A multi-level security site selection method based on networked structure

Abstract

The application discloses a multi-level guarantee site selection method based on a network structure. The application introduces a multi-level site selection method based on a task mission. In view of the actual demand of government operation and management under the epidemic background, different site selection targets are determined according to different guarantee level task missions, thereby completing the construction of a three-level site selection model for epidemic life material guarantee, and improving the authenticity and feasibility of the guarantee site selection model. Moreover, according to the node site selection condition of the lower level, the application selects the node of the upper guarantee level, and forms a stable and convenient network guarantee system. In addition, the application divides the node site selection model of the first guarantee level with a large number of nodes into two stages through a two-stage algorithm, introduces secondary site selection based on heuristic rules for the residential area with high demand, reduces the complexity of the solution of the first stage, and effectively improves the site selection efficiency.

Description

Technical Field

[0001] This invention relates to the field of multi-level addressing technology, and more specifically to a multi-level guaranteed addressing method based on a networked structure. Background Technology

[0002] Currently, the construction of material support systems often adopts a multi-level support system. By gradually breaking down the process of ensuring the supply of daily necessities through the flow of materials between different levels, the pressure on government operation and management is reduced. In a multi-level support system, many factors need to be considered, such as the demand of each level node, the residential areas that the node is responsible for, the locational relationship between nodes at different levels, and the mission of each level's site selection, etc.

[0003] Common methods for emergency facility site selection include the p-central model, the p-median model, and the ensemble coverage model. These methods typically address situations where the number of sites is fixed, neglecting the variable number of sites. The number of sites required is directly related to material and personnel costs and is difficult to determine directly. Given the large number of areas needing to support residents and the large scale and multiple levels of support nodes required, how to select sites for multi-level distribution nodes of essential supplies, with a large number of nodes and uncertain dimensions, to minimize the cost of the supply support system, becomes a new problem that needs to be solved. Summary of the Invention

[0004] In view of this, the present invention provides a multi-level support location method based on a networked structure, which can effectively combine material supply support with warehousing location problems to complete the location selection of multi-level material distribution sites.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A multi-level support site selection method based on a networked structure is proposed for site selection of a life support system with a multi-level support system; specifically, it includes the following steps:

[0007] Step 1: Based on the location and demand information of the areas requiring living assistance, divide the assistance levels into three tiers from low to high: upstream (third-level assistance), midstream (second-level assistance), and downstream (first-level assistance). The first and second levels each contain multiple nodes of varying numbers. Nodes in the first level represent material distribution points in residential areas, while nodes in the second level represent medium-sized material distribution centers. The third level contains one node, representing a large material distribution center in the area. Living assistance supplies are delivered layer by layer in the order of third-level assistance, second-level assistance, first-level assistance, and residential areas.

[0008] Step 2: Site selection for the nodes of the first-level support layer. The specific method is as follows: Based on the population of each residential area requiring essential supplies, statistical analysis of residents' needs is conducted. Combined with the characteristics of the supply distribution nodes, candidate locations for the first-level support layer nodes are determined. Based on the candidate locations and public demand, a two-stage optimization process is used to select node locations. In the first stage, a bi-objective p-median mathematical model is constructed, with the optimization objectives of minimizing the number of first-level support layer nodes and minimizing transportation distance costs, respectively, to initially select node locations. In the second stage, heuristic rules are constructed to perform secondary node location selection to meet the needs of large-scale residential areas.

[0009] Step 3: To meet the material transportation needs from the second-level support layer to the first-level support layer, based on the location of the first-level support layer and the required material storage capacity of each node, the locations of multiple nodes in the second-level support layer are selected. The specific method is as follows: with the optimization objective of minimizing the transportation distance and the number of distribution centers, a bi-objective p-center location model for the nodes of the second-level support layer is constructed, and the solution is obtained through a solution algorithm.

[0010] Step 4: Based on the location information and service conditions of the second-level support layer, determine the demand of each second-level support point to select the location of the third-level support layer. The specific method is as follows: with the goal of minimizing human resources costs, construct a location model for the third-level support layer, and solve the model by using the center of gravity method to calculate the optimal location of the third-level support layer, i.e., the large-scale material distribution center.

