A response human responsibility area division optimization method based on diffusion-repair heuristic

Abstract

The application discloses a response person responsibility area division optimization method based on diffusion-repair heuristic, comprising the following steps: S1, acquiring a region graph; S2, acquiring a candidate response person set; S3, selecting a group of candidate response persons according to a preset rule to form a pre-recruited response person group; S4, generating an initial responsibility field mapping for each candidate response person in the pre-recruited response person group based on the region graph; S5, determining an uncovered region set based on the region graph and the initial responsibility field mapping; S6, when the uncovered region set is not empty, determining a target response person responsible for repairing for each uncovered region unit in the uncovered region set, repairing the responsibility field region set according to whether the target response person belongs to the pre-recruited response person group, and forming a new responsibility field region set; repeating steps S5 and S6 until the uncovered region set is empty or a preset termination condition is reached. The application can quickly and efficiently divide the optimal responsibility area for the response person.

Description

Technical Field

[0001] This invention relates to the fields of out-of-hospital cardiac arrest rescue resource allocation, graph computation, and combinatorial optimization. Specifically, it relates to a method for rapidly generating responder responsibility fields that meet constraints of coverage, connectivity, number of people, and workload by using a diffusion-check-repair closed loop on a rescue area map. Background Technology

[0002] In emergencies such as out-of-hospital cardiac arrest, the effectiveness of rescue is highly time-sensitive. If community volunteers can promptly perform CPR or use an automated external defibrillator (AED) before professional emergency responders arrive, the patient's survival rate will be greatly improved. However, this rapid response is highly dependent on whether reasonable personnel coverage and clear responsibility area allocation have been established beforehand.

[0003] Emergency management departments need to select recruited responders from a large pool of candidates and assign each responder a designated area of ​​responsibility that they must continuously familiarize themselves with. This area of ​​responsibility must cover the area where an accident may occur and connect to the responder's work or living location so that the responder can know the roads, building entrances, locations of first aid equipment, and common routes within the area. This configuration is also subject to several operational constraints: for example, each designated area should be covered by at least one area of ​​responsibility; each area of ​​responsibility should maintain geographical connectivity for responders to become familiar with; the workload of a single responder familiarizing themselves with their area of ​​responsibility cannot exceed their workload limit; and the total number of recruits is also limited by budget or training capacity.

[0004] With the significant increase in the number of urban areas and candidate respondents, the combinations of recruitment choices and the delineation of responsibility field boundaries become massive. Traditional methods using general solvers to directly solve mathematical programming models suffer from a sharp increase in dependent variables, constraints, and optional connectivity, leading to excessively long solution times and huge memory consumption. This makes it difficult to meet the practical business needs of rapid initialization, reconfiguration after personnel changes, or comparison of multiple solutions. Furthermore, the difficulty lies in the cascading effects of local adjustments: adding a responsible person to an uncovered area may lead to exceeding recruitment limits; deleting a person may create a new uncovered area; expanding responsibility fields may exceed workload limits. Therefore, simple greedy allocation by area or one-time allocation methods cannot yield directly implementable solutions.

[0005] The above background information is provided only to aid in understanding the concept and technical solution of this invention. It does not necessarily belong to the prior art of this patent application. In the absence of clear evidence that the above information was disclosed on the filing date of this patent application, the above background information should not be used to evaluate the novelty and inventiveness of this application. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention proposes a responseer responsibility area partitioning optimization method based on diffusion-repair heuristics. Under multiple constraints such as regional coverage, responsibility field connectivity, individual workload, and total number of recruits, this method can quickly and efficiently partition the optimal responsibility area for the responder, thereby overcoming the shortcomings of existing solvers in solving large-scale problems with low efficiency and inability to quickly respond to dynamic changes.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, this invention discloses a response responsibility region partitioning optimization method based on diffusion-repair heuristics, comprising the following steps: S1: Obtain a regional map, which includes multiple regional units representing the geographical area to be rescued, and adjacency information recording the adjacency relationships between the regional units; S2: Obtain a set of candidate respondents, wherein each candidate respondent in the set is associated with a location and a workload parameter representing the workload required to be familiar with the unit of the region; S3: Select a group of candidate respondents from the candidate respondent set according to preset rules to form a pre-recruited respondent group; S4: For each candidate respondent in the pre-recruited respondent group, perform a diffusion step based on the region map to generate an initial responsibility field map, the initial responsibility field map including a set of responsibility field regions corresponding to each candidate respondent; S5: Based on the region map and the initial responsibility field mapping, determine the set of uncovered regions, which includes all the region units that are not included in any of the responsibility field region sets; S6: When the set of uncovered areas is not empty, for each uncovered area unit in the set of uncovered areas, determine the target responder responsible for repair, and perform repair operation on the set of responsible field areas according to whether the target responder belongs to the pre-recruited responder group to form a new set of responsible field areas; Repeat steps S5 and S6 until the set of uncovered areas is empty or a preset termination condition is met.

[0008] Preferably, step S6, which involves performing a repair operation on the responsibility field area set based on whether the target respondent belongs to the pre-recruited respondent group, specifically includes: for each target respondent, When the target respondent belongs to the pre-recruited respondent group, a first repair operation is performed. The first repair operation includes: removing the original responsibility field area set of the target respondent, generating a connected initial area set that includes the location part of the target respondent and the new uncovered area units generated by the removal, and re-performing the diffusion step with the connected initial area set as the starting point to form a new responsibility field area set. When the target respondent does not belong to the pre-recruited respondent group, a second repair operation is performed. The second repair operation includes: removing an existing candidate respondent and its corresponding responsibility field set from the pre-recruited respondent group, adding the target respondent to the pre-recruited respondent group, and performing a diffusion step for it starting from the location part to form a new responsibility field set, replacing the removed responsibility field set.

[0009] Preferably, the step of generating the set of initial connected regions in the first repair operation further includes: The terminal node group is determined, which includes the location of the target responder, all area units in the set of uncovered area units, and new uncovered area units generated due to the removal of the original set of responsibility field areas; Calculate the shortest path between each node in the region graph, and construct a metric complete graph based on the distance of the shortest path; On the metric complete graph, the minimum spanning tree of the terminal node group is obtained; Each edge in the minimum spanning tree is restored to the corresponding shortest path in the region graph, and all nodes traversed by all paths are collected to form the set of connected initial regions.

