A multi-objective coupled geographic stratification method and system based on NSGA-Ⅱ

Abstract

The present invention provides a multi-objective coupling geographic stratification method and system based on NSGA-Ⅱ, which uses NSGA-Ⅱ genetic algorithm to perform geographic stratification on geographical phenomena characterized by multi-objective comprehensiveness, averages and improves the initial population distribution through the optimal point set method, updates the optimal solution set through crossover mutation, and uses the Pareto frontier method to form a non-dominated coupling relationship between multiple objectives, avoiding the complex and uncertain mathematical relationship between multiple objectives. Compared with the traditional method of synthesizing a single objective by adding and subtracting multiple objectives, it is more suitable for solving practical problems. The present invention realizes the measurement of the intensity of spatial stratification heterogeneity of a complex geographical phenomenon, and can also evaluate the degree of explanation of the spatial stratification heterogeneity of geographical phenomena by potential explanatory factors.

Description

Technical Field

[0001] The present invention relates to the field of geographic information science and technology, and in particular to a multi-objective coupling geographic stratification method and system based on NSGA-II. Background Art

[0002] Geographic stratification is a key technology to study the spatial heterogeneity of geographical phenomena and to explore the spatial characteristics and driving factors of geographical phenomena. Existing geographical stratification methods are all single-target methods, that is, for a single geographical indicator, the spatial heterogeneity of the indicator is explained by a single or multiple explanatory factors.

[0003] According to the number of explanatory factors, the existing methods can be divided into single-factor methods and multi-factor methods based on a single objective. Typical single-factor methods include the optimal parameter-based geographic stratifier (OPGD), the multi-scale spatial discretization model (MSD) and the robust geographic detector (RGD); typical multi-factor methods include the interaction detector based on spatial correlation (ISDA) and the optimal region-based spatial heterogeneity model (GOZH). The ISDA method first integrates multiple single-factor discretization methods, such as the natural breakpoint method, the geometric method, the equal distance method, etc. After finding the optimal single-factor geographic stratification scheme, spatial fuzzy superposition is used to obtain a better multi-factor geographic stratification scheme. This integrated optimization method is still limited by the single-factor method, which restricts the model's consideration of multi-factor interactions. To solve this problem, the GOZH method is based on decision tree design. First, it traverses the possible stratification breakpoints of all factors to find an optimal single-factor stratification breakpoint, and then finds the next optimal single-factor stratification breakpoint based on the results of the previous iteration. Through continuous iteration, the optimization of multi-factor geographic stratification is achieved.

[0004] Although the single-objective geographic stratification method can find the optimal geographic stratification scheme based on a single objective to a certain extent, in actual research, geographical phenomena often need to be jointly characterized by multiple geographical indicators. For example, the combined drought and heat wave event (CDHWS) is a composite event consisting of high temperature heat wave and drought events, which cannot be summarized by a single objective variable. The single-objective geographic stratification method cannot be applied to the study of this composite event. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a multi-objective coupled geographic stratification method and system based on NSGA-Ⅱ with high accuracy and good interpretability.

[0006] Technical solution: A multi-objective coupled geographic stratification method based on NSGA-Ⅱ, including the following steps:

[0007] (1) According to the geographical phenomena in the target geographical area, select a number of corresponding explanatory factors and a number of geographical indicators that can characterize the geographical phenomena, and normalize the explanatory factors;

[0008] (2) Using the normalized explanatory factors to construct an initial population, an initial population containing several individuals is obtained. Each individual in the initial population is composed of a series of hyperplane parameters. The hyperplane equation composed of each set of hyperplane parameters and the explanatory factors divides the geographical units in the target geographical area into two types of strata. A series of hyperplane equations corresponding to each individual are calculated, and a target geographical area stratification result is obtained for each individual.

[0009] (3) Using the target geographic region stratification results, the geographic detector q value of each geographic indicator is calculated respectively, and the geographic detector q value of each geographic indicator is used as the value of the objective function of each individual. The initial population is screened by non-dominated sorting and crowding sorting to obtain the parent population;

[0010] (4) Linearly segment the hyperplane parameters of the parent individuals in the parent population, and then perform multi-point crossover to obtain the offspring individuals;

[0011] (5) All parent individuals and offspring individuals in step (4) are merged into one population, and step (3) is repeated on the population to obtain a new parent population;

[0012] (6) Repeat step (5) and determine whether the maximum number of iterations has been reached. If so, stop the iteration and output the target geographic area stratification results. If not, return to step (4) and continue iterating.

