An improved two-step mobile search method considering selection probability and variable radius simultaneously

Abstract

The application provides an improved two-step moving search method considering selection probability and variable radius, which combines the advantages of Huff model and variable radius 2SFCA. The distance attenuation between supply and demand, the service capacity of supply points, the selection probability of the population to the facilities and the variable search radius of supply and demand points are comprehensively considered. The travel time cost between supply and demand is obtained through the path planning interface of Gaode API, the selection probability of demand points to all supply points within the search radius range is calculated according to the Huff model, and the search radius of each demand point and supply point is dynamically determined, and the spatial accessibility of the public service facilities is calculated at the population grid scale and the street scale. Experiments show that the application can minimize the overestimation and underestimation of the accessibility, the spatial distribution result is more continuous and real, and the spatial accessibility of the urban public service facilities can be effectively measured.

Description

Technical Field

[0001] This invention relates to the field of information science and technology, specifically to an improved two-step moving search method that simultaneously considers selection probability and variable radius. Background Technology

[0002] Public service facilities play a vital role in comprehensively improving people's quality of life and promoting sustainable socio-economic development. Therefore, allocating public service facilities equitably and rationally is a key objective in their planning and layout. Studying the spatial accessibility of public service facilities can identify areas with scarce facilities, effectively measuring the spatial equity of their distribution and providing recommendations for reducing regional disparities.

[0003] Currently, this research has attracted widespread attention from scholars both domestically and internationally. Among them, the two-step floating catchment area method (2SFCA) has been widely applied to measure the spatial accessibility of urban public service facilities. This model has been extended to varying degrees to accommodate population choice probabilities and variable search radii. For example, (Luo J, 2014) proposed a 2SFCA method based on the Huff model, using travel impedance and the supply capacity of service facilities to jointly reflect the probability of demand points choosing different facilities. This can reduce the overestimation and underestimation of population demand by supply facilities; however, the fixed search radius used in this method will affect the final accessibility results. (Luo Wei and Whippo, 2012) proposed a variable radius 2SFCA method, which dynamically determines the search radius of each demand point and supply point by gradually increasing the search radius of supply and demand points until a given supply-demand ratio threshold and total population threshold are met. This can more realistically reflect the service range of supply points and the required service level of demand points. However, this method does not consider the probability of demand points choosing different facilities, which may overestimate the spatial accessibility of some areas. Summary of the Invention

[0004] In view of this, the present invention provides an improved two-step movement search method that takes into account both selection probability and variable radius. This method not only overcomes the problems of fixed search radius and distance decay dichotomy in the traditional two-step movement search method, but also considers the distance decay in real-world situations and the selection probability of people for facilities, which can effectively improve the authenticity of accessibility results.

[0005] To achieve the above objectives, the present invention adopts a technical solution: an improved two-step moving search method that simultaneously considers selection probability and variable radius, the specific steps of which are as follows:

[0006] Step S1: Establish facility supply and demand data, where supply data includes the location of public service facilities and various attributes that can characterize the supply capacity of public service facilities; demand data is population grid data within a certain area, including the location and scale of demand points;

[0007] Step S2: Build an accessibility model based on the Gaode API route planning interface, set the travel mode, and obtain the OD travel time cost;

[0008] Step S3: Using each public service facility point and population grid point as the center, calculate the variable search radius of both according to the variable radius 2SFCA method;

[0009] Step S4: Calculate the travel impedance based on the travel time cost obtained in step S2 using the three-segment Gaussian distance attenuation function;

[0010] Step S5: Based on the Huff model, calculate the probability of each population grid point selecting all public service facility points within its search radius;

[0011] Step S6: Based on the variable radius of supply and demand points, population selection probability, travel impedance, location and scale of demand points and supply capacity of supply points obtained in steps S1-S5 above, calculate the supply-demand ratio of each public service facility point. Obtain the accessibility result from the population grid point to the public service facility point from the supply-demand ratio. Then calculate the accessibility of each street according to the average value method.

[0012] Step S7: Using the accessibility ratio difference index, compare the spatial accessibility results of 2SFCA based on the Huff model, 2SFCA with variable radius, and the results of the traditional 2SFCA with the results of the methods in steps S1-S6. Analyze the differences in the spatial distribution pattern of accessibility at the grid point scale, verify the feasibility of the methods in steps S1-S6, and propose corresponding suggestions for improving the rational allocation of public service facility resources.

[0013] Furthermore, the specific steps of step S1 are as follows:

[0014] Step S11: Obtain the address of the public service facility (i.e., the supply point) and relevant attributes that can characterize the supply capacity of the facility, and obtain the latitude and longitude of the supply point based on the address;

[0015] Step S12: Obtain the population, i.e. the location and scale of the demand point. Based on the downloaded population data, resample it into grid cells within a certain area, using the population size as the scale of the demand point.