[0010] Preferably, in the second repair operation, the step of removing an existing candidate responder and its corresponding responsibility field set from the pre-recruited responder group is selected according to a preset priority rule, which includes: prioritizing the selection of candidate responders whose responsibility field set is a completely redundant responsibility field; if none exists, then selecting the candidate responder whose cumulative coverage count of all regional units within its responsibility field set is the largest.

[0011] Preferably, the diffusion step specifically includes: starting from the location associated with the candidate responder, incorporating adjacent regional units layer by layer along the adjacency information until the accumulated workload parameter first exceeds a preset workload upper limit threshold, withdrawing the last layer of included regional units as a candidate set, and solving a subset selection problem in the candidate set to maximize the workload of the included regional units without exceeding the workload upper limit threshold, ultimately forming a responsibility field regional set corresponding to the candidate responder.

[0012] Preferably, the subset selection problem in the diffusion step is solved by constructing a 0-1 knapsack model, wherein each region unit in the candidate set is treated as an item, and its value and weight are both the workload parameters corresponding to that region unit, and the knapsack capacity is the upper limit threshold of workload minus the cumulative workload of the region units already included.

[0013] Preferably, the region map is a hexagonal grid region map generated based on the H3 geospatial indexing system, the region unit is an H3 hexagonal unit, the adjacency information includes the adjacency relationship between two H3 units with a common edge, and the location associated with each candidate responder is mapped to the corresponding H3 unit.

[0014] Preferably, the parameters characterizing the workload required to become familiar with the regional unit in step S2 include at least the response probability, the workload of each regional unit, the upper limit of the number of recruits N, and the upper limit of the workload W; step S3 specifically includes: selecting N candidate responders from the candidate responder set according to the response probability from high to low to form a pre-recruited responder group.

[0015] Preferably, the workload of the regional unit is calculated by normalizing and weighting the road density obtained by the ratio of the total road length in the unit to the unit area, and the building base coverage obtained by the ratio of the union area of ​​the building outline to the unit area. The response probability is estimated by the proportion of valid responses to valid test counts, based on information provided by candidate respondents in the questionnaire, including at least their willingness to respond, available time periods, and work locations.

[0016] Preferably, in step S6, determining the target responder responsible for repairing each uncovered area unit in the set of uncovered areas specifically includes: for each uncovered area unit, determining the nearest responder with the shortest expected response time based on the pre-calculated response time; aggregating the uncovered area units according to the nearest responder, and prioritizing the nearest responder with the largest number of aggregated uncovered area units; The estimated response time is determined by the travel time of the shortest route from the candidate responder's workplace to the target area unit, and the travel time is calculated based on the road network and a preset travel speed.

[0017] In a second aspect, the present invention discloses a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the response responsibility region partitioning optimization method based on diffusion-repair heuristic as described in the first aspect.

[0018] Compared with existing technologies, the beneficial effects of this invention are as follows: The response responsibility area partitioning optimization method based on diffusion-repair heuristic provided by this invention integrates personnel recruitment and responsibility area partitioning into a closed-loop "diffusion-check-repair" process, enabling the direct construction of feasible solutions from the region adjacency graph. First, through the "diffusion" step, the method expands outward layer by layer from the responder's location, introducing a final-layer subset selection mechanism, cleverly ensuring both connectivity within each responsibility area and that individual workload does not exceed limits. Second, through the "check" step, all uncovered areas are explicitly identified, forming clear repair targets. Finally, through the "repair" step, coverage gaps are addressed specifically, and based on whether the target responder has been recruited, the method intelligently selects to reconstruct their responsibility area or replace personnel, thus ensuring that connectivity, workload, and personnel constraints are not violated while repairing gaps. In summary, this invention constructs a closed-loop iterative mechanism of "diffusion-check-repair" to decompose complex multi-constraint global optimization problems into a series of locally constructive and repair subproblems that can be solved quickly. This allows for the stable generation of a feasible solution that satisfies all hard constraints in a very short time, significantly improving the solution efficiency and feasibility of large-scale resource allocation problems.

[0019] In a further embodiment, the present invention also has the following beneficial effects: (1) By dividing the repair operation into a first repair operation and a second repair operation, this method can intelligently adopt different strategies such as "reconstructing the existing personnel responsibility field" or "replacing redundant / high-burden personnel" according to the recruitment status of the target responders, effectively handling the chain problems of connectivity disruption and exceeding the number of personnel that may be caused during the repair process, and ensuring a high success rate of the repair operation.

[0020] (2) By constructing the final layer selection problem in the diffusion step as a 0-1 knapsack model for solution, this method can perform refined region selection at the edge of the workload limit, maximize the utilization of each responder's work capacity, and make the generated responsibility field cover as much area as possible under the premise of satisfying the constraints, thereby improving the overall coverage efficiency of the solution.

[0021] (3) By using the H3 hexagonal grid system to construct the regional map, this method can discretize the continuous geospatial problem into a standard graph computation problem. By utilizing the simple topological relationship and clear adjacency definition of the hexagonal grid, the computational complexity of diffusion and connectivity judgment is greatly simplified, while ensuring the spatial uniformity and practicality of the regional division.

[0022] Other beneficial effects of the embodiments of the present invention will be further described below. Attached Figure Description

[0023] Figure 1This is a schematic diagram of a preferred embodiment of the responder responsibility region partitioning optimization method based on diffusion-repair heuristics of the present invention; Figure 2 This is a schematic diagram of H3 space division and responder responsibility field without optimization by this invention; Figure 3 This is a schematic diagram of the optimized H3 space division and responder responsibility field according to the present invention; Figures 4a to 4d This is the process of generating responsibility fields using the diffusion algorithm in a specific embodiment of the present invention; Figures 5a to 5d This is a fix in a specific embodiment of the present invention when the most recent responder has already been recruited; Figures 6a to 6d This is a replacement and repair method for when the most recent responder has not been recruited, according to a specific embodiment of the present invention. Figure 7 A schematic diagram showing the results of MILP and DRH target values ​​at different scales; Figure 8 A schematic diagram showing the results of the target value under different numbers of candidate responses. Detailed Implementation

[0024] The embodiments of the present invention will be described in detail below. It should be emphasized that the following description is merely exemplary and is not intended to limit the scope and application of the present invention.