[0013] Specifically, in step (1), the normalization calculation formula of the explanatory factor is:

[0014] ,

[0015] Where: x j is the normalized explanatory factor j , is the original data of the explanatory factor, min is the minimum function, and max is the maximum function.

[0016] Specifically, in step (2), the series of hyperplane parameters constituting each individual are:

[0017] ,

[0018] Where: W is a matrix consisting of a series of hyperplane parameters of an individual, k is the number of hyperplanes, n is the number of explanatory factors, r knis the hyperparameter corresponding to the nth explanatory factor of the kth hyperplane, is a constant term, 1≤i≤k;

[0019] The equation for a set of hyperplane parameters and explanatory factors in an individual is:

[0020] ,

[0021] Where: x i is the i-th explanatory factor, 1≤i≤n. According to the equation, if the y value is greater than 0 or less than or equal to 0, the geographical units corresponding to the set of hyperplane parameters are divided into two types of strata.

[0022] Preferably, in step (2), constructing the initial population using the good point set method includes the following sub-steps:

[0023] (21) Calculate the hyperparameter r value corresponding to each explanatory factor on each hyperplane:

[0024] ,

[0025] Where: n is the number of explanatory factors, 1≤j≤n, r j is the hyperparameter of the jth explanatory factor on the hyperplane, m i is the i-th individual in the population;

[0026] (22) Construct a set of good points with m individuals in the population:

[0027] ,

[0028] Where: is the i-th individual, i n represents the hyperplane parameter value of the nth explanatory factor of the ith individual;

[0029] (23) Map the good point set to the feasible region where the population is located to obtain the initial population:

[0030] ,

[0031] Where: a j represents the lower limit of the hyperplane hyperparameter value, b j represents the upper limit of the hyperplane hyperparameter value, Represents the j-th explanatory factor hyperplane parameter value of the ith individual.

[0032] Specifically, in step (3), the calculation formula of the geographic detector q value is as follows:

[0033] ,

[0034] Where: is the q value of the geographic detector of the i-th geographic indicator, SSW is the sum of the variance within the layer, SST is the total variance of the whole area, is the number of geographical units in the stratigraphic layer h, is the intra-layer variance of the dependent variable within layer h, is the total number of geographic units, is the total variance of the dependent variable.

[0035] Specifically, in step (3), the non-dominated sorting includes:

[0036] For any two individuals a and b in the initial population, compare them based on n geographical indicators:

[0037] ,

[0038] Where: represents the geographic detector q value of individual a on the i-th geographic index, represents the geographic detector q value of individual b on the i-th geographic indicator. If the above inequality is satisfied, that is, for any geographic indicator, Are less than or equal to , then individual a dominates individual b if there exists a geographical indicator such that Greater than , then individual a is indistinguishable from individual b;

[0039] Repeat the above steps to obtain the dominance relationship between any two individuals in the population. Mark the individuals that are not dominated by any individual as the optimal individuals on the Pareto front and put them in the first layer, put the individuals that are only dominated by the optimal individuals on the Pareto front into the second layer, and put the remaining individuals into the third layer. According to the stratification results, select a set number of dominant individuals from the first layer in turn to obtain the parent population composed of dominant individuals.

[0040] Specifically, in step (3), the congestion ranking includes:

[0041] When selecting a set number of dominant individuals, when the number of individuals in a certain layer is greater than the number of dominant individuals to be selected in that layer, calculate the crowding degree of each individual in that layer:

[0042] ,

[0043] Where: d j is the crowding degree of the jth individual, m is the total number of individuals in the initial population, represents the geographic detector q value of the xth individual on the i-th geographic indicator;

[0044] The dominant individuals are selected in order from small to large crowding until the number of dominant individuals reaches the set number.

[0045] Specifically, in step (4), when performing multi-point crossover, for each set of hyperplane parameters, a random probability is generated to determine whether the set of hyperplane parameters needs to be mutated. If mutation is required, the set of hyperplane parameters is multiplied by a normal random number within a set range.

[0046] Specifically, the geographic unit is a geographic element to be classified in a target geographic area, and the data type is raster data or vector data.

