Method for optimizing spatial layout of elderly care facilities based on multi-model and reachability analysis

Abstract

The present application relates to the technical field of data processing and spatial operations optimization, and particularly relates to a pension facility spatial layout optimization method based on multi-model and reachability analysis, which obtains the spatial distribution data of the elderly population by constructing a hexagonal grid, introduces a Gaussian distance decay function to improve the two-step moving search method, combines the multi-mode travel time cost and facility service capacity to measure the spatial reachability, identifies the supply-demand mismatch area based on the standard score model, constructs a hierarchical optimization strategy by fusing the P-barycenter location model and the reachability variance minimization model for the area, obtains the location scheme through the location optimization stage respectively, and obtains the configuration scheme by using the quadratic programming algorithm in the service capacity configuration stage, and the present application realizes the organic unification of the pension resource configuration efficiency and spatial fairness through the technical means of multi-model fusion and hierarchical progressive optimization.

Description

Technical Field

[0001] This invention relates to the fields of data processing and spatial operation optimization technology, and in particular to a method for optimizing the spatial layout of elderly care facilities based on multi-model and accessibility analysis. Background Technology

[0002] With the accelerating aging of cities, the scientific and rational spatial layout planning of elderly care facilities has become a core task in improving the urban public service system. In practical planning, it is necessary not only to macroscopically coordinate the distribution of the elderly population and transportation network conditions across the entire area to determine the optimal geographical location of new facilities to reduce the overall travel resistance of the elderly, but also to microscopically match the actual needs of different areas, scientifically allocating corresponding service beds and medical resource capacity to each facility. This dual planning, encompassing both spatial site selection and capacity allocation, is the fundamental guarantee for achieving the equalization and efficient utilization of urban public service resources.

[0003] However, when conducting layout planning, existing technologies typically couple spatial location selection and service capacity configuration into a single multi-objective nonlinear model for simultaneous solution. This approach results in excessively high computational dimensionality and extremely poor solution stability, making it difficult to balance spatial configuration efficiency and resource allocation fairness. Summary of the Invention

[0004] To overcome the above shortcomings, this invention provides a spatial layout optimization method for elderly care facilities based on multi-model and accessibility analysis, aiming to improve the technical defects of existing models that are prone to instability due to strong coupling and cannot balance efficiency and fairness.

[0005] In a first aspect, the present invention provides the following technical solution: a method for optimizing the spatial layout of elderly care facilities based on multi-model and accessibility analysis, comprising:

[0006] S1. Construct a hexagonal grid to aggregate population data at the residential community scale and obtain spatial distribution data of the elderly population;

[0007] S2. Obtain the time cost of multi-mode travel and the comprehensive service capability of facilities, introduce the Gaussian distance decay function to improve the two-step movement search method, combine the time cost of multi-mode travel and the comprehensive service capability of facilities, and perform spatial accessibility measurement based on the spatial distribution data of the elderly population to obtain the accessibility measurement results.

[0008] S3. Based on the standard score model, identify areas of supply-demand mismatch in elderly care facilities according to the accessibility measurement results;

[0009] S4. For the supply-demand mismatch area, integrate the P-centroid location model and the accessibility variance minimization model to construct a hierarchical optimization strategy for the proposed elderly care facility. The hierarchical optimization strategy includes a location optimization stage and a service capacity configuration stage.

[0010] S5. In the site selection optimization stage, the minimization of multimodal travel time cost is used as the objective function and input into the P-center of gravity site selection model to obtain the site selection optimization scheme of the proposed elderly care facility.

[0011] S6. In the service capacity configuration stage, based on the site selection optimization scheme, the accessibility variance minimization model is solved using a quadratic programming algorithm to obtain the service capacity configuration scheme of the proposed elderly care facility.

[0012] Preferably, in step S1, the step of constructing a hexagonal grid and aggregating population data at the residential community scale includes:

[0013] Based on the spatial scale of the study area and the preset walking distance threshold, a continuous hexagonal grid system covering the entire area is generated;

[0014] Establish a mapping relationship between residential community population data and spatial vector boundaries, and use spatial interpolation algorithms to project the community population into the corresponding hexagonal grid;

[0015] The projected grid population data is filtered by age structure, and the elderly population index within a single grid is aggregated and calculated to generate the spatial distribution data of the elderly population.

[0016] Preferably, in step S2, the step of obtaining the multi-modal travel time cost and the comprehensive service capability of facilities includes:

[0017] Extract the road network topology and real-time traffic impedance under various travel modes within the study area, and calculate the shortest time path matrix from each grid to each elderly care facility node;

[0018] An evaluation index system that includes facility scale and medical level is constructed, and the weight of each index is determined by a weight allocation algorithm. The comprehensive service capacity index of the elderly care facility is then calculated.

[0019] Based on the travel preference characteristics of the elderly population, a sharing ratio weight is assigned to the various travel modes, and the multi-mode time path matrix is ​​weighted and fused into a global multi-mode travel time cost matrix.

[0020] Preferably, in step S2, the step of introducing a Gaussian distance decay function to improve the two-step moving search method includes:

[0021] A first-level search domain is formed by setting time cost thresholds for each elderly care facility as the center. The distance impedance attenuation of the elderly population in the domain is calculated using the Gaussian distance attenuation function to obtain the initial supply-demand ratio of each facility.

[0022] A second-level search domain is formed by setting the same time cost threshold as the first-level search domain at the center of each grid, and the Gaussian distance decay function is used to spatially decay weight the initial supply-demand ratio of facilities falling into the domain.

[0023] The weighted supply-demand ratios of each facility are summed to calculate the expected value of elderly care resources for each grid after spatial attenuation weighting, which is used as the accessibility measurement result.