[0011] Step 5: Using the locations and quantities of multiple nodes in the first to third level of the guarantee layer obtained from the above steps, determine the downstream nodes served by the nodes of each level of the guarantee layer from top to bottom, construct a networked multi-level material guarantee system and a directed network guarantee graph, and complete the site selection for multi-level guarantee of living materials based on the networked structure.

[0012] Preferably, the specific method for the two-stage optimized location selection in step two is as follows:

[0013] Step 1: Based on the situation of daily necessities in each residential area, count all cases where the demand exceeds the maximum delivery quantity D. max In this phase, D will be allocated to the region first. max The system first provides living supplies; then, a bi-objective p-median model is adopted, with the goal of minimizing the number of nodes and the transportation distance, and capacity constraints as constraints, to establish a mathematical model for node location, and the Gurobi solver is used to solve the constructed integer programming model.

[0014] Step 2: For residential areas where demand is not being met, heuristic rules are used to add some support nodes to satisfy the demand. For these areas, search for nearby unselected alternative deployment points, select the node to provide services, and repeat this process until the demand of the residential area is met. Subsequently, this process is applied to the remaining areas in order of demand size, thereby completing the secondary site selection of the first-level support layer nodes.

[0015] Beneficial effects

[0016] This invention introduces a multi-level location selection method based on task objectives. Addressing the actual needs of government operation and management, different location selection targets are determined based on the task objectives of different support levels, thereby constructing a three-level location selection model for ensuring the supply of essential goods, improving the realism and feasibility of the support location selection model. Furthermore, this invention selects locations for nodes in the next higher support level based on the location status of nodes in lower levels, forming a stable and convenient networked support system. In addition, this invention uses a two-stage algorithm to divide the location selection model of the first-level support layer, which has a large number of nodes, into two stages. For residential areas with high demand, a heuristic-based secondary location selection is introduced, reducing the complexity of the first-stage solution and effectively improving the location selection efficiency. Attached Figure Description

[0017] Figure 1 Flowchart of multi-level protection site selection method;

[0018] Figure 2 Flowchart of the second-stage heuristic method;

[0019] Figure 3 Site selection results for medium-sized residential areas to the first level of protection;

[0020] Figure 4 Site selection results for large-scale residential areas up to the first level of protection;

[0021] Figure 5 Site selection results for the first and second level of protection layers in medium-sized areas;

[0022] Figure 6 Site selection results for the first and second levels of protection in large areas;

[0023] Figure 7 Site selection results for the second to third level of protection layers in medium-sized areas;

[0024] Figure 8 The site selection results for the second to third level of protection in large areas. Detailed Implementation

[0025] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0026] Example

[0027] This invention provides a multi-level guaranteed addressing method based on a networked structure; such as Figures 1-8 As shown;

[0028] Step 1: Based on the required areas and needs for basic living assistance, and the government's commonly used assistance structure, the assistance levels are divided into three tiers from lowest to highest. The first tier includes multiple nodes of varying numbers, representing material distribution points in residential areas, responsible for receiving materials from the second tier and distributing them to various residential areas. The second tier includes multiple nodes of varying numbers, representing medium-sized material distribution centers, responsible for receiving materials from the third tier and distributing them to the first tier. The third tier includes one node, representing the area's large material distribution center, responsible for distributing all received materials to the nodes in the second tier. The delivery of basic living assistance materials proceeds layer by layer in the order of third tier, second tier, first tier, and residential areas.

[0029] Step Two: Site selection for the nodes of the first-level support layer. The specific method is as follows: Based on the population of each residential area requiring living supplies, information on residents' needs is collected and statistically analyzed. Combining this information with actual conditions, the first-level support layer includes multiple supply distribution points. These points need to directly serve the communities and should be located adjacent to each community. Simultaneously, traffic intersections within each administrative district, being areas with convenient transportation, can quickly deliver supplies; therefore, locations near intersections and communities are considered as candidate points. Since the number of distribution points is a complex variable determined by multiple factors in practice, it needs to be comprehensively determined by considering the location of the distribution points, the user demand, and the location of the communities. Based on the above candidate points and the needs of the residential areas, this invention constructs a two-stage solution method to simultaneously optimize the number and location of distribution points in the first-level support layer. Specifically, it includes the following steps:

[0030] Step 2-1: In the first stage, count all demands that exceed the maximum delivery quantity D. max In this phase, D will be allocated to the community first. max Package supplies. Under the aforementioned requirements, to minimize government operating costs, and with the optimization objectives of minimizing the number of distribution points and minimizing transportation distance costs, a bi-objective p-median model is constructed. The objective function is shown below:

[0031]

[0032]

[0033] The constraints are:

[0034]

[0035] Where K represents the set of preset delivery points, J represents the set of residential areas, Q represents the capacity of the delivery points, and D represents the capacity of the delivery points. j Indicating the needs of residents in the residential area, d ij x represents the Euclidean distance from node i to node j. ij Let ∈{0,1} be the decision variable, representing that if residential area j is assigned to the preset delivery point i, then x ij =1; otherwise x ij =0. y i ∈{0,1} indicates whether the preset delivery point i is selected. p represents the number of preset delivery points that are selected.

[0036] The objective function represents minimizing both the transportation distance cost and the number of delivery points. The five constraints are: capacity is satisfied; each cell can only be served once; only selected delivery points can serve a cell; the number of delivery points equals the number determined by objective two; and all decision variables are integers between 0 and 1.

[0037] Step 2-2: Based on the established p-median optimization model, perform exact planning using the Gurobi solver. The Gurobi solver relaxes the integer programming problem into a linear programming problem and applies a branch and bound algorithm to solve it. This exact algorithm, as a deterministic algorithm, is fast, accurate, and guarantees the optimality of the solution. This yields the node locations and number for the first-level protection layer in the first stage.

[0038] Steps 2-3: For all previous requirements exceeding D max For communities where the actual needs were not met in the first phase, a heuristic approach was adopted to add additional delivery points for the second phase of allocation, thus meeting the actual needs of the communities. The process is as follows: Figure 2 As shown in the diagram. First, all unselected candidate points and all residential areas with unmet needs are statistically analyzed and summarized. Upon detecting unmet needs in a residential area, they are first sorted according to the magnitude of remaining demand. For the residential area with the highest demand, its neighboring candidate delivery points that were not selected in the first phase are searched, and these delivery points are selected to provide services. This process is repeated until the demand of that residential area is met. Subsequently, this process is applied sequentially to the remaining residential areas, thus completing the secondary site selection of delivery points. Through this two-stage site selection of delivery points, the location and number of nodes in the first-level protection layer are optimized.

[0039] Step 3: To meet the downstream material transportation needs of the second-level support layer, based on the location of the first-level support layer nodes and the material storage capacity, optimize the site selection for multiple second-level support layer nodes, namely medium-sized material distribution centers. First, analyze the candidate locations for the second-level support layer nodes. Since medium-sized material distribution centers are long-term, large-scale storage locations, traffic intersections, as well as locations with convenient transportation, can better meet the needs for rapid material transportation and quick relocation. Therefore, traffic intersections are selected as candidate points for planning the location and number of second-level support layer nodes.

[0040] Since the maximum transport distance from medium-sized material distribution centers to various third-level support layer delivery points significantly influences node locations, a dual-objective model is adopted for the site selection of second-level support layer nodes. First, the maximum distance between the first and second-level support layers is minimized, establishing a min-max objective. Second, the number of nodes in the second-level support layer is minimized. Based on the above analysis, the dual-objective p-center model objectives are as follows:

[0041]

[0042]

[0043] The constraints are:

[0044]

[0045] The parameters are described in step 2-2. The objective functions are to minimize the maximum distance between nodes in the first-level and second-level protection layers, and to minimize the number of selected second-level protection layer nodes. The four distance constraints are as follows: each first-level protection layer node can only be served by one second-level protection layer node; only selected second-level protection layer nodes can serve first-level protection layer nodes; the number of second-level protection layer nodes is equal to the number determined by the second optimization objective; and all decision variables are integers between 0 and 1.

[0046] Based on the established p-median optimization model, precise planning is performed using the Gurobi solver. This yields the location and number of medium-sized material distribution centers for the second-level support layer.

