Multi-target joint site selection method for urban convenience service facilities with hierarchical structure

Abstract

The invention relates to the technical field of urban service facility site selection, in particular to a multi-target joint site selection method for urban convenience service facilities with a hierarchical structure, which comprises the following steps: acquiring popularity of each candidate address, a target user set, a travel track set corresponding to the target user set, maximum service capacity and construction cost, and generating each leaf node; clustering all leaf nodes in a multi-level manner by adopting an R + tree structure construction and pruning strategy and taking candidate address popularity corresponding to each leaf node as an index to obtain all generated R + trees; marking each level of the aligned R + tree, and generating an index layer Hash mapping set; and selecting # imgabs0 service centers, # imgabs1 # service centers and # imgabs2 # service centers on the basis of the index layer hash mapping set by adopting a heuristic local greedy strategy under the conditions that the total construction cost of all the selected service centers is smaller than or equal to a total cost threshold value and the popularity sum of all the selected service centers is the highest. According to the invention, the multi-target joint site selection efficiency and effect are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of site selection for urban service facilities, and in particular to a multi-objective joint site selection method for urban public convenience service facilities with a hierarchical structure. Background Art

[0002] Service facilities of the same type are in an equal relationship and are not subordinate to each other. There is no explicit exchange of goods or business between them, such as hospitals, shopping malls, public toilets, etc.; however, the overall service system of some convenience service facilities is a tree-like hierarchical structure, and there are obvious differences in the affiliation of service centers and service outlets, and even the service centers are multi-level; such as logistics express stations, multiple logistics outlets in an urban area always pick up and return related express items to the logistics service center in the area, and then the service center exchanges goods with the service center on the next level; therefore, this type of service facility can be called an urban convenience service facility with a hierarchical structure.

[0003] For non-hierarchical public convenience service facilities, the total popularity of all candidate addresses in the future time period can be directly calculated according to the algorithm model, and then sorted from high to low to select appropriate candidate addresses for construction and deployment; however, for convenience service facilities with a hierarchical structure, this solution is not feasible, mainly because: first, the popularity of convenience service outlets and service centers is calculated in different ways. The popularity of service outlets is generally determined by the number of resident users in the area it can cover, while the popularity of service centers is related to the service outlets and service capacity to which they belong; second, the location strategies of service outlets and service centers are different. Since there is a clear hierarchical relationship between them, different location schemes for lower-level service outlets will significantly affect the further location of upper-level service centers; third, due to their capacity limitations, convenience service outlets generally consider the upper limit of the maximum service capacity in a unit time, while for service centers, profit maximization (serving front-line customers) is not their primary goal. Generally, they need to consider the important factor of cost minimization, and the above-listed factors will affect the calculation of popularity and the implementation of location strategies.

[0004] Under the conditions of considering the maximum service ceiling of service outlets and the comprehensive construction cost constraints of service centers, there is currently little research on the site selection and deployment methods of urban convenience service facilities with a hierarchical structure. Existing methods focus on studying the site selection and construction planning of non-hierarchical similar service facilities. This problem is essentially a classic set cover or integer programming problem, that is, a conditional optimization problem. Therefore, this problem is NP-Hard. The algorithms proposed so far are all heuristic methods with certain restrictions, such as greedy algorithms, hill climbing algorithms, simulated annealing, search space pruning, etc., as well as some index-based algorithms, such as region-based clustering and best-first pruning, B-tree clustering and other index structures, etc.; there are also algorithms that propose the dynamic site selection planning problem of service facilities. Different from the aforementioned fixed site selection, the service facilities are movable in the dynamic site selection case, such as movable breakfast carts, movable trash cans, etc., that is, the subset of candidate addresses that can be deployed in different continuous unit time periods is dynamically changeable, and most of the algorithms used are also heuristic greedy path planning methods. However, dynamic site planning is essentially still a generalization of the non-hierarchical homogeneous service facility site planning problem over multiple continuous time periods.

[0005] At present, a small number of studies have proposed the joint site selection problem of convenient service facilities, such as the joint site selection of charging stations and battery swap stations, and the joint site selection of distributed power sources and sensitive users. The research objects and scope of these methods are mainly concentrated in the field of power facilities; however, the service facilities to be sited and deployed in these methods are mostly complementary services. There is no obvious hierarchical relationship between them, and they are mainly based on minimizing construction costs, rather than minimizing costs and maximizing profits. The algorithms used are mostly heuristic algorithms, such as Nonlinear Mixed Integer Programming, Whale Optimization, Column and Constraint, etc.

[0006] In summary, the existing joint site selection research objects are mainly aimed at similar power-related facilities with non-hierarchical structures, and are not suitable for joint site selection research on urban convenience service facilities with hierarchical structures; in addition, the existing joint site selection research uses minimizing construction costs as the site selection rule, and does not fully consider the characteristics of different types of candidate addresses at different levels (such as service outlets and service centers), and construct a system that adapts to multiple site selection rules (multi-objective). As a result, the effect of multi-objective joint site selection is not good, and there are problems such as low efficiency and low accuracy of joint site selection. Summary of the invention

[0007] To this end, the technical problem to be solved by the present invention is to overcome the lack of support in the prior art for multiple site selection rules for different types of candidate addresses in different hierarchical structures, resulting in poor effect of multi-target joint site selection, low efficiency and low accuracy of joint site selection.

[0008] In order to solve the above technical problems, the present invention provides a multi-objective joint site selection method for urban convenience service facilities with a hierarchical structure, comprising:

[0009] Obtain all candidate addresses of convenient service facilities in the urban road network structure diagram and construct a candidate address set; obtain the popularity, target user set, travel trajectory set corresponding to the target user set, maximum service capacity and construction cost of each candidate address;

[0010] Generate each leaf node based on each candidate address and its popularity, its target user set, the travel trajectory set corresponding to its target user set, its maximum service capacity and its construction cost; Based on all leaf nodes, adopt the R+ tree structure construction and pruning strategy, take the popularity of the candidate address corresponding to each leaf node as the indicator, perform multi-level clustering on all leaf nodes, obtain all generated R+ trees, and build an R+ forest; Align all R+ trees in the R+ forest to obtain each aligned level; Label each aligned level to obtain the index of each level; Based on the candidate addresses corresponding to all leaf nodes in each index layer and their popularity, their target user set, the travel trajectory set corresponding to their target user set, their maximum service capacity and their construction cost, build an index layer node information set; Generate an index layer hash map set with the hierarchical index as the key and the index layer node information set as the value;

[0011] Based on the index layer hash map set, a heuristic local greedy strategy is adopted to select the joint site with the total construction cost of all selected service centers being less than or equal to the total cost threshold and the popularity and maximum of all selected service outlets as conditions. Service Centers and service outlets, including: .

[0012] Preferably, based on the index layer hash map set, a heuristic local greedy strategy is adopted to select the service centers with the total construction cost of all selected service centers being less than or equal to the total cost threshold. After the service centers are selected, the popularity and the highest of all selected service outlets are selected. The service outlets include:

[0013] The total construction cost of all selected service centers is less than or equal to the total cost threshold. Service centers, including:

[0014] If there is an index layer in the index layer hash map collection The number of all candidate addresses in , then calculate the index layer The total construction cost of all candidate addresses in ;

[0015] If the index layer If the total construction cost of all candidate addresses in the index layer is less than or equal to the total cost threshold, All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed;

[0016] If the index layer If the total construction cost of all candidate addresses in is greater than the total cost threshold, the index layer is calculated. The total construction cost of all candidate addresses in each index layer until the index layer is found The total construction cost of all candidate addresses in is less than or equal to the total cost threshold;

[0017] If the index layer The total construction cost of all candidate addresses in is equal to the total cost threshold, then the index layer Satisfy the cost condition and add the index layer All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed;

[0018] If the index layer If the total construction cost of all candidate addresses in the index layer is less than the total cost threshold, a local greedy strategy is adopted to The corresponding does not belong to the index layer All candidate addresses are sorted in descending order according to their corresponding construction costs to form a set ; From the collection Starting from the first element in , the corresponding construction cost is compared with the index layer The total construction cost of all candidate addresses is accumulated until The total construction cost after rounds of accumulation exceeds the total cost threshold and the total number of candidate addresses does not exceed , stop accumulating, and All candidate addresses and index layers accumulated in rounds All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed;

[0019] If an index level does not exist in the index level hash map collection The number of all candidate addresses in , then find the index layer that satisfies The number of corresponding candidate addresses is less than And the index layer The number of corresponding candidate addresses is greater than Two adjacent index layers; calculate the index layer The total construction cost of all candidate addresses in ;

[0020] If the index layer If the total construction cost of all candidate addresses in is equal to the total cost threshold, then the index layer All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed;

[0021] If the index layer If the total construction cost of all candidate addresses in the index layer is less than the total cost threshold, a local greedy strategy is adopted to The corresponding does not belong to the index layer All candidate addresses are sorted in descending order according to their corresponding construction costs to form a set ; From the collection Starting from the first element in, the corresponding construction cost and index layer The total construction cost of all candidate addresses in the above table is accumulated until The total construction cost after rounds of accumulation exceeds the total cost threshold and the total number of candidate addresses does not exceed , stop accumulating, and Round accumulation of candidate addresses and index layers All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed;