[0047] The present invention also provides a multi-objective coupled geographic stratification system based on NSGA-Ⅱ, comprising:

[0048] Preprocessing module: used to select a number of corresponding explanatory factors and a number of geographical indicators that can characterize the geographical phenomena according to the geographical phenomena in the target geographical area, and normalize the explanatory factors;

[0049] Geographical region stratification module: used to construct an initial population using normalized explanatory factors to obtain an initial population containing several individuals. Each individual in the initial population is composed of a series of hyperplane parameters. The hyperplane equation composed of each set of hyperplane parameters and explanatory factors divides the geographical units in the target geographical region into two types of strata. A series of hyperplane equations corresponding to each individual are calculated to obtain a target geographical region stratification result for each individual.

[0050] Initial population screening module: used to calculate the geographic detector q value of each geographic indicator using the target geographic area stratification results, take the geographic detector q value of each geographic indicator as the value of the objective function of each individual, screen the initial population through non-dominated sorting and crowding sorting, and obtain the parent population;

[0051] Crossover mutation module: used to perform linear segmentation on the hyperplane parameters of the parent individuals in the parent population, and then perform multi-point crossover to obtain the offspring individuals;

[0052] Iteration module: used to merge all parent individuals and offspring individuals in the crossover mutation module into one population, and repeatedly run the initial population screening module on the population to iterate and obtain a new parent population;

[0053] Result output module: used to repeatedly run the iteration module and determine whether the maximum number of iterations has been reached. If so, the iteration is stopped and the target geographic area stratification results are output. If the maximum number of iterations has not been reached, the crossover mutation module is repeated to continue the iteration.

[0054] Beneficial effects: Compared with the prior art, the significant effects of the present invention are: the present invention uses the NSGA-Ⅱ genetic algorithm to perform geographical stratification on geographical phenomena characterized by multiple objectives, realizes the measurement of the intensity of spatial stratification heterogeneity of a complex geographical phenomenon, and can evaluate the degree to which potential explanatory factors explain the spatial stratification heterogeneity of geographical phenomena. The initial population distribution is averaged and improved by the optimal point set method, and the optimal solution set is updated by crossover mutation. This discrete search method can escape the local optimum and take into account the global solution space. The Pareto frontier method allows multiple objectives to form a non-dominated coupling relationship, avoiding the complex and uncertain mathematical relationship between multiple objectives. Compared with the traditional method of synthesizing a single objective by adding and subtracting multiple objectives, it is more suitable for solving practical problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a flow chart of the method of embodiment 1 of the present invention.

[0056] Figure 2 This is a temperature-time line graph of Category 1 site in Example 2 of the present invention.

[0057] Figure 3 This is a temperature-time line graph of Category 2 site in Example 2 of the present invention.

[0058] Figure 4 This is a temperature-time line graph of Category 3 site in Example 2 of the present invention.

[0059] Figure 5 This is a temperature-time line graph of Category 4 stations in Example 2 of the present invention.

[0060] Figure 6 This is a temperature-time line graph of Category 5 stations in Example 2 of the present invention.

[0061] Figure 7 This is a temperature-time line graph of Category 6 sites in Example 2 of the present invention.

[0062] Figure 8 This is an hourly scatter density diagram of Example 2 of the present invention. DETAILED DESCRIPTION

[0063] The present invention is further described below in conjunction with the accompanying drawings.

[0064] Embodiment 1:

[0065] See also Figure 1 As shown, this embodiment provides a multi-objective coupled geographic stratification method based on NSGA-Ⅱ, including the following steps:

[0066] (1) According to the geographical phenomena in the target geographical area, select several corresponding explanatory factors and several geographical indicators that can characterize the geographical phenomena, and normalize the explanatory factors. The calculation formula is:

[0067] ,

[0068] Where: x j is the normalized explanatory factor j , is the original data of the explanatory factor, min is the minimum function, and max is the maximum function.

[0069] Geographical phenomena are the external forms and surface features of geographical objects in their occurrence, development and change. In the present invention, geographical phenomena refer to complex geographical phenomena formed by multiple factors, and the geographical indicators representing these geographical phenomena may have various complex relationships such as coordination and conflict. In the present invention, geographical phenomena include three types:

[0070] Complex geographical phenomena, such as plant water stress, compound extreme climate phenomena (compound drought and heat wave events, sudden drought events, etc.);

[0071] Remote sensing data measurement discrepancies and assessments, such as temperature measurement discrepancies;

[0072] Analysis and evaluation of comprehensive human geography indicators, such as evaluation of drivers of rural resilience.