[0024] Preferably, in step S3, the step of identifying areas of supply-demand mismatch in elderly care facilities based on the standard score model and the accessibility measurement results includes:

[0025] Calculate the arithmetic mean and sample standard deviation of the expected global accessibility values ​​to establish a statistical benchmark for the overall supply level of elderly care facilities in the region.

[0026] Substitute the reachability measurement results of each grid into the standard score model to calculate and generate standard score values ​​that characterize the relative dispersion of each grid from the global average level;

[0027] The standard scores are reclassified based on the set significance threshold, and continuous grid groups with standard scores below the negative threshold are selected and marked as the supply-demand mismatch region.

[0028] Preferably, in step S4, the step of integrating the P-centroid location model and the accessibility variance minimization model to construct a hierarchical optimization strategy for the proposed elderly care facility includes:

[0029] A P-centroid location logic framework is constructed with the objective function of minimizing the weighted travel time of the elderly population across the entire region, to characterize spatial configuration efficiency;

[0030] A logical framework for minimizing reachability variance is constructed with the objective function of minimizing the statistical variance of the reachability values ​​of each grid cell, thus characterizing the fairness of resource allocation.

[0031] A cascaded mechanism is constructed that first optimizes space and then allocates resources. The coordinate parameters output by the addressing logic framework are used as the topological input of the variance minimization logic framework to form the hierarchical optimization strategy.

[0032] Preferably, in step S5, the step of minimizing the multimodal travel time cost as the objective function input into the P-center of gravity location model includes:

[0033] A gridded set of candidate points is deployed in the supply-demand mismatch area, and the maximum number of newly planned elderly care facilities is set according to the plan.

[0034] Establish the constraint that grid demand is covered by a single facility, and input the spatial distribution data of the elderly population and the time cost of multimodal travel into the objective function;

[0035] An optimization algorithm is used to iteratively solve the P-centroid location model, and the spatial coordinates of the facility that make the objective function converge are output as the location optimization scheme.

[0036] Preferably, in step S6, the step of solving the reachability variance minimization model using a quadratic programming algorithm includes:

[0037] Substituting the spatial coordinates determined by the site selection optimization scheme into the two-step moving search method improved by introducing the Gaussian distance decay function, a quadratic objective function of global grid reachability variance containing unknown service capability variables is derived.

[0038] Set an upper limit for the total construction scale as an equality constraint, and set upper and lower limits for the scale of each proposed elderly care facility as inequality constraints to construct a quadratic planning solution space;

[0039] The optimization solver is invoked to perform an iterative search in the feasible region along the opposite direction of the objective function gradient, and the solution of the objective variable that minimizes the reachability variance is output as the service capability configuration scheme.

[0040] Secondly, the present invention provides the following technical solution: a spatial layout optimization system for elderly care facilities based on multi-model and accessibility analysis, the system comprising:

[0041] The data aggregation and processing module is used to construct a hexagonal grid to aggregate population data at the residential community scale and obtain spatial distribution data of the elderly population.

[0042] The spatial accessibility measurement module is used to obtain the time cost of multi-modal travel and the comprehensive service capacity of facilities. It introduces a Gaussian distance decay function to improve the two-step movement search method, and combines the time cost of multi-modal travel and the comprehensive service capacity of facilities to perform spatial accessibility measurement based on the spatial distribution data of the elderly population to obtain the accessibility measurement results.

[0043] The mismatch area identification module is used to identify the supply-demand mismatch areas of elderly care facilities based on the standard score model and the accessibility measurement results;

[0044] A hierarchical strategy construction module is used to construct a hierarchical optimization strategy for the proposed elderly care facilities by integrating the P-centroid location model and the accessibility variance minimization model for the supply-demand mismatch area. The hierarchical optimization strategy includes a location optimization stage and a service capacity configuration stage.

[0045] The site selection optimization module is used to input the minimization of multimodal travel time cost as the objective function into the P-center of gravity site selection model during the site selection optimization stage, so as to obtain the site selection optimization scheme of the proposed elderly care facility.

[0046] The service capacity configuration module is used, during the service capacity configuration phase, to solve the accessibility variance minimization model using a quadratic programming algorithm based on the site selection optimization scheme, and to obtain the service capacity configuration scheme for the proposed elderly care facility.

[0047] The present invention has the following beneficial effects:

[0048] 1. In this invention, by constructing a hierarchical optimization strategy that prioritizes spatial optimization before resource allocation, the complex problem of multi-objective collaborative optimization of facility site selection and capacity configuration is decoupled into two cascaded single-objective optimization processes. It cleverly integrates the P-centroid site selection model and the accessibility variance minimization model, thereby achieving an organic unity of efficiency and spatial fairness in the allocation of elderly care resources.

[0049] 2. In this invention, a hexagonal grid is used to perform spatial interpolation and aggregation processing on population data at the residential community scale, thereby achieving a refined representation of the spatial distribution of the elderly population. At the same time, considering the time cost of multi-modal transportation and the comprehensive service capacity of facilities, a Gaussian distance decay function is introduced to improve the two-step movement search method, thereby enhancing the accuracy and scientific nature of the spatial accessibility measurement of elderly care facilities.