[0022] Based on the popularity and highest of all selected service outlets, select Service outlets, including:

[0023] When the index layer corresponding to the location of all selected service centers is , then based on the unchanged level label, delete all the index layer hash map sets that do not contain the index layer All R+ trees of the node update the index layer hash mapping set to be the node candidate hash mapping set;

[0024] When the index layer corresponding to the location of all selected service centers is or and , then based on the unchanged level label, delete all the index layer hash map sets that do not contain the index layer All R+ trees of the node update the index layer hash mapping set to be the node candidate hash mapping set;

[0025] When the index layer corresponding to the location of all selected service centers is or and , then based on the unchanged level label, delete all the index layer hash map sets that do not contain the index layer All R+ trees of the node update the index layer hash mapping set to be the node candidate hash mapping set;

[0026] If there is an index layer in the node candidate hash map set The number of all candidate addresses in , then the index layer All the candidate addresses corresponding to the above are used as the locations of all the selected service outlets, and the location selection of the service outlets is completed;

[0027] If there is no index layer in the node candidate hash map set The number of all candidate addresses in , then find the index layer that satisfies The number of corresponding candidate addresses is less than And the index layer The number of corresponding candidate addresses is greater than The two adjacent index layers; the index layer The corresponding does not belong to the index layer All candidate addresses are sorted in descending order according to their corresponding popularity to form a set ; From the collection Starting from the first element in , a candidate address is selected in each round until The number of candidate addresses and index layers selected after the round The sum of the corresponding candidate addresses in is , stop selecting, All candidate addresses and index layers selected in rounds All the corresponding candidate addresses are used as the locations of all selected service outlets, and the service outlet location selection is completed.

[0028] Preferably, based on the index layer hash map set, a heuristic local greedy algorithm is used to select the service points with the highest popularity of all selected service points as the condition. After the service outlets are built, the total construction cost of all selected service centers is less than or equal to the total cost threshold. The service centers include:

[0029] Based on the popularity and highest of all selected service outlets, select Service outlets, including:

[0030] If there is an index layer in the index layer hash map collection The number of all candidate addresses in , then the index layer All the candidate addresses corresponding to the above are used as the locations of all the selected service outlets, and the location selection of the service outlets is completed;

[0031] If an index level does not exist in the index level hash map collection The number of all candidate addresses in , then find the index layer that satisfies The number of corresponding candidate addresses is less than And the index layer The number of corresponding candidate addresses is greater than The two adjacent index layers; the index layer The corresponding does not belong to the index layer All candidate addresses are sorted in descending order according to their corresponding popularity to form a set ; From the collection Starting from the first element in , a candidate address is selected in each round until The sum of the number of candidate addresses selected after the round and the corresponding number of candidate addresses in the index layer is , stop selecting, All candidate addresses selected in the round and all corresponding candidate addresses in the index layer are used as the locations of all selected service outlets, and the service outlet location selection is completed;

[0032] The total construction cost of all selected service centers is less than or equal to the total cost threshold. Service centers, including:

[0033] When the index layer corresponding to the location of all selected service outlets is , then based on the unchanged level label, delete all the index layer hash map sets that do not contain the index layer All R+ trees of the node update the index layer hash map set to the central candidate hash map set;

[0034] When the index layer corresponding to the location of all selected service outlets is and , then based on the unchanged level label, delete all the index layer hash map sets that do not contain the index layer All R+ trees of the node update the index layer hash map set to the central candidate hash map set;

[0035] If there is an index layer in the central candidate hash map set The number of all candidate addresses in , then calculate the index layer The total construction cost of all candidate addresses in ;

[0036] If the index layer If the total construction cost of all candidate addresses in the index layer is less than or equal to the total cost threshold, All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed;

[0037] If the index layer If the total construction cost of all candidate addresses in is greater than the total cost threshold, the index layer is calculated. The total construction cost of all candidate addresses in each index layer until the index layer is found The total construction cost of all candidate addresses in is less than or equal to the total cost threshold;

[0038] If the index layer If the total construction cost of all candidate addresses in is equal to the total cost threshold, then the index layer All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed;

[0039] If the index layer If the total construction cost of all candidate addresses in the index layer is less than the total cost threshold, a local greedy strategy is adopted to The corresponding does not belong to the index layer All candidate addresses are sorted in descending order according to their corresponding construction costs to form a set ; From the collection Starting from the first element in , the corresponding construction cost is compared with the index layer The total construction cost of all candidate addresses is accumulated until The total construction cost after rounds of accumulation exceeds the total cost threshold and the total number of candidate addresses does not exceed , stop accumulating, and All candidate addresses and index layers accumulated in rounds All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed;

[0040] If there is no index layer in the central candidate hash map set The number of all candidate addresses in , then find the index layer that satisfies The number of corresponding candidate addresses is less than And the index layer The number of corresponding candidate addresses is greater than Two adjacent index layers; calculate the index layer The total construction cost of all candidate addresses in ;

[0041] If the index layer If the total construction cost of all candidate addresses in is equal to the total cost threshold, then the index layer All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed;

[0042] If the index layer If the total construction cost of all candidate addresses in the index layer is less than the total cost threshold, a local greedy strategy is adopted to The corresponding does not belong to the index layer All candidate addresses are sorted in descending order according to their corresponding construction costs to form a set ; From the collection Starting from the first element in, the corresponding construction cost and index layer The total construction cost of all candidate addresses in the above table is accumulated until The total construction cost after rounds of accumulation exceeds the total cost threshold and the total number of candidate addresses does not exceed , stop accumulating, and Round accumulation of candidate addresses and index layers All the corresponding candidate addresses are used as the locations of all selected service centers, and the service center location selection is completed.

[0043] Preferably, obtaining the popularity and target user set of each candidate address includes:

[0044] Obtain the travel trajectory of each user, and based on the additional distance that each user travels after leaving his travel trajectory to each candidate address and then returning to his travel trajectory, obtain the shortest network round-trip distance between each candidate address and each user's travel trajectory, and calculate the attraction value between each candidate address and each user;

[0045] Based on multiple users and their travel trajectories within each candidate address reference area, a user information set covered by each candidate address is constructed; a candidate address hash map set is generated with the candidate address as the key and the user information set covered by the candidate address as the value; wherein each candidate address reference area is centered on each candidate address and has a side length of The candidate data hash mapping set is represented as ; Indicates Candidate addresses The user information set covered; Indicates Candidate addresses The number of all users in the covered user information set;

[0046] Arrange the attraction values ​​between each user and each candidate address containing their travel trajectory in the reference area in descending order, and construct each user attraction information list; generate a user hash map set with the user as the key and the user attraction information list as the value; wherein the user hash map set is represented as ; Indicates The first element of the user attraction information list corresponding to the user; Indicates Users Travel trajectory and candidate addresses The attraction value is the largest;

[0047] Jordi The first of the user information sets covered by the candidate addresses The user belongs to the user hash map set, and the The candidate address and the user information set it covers The attraction value between users is The first element in the user attraction information list, that is , and , then the Users and its corresponding attraction value as the Candidate addresses The candidate data is obtained All the candidate data of the candidate addresses constitute the candidate data set ;

[0048] Jordi The number of users in the candidate data set Less than or equal to its maximum service capacity ,Right now , , then the The sum of all attractiveness values ​​in the candidate data set of candidate addresses is taken as the first The popularity of candidate addresses is expressed as:

[0049] ;

[0050] in, Indicates Candidate addresses popularity; Indicates Candidate addresses The candidate data set The sum of all attraction values ​​in ; represents the maximum service capacity set of all candidate addresses; at the same time, based on the All users in the candidate data set of candidate addresses are constructed The target user set of candidate addresses ,Right now ;

[0051] Jordi The number of users in the candidate data set Greater than its maximum service capacity ,Right now , then for All attractiveness values ​​in the candidate data set of candidate addresses are sorted in descending order, and the cumulative The sum of the attraction values ​​is taken as the The popularity of candidate addresses is expressed as:

[0052] ;

[0053] in, express Before the accumulation The sum of the attraction values; express Index of medium attractiveness value; Indicates the value of the maximum service capacity; at the same time, based on the previous The user corresponding to the attractiveness value is constructed The target user set of candidate addresses , Indicates The number of users in the target user set of candidate addresses, that is , .

[0054] Preferably, the expression of the shortest network round-trip distance between each candidate address and each user travel trajectory is:

[0055] ;

[0056] in, Indicates The candidate address and The shortest round-trip distance between the travel trajectories of users, that is, The user left his travel track to The additional journey from the candidate address to the return path; Indicates Users, , Represents the set of all users in the road network; Indicates The travel trajectory of each user, , Indicates the number of location points on the user's travel trajectory. Indicates Users at location The corresponding timestamp; Indicates Candidate addresses; Indicates Location points on the user's travel trajectory arrive The shortest network distance; Indicates to Location points on the user's travel trajectory The shortest network distance; Indicates The user's travel trajectory from the location point To location The road network trajectory distance.