[0073] In the present invention, the explanatory factors are the geological elements that can explain the spatial heterogeneity of the geographical phenomena under study; and the geographical indicators refer to the geological elements that can be used to characterize the geographical phenomena under study.

[0074] (2) The initial population is constructed using the normalized explanatory factors to obtain an initial population containing several individuals. Each individual in the initial population is composed of a series of hyperplane parameters. The hyperplane equation composed of each set of hyperplane parameters and the explanatory factors divides the geographical units in the target geographical area into two types of strata. The geographical units are the geographical elements to be classified, which are raster data or vector data. A series of hyperplane equations corresponding to each individual are calculated, and a target geographical area stratification result is obtained for each individual.

[0075] Using matrices to represent individuals, a series of hyperplane parameters constituting each individual are:

[0076] ,

[0077] Where: W is a matrix consisting of a series of hyperplane parameters of an individual, k is the number of hyperplanes, n is the number of explanatory factors, r knis the hyperparameter corresponding to the nth explanatory factor of the kth hyperplane, is a constant term, 1≤i≤k;

[0078] The equation for a set of hyperplane parameters and explanatory factors in an individual is:

[0079] ,

[0080] Where: x i is the i-th explanatory factor, 1≤i≤n. According to the equation y value greater than 0 or less than or equal to 0, the geographical units corresponding to the set of hyperplane parameters are divided into two types of strata. Multiple hyperplane equations can be divided into multiple strata. Due to the existence of collinear coincidence of hyperplane equations and the same intersection of multiple hyperplanes, k hyperplanes can divide the geographical units in the target geographical area into at most categories, namely Strata type.

[0081] In this embodiment, randomly generated individuals will cause the population to be unevenly distributed in the solution space, which will in turn affect the convergence speed and robustness of the algorithm. Therefore, a good point set method is introduced to generate an initial population with a relatively uniform distribution, including the following steps:

[0082] (21) Calculate the hyperparameter r value corresponding to each explanatory factor on each hyperplane:

[0083] ,

[0084] Where: n is the number of explanatory factors, 1≤j≤n, r j is the hyperparameter of the jth explanatory factor on the hyperplane, m i is the i-th individual in the population;

[0085] (22) Construct a set of good points with m individuals in the population:

[0086] ,

[0087] Where: is the i-th individual, i n represents the hyperplane parameter value of the nth explanatory factor of the ith individual;

[0088] (23) Map the good point set to the feasible region where the population is located to obtain the initial population:

[0089] ,

[0090] Where: a jrepresents the lower limit of the hyperplane hyperparameter value, b j represents the upper limit of the hyperplane hyperparameter value, Represents the j-th explanatory factor hyperplane parameter value of the ith individual.

[0091] (3) The stratified results of the target geographic areas are used to calculate the geographic detector q value of each geographic indicator. The geographic detector q value of each geographic indicator is used as the value of the objective function of each individual. The initial population is screened by non-dominated sorting and crowding sorting to obtain the parent population.

[0092] The calculation formula of the geographic detector q value is as follows:

[0093] ,

[0094] Where: is the q value of the geographic detector of the i-th geographic indicator, SSW is the sum of the variance within the layer, SST is the total variance of the whole area, is the number of geographical units in the stratigraphic layer h, is the intra-layer variance of the dependent variable within layer h, is the total number of geographic units, is the total variance of the dependent variable.

[0095] Non-dominated sorting includes:

[0096] For any two individuals a and b in the initial population, compare them based on n geographical indicators:

[0097] ,

[0098] Where: represents the geographic detector q value of individual a on the i-th geographic index, represents the geographic detector q value of individual b on the i-th geographic index. If the above inequality is satisfied, a dominates b. If the above inequality is not satisfied, a is indistinguishable from b.

[0099] Repeat the above steps to obtain the dominance relationship between any two individuals in the population. Mark the individuals that are not dominated by any individual as the optimal individuals on the Pareto front and put them in the first layer, put the individuals that are only dominated by the optimal individuals on the Pareto front into the second layer, and put the remaining individuals into the third layer. According to the stratification results, select a set number of dominant individuals from the first layer in turn to obtain the parent population composed of dominant individuals.