[0025] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of the present invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0026] Out-of-hospital cardiac arrest responder systems require assigning responsibility areas to recruited personnel before an incident occurs, ensuring coverage of each rescue zone and enabling responders to continuously familiarize themselves with roads, building entrances, and the location of emergency medical equipment. As urban areas and the number of candidates increase, relying solely on manual, zone-by-zone allocation makes it difficult to create a stable, interconnected, and balanced responsibility area system.

[0027] This problem is constrained by factors such as regional coverage, connectivity of assigned fields, workload familiarity for each individual, and the number of recruits. Expanding an assigned field may exceed the personnel's capacity, while deleting or replacing a person may create new uncovered areas. Local adjustments have cascading effects, and simple nearest-distance allocation or one-time greedy expansion cannot guarantee that the final solution can be implemented directly.

[0028] When using solvers to directly process mathematical programming models, the increase in regions, personnel, and adjacency relationships brings more variables, constraints, and combinations. The solution time and memory consumption increase with the scale, making it difficult to meet business needs such as rapid initialization of responsibility fields, reconfiguration after personnel changes, and rapid comparison of multiple schemes.

[0029] Therefore, the system needs to have the ability to quickly construct responsibility fields directly on regional adjacency relationships, check the coverage status of all regions, and locally repair coverage gaps. Each repair must also simultaneously check the connectivity of responsibility fields, workload, and number of recruits to avoid compromising the feasibility of other regions in order to fill one region.

[0030] This invention employs a closed-loop process of diffusion, inspection, and repair: first, the responsibility field is expanded from the responder's location to adjacent areas; then, uncovered areas are identified region by region; finally, responsibility field reconstruction or personnel replacement is performed based on the recruitment status of the most recent responder. This method can quickly output responsibility field solutions that meet key business constraints and record the reasons for failure, remaining uncovered areas, and termination status.

[0031] Compared to existing technologies that rely on one-time area division, simple area connection, or post-event personnel dispatch, this invention integrates personnel selection, responsibility area allocation, coverage inspection, and gap repair into a closed loop. This allows for local adjustments when personnel or needs change without overturning the original plan. In time-constrained scenarios, this method can quickly generate feasible solutions that meet coverage, connectivity, workload, and personnel requirements. It can also be deployed directly using existing platform data without requiring additional dedicated hardware, offering advantages in efficiency, cost, and implementation, thus overcoming the shortcomings of existing products in pre-planning and dynamic repair.

[0032] To balance computational speed and feasibility, a dedicated algorithm is needed to directly construct responsibility fields on the regional adjacency graph, explicitly check coverage status, and locally repair gaps. Based on this, this invention proposes a diffusion-check-repair closed loop, enabling each adjustment to re-verify coverage, connectivity, workload, and personnel constraints.

[0033] like Figure 1 As shown, a preferred embodiment of the present invention discloses a method for optimizing responder responsibility region partitioning based on a diffusion-repair heuristic, comprising the following steps: S1: Obtain the regional map, which includes multiple regional units representing the geographical area to be rescued, as well as adjacency information recording the adjacency relationships between each regional unit; The regional map is a hexagonal grid regional map generated based on the H3 geospatial indexing system. The regional units are H3 hexagonal cells, and the adjacency information includes the adjacency relationship between two H3 cells sharing a common edge. The location associated with each candidate respondent is mapped to the corresponding H3 cell. By using the H3 geospatial indexing system to construct the hexagonal grid regional map, the spatial uniformity and consistency of the regional units are ensured, avoiding the boundary effects and irregular shape problems caused by traditional administrative boundaries or grid divisions. This results in clearer adjacency definitions, more stable algorithm results, and easier geospatial visualization and implementation.

[0034] S2: Obtain a set of candidate respondents, each of whom is associated with a location and a parameter representing the workload required to be familiar with the unit in that region; Among them, the parameters representing the workload required to become familiar with the regional unit include at least the response probability, the workload of each regional unit, the upper limit of the number of recruits N, and the upper limit of the workload W.

[0035] Furthermore, the workload of a regional unit is calculated using a normalized weighted average of the road density (the ratio of the total road length to the unit area) and the building footprint coverage (the ratio of the union of building outline areas to the unit area). The response probability is estimated by the proportion of valid responses to valid test counts, based on information such as the respondent's willingness to respond, available response time periods, and work location provided in the questionnaire. By specifically defining workload parameters and recruitment rules, the abstract concepts of "familiarity" and "recruitment willingness" are quantified into calculable indicators such as road density, building footprint coverage, and response probability. This makes the optimization model more closely resemble actual business scenarios and provides a more scientific basis for decision-making.

[0036] S3: Select a group of candidate respondents from the candidate respondent set according to preset rules to form a pre-recruitment respondent group; Specifically, step S3 includes: selecting N candidate respondents from the candidate respondent set according to their response probabilities from high to low, forming a pre-recruitment respondent group. Further, if the response probabilities are the same, the candidates are selected according to their unique identifiers.

[0037] S4: For each candidate respondent in the pre-recruited respondent group, perform a diffusion step based on the region map to generate an initial responsibility field map, which includes a set of responsibility field regions corresponding to each candidate respondent; The diffusion step specifically includes: starting from the location associated with the candidate responder, incorporating adjacent regional units layer by layer along the adjacency information until the accumulated workload parameter first exceeds the preset workload upper limit threshold. Then, the last layer of included regional units is withdrawn as a candidate set, and a subset selection problem is solved in the candidate set to maximize the workload of the included regional units without exceeding the workload upper limit threshold, ultimately forming the responsibility field regional set corresponding to the candidate responder.

[0038] In a further scheme, the subset selection problem in the diffusion step is solved using a 0-1 knapsack model. Each region unit in the candidate set is treated as an item, with its value and weight representing the workload parameters corresponding to that unit. The knapsack capacity is the workload cap threshold minus the cumulative workload of the included region units. By solving the final-layer selection problem in the diffusion process using a 0-1 knapsack model, the remaining workload can be fully utilized while ensuring the connectivity of the responsibility fields. This allows the generated responsibility fields to cover and "familiarize" with as many regions as possible while meeting individual workload caps, thus improving the optimization level of the scheme.