[0016] Furthermore, step S2 specifically includes the following steps:

[0017] Step S21: Convert the Earth coordinates of the public service facilities and the center point of the population grid to Mars coordinates, and then call the path planning interface of the Gaode Map API, starting from the center of the population grid and ending at the public service facilities, to simulate the supply and demand scenario of the real population.

[0018] Step S22: By setting the traffic mode of the interface, obtain the OD travel time cost under different traffic modes;

[0019] Furthermore, the specific steps of step S3 are as follows:

[0020] Step S31: Using each public service facility point as the center, the initial value... The initial search radius is used to calculate the total population within that radius. If the total population exceeds a given population threshold, then the initial search radius is adjusted. This is the search radius of the public service facility. If the total number of people is less than the given threshold, then a small increment needs to be added to the initial search radius. Then, recalculate the total number of people under the new search radius, and repeat the process until the total number of people reaches the given threshold.

[0021] Step S32: Using the center point of each population grid as the center, the initial value... The initial search radius is defined as the ratio of the supply capacity of all service facilities to the population within that radius. If this ratio exceeds a given threshold, then the search radius is adjusted accordingly. That is, the search radius of the population grid point. If the ratio is less than a given ratio threshold, then a small increment needs to be added to the initial search radius. Then, the ratio of the supply capacity of all service facilities to the number of people under the new search radius is calculated again, and this process is repeated until the ratio reaches the given ratio threshold.

[0022] Furthermore, the travel impedance expression in step S4 is as follows:

[0023]

[0024] In the formula and These represent two different ranges of search radius thresholds. For population grid points Arrival at public service facilities Time;

[0025] Furthermore, step S5 specifically involves the following steps:

[0026] The probability of each population grid point selecting any public service facility point within its search radius is calculated using the following formula:

[0027]

[0028] In the formula, Population grid points calculated based on the Huff model Arrival at public service facilities The probability of selection by the target population. Indicates population grid points The search radius, For population grid points Reach public service facilities within its search range Right now Travel time at that time It is a public service facility Supply capacity Public service facilities within the search area Right now Supply capacity at the time and These represent population grid points. Arrival Service Facilities Service facilities Travel resistance between them.

[0029] Furthermore, step S6 specifically involves the following steps:

[0030] Step S61: Taking the public service facility as the center, calculate the supply-demand ratio for each public service facility based on all population demand points within the search radius of each facility. ;

[0031] Step S62: Taking each population grid point as the center, sum the supply and demand ratios of all public service facilities within its search range, and simultaneously consider the distance decay effect and the probability of population selection to obtain the spatial accessibility of each population grid point. ;

[0032] Step S63: Calculate the spatial accessibility results of the population grid using the traditional 2SFCA, the 2SFCA based on the Huff model, the variable radius 2SFCA, and the methods in steps S1-S6 respectively. Use the quartile method to divide the accessibility results obtained by these four methods into five levels: very high, high, medium, low, and very low.

[0033] Step S64: Calculate the average spatial accessibility of all population grid points within each street area as the street-scale accessibility;

[0034] Step S65: Calculate the street space accessibility results using the traditional 2SFCA method. The accessibility is divided into four levels using the quartile method: very high, high, medium, and low.

[0035] Furthermore, the expression for calculating the supply-demand ratio of public service facilities is as follows:

[0036]

[0037] The spatial reachability expression for each population grid point is as follows:

[0038]

[0039] The spatial accessibility expressions for public service facilities in each street are as follows:

[0040]

[0041] In the formula, in the formula, For service facilities The supply-demand ratio Service facilities Supply capacity Population grid points calculated based on the Huff model Arrival at service facility The probability of the selected population. For population grid points The population of the area For population grid points With service facilities Travel resistance between Accessibility of public service facilities in each street. The number of population grid points within each street area. The population grid points calculated in step S62 Spatial accessibility.

[0042] Furthermore, step S7 specifically includes the following steps:

[0043] Step S71: Compare and analyze the differences between 2SFCA based on the Huff model and traditional 2SFCA;

[0044] Step S72: Compare the differences between variable radius 2SFCA and traditional 2SFCA;

[0045] Step S73: Compare and analyze the differences between the results of steps S1-S6 and the traditional 2SFCA;

[0046] Step S74: Compare and analyze the differences in the spatial distribution patterns of accessibility at the grid point scale;

[0047] Step S75: Analyze the spatial distribution pattern of accessibility at the grid point scale and street scale to provide suggestions for reducing regional disparities in public service facilities.