[0100] When selecting a set number of dominant individuals, when the number of individuals in a certain layer is greater than the number of dominant individuals to be selected in this layer, it is necessary to calculate the crowding degree of each individual in this layer to further screen the individuals in this layer. The crowding degree calculation formula is:

[0101] ,

[0102] Where: dj is the crowding degree of the jth individual, m is the total number of individuals in the initial population, Represents the geographic detector q value of the xth individual on the ith geographic indicator.

[0103] Crowding is defined as the sum of the normalized differences of adjacent individuals in different target directions. When there is no individual on one side of the two endpoints, the crowding is defined as infinity. Dominant individuals are selected in order of crowding from small to large until the number of dominant individuals reaches the set number, thereby retaining the diversity of the population, that is, retaining the sparse distribution of the hyperplane parameters.

[0104] (4) Linearly segment the hyperplane parameters of the parent individuals in the parent population, and then perform multi-point crossover to obtain the offspring individuals. In order to prevent the hyperplane parameters from being restricted in the solution space, enhance the convergence ability of the algorithm and prevent it from falling into the local optimum too early, when performing multi-point crossover, for each group of hyperplane parameters, a random probability is generated to determine whether the group of hyperplane parameters needs to be mutated. If mutation is required, the group of hyperplane parameters is multiplied by a normal random number α within a set range. In this embodiment, the setting range of the normal random number α is -4≤α≤4.

[0105] (5) All parent individuals and offspring individuals in step (4) are merged into one population, and step (3) is repeated on the population to obtain a new parent population, so as to ensure that the optimal solution is not lost and improve the convergence speed of the algorithm.

[0106] (6) Repeat step (5) and determine whether the maximum number of iterations has been reached. If so, stop the iteration and output the target geographic area stratification results. If not, return to step (4) and continue iterating.

[0107] Embodiment 2:

[0108] This embodiment provides a specific implementation scenario of the multi-objective coupled geographic stratification method based on NSGA-Ⅱ of the above embodiment 1.

[0109] The compound drought and heat wave events in a certain area were selected as the geographical phenomena to be studied, and the normalized vegetation index, chlorophyll fluorescence index, elevation, biodiversity index and land cover category data were selected as explanatory factors. The drought index and surface temperature were used as geographical indicators to characterize the compound drought and heat wave events. That is, the spatial heterogeneity of the compound drought and heat wave events represented by the drought index and surface temperature were explained by the normalized vegetation index, elevation and other explanatory factors.

[0110] The evaluation of the driving factors of rural resilience in a certain area was selected as the geographical phenomenon to be studied, and population density, soil quality, cultivated land capital, and agricultural cultivated land area data were selected as explanatory factors. The labor turnover rate, cultural resource data, per capita agricultural gross output value, and vegetation coverage were used as geographical indicators to characterize the evaluation of the driving factors of rural resilience. That is, the spatial heterogeneity of the evaluation of the driving factors of rural resilience represented by labor turnover rate, cultural resource data, per capita agricultural gross output value, and vegetation coverage was explained by explanatory factors such as population density and soil quality.

[0111] The following is an explanation of a specific implementation scenario. A certain area is taken as the target geographical area, the near-surface temperature estimation problem is taken as the geographical phenomenon to be studied, and the meteorological station is taken as the geographical unit of the target geographical area. The temperature data obtained by interpolation of the MOD07 atmospheric profile product in the MODIS series product data of a certain year and the surface temperature (LST) data of MOD11 are respectively subtracted from the temperature data measured at the meteorological station to obtain the deviations between the two data products and the station temperature data as two geographical indicators:

[0112] ,

[0113] Where: As the first geographical indicator, As the second geographical indicator, is the site temperature data, is the interpolated temperature data, The surface air temperature data.

[0114] Taking elevation (DEM), humidity, normalized difference vegetation index (NDVI), and land surface temperature (LST) as four explanatory factors, the geographical stratification heterogeneity of the deviation between MODIS series product data and the measured temperature data at the station is explained. The number of hyperplanes is set to 4, and the corresponding hyperplane parameter matrix is ​​obtained as follows:

[0115] ,

[0116] Due to the inconsistent dimensions of the explanatory factors, the four explanatory factors are normalized according to step (1) of Example 1, the number of individuals in the initial population is set to 30, and the 30 individuals are evenly distributed in the solution space according to the good point set method in step (2) of Example 1 to improve the convergence rate. The geographic detector q values ​​of the two geographical indicators are calculated according to the method in step (3) of Example 1, and the initial population is screened by non-dominated sorting and crowding sorting in combination with the geographic detector q values ​​to obtain a parent population containing 10 dominant individuals. Steps (4)-(6) in Example 1 are repeated, and the optimal solution set of the target geographical area division result is obtained after 3000 iterations. In order to obtain a final geographical stratification result from the optimal solution set, the present invention uses a voting mechanism as a determination method. For a set of optimal solution sets, each geographical stratification result divides the target geographical area, and each geographical unit, that is, the smallest classification plot, votes for the classification category obtained by different geographical stratification results. The final classification result of the plot is the category that obtains the most votes, thereby determining the final classification result.

[0117] Through the above calculations, the temperature data corresponding to each meteorological station in the region, that is, the geographical unit in this embodiment, is divided into 8 categories. The deviations between the MODIS series product data and the measured temperature data of the station within the category are relatively similar, while there are obvious deviations between the categories. The q values ​​of the two geographical indicators calculated are 0.24 and 0.25, respectively, indicating that the geographical stratification results can reflect the spatial heterogeneity of the deviations between the MODIS series product data and the measured temperature data of the station.

[0118] Select 6 categories and draw a line graph of the temperature data of 1 weather station in each category. Figures 2 to 7 As shown in the figure, the yellow line is LST (surface air temperature), the green line is the interpolated air temperature (ALT), and the blue line is the station air temperature (Station). Figure 2 In category 1, the LST of MOD11 is higher than the station temperature, and the interpolated temperature of MOD07 is lower than the station temperature, and the deviations between the two are relatively consistent, making the station temperature between the time series data of the two temperature products. Figure 3 In category 2, compared with the LST data of MOD11, the MOD07 interpolated temperature has a smaller deviation from the station temperature. Figure 4 In category 3, the three deviations are almost identical and overlap with each other. Figure 5 In category 4, the LST of MOD11 is higher than the station temperature, and the interpolated temperature of MOD07 is lower than the station temperature, but the three overlap in winter. Figure 6 In category 5, the MOD series remote sensing data are all lower than the station air temperature. Figure 7In category 6, the deviation between the LST data of MOD11 and the station temperature is smaller than that of the interpolated temperature of MOD07. It can be seen that there are significant differences between different categories, which verifies the effectiveness of the classification results of this method.

[0119] See also Figures 2 to 7 As shown in the figure, based on the classification results, the temperature data of each type of station with similar systematic deviations are fitted by adjusting the proportional coefficient of the interpolated temperature data of MOD07 and the LST data of MOD11. The red line in the figure is the predicted temperature (Pre), which realizes the estimation of the instantaneous actual temperature for specific geographical units in the target geographical area using only the MODIS series temperature remote sensing data products.

[0120] ,

[0121] Where: a and b represent the proportional coefficients, and their value range is -1 to 1.

[0122] See also Figure 8 As shown in the figure, using the above fitting results, a scatter density map of the measured temperature and the predicted temperature at the station was made. Compared with the mean method currently used to estimate the temperature, this method overall reduced the error by about 1°C and improved the accuracy by about 25%.

[0123] Embodiment 3:

[0124] This embodiment provides a multi-objective coupled geographic stratification system based on NSGA-II corresponding to the multi-objective coupled geographic stratification method based on NSGA-II in the above-mentioned embodiment 1, including:

[0125] Preprocessing module: used to select a number of corresponding explanatory factors and a number of geographical indicators that can characterize the geographical phenomena according to the geographical phenomena in the target geographical area, and normalize the explanatory factors;

[0126] Geographical region stratification module: used to construct an initial population using normalized explanatory factors to obtain an initial population containing several individuals. Each individual in the initial population is composed of a series of hyperplane parameters. The hyperplane equation composed of each set of hyperplane parameters and explanatory factors divides the geographical units in the target geographical region into two types of strata. A series of hyperplane equations corresponding to each individual are calculated to obtain a target geographical region stratification result for each individual.