[0057] Preferably, the expression of the attraction value between each candidate address and each user is:

[0058] ;

[0059] in, Indicates The candidate address and The attractiveness value between users; represents nonlinear log normalization; Indicates The candidate address and The shortest round-trip distance between user travel trajectories; Indicates Users; Indicates The travel trajectory of each user, , Indicates the number of location points on the user's travel trajectory. Indicates the number of times the user travels Location points, Indicates the number of times the user travels The timestamp corresponding to each location point; Indicates Candidate addresses; represents the Euler number; , when the candidate address With users The longer the road network distance, The smaller the value of The itinerary Directly through the candidate address hour, ,at this time, The value of is the largest, .

[0060] Preferably, the R+ tree structure construction and pruning strategy is adopted based on all leaf nodes, the popularity of the candidate address corresponding to each leaf node is used as an indicator, all leaf nodes are clustered at multiple levels, all generated R+ trees are obtained, and the R+ forest is constructed, including:

[0061] S321: taking the leaf node whose number of target users is equal to the maximum service capacity as the root node of the R+ tree, generating an R+ tree as an independent R+ tree;

[0062] S322: taking leaf nodes whose number of target users is less than the maximum service capacity as nodes to be merged, and constructing a set of nodes to be merged;

[0063] S323: Calculate the spherical distance between the candidate addresses corresponding to the two nodes to be merged based on the longitude and latitude radians of the geographical locations where the candidate addresses corresponding to any two nodes to be merged are located;

[0064] Based on the set of nodes to be merged, a pruning strategy is adopted to set the distance threshold , the spherical distance between the corresponding candidate addresses is no greater than The two nodes to be merged constitute a target node pair to be selected, and based on all the target node pairs to be selected, a set of target node pairs to be selected in the initial round is constructed;

[0065] S324: based on the target user sets and their travel trajectory sets corresponding to the two target nodes in the target node pair, obtaining the merged user set and their merged travel trajectory set of the current target node pair;

[0066] Based on the merged user set and merged travel trajectory set of the current candidate node pair, the popularity of the candidate addresses corresponding to the two current candidate nodes is updated respectively to obtain the new popularity of the candidate addresses corresponding to the two current candidate nodes; the higher new popularity of the two current new popularity is selected as the merge function value of the current candidate node pair, and its expression is:

[0067] ;

[0068] in, Represents the target node pair to be selected The combined function value of ; Indicates Target nodes to be selected The new popularity of the corresponding candidate address; Indicates Target nodes to be selected The new popularity of the corresponding candidate address; Indicates Target nodes to be selected The target user set corresponding to the candidate address; Indicates Target nodes to be selected The target user set corresponding to the candidate address; express and The merged user set of express and medium-high new popularity;

[0069] According to the initial round of target node pair set to be selected, a merge function value of each target node pair to be selected in the initial round of target node pair set to be selected is obtained;

[0070] S325: The candidate node pairs with the highest merging function values ​​in the initial round of candidate node pairs are merged to obtain the first merged node in the initial round, and the candidate address corresponding to the candidate node with the larger new popularity among the current two candidate target nodes and its new popularity, its new user set, the new travel trajectory set corresponding to its new user set, its maximum service capacity and its construction cost are used as the candidate address and its popularity, its target user set, the travel trajectory set corresponding to its target user, its maximum service capacity and its construction cost of the first merged node in the initial round;

[0071] S326: remove all the candidate target node pairs that contain any candidate target node corresponding to the first merge node in the initial round from the set of candidate target node pairs in the initial round, and return to execute S325 until the set of candidate target node pairs in the initial round is an empty set, take all the initial merge nodes as parent nodes, take the two candidate target nodes corresponding to the initial merge nodes as child nodes, generate all the initial merge R+ trees, and take each initial merge node as the root node of its corresponding initial merge R+ tree;

[0072] S327: The unmerged candidate target nodes in the initial round of candidate target nodes and the root nodes in the initial round of merged R+ trees whose target user number is less than the maximum service capacity are merged as the candidate target nodes for the next round, until the number of root nodes in the merged R+ trees whose target user number is less than the maximum service capacity after multiple rounds of merging is less than 2, and the merging is completed to obtain all the merged R+ trees generated in the final round;

[0073] S328: Construct an R+ forest based on all the generated independent R+ trees and all the merged R+ trees generated in the final round.

[0074] Preferably, the spherical distance between the candidate addresses corresponding to the two nodes to be merged is calculated based on the radian values ​​of the longitude and latitude of the geographical locations of the candidate addresses corresponding to any two nodes to be merged, and the expression is:

[0075] ;

[0076] in, Indicates Candidate addresses and Candidate addresses The spherical distance between Indicates candidate address The latitude in radians of the geographical location; Indicates candidate address The arc value of longitude of the geographical location; Indicates candidate address The latitude in radians of the geographical location; Indicates candidate address The arc value of longitude of the geographical location; Represents the radius of the Earth.

[0077] Preferably, the candidate address corresponding to the target node with greater new popularity among the two target nodes to be selected, its new popularity, its new user set, its new travel trajectory set corresponding to its new user set, its maximum service capacity and its construction cost, as the candidate address of the first merged node in the initial round, its popularity, its target user set, its travel trajectory set corresponding to its target user, its maximum service capacity and its construction cost, include:

[0078] The two target nodes in the target node pair with the highest merge function value in the initial round of target node pair set are and , whose merged user set is ;

[0079] Based on the merged user collection , get the candidate address The new popularity ,include:

[0080] If the first The user belongs to the candidate address hash map set and the first user exists in the user hash map set. User and The attraction value between candidate addresses, that is, , and , then the Users and its corresponding attraction value are added to the The candidate data set of candidate addresses and thus joined All users in and their corresponding attractiveness values; based on And join All users in and their corresponding attractiveness values ​​are constructed A new candidate data set of candidate addresses ;in, Indicates that the user hash map set exists The element is User and The attractiveness value of the candidate addresses;

[0081] Jordi The number of users in the new candidate data set of candidate addresses Less than or equal to its maximum service capacity ,Right now , , then the The sum of all attractiveness values ​​in the new candidate data set of candidate addresses is taken as the first The new popularity of candidate addresses is expressed as:

[0082] ;

[0083] in, Indicates Candidate addresses The new popularity of Indicates Candidate addresses New candidate data set The sum of all attraction values ​​in ; Represents the maximum service capacity set of the candidate addresses used; at the same time, based on the All users in the new candidate data set of candidate addresses are constructed New user set of candidate addresses ,Right now ;

[0084] Jordi The number of users in the new candidate data set of candidate addresses Greater than its maximum service capacity ,Right now , then for All the attractiveness values ​​in the new candidate data set of candidate addresses are sorted in descending order, and the previous The sum of the attraction values ​​is taken as the The new popularity of candidate addresses is expressed as:

[0085] ;

[0086] in, express Before the accumulation The sum of the attraction values; express Index of medium attractiveness value; Indicates the value of the maximum service capacity; at the same time, based on the previous The user corresponding to the attractiveness value is constructed New user set of candidate addresses , ; Based on the new user set , and obtain the corresponding new travel trajectory set;

[0087] Based on the merged user collection , get the candidate address The new popularity ;

[0088] like , then the target node to be selected Corresponding candidate address and its new popularity, the new user set and new travel trajectory set corresponding to its new popularity, its maximum service capacity, and its construction cost, as the candidate address corresponding to the first merged node in the initial round and its popularity, its target user set, the travel trajectory set corresponding to its target user, its maximum service capacity, and its construction cost;

[0089] like , then the target node to be selected Corresponding candidate address and its new popularity, the new user set and new travel trajectory set corresponding to its new popularity, its maximum service capacity, and its construction cost, as the candidate address corresponding to the first merged node in the initial round and its popularity, its target user set, the travel trajectory set corresponding to its target user, its maximum service capacity, and its construction cost.

[0090] Preferably, aligning all R+ trees in the R+ forest to obtain each level after alignment; labeling each level after alignment to obtain an index of each level includes:

[0091] Align the root nodes of all R+ trees in the R+ forest to the same level, record it as the root node level, and label it as , which is the index layer ;

[0092] Align the child nodes of the root nodes of all R+ trees in the R+ forest to the level below the root node level and mark them as , which is the index layer ;

[0093] Align all the grandchild nodes of the root node in the R+ forest to the next level below the root node level and mark them as , which is the index layer ;

[0094] This process continues in this way until all leaf nodes in all R+ trees are aligned and the hierarchical annotations are completed.