[0048] Furthermore, the difference between 2SFCA based on the Huff model and traditional 2SFCA is expressed as follows:

[0049]

[0050] The difference between variable radius 2SFCA and traditional 2SFCA is expressed as follows:

[0051]

[0052] The difference between the results of steps S1-S6 and the traditional 2SFCA is expressed as follows:

[0053]

[0054] In the formula, , , and These are population grid points Spatial reachability is obtained using steps S1-S6, Huff model-based 2SFCA, variable radius 2SFCA, and traditional 2SFCA.

[0055] Compared with existing technologies, this invention can obtain more continuous and realistic spatial distribution results, and specifically has the following beneficial effects:

[0056] 1. This invention incorporates the Huff model, which considers the selection probability of each public service facility point within the search range of a population grid cell, thus reflecting the actual population demand of each service facility point;

[0057] 2. This invention integrates the variable radius 2SFCA method to dynamically determine the variable search radius of supply and demand points throughout the entire study area, which can minimize the areas of overestimation and underestimation of accessibility;

[0058] 3. This invention uses a population grid unit of 200m*200m or even finer as a starting point, enabling the measurement of spatial accessibility at a finer scale. Attached Figure Description

[0059] Figure 1 This is a flowchart of the steps of the present invention;

[0060] Figure 2 This refers to the population density and spatial distribution of sampling points in the area described in this embodiment of the invention.

[0061] Figure 3This refers to the spatial distribution of the population grid points in this embodiment of the invention, representing the shortest time to reach nearby sampling points.

[0062] Figure 4 The reachability distribution results of the embodiments of the present invention under different models;

[0063] Figure 5 These are the accessibility distribution results obtained using different models at the street scale in embodiments of the present invention;

[0064] Figure 6 The above are the results of the differences in reachability ratios obtained under different models in the embodiments of the present invention. Detailed Implementation

[0065] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0066] In the improved two-step moving search method described above, which simultaneously considers selection probability and variable radius, step S1 first acquires population grid data (demand) and public service facility data (supply) within the research area to construct facility supply and demand data. The population grid data includes the coordinates and population size of each grid center point, while the public service facility data includes location and various attributes characterizing the facility's supply capacity. The specific steps are as follows:

[0067] Step S11: Obtain the address of public service facilities (supply points) and relevant attributes that can characterize the supply capacity of the facilities, such as the area of ​​green space, supporting facilities, etc.; the number of beds and medical staff of medical service institutions, etc.

[0068] Step S12: Calculate the supply capacity of the facilities based on their relevant attributes.

[0069] Step S13: Use the geocoding service of Amap API to obtain latitude and longitude based on the address.

[0070] Step S14: Obtain the location and scale of the demand points. Download population data from Worldpop and resample it into 200m*200m grid cells, using the population size as the scale of the demand points.

[0071] In the improved two-step movement search method described above that simultaneously considers selection probability and variable radius, step S2 obtains the OD travel time cost by calling the Gaode Map API route planning interface, specifically including the following steps:

[0072] Step S21: Convert the Earth coordinates of the public service facility points and the center point of the population grid to Mars coordinates, and then call the path planning interface of the Gaode Map API, with the population grid center as the starting point and the public service facility points as the ending point, to simulate the supply and demand scenario of the real population.

[0073] Step S22: Obtain the OD travel time cost by setting the traffic mode of the interface, such as driving, walking, public transportation, etc.

[0074] In the improved two-step moving search method described above that simultaneously considers selection probability and variable radius, step S3 calculates the variable search radius of each public service facility point and population grid point, respectively, based on the variable radius 2SFCA method, given a population threshold and a supply-demand ratio threshold. Specifically, this includes the following steps:

[0075] Step S31: Using each public service facility point as the center, the initial value... The initial search radius is used to calculate the total population within that radius. If the total population exceeds a given population threshold, then the initial search radius is adjusted. This is the search radius of the service facility point. If the total number of people is less than the given threshold, then a small increment needs to be added to the initial search radius. Then, recalculate the total number of people within the new search radius. Repeat this process until the total number of people reaches the given threshold.

[0076] Step S32: Using the center point of each population grid as the center, the initial value... The search radius is defined as the ratio of the supply capacity of all service facilities to the population within that radius. If this ratio exceeds a given threshold, then the initial search radius is set to [a certain value]. That is, the search radius of the population grid point. If the ratio is less than a given ratio threshold, then a small increment needs to be added to the initial search radius. Then, recalculate the ratio of supply capacity to number of people for all service facilities within the new search radius. Repeat this process until the ratio reaches a given ratio threshold.