[0047] Step Four: After completing the construction of the second-level support layer nodes, determine the node requirements for each second-level support layer based on the location information of the second-level support layer. Within a large region, large-scale distribution centers for daily necessities handle the external receipt of goods and the overall distribution within the region; these centers are large in scale, and each administrative region typically has only one distribution center. Therefore, it is necessary to select the location for the third-level support layer—large-scale distribution centers for daily necessities. A mathematical model is constructed using the center-of-gravity method, with the objective function being human resource cost (the product of demand and distance). The model is constructed as follows:

[0048]

[0049] Among them, V i d represents the number of residents for each i; i Represents the transportation distance between material center i and the location focus, (X i ,Y i (X0, Y0) represents the position of each second-level protection layer, and (X0, Y0) represents the position of the third-level protection layer, which are the variables that need to be optimized.

[0050] For the centroid method model, a first-order gradient search is used to optimize it. The iterative solution steps are as follows:

[0051] Step 4-1: Initialize using the equivalent centroid formula, determine the initial point, and calculate the objective function value D1.

[0052] Right now

[0053] Step 4-2: Apply iterative formulas (11) and (12) to obtain the solution after iteration, and calculate the objective function value D2; the iterative search formula is as follows:

[0054]

[0055]

[0056] When D reaches its minimum value make We can obtain:

[0057]

[0058] Since the above equation is difficult to solve analytically, an iterative method is used to solve it. The iterative formula is:

[0059]

[0060]

[0061] Here, (X'0,Y0') is the solution of this iteration, while (X0,Y0) is the solution obtained in the previous iteration.

[0062] Step 4-3: If the difference between D1 and D2 is less than the set threshold, the iteration process ends and the coordinates at this point are output as the final solution; otherwise, let D1 = D2 and go to step 4-2.

[0063] By following the steps above, the center of gravity model established above is solved, thereby obtaining the location of the third level of protection layer—the large-scale material distribution center.

[0064] Step 5: Calculate the node locations and number of nodes for the first to third level of the support layer using the steps above, identify the child nodes served by each level of nodes, establish corresponding service relationships, construct a networked multi-level material support system and a directed network support graph, and complete the site selection for multi-level support of living materials based on a networked structure.

[0065] For a medium-sized administrative region A and a large administrative region B, this method is used to construct and solve a multi-level support location model. Medium-sized administrative region A has 146 residential areas, with 228,000 people requiring basic living supplies. Large administrative region B has 200 residential areas, with 578,000 people requiring basic living supplies. First, in step two, the number and location of nodes in the first-level support layer are calculated. The relationship between all residential areas and nodes in the first-level support layer is as follows: Figure 3 , 4 As shown in the diagram, circles represent residential areas, their size indicating the material needs of those areas. Triangles represent nodes in the first-level support layer, and lines connecting residential areas to nodes in the first-level support layer represent their service relationships. Through the construction and verification of support systems for medium and large administrative regions, this support method can fully meet the needs of all residential areas. Subsequently, in step three, a directed network support graph from the first-level support layer to the second-level support layer is constructed as shown in the diagram. Figure 5 , 6 As shown in the diagram. The square represents the second-level support layer of the area—a medium-sized material distribution center—and the lines represent the service relationships between nodes in the second-level support layer and nodes in the first-level support layer. Finally, through step four, the location of the third-level support layer, namely the large-scale material distribution center, can be calculated as follows: Figure 7 , 8 As shown in the diagram, the large square represents the third-level support layer node in this area, which will provide material supply services to all second-level support layer nodes within the administrative region. Algorithm verification shows that this support method can fully meet the needs of all residential areas and each sub-node, while minimizing labor and material costs during transportation.

[0066] Based on the above experiments, this method can provide an efficient model and solution for the site selection of regional life support systems of different scales, and optimizes the location and number of support nodes.