[0050] 3. In this invention, the standard score model is used to perform a quantitative analysis of the relative dispersion of spatial accessibility measurement results. By establishing a statistical benchmark for the overall supply level of the region, supply and demand mismatch areas with standard score values ​​below the negative threshold are screened and identified, effectively eliminating the interference of subjective experience and providing a reliable target spatial area for subsequent spatial layout optimization of facilities. Attached Figure Description

[0051] Figure 1 This is a flowchart of the spatial layout optimization method for elderly care facilities based on multi-model and accessibility analysis proposed in this invention;

[0052] Figure 2 This is an architecture diagram of the spatial layout optimization system for elderly care facilities based on multi-model and accessibility analysis proposed in this invention. Detailed Implementation

[0053] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] Example 1

[0055] In the first embodiment of the present invention, the present invention provides a method for optimizing the spatial layout of elderly care facilities based on multi-model and accessibility analysis, such as... Figure 1 As shown, it includes:

[0056] S1. Construct a hexagonal grid to aggregate population data at the residential community scale and obtain spatial distribution data of the elderly population;

[0057] Further, in step S1, the step of constructing a hexagonal grid and aggregating population data at the residential community scale includes: generating a continuous hexagonal grid system covering the entire area based on the spatial scale of the study area and a preset walking distance threshold; establishing a mapping relationship between the residential community population data and the spatial vector boundary, and projecting the community population into the corresponding hexagonal grid using a spatial interpolation algorithm; filtering the age structure of the projected grid population data, aggregating and calculating the elderly population index within a single grid, and generating spatial distribution data of the elderly population.

[0058] Specifically, spatial boundary vector data of the study area is acquired. The radius of the inscribed circle of the hexagonal grid is determined based on a preset walking distance threshold, which is set to a short-distance travel distance suitable for the physical capabilities of elderly individuals. The side length of the hexagon is calculated based on the inscribed circle radius. A continuous hexagonal grid system is generated within the spatial boundary vector data using spatial analysis tools. The geometric area calculation formula for a single hexagonal grid is as follows:

[0059] ;

[0060] In the formula, This represents the area covered by a single hexagonal grid. This indicates the length of one side of a hexagonal grid.

[0061] Collect vector polygon files of residential areas containing census data. Perform a spatial intersection overlay operation between the generated continuous hexagonal grid system and the residential area vector polygon files, segmenting and extracting the geometrically overlapping patches. Establish an area-weighted spatial interpolation model to project and allocate the census population of each residential area into the corresponding hexagonal grid according to the proportion of the overlapping patch area to the total area of ​​the original area. The initial population allocation formula for the grid is as follows:

[0062] ;

[0063] In the formula, Indicates the first The initial population size is obtained by projecting a hexagonal grid. Indicates the first The total census population of each residential community. Indicates the first The hexagonal grid and the first The area of ​​the actual overlapping patches in the spatial arrangement of residential communities. Indicates the first The total area of ​​the residential communities Indicates the relationship with the first The total number of residential communities where hexagonal grids intersect spatially.

[0064] Perform age structure feature filtering on the projected grid population data. Extract the proportion of the population in the residential community that has reached the preset aging threshold. Combine the extracted proportion of the elderly population with the corresponding initial population allocation base of the grid to calculate the absolute number of elderly people in a single grid. The specific formula for calculating the elderly population index is as follows:

[0065] ;

[0066] In the formula, Indicates the first The final elderly population index generated within a hexagonal grid Indicates the first The proportion of elderly people in a residential community to the total census population of that community. The calculation results of all hexagonal grids across the entire area are aggregated and combined to form spatial distribution data of the elderly population with unified geographic coordinates and population attributes.

[0067] This step transforms irregularly shaped and geographically diverse residential population data into standardized cellular grid data, improving the accuracy of population spatial distribution representation.

[0068] S2. Obtain the time cost of multi-modal travel and the comprehensive service capacity of facilities, introduce the Gaussian distance decay function to improve the two-step movement search method, integrate the time cost of multi-modal travel and the comprehensive service capacity of facilities, and measure spatial accessibility based on the spatial distribution data of the elderly population to obtain the accessibility measurement results.

[0069] Furthermore, in step S2, the steps of obtaining multi-modal travel time costs and comprehensive facility service capabilities include: extracting the road network topology and real-time traffic impedance under various travel modes within the study area, calculating the shortest time path matrix from each grid to each elderly care facility node; constructing an evaluation index system that includes facility scale and medical level, using a weight allocation algorithm to determine the weight of each index, and calculating the comprehensive service capability index of elderly care facilities; based on the travel preference characteristics of the elderly population, assigning sharing ratio weights to various travel modes, and weighting and merging the multi-modal time path matrix into a global multi-modal travel time cost matrix.

[0070] Furthermore, in step S2, the two-step moving search method is improved by introducing a Gaussian distance decay function, which includes: setting a time cost threshold centered on each elderly care facility to form a first-level search domain; using the Gaussian distance decay function to calculate the distance impedance decay of the elderly population within the domain to obtain the initial supply-demand ratio of each facility; setting the same time cost threshold as the first-level search domain centered on each grid to form a second-level search domain; using the Gaussian distance decay function to spatially decay-weight the initial supply-demand ratio of facilities falling within the domain; summing the weighted supply-demand ratios of each facility to calculate the expected value of elderly care resources for each grid after spatial decay weighting, which serves as the accessibility measurement result.

[0071] Specifically, the study extracts road network topology vector data and traffic impedance features including real-time congestion coefficients for three travel modes within the study area: walking, public transportation, motor vehicles, and driving. The shortest path algorithm is used to calculate the shortest travel time from the geometric center node of each grid to the spatial nodes of each elderly care facility, generating time path matrices for different travel modes. Matrix elements. Indicates the first From the first travel mode The elderly population grid to the first The shortest travel time between each elderly care facility node.

[0072] An evaluation index system was constructed by extracting attribute data from elderly care facilities. A weighting algorithm was used to determine the weight coefficients of each service indicator. The evaluation indicators were then normalized and weighted summed to calculate the comprehensive service capacity index of each elderly care facility. The formula for calculating the comprehensive service capacity is as follows:

[0073] ;

[0074] In the formula, Indicates the first The comprehensive service capacity index of an elderly care facility This indicates the total number of evaluation indicators, including the ratio of facility beds to medical staff. This represents the result obtained through the weight allocation algorithm. The weight values ​​of each evaluation indicator, Indicates the first The elderly care facility in the Normalized values ​​for each evaluation indicator.