[0095] The above technical solution of the present invention has the following beneficial effects compared with the prior art:

[0096] The present invention discloses a multi-objective joint site selection method for urban convenience service facilities with a hierarchical structure, which performs multi-objective joint site selection on convenience service facilities based on the service capacity of service outlets and the construction cost of service centers. Firstly, the R+ tree structure and pruning strategy are adopted to perform multi-level clustering of candidate addresses in urban areas with the popularity of candidate addresses as an indicator. Urban areas, candidate addresses, user travel trajectories, etc. are divided according to road networks at different levels to form an R+ forest (R+Forest, R+F) index structure. Secondly, based on the R+F index and the local greedy strategy, two multi-objective joint site selection methods are designed between different levels of the R+F index, namely, the highest priority of the service center is prioritized. A top-down joint site selection method with construction cost as the condition and a bottom-up joint site selection method with the highest popularity of service outlets as the condition of giving priority to service outlets are used to find the optimal candidate addresses of multiple service centers and multiple service outlets; therefore, this method takes the service capacity upper limit of the convenience facility service outlets and the construction cost of the service center as the site selection target, and forms an R+F site selection index based on the R+ tree structure, so as to greatly improve the efficiency and effect of multi-objective joint site selection, thereby bringing convenience to the daily work and life of urban residents, reducing the overall production or commercial cost of convenience service facilities, improving the city's service system, and improving the city's comprehensive service capabilities. At the same time, it can also alleviate the city's traffic pressure and environmental pressure and promote social equity. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below according to specific embodiments of the present invention in conjunction with the accompanying drawings, wherein:

[0098] Figure 1 It is a flow chart of a multi-objective joint site selection method for urban convenience service facilities with a hierarchical structure provided by the present invention;

[0099] Figure 2 It is the leaf node generation graph;

[0100] Figure 3 It is a diagram of the node merging, R+F index construction and hierarchical labeling process. DETAILED DESCRIPTION

[0101] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0102] Reference Figure 1 As shown, a flowchart of a multi-objective joint site selection method for urban convenience service facilities with a hierarchical structure provided by the present invention; specifically comprising:

[0103] S1: Obtain all candidate addresses of the convenience service facilities in the urban road network structure diagram and construct a candidate address set; where the urban road network structure is represented as an undirected graph ;in, Represents a set of road network nodes, represents the adjacency matrix, represents the feature matrix, Each element in represents the actual distance between two adjacent road network nodes; all candidate addresses in the road network constitute the candidate address set , candidate address , ,in, and Represents candidate addresses The latitude and longitude values ​​of the geographical location; the set of travel trajectories of taxis, private cars, shared bicycles, etc. left in the road network by urban residents in their daily work and life is , each user's travel trajectory is defined as: , , ;

[0104] The attractiveness of a candidate address to a user is defined as the normalized shortest round-trip distance between the candidate address and the user's trajectory. Therefore, the travel trajectory of each user is obtained. Based on the additional distance that each user travels from his / her travel trajectory to each candidate address and then returns to his / her travel trajectory, the shortest road network round-trip distance between each candidate address and each user's travel trajectory is obtained. Then, the attractiveness value between each candidate address and each user is calculated. The expression is:

[0105] ;

[0106] in, Indicates The candidate address and The attractiveness value between users; represents nonlinear log normalization; Indicates The candidate address and The shortest round-trip distance between user travel trajectories; Indicates Users; Indicates The travel trajectory of each user, , Indicates the number of location points on the user's travel trajectory. Indicates the number of times the user travels Location points, Indicates the number of times the user travels The timestamp corresponding to each location point; Indicates Candidate addresses; represents the Euler number; , when the candidate address With users The longer the road network distance, The smaller the value of The itinerary Directly through the candidate address hour, ,at this time, The value of is the largest, ;

[0107] The expression of the shortest network round-trip distance between each candidate address and each user's travel trajectory is:

[0108] ;

[0109] in, Indicates The candidate address and The shortest round-trip distance between the travel trajectories of users, that is, The user left his travel track to The additional journey from the candidate address to the return path; Indicates Users, , Represents the set of all users in the road network; Indicates The travel trajectory of each user, , Indicates the number of location points on the user's travel trajectory. Indicates Users at location The corresponding timestamp; Indicates Candidate addresses; Indicates Location points on the user's travel trajectory arrive The shortest network distance; Indicates to Location points on the user's travel trajectory The shortest network distance; Indicates The user's travel trajectory from the location point To location The road network trajectory distance.

[0110] S2: Obtain the popularity of each candidate address, the target user set, the travel trajectory set corresponding to the target user set, the maximum service capacity, and the construction cost, including:

[0111] S21: The popularity of a candidate address is defined as the sum of the attractions of those users who have the greatest attraction with the candidate address. In simple terms, we first need to calculate the pairwise attractions between all candidate addresses and all users in the road network. For each candidate address, find the set of users that have the greatest attraction with it, and then sum the attractions of the users in the set. However, urban areas are generally large, and the number of users (trajectories) in the road network is huge. For user trajectories that are far away from the current candidate address, the current candidate address is very likely not able to serve them, and the attraction between users who are far away and the current candidate address is also very small. In order to improve the calculation efficiency of the popularity of the candidate address, there is no need to perform additional calculations. Therefore, a user search space pruning strategy for the attraction to be calculated is adopted, which only considers all users and their travel trajectories in the reference area of ​​each candidate address, that is, for each candidate address, a space with a side length of is defined as the center of its geographical location in the urban road network. The square area is used as the reference area for each candidate address. Then, only the attraction between all users in the reference area of ​​each candidate address and the candidate address is calculated, and two HashMaps are generated; specifically, the following are included:

[0112] Based on multiple users and their travel trajectories within each candidate address reference area, a user information set covered by each candidate address is constructed; a candidate address hash map set is generated with the candidate address as the key and the user information set covered by the candidate address as the value; wherein each candidate address reference area is centered on each candidate address and has a side length of The candidate data hash mapping set is represented as ; Indicates Candidate addresses The user information set covered; Indicates Candidate addresses The number of all users in the covered user information set;

[0113] Arrange the attraction values ​​between each user and each candidate address containing their travel trajectory in the reference area in descending order, and construct each user attraction information list; generate a user hash map set with the user as the key and the user attraction information list as the value; wherein the user hash map set is represented as ; Indicates The first element of the user attraction information list corresponding to the user; Indicates Users Travel trajectory and candidate addresses The attraction value is the largest;

[0114] S22: Calculate the popularity of each candidate address and obtain the target user set and travel trajectory set of each candidate address, including:

[0115] Get the maximum service capacity and construction cost of each candidate address, and construct the maximum service capacity set of all candidate addresses and the construction cost set ;in, Indicates candidate address Maximum service capacity; Indicates candidate address construction costs;

[0116] Jordi The first of the user information sets covered by the candidate addresses The user belongs to the user hash map set, and the The candidate address and the user information set it covers The attraction value between users is The first element in the user attraction information list, that is , and , then the Users and its corresponding attraction value as the Candidate addresses The candidate data is obtained All the candidate data of the candidate addresses constitute the candidate data set ;

[0117] Jordi The number of users in the candidate data set Less than or equal to its maximum service capacity ,Right now , , then the The sum of all attractiveness values ​​in the candidate data set of candidate addresses is taken as the first The popularity of candidate addresses is expressed as:

[0118] ;

[0119] in, Indicates Candidate addresses popularity; Indicates Candidate addresses The candidate data set The sum of all attraction values ​​in ; represents the maximum service capacity set of all candidate addresses; at the same time, based on the All users in the candidate data set of candidate addresses are constructed The target user set of candidate addresses ,Right now ;

[0120] Jordi The number of users in the candidate data set Greater than its maximum service capacity ,Right now , then for All attractiveness values ​​in the candidate data set of candidate addresses are sorted in descending order, and the cumulative The sum of the attraction values ​​is taken as the The popularity of candidate addresses is expressed as:

[0121] ;

[0122] in, express Before the accumulation The sum of the attraction values; express Index of medium attractiveness value; Indicates the value of the maximum service capacity; at the same time, based on the previous The user corresponding to the attractiveness value is constructed The target user set of candidate addresses , Indicates The number of users in the target user set of candidate addresses, that is , ;

[0123] S23: Finally, the popularity of each candidate address, the target user set, the travel trajectory set corresponding to the target user set, the maximum service capacity and the construction cost can be obtained;

[0124] S3: Build R+F hierarchical index, such as Figure 3 As shown, including:

[0125] S31: Generate each leaf node based on each candidate address and its popularity, its target user set, the travel trajectory set corresponding to its target user set, its maximum service capacity and its construction cost, such as Figure 2 As shown in the figure, for each candidate address whose popularity is not 0, a corresponding leaf node can be generated; each leaf node represents its corresponding candidate address service with the candidate address as the center and the edge length is All users in the square area;

[0126] S32: Based on all leaf nodes, adopt the R+ tree structure construction and pruning strategy, take the popularity of the candidate address corresponding to each leaf node as an indicator, perform multi-level clustering on all leaf nodes, obtain all generated R+ trees, and construct an R+ forest, including:

[0127] In order to construct an R+ tree, it is necessary to merge qualified leaf nodes layer by layer in pairs to form a new parent node. The structure of the parent node is the same as that of the child node. The candidate address of the parent node is one of the candidate addresses of the two child nodes, and the two originally merged leaf nodes become the two child nodes of the parent node respectively. The leaf node with a larger candidate address popularity is the left child node, and the leaf node with a smaller candidate address popularity is the right child node.

[0128] The merging condition corresponding to any two qualified leaf nodes is: based on the merged user set of the current two leaf nodes and their corresponding travel trajectory set, one of the candidate addresses corresponding to the current two leaf nodes generates the highest popularity value without exceeding its maximum service capacity;

[0129] In order to calculate which two candidate addresses can generate the highest popularity when merged, it is generally necessary to calculate the updated popularity of all candidate addresses that are combined with each other. However, in urban areas, even if two candidate addresses that are geographically far away are merged, the updated popularity will be very small. Therefore, in order to further improve the efficiency of the node merging process, a pruning strategy is adopted for the search space of candidate leaf nodes that meet the merging conditions.