[0077] In the improved two-step movement search method described above that simultaneously considers selection probability and variable radius, step S4 uses the time cost returned from step S2 as the travel time distance cost in the model, and sets a three-segment Gaussian distance decay function as the travel impedance to simulate the phenomenon that the service capacity of public service facilities gradually decreases with increasing distance in real-world scenarios. The formula is as follows:

[0078]

[0079] In the formula and These represent two different ranges of search radius thresholds. For population grid points Arrival at public service facilities The time. Within less than Travel impedance within range This indicates that there is no distance attenuation within the area, meaning it has optimal spatial accessibility. Based on the 15-minute living circle proposed in the "Urban Residential Area Planning and Design Standard" (GB50180—2018), it is possible to establish... It lasts for 15 minutes; to The travel impedance within the range is a Gaussian decay function. Based on the longest walking limit of the population, we can set... For 30 minutes; greater than Regional travel resistance This indicates that these areas are inaccessible.

[0080] In the improved two-step moving search method described above, which simultaneously considers selection probability and variable radius, step S5 specifically involves calculating the selection probability of each population grid point for all service facility points within its search radius based on the Huff model. The formula is as follows:

[0081]

[0082] In the formula, Population grid points calculated based on the Huff model Arrival at service facility The probability of selection by the target population. Indicates population grid points The search radius, For population grid points Reaching its search range ( ) service facilities Travel time, Service facilities Supply capacity Within the search range ( Service facilities Supply capacity and These represent population grid points. Arrival Service Facilities Service facilities The travel impedance between them can be found in step S4.

[0083] In the improved two-step movement search method described above, which simultaneously considers selection probability and variable radius, step S6 calculates the supply-demand ratio for each service facility point based on the variable radius of supply and demand points, population selection probability, travel impedance, location and size of demand points, and supply capacity of supply points obtained in steps S1-S5. The accessibility from the population grid point to the public service facility point is then obtained from the supply-demand ratio, and finally, the accessibility of each street is calculated using the average value method. Specifically, the steps include the following:

[0084] Step S61: Taking the public service facility as the center, calculate the supply-demand ratio for each service facility based on all population demand points within the search radius of each service facility. The formula is as follows:

[0085]

[0086] In the formula, For service facilities The supply-demand ratio Service facilities Supply capacity Population grid points calculated based on the Huff model Arrival at service facility The probability of the selected population. For population grid points The population of the area For population grid points With service facilities Travel resistance between them.

[0087] Step S62: Taking each population grid point as the center, sum the supply and demand ratios of all service facility points within its search range, and simultaneously consider the distance decay effect and the probability of population selection to obtain the spatial accessibility of public service facilities for each population grid point. The formula is as follows:

[0088]

[0089] Step S63: Calculate the spatial accessibility results of the population grid using traditional 2SFCA, Huff model-based 2SFCA, and variable radius 2SFCA respectively. Then, use the quartile method to divide the accessibility results obtained by these four methods into five levels: very high, high, medium, low, and very low. This facilitates subsequent comparison with the present invention.

[0090] Step S64: Calculate the average spatial accessibility of all population grid points within each street area as the street-scale accessibility, using the following formula:

[0091]

[0092] In the formula, Accessibility of public service facilities in each street. The number of population grid points within each street area. The population grid points calculated in step S62 Spatial accessibility.

[0093] Step S65: Calculate the street spatial accessibility results using the traditional 2SFCA method. Similarly, the quartile method is used to divide accessibility into four levels: very high, high, medium, and low. This facilitates subsequent comparison with the present invention.

[0094] In the improved two-step movement search method described above, which simultaneously considers selection probability and variable radius, step S7 uses the Accessibility Ratio Difference (ARD) index to compare the spatial accessibility results of 2SFCA based on the Huff model, 2SFCA with variable radius, and the method of this invention with the results of traditional 2SFCA. This analyzes the differences in the spatial distribution pattern of accessibility at the grid point scale and verifies the feasibility of the method of this invention. Finally, corresponding suggestions are proposed to improve the rational allocation of public service facility resources. Specifically, the steps are as follows:

[0095] Step S71: Compare and analyze the differences between 2SFCA based on the Huff model and traditional 2SFCA, using the following formula:

[0096]

[0097] Step S72: Compare the differences between variable radius 2SFCA and traditional 2SFCA, using the following formula:

[0098]

[0099] Step S73: Compare and analyze the differences between the results of this invention and the traditional 2SFCA, using the following formula:

[0100]

[0101] In the formula, , , and These are population grid points Spatial reachability obtained using the present invention, Huff model-based 2SFCA, variable radius 2SFCA, and conventional 2SFCA.