[0075] Based on the actual travel preferences of the elderly population, corresponding modal share weights are assigned to walking, public transportation, and driving. The shortest time path matrices of these three modes are then weighted and fused to generate a global multimodal travel time cost matrix. The formula for calculating the global multimodal travel time cost is as follows:

[0076] ;

[0077] In the formula, Indicates from the first The elderly population grid to the first Global multimodal travel time cost for individual elderly care facility nodes Represents a set of travel modes. Indicates the first The sharing ratio weights of each travel mode are assigned, and the sum of the weights of each mode is 1.

[0078] A Gaussian distance attenuation function is introduced to calculate the continuous attenuation of travel time impedance. The formula for calculating the Gaussian distance attenuation weight is as follows:

[0079] ;

[0080] In the formula, This represents the Gaussian distance decay weight value after time cost threshold normalization. This represents the preset limit of time cost threshold, when Less than or equal to Calculate the weight when Greater than The weight is then assigned a value of 0.

[0081] Centered on the spatial nodes where each elderly care facility is located, the extreme time cost threshold is set as the boundary of the first-level search domain. All coverage grids with a global multimodal travel time cost less than or equal to this time cost threshold are selected. Using the aforementioned Gaussian distance decay function, distance impedance attenuation is calculated for the number of elderly people in each grid falling within this search domain. The comprehensive service capacity index of each elderly care facility is then divided by the weighted sum of the attenuated elderly population to obtain the initial supply-demand ratio for each facility. The formula for calculating the initial supply-demand ratio is as follows:

[0082] ;

[0083] In the formula, Indicates the first The initial supply-demand ratio of an elderly care facility, For the first The comprehensive service capacity index of an elderly care facility Indicates up to the A grid set whose global multimodal travel time cost for each elderly care facility is less than or equal to the limit time cost threshold. Indicates the first [item] falling within the search domain The indicator of the number of elderly people within each grid, For the first The grid number to the first Gaussian distance decay weighting values ​​for each elderly care facility.

[0084] Centered on the geometric center of each elderly population distribution grid, a second-level search domain is formed by setting the same extreme time cost threshold as the first-level search domain. All elderly care facilities covered within the reachable time range are then selected. The same Gaussian distance decay function is used to spatially attenuate and weight the initial supply-demand ratio of each elderly care facility falling within the second-level search domain. The weighted supply-demand ratios of each elderly care facility are then linearly summed to calculate the expected value of elderly care resources actually acquired by each grid after overcoming distance impedance. This value is used as the spatial accessibility measure result. The formula for calculating the spatial accessibility measure result is as follows:

[0085] ;

[0086] In the formula, Indicates the first Spatial accessibility measurement results of an elderly population distribution grid Indicates up to the A set of elderly care facilities whose global multimodal travel time cost per grid is less than or equal to the limit time cost threshold. For the first to fall within the search domain The initial supply-demand ratio of an elderly care facility, For the first The grid number to the first Gaussian distance decay weighting values ​​for each elderly care facility.

[0087] This step takes into account the differences in facility size and the reality of mixed travel using multiple modes of transportation, thus improving the accuracy of measuring the spatial accessibility of elderly care facilities.

[0088] S3. Based on the standard score model, identify areas of supply-demand mismatch in elderly care facilities according to the accessibility measurement results;

[0089] Further, in step S3, the step of identifying supply-demand mismatch areas of elderly care facilities based on the standard score model and the accessibility measurement results includes: calculating the arithmetic mean and sample standard deviation of the global accessibility expectation value to establish a statistical benchmark for the overall supply level of elderly care facilities in the region; substituting the accessibility measurement results of each grid into the standard score model to calculate and generate standard score values ​​that characterize the relative dispersion of each grid from the global average level; reclassifying the standard score values ​​according to the set significance threshold, and selecting continuous grid groups with standard score values ​​below the negative threshold as supply-demand mismatch areas.

[0090] Specifically, the spatial accessibility measurement results of all hexagonal grids within the study area are extracted. The arithmetic mean of the expected global accessibility values ​​is calculated to establish an absolute statistical benchmark for the overall supply level of elderly care facilities in the region. The formula for calculating the global arithmetic mean is as follows:

[0091] ;

[0092] In the formula, This represents the arithmetic mean of global reachability across all grids within the study area. This represents the total number of hexagonal grids containing elderly people within the study area. Indicates the first Spatial accessibility measurement results of an elderly population distribution grid.

[0093] The sample standard deviation of all grid accessibility measures relative to the arithmetic mean is calculated to quantify the discrete distribution characteristics of the overall supply level of elderly care facilities in the region. The formula for calculating the sample standard deviation is as follows:

[0094] ;

[0095] In the formula, The sample standard deviation represents the global accessibility measurement results and is used to assess the degree of uneven distribution of elderly care resources among different grids.

[0096] The reachability measure results of each grid are substituted into the standard score model for linear transformation to calculate a standard score value representing the relative dispersion of each grid from the global average level. The specific formula for calculating the standard score value is as follows:

[0097] ;

[0098] In the formula, Indicates the first The standard score value of each grid representing the distribution of the elderly population reflects the relative position of the grid's actual access to elderly care resources within the global statistical distribution.

[0099] A negative threshold value for the standard score was determined based on a set statistical significance level. Spatial reclassification was performed on the standard scores of all grid cells in the geographic information system. Grid cells with standard scores strictly below the negative threshold were extracted. These grid cells indicate that their accessibility to elderly care facilities is significantly worse than the regional average and that there is a high demand gap. Spatial connectivity analysis was performed on the extracted grid cells to remove isolated and singular grid patches, and to screen out low-standard-score grid groups that are spatially adjacent and continuous. These continuous grid groups were uniformly extracted from the spatial database and marked as areas of supply-demand mismatch for elderly care facilities, serving as target spatial areas for subsequent site selection and capacity allocation of proposed elderly care facilities.