[0130] S321: taking the leaf node whose number of target users is equal to the maximum service capacity as the root node of the R+ tree, generating an R+ tree as an independent R+ tree;

[0131] S322: taking leaf nodes whose number of target users is less than the maximum service capacity as nodes to be merged, and constructing a set of nodes to be merged;

[0132] S323: Based on the longitude and latitude radians of the geographical locations of the candidate addresses corresponding to any two nodes to be merged, the spherical distance between the candidate addresses corresponding to the current two nodes to be merged is calculated, and the expression is:

[0133] ;

[0134] in, Indicates Candidate addresses and Candidate addresses The spherical distance between Indicates candidate address The latitude in radians of the geographical location; Indicates candidate address The arc value of longitude of the geographical location; Indicates candidate address The latitude in radians of the geographical location; Indicates candidate address The arc value of longitude of the geographical location; represents the radius of the Earth;

[0135] Based on the set of nodes to be merged, a pruning strategy is adopted to set the distance threshold , the spherical distance between the corresponding candidate addresses is no greater than The two nodes to be merged constitute a target node pair to be selected, and based on all the target node pairs to be selected, a set of target node pairs to be selected in the initial round is constructed;

[0136] S324: based on the target user sets and their travel trajectory sets corresponding to the two target nodes in the target node pair, obtaining the merged user set and their merged travel trajectory set of the current target node pair;

[0137] Based on the merged user set and merged travel trajectory set of the current candidate node pair, the popularity of the candidate addresses corresponding to the two current candidate nodes is updated respectively to obtain the new popularity of the candidate addresses corresponding to the two current candidate nodes; the higher new popularity of the two current new popularity is selected as the merge function value of the current candidate node pair, and its expression is:

[0138] ;

[0139] in, Represents the target node pair to be selected The combined function value of ; Indicates Target nodes to be selected The new popularity of the corresponding candidate address; Indicates Target nodes to be selected The new popularity of the corresponding candidate address; Indicates Target nodes to be selected The target user set corresponding to the candidate address; Indicates Target nodes to be selected The target user set corresponding to the candidate address; express and The merged user set of express and medium-high new popularity;

[0140] According to the initial round of target node pair set to be selected, a merge function value of each target node pair to be selected in the initial round of target node pair set to be selected is obtained;

[0141] S325: The candidate node pairs with the highest merging function values ​​in the initial round of candidate node pairs are merged to obtain the first merged node in the initial round, and the candidate address corresponding to the candidate node with the larger new popularity among the current two candidate target nodes and its new popularity, its new user set, the new travel trajectory set corresponding to its new user set, its maximum service capacity and its construction cost are used as the candidate address and its popularity, its target user set, the travel trajectory set corresponding to its target user, its maximum service capacity and its construction cost of the first merged node in the initial round;

[0142] Specifically, obtaining the candidate address of the first merged node in the initial round and its popularity, its target user set, the travel trajectory set corresponding to its target user, its maximum service capacity, and its construction cost includes:

[0143] The two target nodes in the target node pair with the highest merge function value in the initial round of target node pair set are and , whose merged user set is ;

[0144] Based on the merged user collection , get the candidate address The new popularity ,include:

[0145] If the first The user belongs to the candidate address hash map set and the first user exists in the user hash map set. User and The attraction value between candidate addresses, that is, , and , then the Users and its corresponding attraction value are added to the The candidate data set of candidate addresses and thus joined All users in and their corresponding attractiveness values; based on And join All users in and their corresponding attractiveness values ​​are constructed A new candidate data set of candidate addresses ;in, Indicates that the user hash map set exists The element is User and The attractiveness value of the candidate addresses;

[0146] Jordi The number of users in the new candidate data set of candidate addresses Less than or equal to its maximum service capacity ,Right now , , then the The sum of all attractiveness values ​​in the new candidate data set of candidate addresses is taken as the first The new popularity of candidate addresses is expressed as:

[0147] ;

[0148] in, Indicates Candidate addresses The new popularity of Indicates Candidate addresses New candidate data set The sum of all attraction values ​​in ; Represents the maximum service capacity set of the candidate addresses used; at the same time, based on the All users in the new candidate data set of candidate addresses are constructed New user set of candidate addresses ,Right now ;

[0149] Jordi The number of users in the new candidate data set of candidate addresses Greater than its maximum service capacity ,Right now , then for All the attractiveness values ​​in the new candidate data set of candidate addresses are sorted in descending order, and the previous The sum of the attraction values ​​is taken as the The new popularity of candidate addresses is expressed as:

[0150] ;

[0151] in, express Before the accumulation The sum of attraction values express Index of medium attractiveness value; Indicates the value of the maximum service capacity; at the same time, based on the previous The user corresponding to the attractiveness value is constructed New user set of candidate addresses , ; Based on the new user set , and obtain the corresponding new travel trajectory set;

[0152] Based on the merged user collection , get the candidate address The new popularity ;

[0153] like , then the target node to be selected Corresponding candidate address and its new popularity, the new user set and new travel trajectory set corresponding to its new popularity, its maximum service capacity, and its construction cost, as the candidate address corresponding to the first merged node in the initial round and its popularity, its target user set, the travel trajectory set corresponding to its target user, its maximum service capacity, and its construction cost;

[0154] like , then the target node to be selected Corresponding candidate address and its new popularity, the new user set and new travel trajectory set corresponding to its new popularity, its maximum service capacity, and its construction cost, as the candidate address corresponding to the first merged node in the initial round and its popularity, its target user set, the travel trajectory set corresponding to its target user, its maximum service capacity, and its construction cost;

[0155] S326: remove all the candidate target node pairs that contain any candidate target node corresponding to the first merge node in the initial round from the set of candidate target node pairs in the initial round, and return to execute S325 until the set of candidate target node pairs in the initial round is an empty set, take all the initial merge nodes as parent nodes, take the two candidate target nodes corresponding to the initial merge nodes as child nodes, generate all the initial merge R+ trees, and take each initial merge node as the root node of its corresponding initial merge R+ tree;

[0156] S327: The unmerged candidate target nodes in the initial round of candidate target nodes and the root nodes in the initial round of merged R+ trees whose target user number is less than the maximum service capacity are merged as the candidate target nodes for the next round, until the number of root nodes in the merged R+ trees whose target user number is less than the maximum service capacity after multiple rounds of merging is less than 2, and the merging is completed to obtain all the merged R+ trees generated in the final round;

[0157] S328: construct an R+ forest based on all the generated independent R+ trees and all the merged R+ trees generated in the final round;

[0158] S33: Align all R+ trees in the R+ forest to obtain each level after alignment; annotate each level after alignment to obtain the index of each level, including:

[0159] Align the root nodes of all R+ trees in the R+ forest to the same level, record it as the root node level, and label it as , which is the index layer ;

[0160] Align the child nodes of the root nodes of all R+ trees in the R+ forest to the level below the root node level and mark them as , which is the index layer ;

[0161] Align all the grandchild nodes of the root node in the R+ forest to the next level below the root node level and mark them as , which is the index layer ;

[0162] This process continues in this way until all leaf nodes in all R+ trees are aligned and the hierarchical annotations are completed;

[0163] In summary, first, all generated R+ trees (including R+ trees with only a single leaf node) are aligned starting from the root node, that is, all root nodes are at one level, all child nodes of the root node are at the next level, all grandchild nodes of the root node are at the next level, and so on, until all leaf nodes are aligned; then, the level identification is performed starting from the root node level, and the root node level is marked as , the next level of the root node (child node level, if any) is marked as , the next level down from the root node (grandchild level, if any) is marked as , and so on, until all levels are marked;

[0164] S34: Based on the candidate addresses corresponding to all leaf nodes in each index layer and their popularity, their target user sets, the travel trajectory sets corresponding to their target user sets, their maximum service capacity and their construction costs, an index layer node information set is constructed; with the hierarchical index as the key and the index layer node information set as the value, an index layer hash map set is generated, denoted as .

[0165] In summary, the optimal time complexity of the joint site selection problem of multiple service centers and service outlets with service center construction cost constraints and service outlet service capacity constraints is NP-Hard. Therefore, in order to efficiently solve this problem in polynomial time, a hierarchical index structure R+ forest (R+F) is designed. The index adopts R+ tree, and the popularity of candidate addresses is used as an indicator to perform multi-level clustering on different candidate addresses, thereby dividing urban areas, candidate addresses, and user trajectories into rectangles at different levels; on this basis, the designed efficient heuristic greedy algorithm can be used to directly perform joint site selection queries on service centers and service outlets at higher and lower levels of the R+F index.