[0127] Initial population screening module: used to calculate the geographic detector q value of each geographic indicator using the target geographic area stratification results, take the geographic detector q value of each geographic indicator as the value of the objective function of each individual, screen the initial population through non-dominated sorting and crowding sorting, and obtain the parent population;

[0128] Crossover mutation module: used to perform linear segmentation on the hyperplane parameters of the parent individuals in the parent population, and then perform multi-point crossover to obtain the offspring individuals;

[0129] Iteration module: used to merge all parent individuals and offspring individuals in the crossover mutation module into one population, and repeatedly run the initial population screening module on the population to iterate and obtain a new parent population;

[0130] Result output module: used to repeatedly run the iteration module and determine whether the maximum number of iterations has been reached. If so, the iteration is stopped and the target geographic area stratification results are output. If the maximum number of iterations has not been reached, the crossover mutation module is repeated to continue the iteration.

Claims

1. A multi-objective coupled geographic stratification method based on NSGA-Ⅱ, characterized in that: The following steps are involved: (1) According to the geographical phenomena in the target geographical area, select a number of corresponding explanatory factors and a number of geographical indicators that can characterize the geographical phenomena, and normalize the explanatory factors; (2) Using the normalized explanatory factors to construct an initial population, an initial population containing several individuals is obtained. Each individual in the initial population is composed of a series of hyperplane parameters. The hyperplane equation composed of each set of hyperplane parameters and the explanatory factors divides the geographical units in the target geographical area into two types of strata. A series of hyperplane equations corresponding to each individual are calculated, and a target geographical area stratification result is obtained for each individual. (3) Using the target geographic area stratification results, the geographic detector q value of each geographic indicator is calculated respectively, and the geographic detector q value of each geographic indicator is used as the value of the objective function of each individual. The initial population is screened by non-dominated sorting and crowding sorting to obtain the parent population; the non-dominated sorting includes: For any two individuals a and b in the initial population, compare them based on n geographical indicators: ， Where: represents the geographic detector q value of individual a on the i-th geographic index, represents the geographic detector q value of individual b on the i-th geographic index. If it satisfies any geographic index, Are less than or equal to , then individual a dominates individual b if there exists a geographical indicator such that Greater than , then individual a is indistinguishable from individual b; Repeat the above steps to obtain the dominance relationship between any two individuals in the population. Mark the individuals that are not dominated by any individual as the optimal individuals on the Pareto front and put them in the first layer. Put the individuals that are only dominated by the optimal individuals on the Pareto front into the second layer, and put the remaining individuals into the third layer. According to the stratification results, select a set number of dominant individuals from the first layer in turn to obtain the parent population composed of dominant individuals. The congestion ranking includes: When selecting a set number of dominant individuals, when the number of individuals in a certain layer is greater than the number of dominant individuals to be selected in that layer, calculate the crowding degree of each individual in that layer: ， Where: d j is the crowding degree of the jth individual, m is the total number of individuals in the initial population, represents the geographic detector q value of the xth individual on the i-th geographic indicator; The dominant individuals are selected in order from small to large crowding degree until the number of dominant individuals reaches the set number; (4) Linearly segment the hyperplane parameters of the parent individuals in the parent population, and then perform multi-point crossover to obtain the offspring individuals; (5) All parent individuals and offspring individuals in step (4) are merged into one population, and step (3) is repeated on the population to obtain a new parent population; (6) Repeat step (5) and determine whether the maximum number of iterations has been reached. If so, stop the iteration and output the target geographic area stratification results. If not, return to step (4) and continue iterating.

2. The multi-objective coupled geographic stratification method according to claim 1 is characterized by: In step (1), the normalization calculation formula of the explanatory factor is: ， Where: x j is the normalized explanatory factor j , is the original data of the explanatory factor, min is the minimum function, and max is the maximum function.

3. The multi-objective coupled geographic stratification method according to claim 1 is characterized in that: In step (2), a series of hyperplane parameters constituting each individual are: ， Where: W is a matrix consisting of a series of hyperplane parameters of an individual, k is the number of hyperplanes, n is the number of explanatory factors, r kn is the hyperparameter corresponding to the nth explanatory factor of the kth hyperplane, is a constant term, 1≤i≤k; The equation for a set of hyperplane parameters and explanatory factors in an individual is: ， Where: x i is the i-th explanatory factor, 1≤i≤n. According to the equation, if the y value is greater than 0 or less than or equal to 0, the geographical units corresponding to the set of hyperplane parameters are divided into two types of strata.