[0067] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-level guaranteed addressing method based on a networked structure, characterized in that... Includes the following steps: Step 1: Based on the location and needs of the areas requiring living support, divide the support levels into three levels from low to high: Level 3, Level 2, and Level 1. Deliver living support supplies layer by layer in the order of Level 3, Level 2, Level 1, and residential areas. Step 2: Select locations for the nodes of the first-level protection layer; Step 3: Select the node locations for the second-level protection layer based on the location of the first-level protection layer and the required material storage capacity of each node; Step 4: Based on the location information and service conditions of the second-level protection layer, select the location for the third-level protection layer; Step 5: Based on the node locations and quantities obtained in the first, second, and third protection layers, construct a networked multi-level material support system and a directed network support graph, and complete the site selection for the networked multi-level material support system. The specific method for selecting the locations of nodes in the first-level protection layer is as follows: based on the number of residents in each residential area that needs living supplies, information on residents' needs is collected, and combined with the characteristics of the supply distribution nodes, candidate locations for the first-level protection layer nodes are determined; based on the candidate locations and the needs of the people, a two-stage optimization method is used to select the locations of the nodes. When using a two-stage optimization approach for node location selection, in the first stage, a bi-objective p-median mathematical model is constructed, with the optimization objectives of minimizing the number of nodes selected in the first-level protection layer and minimizing transportation distance costs, respectively, to perform preliminary node location selection; in the second stage, heuristic rules are constructed to perform secondary node location selection to meet the needs of large-scale residential areas. The specific method for preliminary site selection is as follows: Based on the situation of daily necessities in each residential area, statistics were compiled on all cases where demand exceeded the maximum delivery quantity. The area is allocated first. Daily necessities; Subsequently, a bi-objective p-median model was adopted to establish a node location mathematical model with the goal of minimizing the number of nodes and transportation distance, and with capacity constraints as constraints. The Gurobi solver was then used to solve the constructed integer programming model. The specific method for secondary addressing is as follows: For residential areas where demand is not met, heuristic rules are used to add some guarantee nodes to meet their needs. For the above-mentioned areas, search for nearby unselected alternative deployment points, select the node to provide services, and repeat the process until the demand of the residential area is met. Then, in order of demand size, this process is applied to the remaining areas to complete the secondary site selection of the first-level guarantee layer nodes.

2. The multi-level guaranteed addressing method based on a networked structure according to claim 1, characterized in that: In step one, the first level of protection layer contains multiple nodes, which represent material distribution points in residential areas; the second level of protection layer contains multiple nodes, which represent medium-sized material distribution centers; and the third level of protection layer contains one node, which represents a large material distribution center in the area.

3. The multi-level guaranteed addressing method based on a networked structure according to claim 1, characterized in that: In step three, the specific method for selecting the node locations of the second-level protection layer is as follows: with the optimization objective of minimizing the transportation distance and the number of distribution centers, a bi-objective p-center location model for the nodes of the second-level protection layer is constructed, and the model is solved using a solution algorithm.

4. The multi-level guaranteed addressing method based on a networked structure according to claim 3, characterized in that: In step four, the specific method for selecting the location of the third-level support layer is as follows: with the goal of minimizing human resource costs, a location model for the third-level support layer is constructed, and the model is solved by using the center of gravity method to calculate the optimal location of the third-level support layer, i.e., the large-scale material distribution center.

5. The multi-level guaranteed addressing method based on a networked structure according to claim 4, characterized in that: The constructed bi-objective p-median model is as follows: （1） （2） The constraints are: （3） in, This represents the set of preset delivery points. It represents a collection of residential areas. Indicates the capacity of the delivery point. This indicates the needs of residents in the residential area. Represents a node To the node Euclidean distance, Let be the decision variable, representing if the residential area Assigned to preset delivery points ,but ;otherwise , Indicates the preset delivery point Whether it is selected or not This indicates the number of preset delivery points selected.

6. The multi-level guaranteed addressing method based on a networked structure according to claim 5, characterized in that: The objectives of constructing a bi-objective p-centered model are as follows: （4） （5） The constraints are: （6）。 7. The multi-level guaranteed addressing method based on a networked structure according to claim 4, characterized in that: In step four, when selecting the location for the third-level protection layer, the centroid method is used to construct a mathematical model, and the constructed model is as follows: （7） in, Indicate each The number of residents; Indicates the material center Transportation distance relative to the location focus; Indicates the location of each second-level protection layer node; This indicates the location of the third-level protection layer, which is the variable that needs to be optimized; The optimization is performed using a first-order gradient search, and the iterative solution steps are as follows: Step 4-1: Initialize using the equivalent centroid formula, determine the initial point, and calculate the objective function value. ;Right now ; Step 4-2: Apply iterative formulas (11) and (12) to obtain the solution after iteration, and calculate the objective function value. The iterative search formula is shown below: （8） （9） when When the minimum value is obtained, ,make ,have to: （10） The iterative formula is: in, This is the solution for this iteration. This is the solution obtained from the previous iteration.

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