[0039] S5: Based on the regional map and the initial responsibility field mapping, determine the set of uncovered regions, which includes all regional units not included in any responsibility field region set; S6: When the set of uncovered areas is not empty, for each uncovered area unit in the set of uncovered areas, determine the target responder responsible for repair, and perform repair operations on the set of responsible field areas according to whether the target responder belongs to the pre-recruited responder group to form a new set of responsible field areas; Specifically, for each uncovered area unit in the set of uncovered areas, determining the target responder responsible for repair includes: for each uncovered area unit, determining the nearest responder with the shortest expected response time based on a pre-calculated response time; aggregating uncovered area units by nearest responder, prioritizing the nearest responder with the largest number of aggregated uncovered area units; if the number of aggregated nearest responders is tied, the order is determined by the responder's unique identifier. Furthermore, the expected response time is determined by the travel time of the shortest route from the candidate responder's work location to the target area unit, calculated based on the road network and a preset travel speed. By explicitly estimating the response time and using it as the basis for determining the "nearest responder," repair operations can prioritize addressing coverage gaps that have the greatest impact on response time, thereby improving overall response efficiency.

[0040] This includes repairing the responsibility field set based on whether the target respondent belongs to the pre-recruited respondent group, specifically including: for each target respondent, When the target respondent belongs to the pre-recruited respondent group, the first repair operation is performed. The first repair operation includes: removing the original responsibility field area set of the target respondent, generating a connected initial area set containing the location of the target respondent and the new uncovered area units generated by the removal, and re-performing the diffusion step with the connected initial area set as the starting point to form a new responsibility field area set. When the target respondent does not belong to the pre-recruited respondent group, a second repair operation is performed. The second repair operation includes: removing an existing candidate respondent and its corresponding responsibility field set from the pre-recruited respondent group, adding the target respondent to the pre-recruited respondent group, and performing a diffusion step for it starting from the location part to form a new responsibility field set, replacing the removed responsibility field set.

[0041] By subdividing the repair operation into a first repair operation and a second repair operation, the algorithm can flexibly cope with two scenarios: responsibility field reconstruction and personnel replacement, thereby improving the pertinence and effectiveness of the repair strategy.

[0042] The diffusion step in the first and second repair operations also specifically includes: starting from the location associated with the candidate responder, the adjacent regional units are included layer by layer along the adjacency information until the cumulative workload parameter exceeds the preset workload upper limit threshold for the first time. Then, the regional units included in the last layer are withdrawn as a candidate set, and a subset selection problem is solved in the candidate set to maximize the workload of the included regional units without exceeding the workload upper limit threshold, and finally a responsibility field regional set corresponding to the candidate responder is formed.

[0043] In a further scheme, the step of generating the initial set of connected regions in the first repair operation includes: The terminal node group is determined, which includes the location of the target responder, all area units in the set of uncovered area units, and new uncovered area units resulting from the removal of the original set of responsibility field areas; Calculate the shortest path between all nodes in the region graph, and construct a metric complete graph based on the distance of the shortest path; On a metric complete graph, find the minimum spanning tree of the terminal node subset; For each edge in the minimum spanning tree, convert it into the corresponding shortest path in the region graph, and collect all the nodes traversed by all paths to form a set of connected initial regions.

[0044] In the first repair operation, a set of initial connected regions was generated by introducing a method based on minimum spanning tree and shortest path restoration. This ensured that the reconstructed responsibility field could maintain connectivity in the simplest and most economical way while including all necessary nodes (such as responder locations and uncovered areas), providing a high-quality starting point for subsequent diffusion optimization.

[0045] In a further scheme, the second repair operation, the step of removing an existing candidate respondent and its corresponding responsibility field set from the pre-recruited respondent group, is selected according to a preset priority rule. The priority rule includes: prioritizing the selection of candidate respondents whose responsibility field set is a completely redundant responsibility field; if no such candidate is found, then selecting the candidate respondent whose cumulative coverage count of all area units within its responsibility field set is the largest.

[0046] In the second repair operation, by setting a priority rule of "prioritizing the removal of completely redundant responsibility fields, followed by removing responsibility fields with the highest cumulative coverage count", the negative impact of personnel replacement on the existing coverage pattern was minimized, making the repair process smoother and more efficient.

[0047] Repeat steps S5 and S6 until the set of uncovered areas is empty or the preset termination condition is met.

[0048] In a preferred embodiment of this invention, a closed-loop heuristic framework of "diffusion-repair" is employed, enabling the direct construction of responsibility fields on the regional adjacency graph. First, through constrained diffusion along adjacency information from each responder's location, initial responsibility fields satisfying connectivity and single-person workload constraints are generated in one step. Subsequently, uncovered region units are identified through explicit inspection, and target responders are intelligently selected for repair. This "diffusion-inspection-repair" mechanism decomposes the complex multi-constraint global optimization problem into a series of computationally inexpensive local construction and repair steps, avoiding the computational bottleneck caused by the explosion of dependent variables and constraint combinations in traditional solvers. Therefore, fundamentally, this invention achieves the generation of high-quality feasible solutions satisfying all constraints of coverage, connectivity, workload, and number of responders in an extremely short time (sub-second), significantly improving the efficiency and dynamic adaptability of large-scale responder responsibility region partitioning, and solving the problems of slow computation and inability to meet real-time business requirements in existing technologies.

[0049] The following detailed description of the preferred embodiment of the present invention, based on the diffusion-repair heuristic, optimizes the responder responsibility region partitioning method.

[0050] This specific embodiment uses the H3 geospatial indexing system to discretize continuous urban areas into hexagonal regional units with uniform scale, each unit uniquely identified by an H3 index. The work location coordinates, roads, buildings, and historical emergency rescue events of candidate responders are mapped to corresponding H3 units; two H3 units with a common boundary are defined as adjacent areas, and a regional map is constructed accordingly. The H3 resolution is pre-set based on the planning area scale and the accuracy of farmland management, and the same resolution is used for the same calculation instance.

[0051] like Figure 2 The diagram shown is a schematic of H3 spatial division and responder responsibility field without optimization by this invention, illustrating the construction process from continuous urban space to responder responsibility field. Figure 2 The left figure shows the city map and the location of the respondents. After spatial discretization using the H3 grid system, the original recruitment and responsibility field division problem can be transformed into the selection of respondents and the allocation of areas to individuals. Figure 2 The right-hand diagram shows a region map composed of hexagonal cells, cell numbers, and responder locations, thus completing the mapping between responder locations and region cells. For example... Figure 3 The diagram shown illustrates the optimized H3 spatial partitioning and responder responsibility fields, where the results are represented after executing the diffusion-check-repair algorithm. Adjacent hexagons of the same color constitute a connected responsibility field for one responder, and circular markers indicate the region where the responder is located. Figure 2 In contrast, after optimization, each responsibility field contains the location area of ​​the corresponding responder and forms a continuous range through adjacent areas; connected areas of the same color represent responsibility fields assigned to the corresponding responder. Figure 3 The diagram illustrates the configuration of responsibility fields after applying this invention. The diffusion and repair process adjusts the boundaries while maintaining the connectivity of responsibility fields and keeping the workload controllable, making the personnel's responsibility area more continuous and reducing coverage gaps.