4. The multi-objective coupled geographic stratification method according to claim 1, characterized in that: In step (2), the initial population is constructed using the good point set method, which includes the following sub-steps: (21) Calculate the hyperparameter r value corresponding to each explanatory factor on each hyperplane: ， Where: n is the number of explanatory factors, 1≤j≤n, r j is the hyperparameter of the jth explanatory factor on the hyperplane, m i is the i-th individual in the population; (22) Construct a set of good points with m individuals in the population: ， Where: is the i-th individual, i n represents the hyperplane parameter value of the nth explanatory factor of the ith individual; (23) Map the good point set to the feasible region where the population is located to obtain the initial population: ， Where: a j represents the lower limit of the hyperplane hyperparameter value, b j represents the upper limit of the hyperplane hyperparameter value, Represents the j-th explanatory factor hyperplane parameter value of the ith individual.

5. The multi-objective coupled geographic stratification method according to claim 1, characterized in that: In step (3), the calculation formula of the geographic detector q value is as follows: ， Where: is the q value of the geographic detector of the i-th geographic indicator, SSW is the sum of the variance within the layer, SST is the total variance of the whole area, is the number of geographical units in the stratigraphic layer h, is the intra-layer variance of the dependent variable within layer h, is the total number of geographic units, is the total variance of the dependent variable.

6. The multi-objective coupled geographic stratification method according to claim 1, characterized in that: In the step (4), when performing multi-point crossover, for each set of hyperplane parameters, a random probability is generated to determine whether the set of hyperplane parameters needs to be mutated. If mutation is required, the set of hyperplane parameters is multiplied by a normal random number within a set range.

7. The multi-objective coupled geographic stratification method according to claim 1, characterized in that: The geographic unit is a geographic element to be classified in the target geographic area, and the data type is raster data or vector data.

8. A multi-objective coupled geographic stratification system based on NSGA-Ⅱ, characterized by: include: Preprocessing module: used to select a number of corresponding explanatory factors and a number of geographical indicators that can characterize the geographical phenomena according to the geographical phenomena in the target geographical area, and normalize the explanatory factors; Geographical region stratification module: used to construct an initial population using normalized explanatory factors to obtain an initial population containing several individuals. Each individual in the initial population is composed of a series of hyperplane parameters. The hyperplane equation composed of each set of hyperplane parameters and explanatory factors divides the geographical units in the target geographical region into two types of strata. A series of hyperplane equations corresponding to each individual are calculated to obtain a target geographical region stratification result for each individual. Initial population screening module: used to calculate the geographic detector q value of each geographic indicator respectively using the target geographic area stratification results, taking the geographic detector q value of each geographic indicator as the value of the objective function of each individual, screening the initial population through non-dominated sorting and crowding sorting to obtain the parent population; the non-dominated sorting includes: For any two individuals a and b in the initial population, compare them based on n geographical indicators: ， Where: represents the geographic detector q value of individual a on the i-th geographic index, represents the geographic detector q value of individual b on the i-th geographic index. If it satisfies any geographic index, Are less than or equal to , then individual a dominates individual b if there exists a geographical indicator such that Greater than , then individual a is indistinguishable from individual b; Repeat the above steps to obtain the dominance relationship between any two individuals in the population. Mark the individuals that are not dominated by any individual as the optimal individuals on the Pareto front and put them in the first layer. Put the individuals that are only dominated by the optimal individuals on the Pareto front into the second layer, and put the remaining individuals into the third layer. According to the stratification results, select a set number of dominant individuals from the first layer in turn to obtain the parent population composed of dominant individuals. The congestion ranking includes: When selecting a set number of dominant individuals, when the number of individuals in a certain layer is greater than the number of dominant individuals to be selected in that layer, calculate the crowding degree of each individual in that layer: ， Where: d j is the crowding degree of the jth individual, m is the total number of individuals in the initial population, represents the geographic detector q value of the xth individual on the i-th geographic indicator; The dominant individuals are selected in order from small to large crowding degree until the number of dominant individuals reaches the set number; Crossover mutation module: used to linearly segment the hyperplane parameters of the parent individuals in the parent population, and then perform multi-point crossover to obtain the offspring individuals; Iteration module: used to merge all parent individuals and offspring individuals in the crossover mutation module into one population, and repeatedly run the initial population screening module on the population to iterate and obtain a new parent population; Result output module: used to repeatedly run the iteration module and determine whether the maximum number of iterations has been reached. If so, the iteration is stopped and the target geographic area stratification results are output. If the maximum number of iterations has not been reached, the crossover mutation module is repeated to continue the iteration.

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