[0102] Step S74: Compare and analyze the differences in the spatial distribution patterns of accessibility at the grid point scale to verify the feasibility of the method of the present invention.

[0103] Step S75: Based on the spatial distribution of accessibility results at different levels, analyze the spatial distribution pattern of accessibility at the grid point scale and street scale, and provide suggestions for reducing regional differences in public service facilities.

[0104] Example

[0105] Reference Figure 1 This invention provides an improved two-step movement search method that simultaneously considers selection probability and variable radius. It selects sampling points in a city as the public service facilities to be studied, thereby measuring the spatial accessibility of sampling points within the study area. Specifically, it includes the following steps:

[0106] Step S1: Obtain sampling point data (supply) and population grid data (demand) to establish facility supply and demand data. The supply data includes the location and service duration of the supply facilities, and the demand data includes the location and scale of the demand points.

[0107] Step S2: Build an accessibility model based on the Gaode API route planning interface, set the walking travel mode, and obtain the OD travel time cost;

[0108] Step S3: Using each sampling point and population grid point as the center, calculate the variable search radius of both according to the variable radius 2SFCA method;

[0109] Step S4: Calculate the travel impedance based on the travel time cost obtained in step S2 using the three-segment Gaussian distance attenuation function;

[0110] Step S5: Based on the Huff model, calculate the selection probability of each population grid point for all sampling points within its search radius;

[0111] Step S6: Calculate the accessibility results from the population grid point to the free sampling facility point based on the variable radius of the supply point and demand point, the population selection probability, travel impedance, the location and size of the demand point, and the supply capacity of the supply point, and calculate the accessibility of each street according to the average method.

[0112] Step S7: Using the Accessibility Ratio Difference (ARD) index, the spatial accessibility results of 2SFCA based on the Huff model, 2SFCA with variable radius, and the present invention are compared with the results of traditional 2SFCA to verify the feasibility of the present invention. Finally, the spatial distribution pattern of accessibility at the grid point scale and street scale is analyzed, and corresponding suggestions are made to improve the rational allocation of sampling point resources.

[0113] In this implementation, step S1 uses the central urban area of ​​a city as the research scope, divides the research units using a population grid, and constructs supply and demand data. For example... Figure 2 The figure shows the population density and spatial distribution of sampling points in a certain city, specifically including the following steps:

[0114] Step S11: Obtain the address and service time period of the sampling points in a certain city. In this example, we expanded the data selection range of the sampling points by 1km outward from the Third Ring Road, and considered the sampling points in the edge area close to the Third Ring Road to reduce the impact of the "edge effect" on the spatial accessibility results of the edge area.

[0115] Step S12: Calculate the supply capacity of the sampling points. Calculate the average weekly service duration of the sampling points as the facility's supply capacity.

[0116] Step S13: Obtain the latitude and longitude of the sampling points based on their addresses. Using the geocoding service of the Amap API, convert the sampling point addresses to Mars coordinates. After converting them to Earth coordinates using the sampling coordinate conversion system, load them into ArcGIS to obtain point shapefiles, and then check and correct them against the map. Finally, use the spatial connectivity tool to connect the sampling point's capabilities to the point shapefile.

[0117] Step S14: Obtain the location and size of the demand point. Download the 2020 population grid data of a certain city (200m*200m) from Worldpop, remove water bodies and uninhabited areas, and use ArcGIS computational geometry tools to obtain its geographic coordinates as the location of the demand point, and use the population size as the size of the demand point.

[0118] In this implementation, step S2 obtains the OD time cost based on walking mode by calling the Gaode Map API route planning interface, specifically including the following steps:

[0119] Step S21: Based on the coordinate transformation system, convert the sampling points and population grid points in ArcGIS from Earth coordinates to Mars coordinates. Then, call the Gaode Map API path planning interface, using the center of the population grid point as the starting point and the sampling point as the ending point, to simulate a real-world population sampling scenario. The interface call is as follows:

[0120] https: / / restapi.amap.com / v3 / direction / walking?origin={}&destination={}&ak={user's key}

[0121] Step S22: Set the traffic mode of the interface to walking and obtain the OD travel time cost;

[0122] In this implementation, step S3 calculates the search radius of each sampling point and population grid point using the variable radius 2SFCA method, given a population threshold and a supply-demand ratio threshold. Specifically, it includes the following steps:

[0123] Step S31: Using each sampling point as the center, initialize the value. The initial search radius is used to calculate the total population within that radius. If the total population exceeds a given population threshold, then the initial search radius is adjusted. That is, the search radius of the sampling point. If the total number of people is less than the given threshold, then a small increment needs to be added to the initial search radius. Then, the total number of people within the new search radius is recalculated, and this process is repeated until the total number of people reaches a given threshold. In this example, the threshold is set to 3000 people.