[0100] This step quantifies the resource scarcity of each spatial unit using a unified statistical scale, eliminating the interference of subjective experience and accurately identifying areas that require key optimization of the layout.

[0101] S4. For areas with supply-demand mismatch, integrate the P-centroid location model and the accessibility variance minimization model to construct a hierarchical optimization strategy for proposed elderly care facilities. The hierarchical optimization strategy includes a location optimization stage and a service capacity configuration stage.

[0102] Furthermore, in step S4, the steps of integrating the P-centroid location model and the accessibility variance minimization model to construct a hierarchical optimization strategy for the proposed elderly care facility include: constructing a P-centroid location logic framework with the objective function of minimizing the weighted travel time of the entire elderly population, representing spatial configuration efficiency; constructing an accessibility variance minimization logic framework with the objective function of minimizing the statistical variance of the accessibility values ​​of each grid unit, representing the fairness of resource allocation; and constructing a cascade mechanism of first spatial optimization and then resource allocation, using the coordinate parameters output by the location logic framework as the topological input of the variance minimization logic framework to form a hierarchical optimization strategy.

[0103] Specifically, the geometric centers of all hexagonal grids within the supply-demand mismatch area are extracted as the candidate spatial node set for proposed elderly care facilities. A P-centroid location logic framework is constructed with the objective function of minimizing the weighted travel time of the entire elderly population. This framework introduces Boolean decision variables to represent the spatial allocation relationship between grid demand points and candidate facility points, and sets the maximum number of proposed elderly care facilities as a boundary constraint. The objective function calculation formula for the P-centroid location logic framework is as follows:

[0104] ;

[0105] In the formula, This represents the total weighted travel time cost for the entire elderly population to overcome spatial resistance and reach the proposed elderly care facility. This represents the total number of grids in the entire region that include the elderly population. This represents the total number of candidate elderly care facility nodes deployed in areas with supply-demand mismatch. Indicates the first The absolute number of elderly people within each grid Indicates from the first The grid number to the first Global multimodal travel time cost for each candidate elderly care facility node Assign Boolean decision variables to the space, when the first The travel needs of the elderly population in the first grid were allocated to the second grid. The value is 1 when there are candidate elderly care facility nodes, and 0 when no node is assigned. This logical framework represents the spatial allocation efficiency of elderly care resources by minimizing the overall travel time cost for the elderly population.

[0106] A logical framework for minimizing accessibility variance is constructed, with the objective function being the minimization of the statistical variance of the accessibility values ​​of each grid cell. This framework concretizes the comprehensive service capacity of the proposed elderly care facility into variable, continuous numerical measures, such as the number of newly planned beds. The objective function of the accessibility variance minimization logical framework is calculated as follows:

[0107] ;

[0108] In the formula, This represents the statistical variance of the spatial accessibility measurement results for each grid in the entire region after the introduction of the proposed elderly care facility resources. This represents the total number of grids in the entire region that include the elderly population. This indicates the result of combining the existing elderly care facility service capacity with the proposed comprehensive elderly care facility service capacity. Expected spatial reachability of each grid after update Indicates the first The expected spatial accessibility value after grid updates. This logical framework characterizes the fairness of resource allocation by reducing the degree of difference in the amount of access to elderly care resources between different spatial grids within a region.

[0109] A cascaded coupling mechanism is constructed, prioritizing spatial optimization followed by resource allocation. The aforementioned P-center-of-gravity location logic framework is divided into a location optimization stage within a hierarchical optimization strategy. The optimal facility spatial latitude and longitude coordinate parameters and the corresponding grid spatial allocation relation matrix are extracted from the framework's solution. The output latitude and longitude coordinate parameters and allocation relation matrix are then unidirectionally input into the reachability variance minimization logic framework as known parameters of a fixed network topology. This variance minimization logic framework is further divided into a service capacity configuration stage within the hierarchical optimization strategy. Under the premise of locking spatial coordinate variables and the allocation relation network, the optimal integrated service capacity configuration scale is solved separately. A hierarchical optimization strategy based on unidirectional parameter transfer is formed, achieving dimensionality reduction.

[0110] This step decouples the complex multi-objective nonlinear collaborative optimization problem of facility site selection and capacity configuration into two cascaded single-objective optimization processes, reducing computational dimensionality and ensuring the stability of the solution.

[0111] S5. In the site selection optimization stage, the minimization of multimodal travel time cost is used as the objective function input into the P-centroid site selection model to obtain the site selection optimization scheme for the proposed elderly care facility.

[0112] Furthermore, in step S5, the step of minimizing the multimodal travel time cost as the objective function input into the P-centroid location model includes: deploying a gridded candidate point set in the supply-demand mismatch area, setting the maximum number of newly built elderly care facilities allowed according to the plan; establishing the constraint that grid demand is covered by a single facility, and inputting the spatial distribution data of the elderly population and the multimodal travel time cost into the objective function; using an optimization algorithm to iteratively solve the P-centroid location model, and outputting the facility spatial coordinates that make the objective function converge as the location optimization scheme.

[0113] Specifically, the spatial geometric centers of all hexagonal grids within the supply-demand mismatch area are extracted and used as the discrete candidate point set for proposed elderly care facilities. The maximum number of newly permitted elderly care facilities is obtained from urban planning data and set as a positive integer constant parameter in the site selection model.