[0052] The following five parts describe the response responsibility region partitioning optimization method based on the diffusion-repair heuristic in specific embodiments.

[0053] 1. Problem Data and Constraints The input processed by this invention includes a set of regions. Adjacent edge set Regional map Regional workload Candidate Respondent Set Response location area Response probability Regional response time Maximum number of recruits and the upper limit of the workload of the contracted field .

[0054] The output includes the responder recruitment status and the mapping of responsibility fields. It also includes the results of the overlay inspection and the termination status.

[0055] in, This parameter represents the workload required to familiarize oneself with the roads and building environment within unit z. The road density is obtained by dividing the total road length within the unit by the unit area, and the building footprint coverage is obtained by dividing the building outline union area by the unit area. These two indicators are then normalized and weighted for calculation.

[0056] This parameter represents the probability that a candidate respondent r will accept and respond to a call. Information regarding the candidate respondent's willingness to respond, available response time periods, and work location was collected through a questionnaire before recruitment, and the parameter was estimated as the proportion of valid responses to valid test runs.

[0057] This represents the estimated travel time for candidate responder r to travel from their workplace to cell z. This parameter is generated from the candidate responder's workplace, the Open Street Map road network, road lengths, and a set travel speed, using the shortest route travel time from the workplace to the target cell's representative point as the value.

[0058] The above data is used to constrain the responsibility field to include the respondent's area, maintain internal connectivity, meet the single-person workload limit, and ensure that all designated areas are covered and the number of recruits does not exceed the given limit.

[0059] Let the region adjacency graph be The responsibility area of ​​a certain first responder is a subset of the region. The connection of responsibility fields refers to the connection of... Subgraphs induced in the region adjacency graph It is a connected graph, meaning that for any two regions within the assigned field... There exists a path from arrive The path, and all areas traversed by the path belong to A responsibility field containing only one region can be considered connected according to graph theory.

[0060] 2. Diffusion-Repair Overall Framework The diffusion-repair framework includes the following steps: A1: Select the candidate responder with the highest probability of response from the set of candidate responders. A number of respondents were selected to form a pre-recruitment pool. .

[0061] A2: For each belonging to respondent , by location area The diffusion algorithm is invoked for the initial set to form the original responsibility field mapping. .

[0062] A3: Call the feasibility checker to calculate the region group mapping. and uncovered sets .

[0063] A4: If If not empty, then call the repair algorithm to update. And re-examine until a feasible solution is found or an explicit infeasibility / rollback state is triggered.

[0064] 3. Diffusion Algorithm and Last Layer Selection Given respondent and its location area Initialize the responsibility field in this location area. And add layer by layer along the region map. Rank Neighborhood The cumulative workload exceeded [a certain amount] for the first time. When the last layer is withdrawn, the newly added candidate region of the last layer is recorded as... The final selection problem maximizes the workload of the included region within the remaining capacity.

[0065] This invention constructs a mathematical programming model for the final-level selection problem. This represents the cumulative workload of all preceding layers already included in the current responsibility field before entering the final layer selection. During initialization, the responsibility field only contains the responder's location area. Therefore ; thereafter, for each new layer added, the workload of each layer is accumulated. When entering the final selection layer, the following conditions must be met: ,therefore This indicates the remaining available workload for the assigned field.

[0066] (1) (2) (3) Equation (1) uses the total workload of the candidate region at the last layer as the benefit, and fills the responsibility field as much as possible within the remaining capacity.

[0067] Equation (2) ensures that the workload of the selected final layer area does not exceed the remaining workload before entering the final layer. .

[0068] Equation (3) specifies the variables for selecting the last layer region. It is a binary variable.

[0069] Since the candidate region comes from the neighboring layer that first exceeds the limit when spreading layer by layer from the responder's location area, the selected region together with the preceding layer constitutes a connected responsibility field.

[0070] This problem is solved by the following steps: First, sort the candidate regions in the last layer according to their unique regional numbers; then, generate all candidate subsets sequentially by combining enumerations from 1 to the total number of candidate regions in the last layer according to the number of selected regions, and retain the subsets whose total workload does not exceed the remaining capacity, while not selecting any last layer regions as candidates; finally, sort the candidate responsibility fields in descending order of cumulative workload, and select the scheme with the largest cumulative workload as the last layer selection result.

[0071] The final layer selection result is used to update the responsibility field mapping χ[r] and the regional cover reverse mapping. .

[0072] This is a mapping of responsibility fields, with the responder as the key. Indicates assignment to the responder The set of responsibility field areas; the mapping value of unrecruited responders is an empty set.

[0073] This is a reverse mapping for region coverage, where the key is the region. This indicates the area included in the responsibility field. The collection of all recruited respondents.

[0074] therefore, For the region The number of times it is covered; when Time, region This is an uncovered area. Updates should be made synchronously after each addition, deletion, or replacement of assigned fields. and corresponding areas If no candidate region is selected in the last layer model, the first k-1 layers are retained as the current responsibility field, and then the coverage check is performed.

[0075] by Figures 4a to 4d For example, set the regional span 2. Maximum workload The value is 1, and the respondent is located in the region. . Figure 4a This is the initial state. Figure 4b To initialize the responsibility field based on the area where the respondent is located, Figure 4c To expand the responsibility field to adjacent areas, Figure 4d For the final generated responsibility fields, Figures 4a to 4d The process of the diffusion algorithm generating responsibility fields from the responder's location area is described sequentially. Among them, Figure 4a This represents the initial area network and the workload of each area; Figure 4bIndicates the respondent Location Initialize the responsibility field; at this time, the responsibility field is... ; Figure 4c Indicates will First-order adjacency region When added as the next diffusion layer, the cumulative workload after addition is 1.5, exceeding the workload limit. Therefore, this layer is withdrawn and included in the candidate set for the final layer. Figure 4d This indicates solving the final-level selection problem within the remaining capacity, selecting... Ultimately, they received the assigned farmland. .thus, Figure 3 It embodies the complete responsibility field generation process of "location area initialization → layer-by-layer neighborhood diffusion → withdrawal to the last layer after the first over-limit → selection of feasible subsets from the candidate regions of the last layer".