[0124] Step S32: Using the center point of each population grid as the center, the initial value... The initial search radius is defined as the ratio of the number of sampling points to the population within that radius. If this ratio is greater than a given threshold, then the initial search radius is adjusted. That is, the search radius of the population grid point. If the ratio is less than a given ratio threshold, then a small increment needs to be added to the initial search radius. Then, the ratio of the number of sampling points to the number of people under the new search radius is recalculated. This process is repeated until the ratio reaches a given ratio threshold. Similarly, in this implementation, the given ratio threshold is set to 1:3000.

[0125] In this implementation, step S4 uses the time cost returned in step S2 as the travel time distance cost in the model, and sets a three-segment Gaussian distance decay function as the travel impedance to simulate the phenomenon that the service capacity of the sampled service gradually decreases with increasing distance in real-world scenarios. The formula is as follows:

[0126]

[0127] In the formula and These represent two different ranges of search radius thresholds. For population grid points Arrival at the sampling point The walking time. The three-segment Gaussian distance decay function is established for two reasons: First, the planning of various cities considers the distance requirement of a "15-minute walking circle," therefore, in this implementation, the walking time will be... Setting it to 15 minutes indicates that there is no distance decay within a 15-minute radius, and that this area has optimal spatial accessibility. Secondly, most people's maximum acceptable walking time is 30 minutes, therefore, in this implementation, [the following will be used]. Set to 30 minutes, define the area between 15 and 30 minutes as Gaussian decay, and the reachability of areas outside 30 minutes is 0, indicating that these areas are inaccessible.

[0128] In this implementation, step S5 involves calculating the selection probability of each population grid point within its search radius based on the Huff model, using the following formula:

[0129]

[0130] In the formula, Population grid points calculated based on the Huff model Arrival at the sampling point The probability of selection by the target population. Indicates population grid points The search radius, For population grid points Reaching its search range ( sampling points Travel time, Sampling points Supply capacity Within the search range ( Sampling points Supply capacity and These represent population grid points. Arrival at the sampling point and sampling points The travel impedance between them can be found in step S4.

[0131] In this implementation, step S6 calculates the supply-demand ratio for each sampling point based on the variable radius of the supply and demand points, population selection probability, travel impedance, location and size of the demand points, and supply capacity of the supply points obtained from steps S1-S5. The accessibility from the population grid points to the sampling facility points is then obtained from the supply-demand ratio, and finally, the accessibility of each street is calculated using the average value method. Specifically, the steps include the following:

[0132] Step S61: Using the sampling point as the center, calculate the supply-demand ratio for each sampling point based on all population demand points within the search radius of each sampling point. The formula is as follows:

[0133]

[0134] In the formula, Sampling points The supply-demand ratio Sampling points Supply capacity Population grid points calculated based on the Huff model Arrival at the sampling point The probability of the selected population. For population grid points The population of the area For population grid points With sampling points Travel resistance between them.

[0135] Step S62: Centered on each population grid point, sum the supply and demand ratios of all sampling points within its search range, while considering distance decay and population selection probability, to obtain the sampling spatial accessibility of each population grid point. The formula is as follows:

[0136]

[0137] Step S63: Calculate the spatial reachability results of the population grid under the traditional 2SFCA, the 2SFCA based on the Huff model, and the variable radius 2SFCA in this embodiment, respectively, so as to facilitate subsequent comparison with the present invention.

[0138] Step S64: Generate a table of accessibility results from the four methods. Using ArcGIS spatial connectivity tools, connect the spatial accessibility of each population grid point to the population grid surface layer based on the population grid index. The resulting image is shown in... Figure 4 middle, Figure 4 (a) to Figure 4 (d) These figures represent the spatial accessibility results of the population grid obtained by traditional 2SFCA, Huff model-based 2SFCA, variable radius 2SFCA, and the method of this invention, respectively. These figures represent accessibility results obtained using different methods, and are all divided into five levels using the quartile method: very high, high, medium, low, and very low. The same color scheme is used for explanation; a darker hue indicates higher spatial accessibility in the region, and a lighter hue indicates lower spatial accessibility.

[0139] Step S65: Calculate the average spatial accessibility of all population grid points within each street area as the street-scale accessibility, using the following formula:

[0140]

[0141] In the formula, Spatial accessibility of sampling points for each street, The number of population grid points within each street area. The population grid points calculated in step S62 Spatial accessibility.