[0114] A strict constraint system is established to ensure that grid demand is covered by a single facility. First, the total number of facilities actually constructed is strictly equal to the maximum number set in the plan. Second, each grid demand containing elderly residents can only be allocated to one and only one proposed elderly care facility to avoid demand fragmentation. Finally, a logical dependency constraint is established, requiring that elderly population demand from a grid can only be allocated to a candidate site after the construction of a facility is confirmed. The formula for calculating the constraint system of the P-centroid location model is as follows:

[0115] ;

[0116] ;

[0117] ;

[0118] In the formula, This represents the total number of candidate points within the supply-demand mismatch area. This indicates the maximum number of new proposed elderly care facilities that are permitted to be built. As a variable in facility construction decisions, when in the first... When a candidate site is selected for the proposed construction of elderly care facilities, the value is 1; otherwise, the value is 0. Assign decision variables to the space, when the first The travel needs of the elderly population in the first grid were allocated to the second grid. The value is 1 if there are 1 candidate points, otherwise it is 0. Based on the above constraints, the absolute number of elderly people in each grid and the global multimodal travel time cost are input into the P-centroid location objective function, which aims to minimize the weighted travel time across the entire region.

[0119] Heuristic optimization algorithms, such as genetic algorithms, are used to iteratively solve the constructed P-centroid location model. The facility construction decision variables are encoded as binary chromosome sequences of length equal to the total number of candidate points, with the number of gene positions with a value of 1 strictly limited to this maximum value. The reciprocal of the objective function for minimizing the weighted travel time across the entire domain is set as the fitness evaluation function of the genetic algorithm. Roulette wheel selection with single-point crossover and basic position mutation operations is used to perform nonlinear iterative optimization in the solution space. When the calculated fitness function value remains unchanged for multiple consecutive preset iteration periods or reaches the set maximum number of iterations, the objective function is considered to have converged. The chromosome with the highest fitness value at this point is decoded, and the spatial latitude and longitude coordinates of the candidate points corresponding to the gene positions with a value of 1 are extracted and combined as the optimized location scheme for the proposed elderly care facility.

[0120] This step determined the specific latitude and longitude locations of new facilities under the boundary condition of limited facility construction, minimizing the overall transportation resistance of the elderly population in the area.

[0121] S6. In the service capacity configuration phase, based on the site selection optimization scheme, the quadratic programming algorithm is used to solve the accessibility variance minimization model to obtain the service capacity configuration scheme of the proposed elderly care facility.

[0122] Further, in step S6, the step of using a quadratic programming algorithm to solve the accessibility variance minimization model includes: substituting the spatial coordinates determined by the site selection optimization scheme into the two-step moving search method improved by introducing the Gaussian distance decay function, and deriving the quadratic objective function of global grid accessibility variance containing unknown service capacity variables; setting the upper limit of the total construction scale as an equality constraint, and setting the upper and lower limits of the scale of each proposed elderly care facility as inequality constraints, and constructing the quadratic programming solution space; calling the optimization solver to perform an iterative search in the feasible region along the opposite direction of the objective function gradient, and outputting the objective variable solution that minimizes the accessibility variance as the service capacity configuration scheme.

[0123] Specifically, the spatial latitude and longitude coordinates of the proposed elderly care facility output from the site selection optimization stage are extracted and used as known spatial nodes. The comprehensive service capacity of the proposed elderly care facility is set as an unknown service capacity variable, specifically represented by the number of newly added elderly care beds to be allocated. The known spatial latitude and longitude coordinates and the unknown service capacity variable are substituted into a two-step moving search method improved with a Gaussian distance decay function to calculate the first... The expected spatial accessibility value of the entire region after overlaying the proposed elderly care facilities on a grid. The formula for calculating the expected spatial accessibility value of the entire region is as follows:

[0124] ;

[0125] In the formula, Indicates the first The expected spatial accessibility of the entire area after overlaying the proposed elderly care facilities on a grid. Indicates the first Each grid relies solely on existing spatial accessibility measurements of elderly care facilities. This indicates the total number of proposed elderly care facilities determined by the site selection optimization plan. Indicates the first The unknown service capacity variable of the proposed elderly care facility Indicates the first The grid number to the first Gaussian distance decay weighting value for a proposed elderly care facility. Indicates falling into the first A set of grids within the search domain for the ultimate time cost threshold of a proposed elderly care facility. Indicates the number of items falling within this search domain. The indicator of the number of elderly people within each grid, Indicates the first The grid number to the first The Gaussian distance attenuation weight value for each proposed elderly care facility. Substituting the above expression into the accessibility variance calculation formula, a quadratic objective function for global grid accessibility variance, including unknown service capacity variables, is derived.

[0126] Obtain the total control indicators for newly added elderly care resources from the regional construction planning data, and set an upper limit for the total construction scale as an equality constraint. Set a minimum bed capacity and a maximum bed capacity limit for each proposed elderly care facility in actual operation as inequality constraints. Construct a quadratic programming solution space by simultaneously solving the quadratic objective function and the above constraints. The mathematical model formula for the quadratic programming solution space is as follows:

[0127] ;

[0128] ;

[0129] ;

[0130] In the formula, This represents the total number of grids in the entire region that include the elderly population. Indicates the first The expected spatial accessibility of the entire area after overlaying the proposed elderly care facilities on a grid. This represents the equation constraint parameter representing the upper limit of the total construction scale set in the regional plan. and These represent the lower and upper limits of the inequality constraint parameters for the construction scale of a single proposed elderly care facility, respectively.

[0131] The mathematical optimization solver, incorporating the interior-point method, is invoked to iteratively compute the constructed quadratic programming solution space. An initial iterative search point is set within the multidimensional feasible region, comprised of equality and inequality constraints. The first derivative vector of the quadratic objective function representing the global grid reachability variance at that point is calculated, i.e., the gradient vector. The optimal search step size is determined through a one-dimensional search along the inverse direction of the objective function gradient, updating the position of the current iteration point. This process of calculating the gradient and updating the iteration point is repeated until the change in the objective function value between two consecutive iterations is less than the set minimum convergence precision, at which point the iterative search process is considered converged. The corresponding solution for the unknown service capacity variable is output as the objective variable solution that minimizes the global grid reachability variance. This objective variable solution is then transformed into the specific number of beds for each proposed elderly care facility, generating and outputting the final service capacity configuration scheme.