[0076] 4. Feasibility Checker The diffusion algorithm guarantees connectivity of responsibility fields, a maximum workload limit, and a limit on the number of participants. Therefore, the feasibility of the original solution is equivalent to checking whether each region is covered by at least one responsibility field. For each region within a responsibility field, the responders are added to... ;like If empty, then the region... Add to collection .

[0077] (4) Equation (4) maps the region coverage. All empty regions are grouped into an uncovered set. This formula only determines coverage gaps; the connectivity of responsibility fields, individual workload, and pre-recruitment limits are guaranteed by the diffusion phase.

[0078] The inspector simultaneously saves the reverse mapping from the region to the person covering the response. And pass the result of equation (4) to the repair algorithm; when If empty, the current configuration passes the overwrite check.

[0079] 5. Repair Algorithm The system generates a unique internal number for each candidate respondent upon registration, which remains unchanged throughout the optimization process. The repair algorithm first establishes a deterministic mapping from uncovered areas to the nearest valid respondent, then aggregates the areas to be processed by respondent; when the expected response times are equal, the processing objects are determined by a fixed ascending order of the internal numbers.

[0080] (5) (6) (7) in, This refers to the group of qualified responders who can reach the area before an emergency vehicle arrives. Equation (5) determines the effective responder with the shortest expected response time for each uncovered area. .

[0081] Equation (6) gathers the most recent responders corresponding to at least one uncovered area to form a set. .

[0082] Equation (7) categorizes uncovered areas into sets based on the most recent responder. Algorithm priority processing | The largest number of respondents, in case of a tie, will be ordered by their unique ID.

[0083] The specific remediation steps are divided into the following two scenarios depending on whether the selected most recent responder has been recruited: Scenario 1: The selected respondent has already been recruited.

[0084] The terminal set consists of the responder's location area, the previously uncovered areas, and the newly added uncovered areas after deleting the original responsibility areas. .

[0085] In the regional map Construct a Steiner tree containing all terminal nodes: this tree must be connected. All nodes in the list, and simultaneously allow selection. Non-terminal nodes in the tree are designated as Steiner nodes, and the goal is to minimize the total edge weight of the tree. The set of regions contained in the resulting Steiner tree is denoted as the initial connected path. , and then Perform the diffusion algorithm on the initial set.

[0086] The initial path to connectivity is generated using NetworkX's Steiner tree approximation function.

[0087] First, the location area of ​​the selected responder, the original uncovered area, and the newly added uncovered area after deleting the original responsibility field are combined into a terminal set; Then, calculate the shortest path and distance between nodes in the region graph, construct the metric closure, and take the induced complete graph of the terminal set in the metric closure; Then, using the shortest path distance between terminals as the edge weight, find the minimum spanning tree of the complete graph; Finally, each edge of the minimum spanning tree is restored to the corresponding shortest path in the original region graph. All nodes contained in the path are taken as the initial connected region set, and the diffusion is continued with this set as the initial responsibility field.

[0088] refer to Figures 5a to 5d This indicates the process of restoring the responsibility field when the most recent responder has been recruited. Figure 5a The original solution, in which the respondent and All have been recruited, and their assigned farmland is as follows: and ,area Not covered; Figure 5b Select distance based on estimated response time Recent Respondent ; Figure 5c delete The original contracted farmland now needs to be covered by new contracted farmland. The location area, the originally uncovered area, and the newly added uncovered area after deletion, i.e., the terminal area. ; Figure 5d New responsibility fields are generated based on the uncovered areas. Specifically, first, initial connectivity paths connecting the aforementioned terminal areas are generated, and then diffusion is performed using these paths as the initial set to obtain... New responsibility field After the update, all areas have been covered by at least one responder, completing this fix.

[0089] Scenario 2: The selected respondent has not yet been recruited.

[0090] To maintain the recruitment cap, first select a replacement from the existing responsibility fields; the newly uncovered areas generated after removal are added to the set to be repaired, and then responsibility fields are constructed for the new respondent.

[0091] (8) (9) Equation (8) defines the set of completely redundant responsibility fields. This means that each area within a designated responsibility field is covered at least twice. In the algorithm implementation, this can be efficiently determined by checking whether each area within the responsibility field is covered by at least one other different responsibility field.

[0092] Equation (9) specifies the replacement object: Let This indicates the original responsibility field that was selected in the current repair iteration and is ready to be deleted, to be replaced by a new responsibility field that has not recruited the most recent responder. When not empty, select one responsibility field as... ; When the field is empty, select the responsibility field with the highest cumulative coverage count as the responsibility field. In the event of a tie, the fixed responsibility field number will be used to determine the appropriate number, in order to ensure that the algorithm can be reproduced.

[0093] refer to Figures 6a to 6dThis indicates the process of replacing the responsibility field when the most recent responder has not yet been recruited. Figure 6a The original solution, the respondent and Recruited, their assigned farmland is as follows: and ,area Not covered; Figure 6b China has determined The most recent respondent is someone who has not yet been recruited. Therefore, it is necessary to select a replacement responsibility field from the existing ones. In the absence of completely redundant responsibility fields, the one with the highest cumulative coverage count should be selected. As the responsibility field ; Figure 6c After deleting the assigned field, This constitutes the set of currently uncovered areas; Figure 6d Recruitment Starting from its location area, the diffusion process is performed to generate new responsibility fields covering the previously uncovered areas. The original responsibility field was then replaced with the new one. After the replacement, all areas were covered by at least one responder, completing the repair.

[0094] The following numerical experiments further illustrate and verify the response responsibility region partitioning optimization method based on diffusion-repair heuristic proposed in a specific embodiment of the present invention.