[0166] S4: Based on the index layer hash map set, a heuristic local greedy strategy is adopted to select joint sites with the total construction cost of all selected service centers being less than or equal to the total cost threshold and the popularity and maximum of all selected service outlets as conditions. Service Centers and service outlets, including: ,include:

[0167] Based on the R+F index, an efficient heuristic local greedy algorithm is designed to search for Service Centers and The number of service centers is less than the number of service centers, and the total construction cost of the service center is controlled within the total cost threshold. The service outlets have the highest popularity; there are two ways of multi-level joint site selection: top-down method (service center first, then service outlets) and bottom-up method (service outlets first, then service center). The top-down method gives priority to ensuring that the best location is selected within the construction cost range of the service center. service center, and then make sure to select The service outlets have the highest popularity; the bottom-up rule gives priority to the selected The service outlets have the highest popularity, and then ensure that the best choice is made within the construction cost range of the service center. service centers;

[0168] S41: Based on the index layer hash map set, a heuristic local greedy strategy is adopted to select the service centers with the total construction cost of all selected service centers less than or equal to the total cost threshold. After the service centers are selected, the popularity and the highest of all selected service outlets are selected. The service outlets include:

[0169] The total construction cost of all selected service centers is less than or equal to the total cost threshold As condition, select Service centers, including:

[0170] If there is an index layer in the index layer hash map collection The number of all candidate addresses in ,Right now , then calculate the index layer The total construction cost of all candidate addresses in ;in, Represents the index layer in the index layer hash map collection The number of all candidate addresses in ;

[0171] If the index layer The total construction cost of all candidate addresses in is less than or equal to the total cost threshold, that is, , then the index layer All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed;

[0172] If the index layer The total construction cost of all candidate addresses in is greater than the total cost threshold, that is, , then calculate the index layer The total construction cost of all candidate addresses in each index layer until the index layer is found The total construction cost of all candidate addresses in is less than or equal to the total cost threshold, that is, ; Among them, if the index layer If the total construction cost of all candidate addresses in each index layer is not less than or equal to the total cost threshold, the candidate address set is obtained again, and the appropriate service center is selected based on the condition that the total construction cost of all selected service centers is less than or equal to the total cost threshold;

[0173] If the index layer The total construction cost of all candidate addresses in is equal to the total cost threshold, that is, , then the index layer Satisfy the cost condition and add the index layer All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed;

[0174] If the index layer The total construction cost of all candidate addresses in is less than the total cost threshold, that is, , then a local greedy strategy is adopted to convert the index layer The corresponding does not belong to the index layer All candidate addresses are sorted in descending order according to their corresponding construction costs to form a set ; From the collection Starting from the first element in , the corresponding construction cost is compared with the index layer The total construction cost of all candidate addresses is accumulated until The total construction cost after rounds of accumulation exceeds the total cost threshold and the total number of candidate addresses does not exceed , stop accumulating, and All candidate addresses and index layers accumulated in rounds All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed;

[0175] If an index level does not exist in the index level hash map collection The number of all candidate addresses in , then find the index layer that satisfies The number of corresponding candidate addresses is less than And the index layer The number of corresponding candidate addresses is greater than The two adjacent index layers, namely ; Calculate index layer The total construction cost of all candidate addresses corresponds to Represents the index layer in the index layer hash map collection The number of all candidate addresses in ; Represents the index layer in the index layer hash map collection The number of all candidate addresses in ;

[0176] If the index layer The total construction cost of all candidate addresses in is equal to the total cost threshold, that is, , then the index layer All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed;

[0177] If the index layer The total construction cost of all candidate addresses in is less than the total cost threshold, that is, , then a local greedy strategy is adopted to convert the index layer The corresponding does not belong to the index layer All candidate addresses are sorted in descending order according to their corresponding construction costs to form a set ; From the collection Starting from the first element in, the corresponding construction cost and index layer The total construction cost of all candidate addresses in the above table is accumulated until The total construction cost after rounds of accumulation exceeds the total cost threshold and the total number of candidate addresses does not exceed , stop accumulating, and Round accumulation of candidate addresses and index layers All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of service centers is completed.

[0178] Based on the popularity and highest of all selected service outlets, select Service outlets, including:

[0179] When the index layer corresponding to the location of all selected service centers is , then based on the unchanged level label, delete all the index layer hash map sets that do not contain the index layer All R+ trees of the node, update the index layer hash map set to the node candidate hash map set ;

[0180] When the index layer corresponding to the location of all selected service centers is or and , then based on the unchanged level label, delete all the index layer hash map sets that do not contain the index layer All R+ trees of the node, update the index layer hash map set to the node candidate hash map set ;

[0181] When the index layer corresponding to the location of all selected service centers is or and , then based on the unchanged level label, delete all the index layer hash map sets that do not contain the index layer All R+ trees of the node, update the index layer hash map set to the node candidate hash map set ;

[0182] If there is an index layer in the node candidate hash map set The number of all candidate addresses in ,Right now , then the index layer All candidate addresses in the above are used as the location of all selected service outlets, and the location selection of service outlets is completed; among them, Represents the index layer in the hash map set of network nodes to be selected The number of all candidate addresses in ;

[0183] If there is no index layer in the node candidate hash map set The number of all candidate addresses in , then find the index layer that satisfies The number of corresponding candidate addresses is less than And the index layer The number of corresponding candidate addresses is greater than The two adjacent index layers, namely ; Index layer The corresponding does not belong to the index layer All candidate addresses are sorted in descending order according to their corresponding popularity to form a set ; From the collection Starting from the first element in , a candidate address is selected in each round until The number of candidate addresses and index layers selected after the round The sum of the corresponding candidate addresses in is , stop selecting, All candidate addresses and index layers selected in rounds All candidate addresses in the above are used as the location of all selected service outlets, and the location selection of service outlets is completed; among them, Represents the index layer in the hash map set of network nodes to be selected The number of all candidate addresses in ; Represents the index layer in the hash map set of network nodes to be selected The number of all candidate addresses in ;

[0184] S42: Based on the index layer hash map set, a heuristic local greedy algorithm is used to select the service points with the highest popularity of all selected service points as the condition. After the service outlets are built, the total construction cost of all selected service centers is less than or equal to the total cost threshold. The service centers include:

[0185] Based on the popularity and highest of all selected service outlets, select Service outlets, including:

[0186] If there is an index layer in the index layer hash map collection The number of all candidate addresses in ,Right now , then the index layer All candidate addresses in the above are used as the location of all selected service outlets, and the location selection of service outlets is completed; among them, Represents the index layer in the index layer hash map collection The number of all candidate addresses in ;

[0187] If an index level does not exist in the index level hash map collection The number of all candidate addresses in , then find the index layer that satisfies The number of corresponding candidate addresses is less than And the index layer The number of corresponding candidate addresses is greater than The two adjacent index layers, namely ; Index layer The corresponding does not belong to the index layer All candidate addresses are sorted in descending order according to their corresponding popularity to form a set ; From the collection Starting from the first element in , a candidate address is selected in each round until The sum of the number of candidate addresses selected after the round and the corresponding number of candidate addresses in the index layer is , stop selecting, All candidate addresses selected in the round and all corresponding candidate addresses in the index layer are used as the locations of all selected service outlets, and the service outlet location selection is completed; wherein, Represents the index layer in the index layer hash map collection The number of all candidate addresses in ; Represents the index layer in the index layer hash map collection The number of all candidate addresses in ;

[0188] The total construction cost of all selected service centers is less than or equal to the total cost threshold. Service centers, including:

[0189] When the index layer corresponding to the location of all selected service outlets is , then based on the unchanged level label, delete all the index layer hash map sets that do not contain the index layer All R+ trees of the node update the index layer hash map set to the central candidate hash map set ;

[0190] When the index layer corresponding to the location of all selected service outlets is and , then based on the unchanged level label, delete all the index layer hash map sets that do not contain the index layer All R+ trees of the node update the index layer hash map set to the central candidate hash map set ;

[0191] If there is an index layer in the central candidate hash map set The number of all candidate addresses in ,Right now , then calculate the index layer The total construction cost of all candidate addresses corresponds to Represents the index layer in the central candidate hash map set The number of all candidate addresses in ;

[0192] If the index layer The total construction cost of all candidate addresses in is less than or equal to the total cost threshold, that is, , then the index layer All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed;

[0193] If the index layer The total construction cost of all candidate addresses in is greater than the total cost threshold, that is, , then calculate the index layer The total construction cost of all candidate addresses in each index layer until the index layer is found The total construction cost of all candidate addresses in is less than or equal to the total cost threshold; if the index layer If the total construction cost of all candidate addresses in each index layer is not less than or equal to the total cost threshold, the candidate address set is obtained again, and the appropriate service center is selected based on the condition that the total construction cost of all selected service centers is less than or equal to the total cost threshold;

[0194] If the index layer The total construction cost of all candidate addresses in is equal to the total cost threshold, that is, , then the index layer All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed;

[0195] If the index layer The total construction cost of all candidate addresses in is less than the total cost threshold, that is, , then a local greedy strategy is adopted to convert the index layer The corresponding does not belong to the index layer All candidate addresses are sorted in descending order according to their corresponding construction costs to form a set ; From the collection Starting from the first element in , the corresponding construction cost is compared with the index layer The total construction cost of all candidate addresses is accumulated until The total construction cost after rounds of accumulation exceeds the total cost threshold and the total number of candidate addresses does not exceed , stop accumulating, and All candidate addresses and index layers accumulated in rounds All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed;

[0196] If there is no index layer in the central candidate hash map set The number of all candidate addresses in , then find the index layer that satisfies The number of corresponding candidate addresses is less than And the index layer The number of corresponding candidate addresses is greater than The two adjacent index layers, namely ; Calculate index layer The total construction cost of all candidate addresses corresponds to Represents the index layer in the central candidate hash map set The number of all candidate addresses in ; Represents the index layer in the central candidate hash map set The number of all candidate addresses in ;

[0197] If the index layer The total construction cost of all candidate addresses in is equal to the total cost threshold, that is, , then the index layer All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed;

[0198] If the index layer The total construction cost of all candidate addresses in is less than the total cost threshold, that is, , then a local greedy strategy is adopted to convert the index layer The corresponding does not belong to the index layer All candidate addresses are sorted in descending order according to their corresponding construction costs to form a set ; From the collection Starting from the first element in, the corresponding construction cost and index layer The total construction cost of all candidate addresses in the above table is accumulated until The total construction cost after rounds of accumulation exceeds the total cost threshold and the total number of candidate addresses does not exceed , stop accumulating, and Round accumulation of candidate addresses and index layers All the corresponding candidate addresses are used as the locations of all selected service centers, and the service center location selection is completed.