[0132] This step rationally allocated specific facility capacity based on the determined optimal spatial location, effectively alleviating the contradiction of uneven distribution of elderly care resources among regions.

[0133] Example 2

[0134] In layout planning, spatial site selection and service capacity configuration are typically forcibly coupled into a single multi-objective nonlinear model for simultaneous solution. This approach results in excessively high model dimensionality and extremely poor solution stability, making it difficult to balance spatial configuration efficiency and resource allocation fairness. To address these issues, this invention provides a spatial layout optimization system for elderly care facilities based on multi-model and accessibility analysis, the structure of which is as follows: Figure 2 As shown. The specific implementation process of this system is as follows:

[0135] The data aggregation and processing module is used to construct a hexagonal grid to aggregate population data at the residential community scale and obtain spatial distribution data of the elderly population.

[0136] The spatial accessibility measurement module is used to obtain the time cost of multi-modal travel and the comprehensive service capacity of facilities. It introduces a Gaussian distance decay function to improve the two-step movement search method, and combines the time cost of multi-modal travel and the comprehensive service capacity of facilities to perform spatial accessibility measurement based on the spatial distribution data of the elderly population to obtain the accessibility measurement results.

[0137] The mismatch area identification module is used to identify the supply-demand mismatch areas of elderly care facilities based on the standard score model and the accessibility measurement results;

[0138] A hierarchical strategy construction module is used to construct a hierarchical optimization strategy for the proposed elderly care facilities by integrating the P-centroid location model and the accessibility variance minimization model for the supply-demand mismatch area. The hierarchical optimization strategy includes a location optimization stage and a service capacity configuration stage.

[0139] The site selection optimization module is used to input the minimization of multimodal travel time cost as the objective function into the P-center of gravity site selection model during the site selection optimization stage, so as to obtain the site selection optimization scheme of the proposed elderly care facility.

[0140] The service capacity configuration module is used, during the service capacity configuration phase, to solve the accessibility variance minimization model using a quadratic programming algorithm based on the site selection optimization scheme, and to obtain the service capacity configuration scheme for the proposed elderly care facility.

[0141] Specifically, the data aggregation and processing module first converts the irregular residential population data into spatial distribution data of the elderly population in a standard hexagonal grid. Then, the spatial accessibility measurement module calculates the expected accessibility value of each grid based on this data, combining multi-modal traffic impedance and a Gaussian decay function. Next, the mismatch area identification module uses statistical benchmarks to accurately pinpoint target areas of supply-demand mismatch that urgently need optimization. For these target areas, the hierarchical strategy construction module establishes a dimensionality reduction and decoupling mechanism that prioritizes spatial optimization followed by resource allocation. Finally, the site selection optimization module executes the first stage of optimization, solving for P under the constraint of controlling the total quantity. - The center-of-gravity location model outputs the specific latitude and longitude coordinates of the proposed facilities. Finally, the service capacity configuration module uses these coordinates as a fixed topology input. In the second stage, a quadratic programming algorithm is used to specifically solve the optimal service capacity quota for each proposed facility. Through the unidirectional flow of data and step-by-step calculation between the above modules, this system cleverly transforms the originally high-dimensional and easily unstable multi-objective strongly coupled problem into two serial single-objective optimization processes. While significantly reducing the computational complexity of the algorithm, it ensures that the final output layout scheme can perfectly balance the spatial configuration efficiency of facilities and the fairness of the allocation of elderly care resources.

[0142] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing the spatial layout of elderly care facilities based on multi-model and accessibility analysis, characterized in that, include: S1. Construct a hexagonal grid to aggregate population data at the residential community scale and obtain spatial distribution data of the elderly population; S2. Obtain the time cost of multi-mode travel and the comprehensive service capability of facilities, introduce the Gaussian distance decay function to improve the two-step movement search method, combine the time cost of multi-mode travel and the comprehensive service capability of facilities, and perform spatial accessibility measurement based on the spatial distribution data of the elderly population to obtain the accessibility measurement results. S3. Based on the standard score model, identify areas of supply-demand mismatch in elderly care facilities according to the accessibility measurement results; S4. For the supply-demand mismatch area, integrate the P-centroid location model and the accessibility variance minimization model to construct a hierarchical optimization strategy for the proposed elderly care facility. The hierarchical optimization strategy includes a location optimization stage and a service capacity configuration stage. S5. In the site selection optimization stage, the minimization of multimodal travel time cost is used as the objective function and input into the P-center of gravity site selection model to obtain the site selection optimization scheme of the proposed elderly care facility. S6. In the service capacity configuration stage, based on the site selection optimization scheme, the accessibility variance minimization model is solved using a quadratic programming algorithm to obtain the service capacity configuration scheme of the proposed elderly care facility.

2. The method for optimizing the spatial layout of elderly care facilities based on multi-model and accessibility analysis according to claim 1, characterized in that, In step S1, the step of constructing a hexagonal grid and aggregating population data at the residential community scale includes: Based on the spatial scale of the study area and the preset walking distance threshold, a continuous hexagonal grid system covering the entire area is generated; Establish a mapping relationship between residential community population data and spatial vector boundaries, and use spatial interpolation algorithms to project the community population into the corresponding hexagonal grid; The projected grid population data is filtered by age structure, and the elderly population index within a single grid is aggregated and calculated to generate the spatial distribution data of the elderly population.