[0095] To test the solution efficiency of the method of the present invention under different region sizes, different calculation methods, different number of candidate responses, and different recruitment numbers, 41 test cases, E1-E41, were constructed. Among them, E1-E12 used regular hexagonal region networks, with the number of regions being 7, 7, 19, 19, 37, 61, 91, 127, 169, 217, 271, and 331 respectively, representing the number of candidate first responses. The numbers are 7, 9, 19, 24, 47, 77, 114, 159, 212, 272, 339, and 414, representing the planned recruitment numbers. The numbers are 6, 7, 17, 19, 37, 61, 91, 127, 169, 217, 271, and 331, respectively. For regions E13-E21, the number of regions and the number of pre-recruited personnel are both 19, and the number of first-responder candidates is set to 19, 24, 29, 34, 38, 43, 48, 53, and 57, respectively, to analyze the impact of increasing the number of candidate respondents. For regions E32-E41, the number of regions is 127, the number of first-responder candidates is 159, and the number of pre-recruited personnel is set to 88, 96, 104, 112, 120, 128, 136, 144, 152, and 159, respectively, to analyze the impact of changes in responder supply levels on algorithm performance.

[0096] The experiments were conducted using Python 3.9 and Gurobi 11.0.2 on a Windows computer with an Intel Core i7-10700 2.90GHz processor, 32GB of RAM. The following compares the diffuse-then-repair heuristic (DRH) algorithm of this invention with existing mixed-integer linear programming (MILP) models. Metrics include the objective value Obj, the optimality gap Gap (Gap = (UB - LB) / LB × 100, where for a maximization problem, UB is the upper bound of the objective given by the solver, and LB is the current best feasible solution objective value), and the heuristic gap Gap. heu (Gap) heu = (Obj DRH - Obj MILP ) / Obj MILP ×100, where, Obj DRH This represents the target value of DRH, Obj MILP The values ​​represent the target value of MILP, the model state (MS), and the CPU time; OPT (Optimal) indicates that the solver has proven the current solution to be the global optimum, and TL (Time Limit) indicates the preset solution time limit of 36,000 seconds.

[0097] Refer to Table 1 for the performance results of MILP and DRH at different scales. Figure 7 This diagram illustrates the results of MILP and DRH target values ​​at different scales.

[0098] Table 1 Results of MILP and DRH on instances of different sizes.

[0099] Table 1 shows the average heuristic gap between DRH and the current results of MILP in the small-scale experimental records of E1-E8. heu The average value is approximately 1.12%, with CPU time ranging from 0.0009 to 0.1661 seconds. From Figure 7 It can be seen that in the last four larger-scale records, MILP did not converge within the 10-hour time limit, and the DRH objective value was 13.24%–19.08% higher than the feasible solution of MILP at that time; this comparison only reflects the quality of feasible solutions within the time limit and does not indicate that the heuristic exceeds the unknown global optimal solution of MILP.

[0100] Refer to Table 2 for the performance results under different numbers of candidate responses. Figure 8 This is a schematic diagram showing the results of MILP and DRH target values ​​under different numbers of candidate responses.

[0101] Table 2. MILP and DRH results with different numbers of candidate responses

[0102] From Table 2 and Figure 8 It can be seen that, except for the record with the largest number of candidate responses, the difference between DRH and MILP is 0.92%–2.87%, and the CPU time is 0.0028–0.0040 seconds. Row E21 of Table 2 shows that when MILP reaches the 36000-second solution time limit, the target value obtained is 5.6334, with a gap of 235.30%; DRH obtains a feasible target value of 6.7966, with a runtime of 0.0037 seconds, corresponding to… Figure 8 The final example shows that the objective function of MILP is significantly lower than that of DRH. This result indicates that, in this instance and given the solution time limit, MILP has not yet completed optimality verification, while DRH can quickly obtain a feasible solution.

[0103] Refer to Table 3 for the results of the repair features under different recruitment numbers.

[0104] Table 3. DRH Results for Different Numbers of Recruits

[0105] In this set of examples The meanings of each field in Table 3 are as follows: Instance ID represents the test instance number; This indicates the number of first responders to be recruited. This indicates the number of areas not yet covered after the diffusion algorithm generates the original scheme; This indicates the number of times "the most recent responder in the uncovered area has been recruited" has been repaired during the repair phase; This indicates the number of times during the repair phase that "the most recent responder in the uncovered area has not yet been recruited, so it is necessary to replace a recruited responder"; Obj represents the overall target value of the final plan across the entire study area, i.e., the overall expected success rate of the rescue. This represents the average target value contribution of each pre-recruited first responder, calculated using the following formula: ; CPU(s) represents the total computation time taken by the DRH algorithm to complete this instance, in seconds.

[0106] As shown in Table 3, when the number of recruits increased from 88 to 159, the number of uncovered areas in the original solution decreased from 3 to 1, the overall target value continued to increase, and the CPU time remained within the range of 0.08 to 0.16 seconds. The average contribution per person showed a decreasing trend, indicating that a balance needs to be struck between coverage integrity, cost, and marginal benefits.

[0107] In a further embodiment, the response responsibility region partitioning optimization method based on diffusion-repair heuristic of the present invention includes the following steps: B1: Read the region map, workload, responder location, response probability and response time, and verify the region connectivity and parameter range.

[0108] B2: Select N pre-recruited responders according to the response probability, and perform diffusion and final layer 0-1 selection on each responder.

[0109] B3: Generate region group mappings and identify uncovered regions.

[0110] B4: Select repair responders based on the shortest response time and the number of uncovered areas, and perform repairs in two categories: recruited and unrecruited.

[0111] B5: Review coverage, connectivity, workload, and personnel constraints, and output responsibility field mapping and status codes.

[0112] B6: Record input version, iteration trajectory, rollback reason and manual adjustment to support rapid initialization of responsibility fields, real-time reconfiguration and accurate algorithm warm start.

[0113] Another preferred embodiment of the present invention discloses a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the response responsibility region partitioning optimization method based on the diffusion-repair heuristic as described in the preferred embodiment above.

[0114] Optionally, the aforementioned storage media may include, but are not limited to, USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks, and other media capable of storing computer programs.

[0115] The background section of this invention may include background information about the problems or circumstances surrounding the invention, rather than a description of prior art by others. Therefore, the content included in the background section is not an admission of prior art by the applicant.