[0199] To sum up, the multi-objective joint site selection method for urban convenience service facilities with a hierarchical structure provided by the present invention is different from the existing site selection method that only considers power and electrical facilities. The present method is aimed at convenience service facilities in the field of urban planning that are closely related to the daily work and life of residents; the present invention takes the service capacity upper limit of convenience facility service points and the construction cost of the service center as site selection targets, and forms an R+F site selection index based on the R+ tree structure, thereby greatly improving the efficiency and effect of multi-objective joint site selection.

[0200] Obviously, the above embodiments are merely examples for the purpose of clear explanation and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived therefrom are still within the scope of protection of the present invention.

Claims

1. A multi-objective joint site selection method for urban convenience service facilities with a hierarchical structure, characterized in that: include: Obtain all candidate addresses of convenient service facilities in the urban road network structure diagram and construct a candidate address set; obtain the popularity, target user set, travel trajectory set corresponding to the target user set, maximum service capacity and construction cost of each candidate address; Generate each leaf node based on each candidate address and its popularity, its target user set, the travel trajectory set corresponding to its target user set, its maximum service capacity and its construction cost; Based on all leaf nodes, the R+ tree structure construction and pruning strategy is adopted. The popularity of the candidate address corresponding to each leaf node is used as an indicator to perform multi-level clustering on all leaf nodes, obtain all generated R+ trees, and construct an R+ forest; Align all R+ trees in the R+ forest and get each level after alignment; Label each level after alignment to obtain the index of each level; construct the index layer node information set based on the candidate addresses corresponding to all leaf nodes in each index layer and their popularity, their target user set, the travel trajectory set corresponding to their target user set, their maximum service capacity and their construction cost; Generate an index layer hash map set with the hierarchical index as the key and the index layer node information set as the value; Based on the index layer hash map set, a heuristic local greedy strategy is adopted to select the joint site with the total construction cost of all selected service centers being less than or equal to the total cost threshold and the popularity and maximum of all selected service outlets as conditions. Service Centers and service outlets, including: .

2. According to the multi-objective joint site selection method of a hierarchical urban convenience service facility according to claim 1, it is characterized in that: Based on the index layer hash map set, a heuristic local greedy strategy is adopted to select the selected service centers under the condition that the total construction cost of all selected service centers is less than or equal to the total cost threshold. After the service centers are selected, the popularity and the highest of all selected service outlets are selected. The service outlets include: The total construction cost of all selected service centers is less than or equal to the total cost threshold. Service centers, including: If there is an index layer in the index layer hash map collection The number of all candidate addresses in , then calculate the index layer The total construction cost of all candidate addresses in ; If the index layer If the total construction cost of all candidate addresses in the index layer is less than or equal to the total cost threshold, All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed; If the index layer If the total construction cost of all candidate addresses in is greater than the total cost threshold, the index layer is calculated. The total construction cost of all candidate addresses in each index layer until the index layer is found The total construction cost of all candidate addresses in is less than or equal to the total cost threshold; If the index layer The total construction cost of all candidate addresses in is equal to the total cost threshold, then the index layer Satisfy the cost condition and add the index layer All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed; If the index layer If the total construction cost of all candidate addresses in the index layer is less than the total cost threshold, a local greedy strategy is adopted to The corresponding does not belong to the index layer All candidate addresses are sorted in descending order according to their corresponding construction costs to form a set ; From the collection Starting from the first element in , the corresponding construction cost is compared with the index layer The total construction cost of all candidate addresses is accumulated until The total construction cost after rounds of accumulation exceeds the total cost threshold and the total number of candidate addresses does not exceed , stop accumulating, and All candidate addresses and index layers accumulated in rounds All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed; If an index level does not exist in the index level hash map collection The number of all candidate addresses in , then find the index layer that satisfies The number of corresponding candidate addresses is less than And the index layer The number of corresponding candidate addresses is greater than Two adjacent index layers; calculate the index layer The total construction cost of all candidate addresses in ; If the index layer If the total construction cost of all candidate addresses in is equal to the total cost threshold, then the index layer All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed; If the index layer If the total construction cost of all candidate addresses in the index layer is less than the total cost threshold, a local greedy strategy is adopted to The corresponding does not belong to the index layer All candidate addresses are sorted in descending order according to their corresponding construction costs to form a set ; From the collection Starting from the first element in, the corresponding construction cost and index layer The total construction cost of all candidate addresses in the above table is accumulated until The total construction cost after rounds of accumulation exceeds the total cost threshold and the total number of candidate addresses does not exceed , stop accumulating, and Round accumulation of candidate addresses and index layers All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed; Based on the popularity and highest of all selected service outlets, select Service outlets, including: When the index layer corresponding to the location of all selected service centers is , then based on the unchanged level label, delete all the index layer hash map sets that do not contain the index layer All R+ trees of the node update the index layer hash mapping set to be the node candidate hash mapping set; When the index layer corresponding to the location of all selected service centers is or and , then based on the unchanged level label, delete all the index layer hash map sets that do not contain the index layer All R+ trees of the node update the index layer hash mapping set to be the node candidate hash mapping set; When the index layer corresponding to the location of all selected service centers is or and , then based on the unchanged level label, delete all the index layer hash map sets that do not contain the index layer All R+ trees of the node update the index layer hash mapping set to be the node candidate hash mapping set; If there is an index layer in the node candidate hash map set The number of all candidate addresses in , then the index layer All the candidate addresses corresponding to the above are used as the locations of all the selected service outlets, and the location selection of the service outlets is completed; If there is no index layer in the node candidate hash map set The number of all candidate addresses in , then find the index layer that satisfies The number of corresponding candidate addresses is less than And the index layer The number of corresponding candidate addresses is greater than The two adjacent index layers; the index layer The corresponding does not belong to the index layer All candidate addresses are sorted in descending order according to their corresponding popularity to form a set ; From the collection Starting from the first element in , a candidate address is selected in each round until The number of candidate addresses and index layers selected after the round The sum of the corresponding candidate addresses in is , stop selecting, All candidate addresses and index layers selected in rounds All the corresponding candidate addresses are used as the locations of all selected service outlets, and the service outlet location selection is completed.