[0142] Step S66: Using the same steps, calculate the street spatial accessibility results obtained using the traditional 2SFCA method in this embodiment. Using the ArcGIS spatial connectivity tool, connect the spatial accessibility calculation results of each street face to the street face layer based on the street's isometric layer index. The result image is reflected in... Figure 5 In the image, from left to right, the street spatial accessibility is represented by: the traditional 2SFCA method and the method of this invention. It is divided into four levels using the quartile method: very high, high, medium, and low. The same color scheme is used for explanation; a darker hue indicates higher spatial accessibility, and a lighter hue indicates lower spatial accessibility.

[0143] In this implementation, step S7 uses the Accessibility Ratio Difference (ARD) index to compare the spatial accessibility results of 2SFCA based on the Huff model, 2SFCA with a variable radius, and the method of this invention with the results of traditional 2SFCA. This analyzes the differences in the spatial distribution pattern of accessibility at the grid point scale and verifies the feasibility of the method of this invention. Finally, corresponding suggestions are proposed to improve the rational allocation of sampling point resources. Specifically, the steps are as follows:

[0144] Step S71: Compare and analyze the differences between 2SFCA based on the Huff model and traditional 2SFCA. See the results in the figure below. Figure 6 (a) The formula is as follows:

[0145]

[0146] Step S72: Compare the differences between variable radius 2SFCA and traditional 2SFCA. See the results in the figure below. Figure 6 (b), the formula is as follows:

[0147]

[0148] Step S73: Compare and analyze the differences between the results of this invention and the traditional 2SFCA. See the results figure. Figure 6 (c) The formula is as follows:

[0149]

[0150] In the formula, , , and These are population grid points Spatial reachability is obtained using the method of this invention, 2SFCA based on the Huff model, variable radius 2SFCA, and conventional 2SFCA.

[0151] Step S74: Compare and analyze the differences in the spatial distribution patterns of accessibility at the grid point scale to verify the feasibility of the method of the present invention.

[0152] Step S75: According to this embodiment Figure 4 and Figure 5 The spatial distribution results of accessibility at the population grid scale and street scale reveal areas with low accessibility in some sampled spaces, which can be combined with this embodiment. Figure 3 For areas outside the "15-minute walking circle" in the sampling area, corresponding suggestions can be made to improve the rational allocation of sampling point resources.

[0153] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any changes or modifications made to the above embodiments based on the technical essence of the present invention are within the scope of the present invention.

Claims

1. An improved two-step move search method that simultaneously considers selection probability and variable radius, characterized in that, The specific steps are as follows: Step S1: Establish facility supply and demand data, where supply data includes the location of public service facilities and various attributes that can characterize the supply capacity of public service facilities; demand data is population grid data within a certain area, including the location and scale of demand points; Step S2: Build an accessibility model based on the Gaode API route planning interface, set the travel mode, and obtain the OD travel time cost; Step S3: Using each public service facility point and population grid point as the center, calculate the variable search radius for both using the 2SFCA method with variable radius; the specific steps are as follows: Step S31: Using each public service facility point as the center, the initial value... The initial search radius is used to calculate the total population within that radius. If the total population exceeds a given population threshold, then the initial search radius is adjusted. This is the search radius of the public service facility. If the total number of people is less than the given threshold, then a small increment needs to be added to the initial search radius. Then, recalculate the total number of people under the new search radius, and repeat the process until the total number of people reaches the given threshold. Step S32: Using the center point of each population grid as the center, the initial value... The initial search radius is defined as the ratio of the supply capacity of all service facilities to the population within that radius. If this ratio exceeds a given threshold, then the search radius is adjusted accordingly. That is, the search radius of the population grid point. If the ratio is less than a given ratio threshold, then a small increment needs to be added to the initial search radius. Then, recalculate the ratio of the supply capacity of all service facilities to the number of people under the new search radius, and repeat the process until the ratio reaches the given ratio threshold. Step S4: Calculate the travel impedance based on the travel time cost obtained in step S2 using the three-segment Gaussian distance attenuation function; Step S5: Based on the Huff model, calculate the probability of each population grid point selecting all public service facility points within its search radius; Step S6: Based on the variable radius of supply and demand points, population choice probability, travel impedance, location and size of demand points, and supply capacity of supply points obtained in steps S1-S5 above, calculate the supply-demand ratio for each public service facility point. Obtain the accessibility results from the population grid points to the public service facility points from the supply-demand ratio, and then calculate the accessibility of each street using the average value method. The specific steps are as follows: Step S61: Taking the public service facility as the center, calculate the supply-demand ratio for each public service facility based on all population demand points within the search radius of each facility. ; Step S62: Centered on each population grid point, sum the supply and demand ratios of all public service facilities within its search range, while considering distance decay and population selection probability, to obtain the spatial accessibility of each population grid point. ; Step S63: Calculate the spatial accessibility results of the population grid using the traditional 2SFCA, the 2SFCA based on the Huff model, the variable radius 2SFCA, and the methods in steps S1-S5 respectively. Use the quartile method to divide the accessibility results obtained by these four methods into five levels: very high, high, medium, low, and very low. Step S64: Calculate the average spatial accessibility of all population grid points within each street area as the street-scale accessibility; Step S65: Calculate the street spatial accessibility results using the traditional 2SFCA method, and divide the accessibility into four levels using the quartile method: very high, high, medium and low. Step S7: Using the accessibility ratio difference index, compare the spatial accessibility results of 2SFCA based on the Huff model, 2SFCA with variable radius, and the results of the traditional 2SFCA with the results of the methods in steps S1-S6. Analyze the differences in the spatial distribution pattern of accessibility at the grid point scale, verify the feasibility of the methods in steps S1-S6, and propose corresponding suggestions for improving the rational allocation of public service facility resources.