3. The method for optimizing the spatial layout of elderly care facilities based on multi-model and accessibility analysis according to claim 1, characterized in that, Step S2, the step of obtaining multi-modal travel time costs and integrated facility service capabilities, includes: Extract the road network topology and real-time traffic impedance under various travel modes within the study area, and calculate the shortest time path matrix from each grid to each elderly care facility node; An evaluation index system that includes facility scale and medical level is constructed, and the weight of each index is determined by a weight allocation algorithm. The comprehensive service capacity index of the elderly care facility is then calculated. Based on the travel preference characteristics of the elderly population, a sharing ratio weight is assigned to the various travel modes, and the multi-mode time path matrix is ​​weighted and fused into a global multi-mode travel time cost matrix.

4. The method for optimizing the spatial layout of elderly care facilities based on multi-model and accessibility analysis according to claim 1, characterized in that, In step S2, the step of introducing a Gaussian distance decay function to improve the two-step moving search method includes: A first-level search domain is formed by setting time cost thresholds for each elderly care facility as the center. The distance impedance attenuation of the elderly population in the domain is calculated using the Gaussian distance attenuation function to obtain the initial supply-demand ratio of each facility. A second-level search domain is formed by setting the same time cost threshold as the first-level search domain at the center of each grid, and the Gaussian distance decay function is used to spatially decay weight the initial supply-demand ratio of facilities falling into the domain. The weighted supply-demand ratios of each facility are summed to calculate the expected value of elderly care resources for each grid after spatial attenuation weighting, which is used as the accessibility measurement result.

5. The method for optimizing the spatial layout of elderly care facilities based on multi-model and accessibility analysis according to claim 1, characterized in that, Step S3, the step of identifying areas of supply-demand mismatch in elderly care facilities based on the standard score model and the accessibility measurement results, includes: Calculate the arithmetic mean and sample standard deviation of the expected global accessibility values ​​to establish a statistical benchmark for the overall supply level of elderly care facilities in the region. Substitute the reachability measurement results of each grid into the standard score model to calculate and generate standard score values ​​that characterize the relative dispersion of each grid from the global average level; The standard scores are reclassified based on the set significance threshold, and continuous grid groups with standard scores below the negative threshold are selected and marked as the supply-demand mismatch region.

6. The method for optimizing the spatial layout of elderly care facilities based on multi-model and accessibility analysis according to claim 1, characterized in that, Step S4, the step of integrating the P-centroid location model and the accessibility variance minimization model to construct a hierarchical optimization strategy for the proposed elderly care facility, includes: A P-centroid location logic framework is constructed with the objective function of minimizing the weighted travel time of the elderly population across the entire region, to characterize spatial configuration efficiency; A logical framework for minimizing reachability variance is constructed with the objective function of minimizing the statistical variance of the reachability values ​​of each grid cell, thus characterizing the fairness of resource allocation. A cascaded mechanism is constructed that first optimizes space and then allocates resources. The coordinate parameters output by the addressing logic framework are used as the topological input of the variance minimization logic framework to form the hierarchical optimization strategy.

7. The method for optimizing the spatial layout of elderly care facilities based on multi-model and accessibility analysis according to claim 1, characterized in that, Step S5, the step of minimizing the multimodal travel time cost as the objective function input into the P-center of gravity location model, includes: A gridded set of candidate points is deployed in the supply-demand mismatch area, and the maximum number of newly planned elderly care facilities is set according to the plan. Establish the constraint that grid demand is covered by a single facility, and input the spatial distribution data of the elderly population and the time cost of multimodal travel into the objective function; An optimization algorithm is used to iteratively solve the P-centroid location model, and the spatial coordinates of the facility that make the objective function converge are output as the location optimization scheme.

8. The method for optimizing the spatial layout of elderly care facilities based on multi-model and accessibility analysis according to claim 1, characterized in that, Step S6, the step of using a quadratic programming algorithm to solve the reachability variance minimization model, includes: Substituting the spatial coordinates determined by the site selection optimization scheme into the two-step moving search method improved by introducing the Gaussian distance decay function, a quadratic objective function of global grid reachability variance containing unknown service capability variables is derived. Set an upper limit for the total construction scale as an equality constraint, and set upper and lower limits for the scale of each proposed elderly care facility as inequality constraints to construct a quadratic planning solution space; The optimization solver is invoked to perform an iterative search in the feasible region along the opposite direction of the objective function gradient, and the solution of the objective variable that minimizes the reachability variance is output as the service capability configuration scheme.

9. A spatial layout optimization system for elderly care facilities based on multi-model and accessibility analysis, characterized in that, The system for the spatial layout optimization method for elderly care facilities based on multi-model and accessibility analysis as described in any one of claims 1-8 comprises: The data aggregation and processing module is used to construct a hexagonal grid to aggregate population data at the residential community scale and obtain spatial distribution data of the elderly population. The spatial accessibility measurement module is used to obtain the time cost of multi-modal travel and the comprehensive service capacity of facilities. It introduces a Gaussian distance decay function to improve the two-step movement search method, and combines the time cost of multi-modal travel and the comprehensive service capacity of facilities to perform spatial accessibility measurement based on the spatial distribution data of the elderly population to obtain the accessibility measurement results. The mismatch area identification module is used to identify the supply-demand mismatch areas of elderly care facilities based on the standard score model and the accessibility measurement results; A hierarchical strategy construction module is used to construct a hierarchical optimization strategy for the proposed elderly care facilities by integrating the P-centroid location model and the accessibility variance minimization model for the supply-demand mismatch area. The hierarchical optimization strategy includes a location optimization stage and a service capacity configuration stage. The site selection optimization module is used to input the minimization of multimodal travel time cost as the objective function into the P-center of gravity site selection model during the site selection optimization stage, so as to obtain the site selection optimization scheme of the proposed elderly care facility. The service capacity configuration module is used, during the service capacity configuration phase, to solve the accessibility variance minimization model using a quadratic programming algorithm based on the site selection optimization scheme, and to obtain the service capacity configuration scheme for the proposed elderly care facility.

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