[0116] The above description provides a further detailed explanation of the present invention in conjunction with specific / preferred embodiments, and it should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various substitutions or modifications can be made to these described embodiments without departing from the concept of the present invention, and all such substitutions or modifications should be considered within the scope of protection of the present invention. In the description of this specification, the reference to terms such as "an embodiment," "some embodiments," "preferred embodiment," "example," "specific example," or "some examples," etc., indicates that the specific features, structures, materials, or characteristics described in connection with that embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any suitable manner in one or more embodiments or examples. Furthermore, those skilled in the art can combine and integrate different embodiments or examples and features of different embodiments or examples described in this specification without contradiction. Although the embodiments of the present invention and their advantages have been described in detail, it should be understood that various changes, substitutions, and modifications can be made herein without departing from the scope defined by the appended claims.

Claims

1. A response responsibility region partitioning optimization method based on diffusion-repair heuristic, characterized in that, Includes the following steps: S1: Obtain a regional map, which includes multiple regional units representing the geographical area to be rescued, and adjacency information recording the adjacency relationships between the regional units; S2: Obtain a set of candidate respondents, wherein each candidate respondent in the set is associated with a location and a workload parameter representing the workload required to be familiar with the unit of the region; S3: Select a group of candidate respondents from the candidate respondent set according to preset rules to form a pre-recruited respondent group; S4: For each candidate respondent in the pre-recruited respondent group, perform a diffusion step based on the region map to generate an initial responsibility field map, the initial responsibility field map including a set of responsibility field regions corresponding to each candidate respondent; S5: Based on the region map and the initial responsibility field mapping, determine the set of uncovered regions, which includes all the region units that are not included in any of the responsibility field region sets; S6: When the set of uncovered areas is not empty, for each uncovered area unit in the set of uncovered areas, determine the target responder responsible for repair, and perform repair operation on the set of responsible field areas according to whether the target responder belongs to the pre-recruited responder group to form a new set of responsible field areas; Repeat steps S5 and S6 until the set of uncovered areas is empty or a preset termination condition is met.

2. The response responsibility region partitioning optimization method based on diffusion-repair heuristic as described in claim 1, characterized in that, Step S6 involves performing a repair operation on the responsibility field area set based on whether the target respondent belongs to the pre-recruited respondent group. Specifically, this includes: for each target respondent, When the target respondent belongs to the pre-recruited respondent group, a first repair operation is performed. The first repair operation includes: removing the original responsibility field area set of the target respondent, generating a connected initial area set that includes the location part of the target respondent and the new uncovered area units generated by the removal, and re-performing the diffusion step with the connected initial area set as the starting point to form a new responsibility field area set. When the target respondent does not belong to the pre-recruited respondent group, a second repair operation is performed. The second repair operation includes: removing an existing candidate respondent and its corresponding responsibility field set from the pre-recruited respondent group, adding the target respondent to the pre-recruited respondent group, and performing a diffusion step for it starting from the location part to form a new responsibility field set, replacing the removed responsibility field set.

3. The response responsibility region partitioning optimization method based on diffusion-repair heuristic as described in claim 2, characterized in that, The step of generating the initial connected region set in the first repair operation further includes: The terminal node group is determined, which includes the location of the target responder, all area units in the set of uncovered area units, and new uncovered area units generated due to the removal of the original set of responsibility field areas; Calculate the shortest path between each node in the region graph, and construct a metric complete graph based on the distance of the shortest path; On the metric complete graph, the minimum spanning tree of the terminal node group is obtained; Each edge in the minimum spanning tree is restored to the corresponding shortest path in the region graph, and all nodes traversed by all paths are collected to form the set of connected initial regions.

4. The response responsibility region partitioning optimization method based on diffusion-repair heuristic as described in claim 2, characterized in that, In the second repair operation, the step of removing an existing candidate responder and its corresponding responsibility field area set from the pre-recruited responder group is selected according to a preset priority rule. The priority rule includes: prioritizing the selection of candidate responders whose responsibility field area set is a completely redundant responsibility field; if it does not exist, then selecting the candidate responder whose cumulative coverage count of all area units in its responsibility field area set is the largest.

5. The response responsibility region partitioning optimization method based on diffusion-repair heuristic as described in claim 1 or 2, characterized in that, The diffusion step specifically includes: starting from the location associated with the candidate responder, incorporating adjacent regional units layer by layer along the adjacency information until the accumulated workload parameter first exceeds the preset workload upper limit threshold. Then, the last layer of included regional units is withdrawn as a candidate set, and a subset selection problem is solved in the candidate set to maximize the workload of the included regional units without exceeding the workload upper limit threshold, ultimately forming the responsibility field regional set corresponding to the candidate responder.

6. The response responsibility region partitioning optimization method based on diffusion-repair heuristic as described in claim 5, characterized in that, The subset selection problem in the diffusion step is solved by constructing a 0-1 knapsack model, wherein each region unit in the candidate set is treated as an item, and its value and weight are the workload parameters corresponding to that region unit. The knapsack capacity is the upper limit threshold of workload minus the cumulative workload of the region units already included.

7. The response responsibility region partitioning optimization method based on diffusion-repair heuristic as described in claim 1, characterized in that, The parameters representing the workload required to become familiar with the regional unit in step S2 include at least the response probability, the workload of each regional unit, the upper limit of the number of recruits N, and the upper limit of the workload W; Step S3 specifically includes: selecting N candidate responders from the candidate responder set according to the response probability from high to low to form a pre-recruited responder group.

8. The response responsibility region partitioning optimization method based on diffusion-repair heuristic as described in claim 7, characterized in that, The workload of the regional unit is calculated by normalizing and weighting the road density obtained by the ratio of the total road length in the unit to the unit area, and the building base coverage obtained by the ratio of the union area of ​​the building outline to the unit area. The response probability is estimated by the proportion of valid responses to valid test counts, based on information provided by candidate respondents in the questionnaire, including at least their willingness to respond, available time periods, and work locations.

9. The response responsibility region partitioning optimization method based on diffusion-repair heuristic as described in claim 1, characterized in that, Step S6 involves determining the target responder responsible for repairing each uncovered area unit in the set of uncovered areas. Specifically, this includes: for each uncovered area unit, determining the nearest responder with the shortest expected response time based on a pre-calculated response time; aggregating the uncovered area units according to the nearest responder, and prioritizing the nearest responder with the largest number of aggregated uncovered area units. The estimated response time is determined by the travel time of the shortest route from the candidate responder's workplace to the target area unit, and the travel time is calculated based on the road network and a preset travel speed.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the response responsibility region partitioning optimization method based on the diffusion-repair heuristic as described in any one of claims 1 to 9.

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