le Number{\text{ }}of{\text{ }}means{\text{ }}of{\text{ }}transportation\left( {{D_{12}}} \right) \\ \times \left[ {{e_i} + {\theta _{12}}\left( {1 - {e_i}} \right)} \right] \times {h_i} \\ \end{array}$$

In equation (14), a₁₀₁, a₁₀₂ and a₁₀₃ are the average amount of transportation applicable to domestic tourists, overseas tourists and rural residents in the corresponding satisfaction level, and K₁, K₂ and K₃ are the percentages of domestic tourists, overseas tourists and rural residents who take this mode of transportation in that order.

Constraints on health care service facility indicators: (15)a111*t1λ111x1+a112*t2λ112x2+a113*t3λ113x3 ≤Numberofurbanhealthcarebeds(D14) ×[ei+θ14(1−ei)]×hi$$\begin{array}{l} \frac{{{a_{111}}*{t_1}}}{{{\lambda _{111}}}}{x_1} + \frac{{{a_{112}}*{t_2}}}{{{\lambda _{112}}}}{x_2} + \frac{{{a_{113}}*{t_3}}}{{{\lambda _{113}}}}{x_3} \\ \le Number{\text{ }}of{\text{ }}urban{\text{ }}healthcare{\text{ }}beds\left( {{D_{14}}} \right) \\ \times \left[ {{e_i} + {\theta _{14}}\left( {1 - {e_i}} \right)} \right] \times {h_i} \\ \end{array}$$

Eq. (15) in a₁₁₁, a₁₁₂, a₁₁₃ in turn for domestic tourists, overseas tourists and rural residents in the corresponding satisfaction per person per day bed use.

Constraints for tourists and residents of rural tourist attractions (1)

Constraints for domestic tourists: (16)minx1*(1−S1)≤x1≤maxx1*(1+S1)$$\min {x_1}*\left( {1 - {S_1}} \right) \le {x_1} \le \max {x_1}*\left( {1 + {S_1}} \right)$$

In equation (16), S₁ is the floating value of the number of domestic tourists.

Constraints on overseas tourists: (17)minx2*(1−S2)≤x2≤max2*(1+S2)$$\min {x_2}*\left( {1 - {S_2}} \right) \le {x_2} \le {\max _2}*\left( {1 + {S_2}} \right)$$

S₂ in equation (17) is the floating value of the number of overseas tourists.

Constraints on rural residents: (18)minx3*(1−S1)≤x3≤max3*(1+S1)$$\min {x_3}*\left( {1 - {S_1}} \right) \le {x_3} \le {\max _3}*\left( {1 + {S_1}} \right)$$

In equation (18), S₃ is the floating value of the number of urban residents.

Evaluate fitness: evaluate the fitness of each individual and calculate its objective function value.

Fast non-dominated sorting: non-dominated sorting is performed on the individuals in the population, and the individuals are divided into different ranks, i.e. non-dominated tiers. The lower the non-dominated tier, the better the individual.

Calculation of crowding distance: Crowding distance is calculated for each non-dominated tier. The crowding degree value is used to measure the distance and distribution between individuals to maintain diversity on the frontier.

Selection operation: High-quality individuals are selected from the current population by using the non-dominated ordering and the crowding degree value.

Crossover operation: use crossover operation to generate new individuals. One or more crossover methods are usually used to combine two parent individuals to generate offspring individuals.

Mutation operation: Mutation operation is performed on some individuals to introduce randomness to increase the diversity of the population and assist the algorithm to better explore the search space.

Judgment of termination conditions: Judge whether the termination conditions are satisfied, such as reaching the maximum number of iterations, finding a good enough Pareto frontier solution, etc. If the termination conditions are satisfied, the algorithm ends. Otherwise, return to step (2) and continue with the next generation of optimization.

Crowding degree operator

The main goal of the crowding degree calculation is to make the distribution of individuals on the Pareto front even, in order to avoid individuals being overly concentrated in certain regions, and to find high-quality solutions while improving the search diversity. The distance calculation formula for congestion degree is as follows: (19)di=∑k=1m(|fki+1−fki−1|)$${d_i} = \sum\limits_{k = 1}^m {\left( {\left| {f_k^{i + 1} - f_k^{i - 1}} \right|} \right)}$$

Where: fki$$f_k^i$$ is the target value of individual i on the krd objective and the essence of crowding is the perimeter of the largest rectangle that surrounds only individual i.

Elite retention strategy

The operation of the elite retention strategy is shown schematically in Fig. 2. Elite retention strategy is a strategy for retaining high-quality solutions, combining the parent population P_l with the offspring population Q_l together to form a new population Rl(Rt=Pt∪Qt)$${R_l}\left( {{R_t} = {P_t} \cup {Q_t}} \right)$$ of size 2N, executing non-dominated sorting and crowding computation on the newly generated population R_t, and selecting the currently known optimal N individuals by comparison to form a new generation of the parent population. The parent and offspring populations compete together, ensuring that the excellent individuals in the set of non-inferior solutions are not lost during the evolutionary process, effectively preventing the loss of excellent genes, maintaining the diversity and convergence of the populations, and further optimizing the accuracy of the results.