2. The improved two-step movement search method that simultaneously considers selection probability and variable radius according to claim 1, characterized in that, The specific steps of step S1 are as follows: Step S11: Obtain the address of the public service facility (i.e., the supply point) and relevant attributes that can characterize the supply capacity of the facility, and obtain the latitude and longitude of the supply point based on the address; Step S12: Obtain the population, i.e. the location and scale of the demand point. Based on the downloaded population data, resample it into grid cells within a certain area, using the population size as the scale of the demand point.

3. The improved two-step movement search method that simultaneously considers selection probability and variable radius according to claim 1, characterized in that, The specific steps of step S2 are as follows: Step S21: Convert the Earth coordinates of the public service facilities and the center point of the population grid to Mars coordinates, and then call the path planning interface of the Gaode Map API, starting from the center of the population grid and ending at the public service facilities, to simulate the supply and demand scenario of the real population. Step S22: By setting the traffic mode of the interface, obtain the OD travel time cost under different traffic modes.

4. An improved two-step movement search method that simultaneously considers selection probability and variable radius according to claim 1, characterized in that, The travel impedance expression in step S4 is as follows: In the formula and These represent two different ranges of search radius thresholds. For population grid points Arrival at public service facilities The time.

5. An improved two-step movement search method that simultaneously considers selection probability and variable radius according to claim 1, characterized in that, The specific steps of step S5 are as follows: The probability of each population grid point selecting any public service facility point within its search radius is calculated using the following formula: In the formula, Population grid points calculated based on the Huff model Arrival at public service facilities The probability of the selected population. Indicates population grid points The search radius, For population grid points Reach public service facilities within its search range Right now Travel time at that time It is a public service facility Supply capacity Public service facilities within the search area Right now Supply capacity at the time and These represent population grid points. Arrival Service Facilities Service facilities Travel resistance between them.

6. An improved two-step movement search method that simultaneously considers selection probability and variable radius according to claim 1, characterized in that, The expression for calculating the supply-demand ratio of public service facilities is as follows: The spatial reachability expression for each population grid point is as follows: The spatial accessibility expressions for public service facilities in each street are as follows: In the formula, in the formula, For service facilities The supply-demand ratio Service facilities Supply capacity Population grid points calculated based on the Huff model Arrival at service facility The probability of the selected population. For population grid points The population of the area For population grid points With service facilities Travel resistance between Accessibility of public service facilities in each street. The number of population grid points within each street area. The population grid points calculated in step S62 Spatial accessibility.

7. An improved two-step movement search method that simultaneously considers selection probability and variable radius according to claim 1, characterized in that, Step S7 specifically includes the following steps: Step S71: Compare and analyze the differences between 2SFCA based on the Huff model and traditional 2SFCA; Step S72: Compare the differences between variable radius 2SFCA and traditional 2SFCA; Step S73: Compare and analyze the differences between the results of steps S1-S6 and the traditional 2SFCA; Step S74: Compare and analyze the differences in the spatial distribution patterns of accessibility at the grid point scale; Step S75: Analyze the spatial distribution pattern of accessibility at the grid point scale and street scale to provide suggestions for reducing regional disparities in public service facilities.

8. An improved two-step movement search method that simultaneously considers selection probability and variable radius according to claim 7, characterized in that, The difference between the Huff model-based 2SFCA and the traditional 2SFCA is expressed as follows: The difference between variable radius 2SFCA and traditional 2SFCA is expressed as follows: The difference between the results of steps S1-S6 and the traditional 2SFCA is expressed as follows: In the formula, , , and These are population grid points Spatial reachability is obtained using steps S1-S6, Huff model-based 2SFCA, variable radius 2SFCA, and traditional 2SFCA.

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