3. According to the multi-objective joint site selection method of a hierarchical urban convenience service facility according to claim 1, it is characterized in that: Based on the index layer hash map set, a heuristic local greedy algorithm is used to select the service points with the popularity and the highest value of all selected service points as the condition. After the service outlets are built, the total construction cost of all selected service centers is less than or equal to the total cost threshold. The service centers include: Based on the popularity and highest of all selected service outlets, select Service outlets, including: If there is an index layer in the index layer hash map collection The number of all candidate addresses in , then the index layer All the candidate addresses corresponding to the above are used as the locations of all the selected service outlets, and the location selection of the service outlets is completed; If an index level does not exist in the index level hash map collection The number of all candidate addresses in , then find the index layer that satisfies The number of corresponding candidate addresses is less than And the index layer The number of corresponding candidate addresses is greater than The two adjacent index layers; the index layer The corresponding does not belong to the index layer All candidate addresses are sorted in descending order according to their corresponding popularity to form a set ; From the collection Starting from the first element in , a candidate address is selected in each round until The sum of the number of candidate addresses selected after the round and the corresponding number of candidate addresses in the index layer is , stop selecting, All candidate addresses selected in the round and all corresponding candidate addresses in the index layer are used as the locations of all selected service outlets, and the service outlet location selection is completed; The total construction cost of all selected service centers is less than or equal to the total cost threshold. Service centers, including: When the index layer corresponding to the location of all selected service outlets is , then based on the unchanged level label, delete all the index layer hash map sets that do not contain the index layer All R+ trees of the node update the index layer hash map set to the central candidate hash map set; When the index layer corresponding to the location of all selected service outlets is and , then based on the unchanged level label, delete all the index layer hash map sets that do not contain the index layer All R+ trees of the node update the index layer hash map set to the central candidate hash map set; If there is an index layer in the central candidate hash map set The number of all candidate addresses in , then calculate the index layer The total construction cost of all candidate addresses in ; If the index layer If the total construction cost of all candidate addresses in the index layer is less than or equal to the total cost threshold, All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed; If the index layer If the total construction cost of all candidate addresses in is greater than the total cost threshold, the index layer is calculated. The total construction cost of all candidate addresses in each index layer until the index layer is found The total construction cost of all candidate addresses in is less than or equal to the total cost threshold; If the index layer If the total construction cost of all candidate addresses in is equal to the total cost threshold, then the index layer All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed; If the index layer If the total construction cost of all candidate addresses in the index layer is less than the total cost threshold, a local greedy strategy is adopted to The corresponding does not belong to the index layer All candidate addresses are sorted in descending order according to their corresponding construction costs to form a set ; From the collection Starting from the first element in , the corresponding construction cost is compared with the index layer The total construction cost of all candidate addresses is accumulated until The total construction cost after rounds of accumulation exceeds the total cost threshold and the total number of candidate addresses does not exceed , stop accumulating, and All candidate addresses and index layers accumulated in rounds All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed; If there is no index layer in the central candidate hash map set The number of all candidate addresses in , then find the index layer that satisfies The number of corresponding candidate addresses is less than And the index layer The number of corresponding candidate addresses is greater than Two adjacent index layers; calculate the index layer The total construction cost of all candidate addresses in ; If the index layer If the total construction cost of all candidate addresses in is equal to the total cost threshold, then the index layer All candidate addresses in the above are used as the locations of all selected service centers, and the location selection of the service center is completed; If the index layer If the total construction cost of all candidate addresses in the index layer is less than the total cost threshold, a local greedy strategy is adopted to The corresponding does not belong to the index layer All candidate addresses are sorted in descending order according to their corresponding construction costs to form a set ; From the collection Starting from the first element in, the corresponding construction cost and index layer The total construction cost of all candidate addresses in the above table is accumulated until The total construction cost after rounds of accumulation exceeds the total cost threshold and the total number of candidate addresses does not exceed , stop accumulating, and Round accumulation of candidate addresses and index layers All the corresponding candidate addresses are used as the locations of all selected service centers, and the service center location selection is completed.

4. According to the multi-objective joint site selection method of a hierarchical urban convenience service facility according to claim 1, it is characterized in that: The step of obtaining the popularity and target user set of each candidate address includes: Obtain the travel trajectory of each user, and based on the additional distance that each user travels after leaving his travel trajectory to each candidate address and then returning to his travel trajectory, obtain the shortest network round-trip distance between each candidate address and each user's travel trajectory, and calculate the attraction value between each candidate address and each user; Based on multiple users and their travel trajectories within each candidate address reference area, a user information set covered by each candidate address is constructed; a candidate address hash map set is generated with the candidate address as the key and the user information set covered by the candidate address as the value; wherein each candidate address reference area is centered on each candidate address and has a side length of The candidate data hash mapping set is represented as ; Indicates Candidate addresses The user information set covered; Indicates Candidate addresses The number of all users in the covered user information set; Arrange the attraction values ​​between each user and each candidate address containing their travel trajectory in the reference area in descending order, and construct each user attraction information list; generate a user hash map set with the user as the key and the user attraction information list as the value; wherein the user hash map set is represented as ; Indicates The first element of the user attraction information list corresponding to the user; Indicates Users Travel trajectory and candidate addresses The attraction value is the largest; Jordi The first of the user information sets covered by the candidate addresses The user belongs to the user hash map set, and the The candidate address and the user information set it covers The attraction value between users is The first element in the user attraction information list, that is , and , then the Users and its corresponding attraction value as the Candidate addresses The candidate data is obtained All the candidate data of the candidate addresses constitute the candidate data set ; Jordi The number of users in the candidate data set Less than or equal to its maximum service capacity ,Right now , , then the The sum of all attractiveness values ​​in the candidate data set of candidate addresses is taken as the first The popularity of candidate addresses is expressed as: ； in, Indicates Candidate addresses popularity; Indicates Candidate addresses The candidate data set The sum of all attraction values ​​in ; Represents the maximum service capacity set of all candidate addresses; at the same time, based on the All users in the candidate data set of candidate addresses are constructed The target user set of candidate addresses ,Right now ; Jordi The number of users in the candidate data set Greater than its maximum service capacity ,Right now , then for All attractiveness values ​​in the candidate data set of candidate addresses are sorted in descending order, and the cumulative The sum of the attraction values ​​is taken as the The popularity of candidate addresses is expressed as: ； in, express Before the accumulation The sum of the attraction values; express Index of medium attractiveness value; Indicates the value of the maximum service capacity; at the same time, based on the previous The user corresponding to the attractiveness value is constructed The target user set of candidate addresses , Indicates The number of users in the target user set of candidate addresses, that is , .

5. According to claim 4, a multi-objective joint site selection method for urban public service facilities with a hierarchical structure is characterized in that: The expression of the shortest path network round-trip distance between each candidate address and each user's travel trajectory is: ； in, Indicates The candidate address and The shortest round-trip distance between the travel trajectories of users, that is, The user left his travel track to The additional journey from the candidate address to the return path; Indicates Users, , Represents the set of all users in the road network; Indicates The travel trajectory of each user, , Indicates the number of location points on the user's travel trajectory. Indicates Users at location The corresponding timestamp; Indicates Candidate addresses; Indicates Location points on the user's travel trajectory arrive The shortest network distance; Indicates to Location points on the user's travel trajectory The shortest network distance; Indicates The user's travel trajectory from the location point To location The road network trajectory distance.

6. According to claim 4, a multi-objective joint site selection method for urban public service facilities with a hierarchical structure is characterized in that: The expression of the attraction value between each candidate address and each user is: ； in, Indicates The candidate address and The attractiveness value between users; represents nonlinear log normalization; Indicates The candidate address and The shortest round-trip distance between user travel trajectories; Indicates Users; Indicates The travel trajectory of each user, , Indicates the number of location points on the user's travel trajectory. Indicates the number of times the user travels location points, Indicates the number of times the user travels The timestamp corresponding to each location point; Indicates Candidate addresses; represents the Euler number; , when the candidate address With users The longer the road network distance, The smaller the value of The itinerary Directly through the candidate address hour, ,at this time, The value of is the largest, .

7. According to claim 4, a multi-objective joint site selection method for urban public service facilities with a hierarchical structure is characterized in that: The R+ tree structure construction and pruning strategy is adopted based on all leaf nodes, and the popularity of the candidate address corresponding to each leaf node is used as an indicator to perform multi-level clustering on all leaf nodes, obtain all generated R+ trees, and construct an R+ forest, including: S321: taking the leaf node whose number of target users is equal to the maximum service capacity as the root node of the R+ tree, generating an R+ tree as an independent R+ tree; S322: taking leaf nodes whose number of target users is less than the maximum service capacity as nodes to be merged, and constructing a set of nodes to be merged; S323: Calculate the spherical distance between the candidate addresses corresponding to the two nodes to be merged based on the longitude and latitude radians of the geographical locations where the candidate addresses corresponding to any two nodes to be merged are located; Based on the set of nodes to be merged, a pruning strategy is adopted to set the distance threshold , the spherical distance between the corresponding candidate addresses is no greater than The two nodes to be merged constitute a target node pair to be selected, and based on all the target node pairs to be selected, a set of target node pairs to be selected in the initial round is constructed; S324: based on the target user sets and their travel trajectory sets corresponding to the two target nodes in the target node pair, obtaining the merged user set and their merged travel trajectory set of the current target node pair; Based on the merged user set and merged travel trajectory set of the current candidate node pair, the popularity of the candidate addresses corresponding to the two current candidate nodes is updated respectively to obtain the new popularity of the candidate addresses corresponding to the two current candidate nodes; the higher new popularity of the two current new popularity is selected as the merge function value of the current candidate node pair, and its expression is: ； in, Represents the target node pair to be selected The combined function value of ; Indicates Target nodes to be selected The new popularity of the corresponding candidate address; Indicates Target nodes to be selected The new popularity of the corresponding candidate address; Indicates Target nodes to be selected The target user set corresponding to the candidate address; Indicates Target nodes to be selected The target user set corresponding to the candidate address; express and The merged user set of express and medium-high new popularity; According to the initial round of target node pair set to be selected, a merge function value of each target node pair to be selected in the initial round of target node pair set to be selected is obtained; S325: The candidate node pairs with the highest merging function values ​​in the initial round of candidate node pairs are merged to obtain the first merged node in the initial round, and the candidate address corresponding to the candidate node with the larger new popularity among the current two candidate target nodes and its new popularity, its new user set, the new travel trajectory set corresponding to its new user set, its maximum service capacity and its construction cost are used as the candidate address and its popularity, its target user set, the travel trajectory set corresponding to its target user, its maximum service capacity and its construction cost of the first merged node in the initial round; S326: remove all the candidate target node pairs that contain any candidate target node corresponding to the first merge node in the initial round from the set of candidate target node pairs in the initial round, and return to execute S325 until the set of candidate target node pairs in the initial round is an empty set, take all the initial merge nodes as parent nodes, take the two candidate target nodes corresponding to the initial merge nodes as child nodes, generate all the initial merge R+ trees, and take each initial merge node as the root node of its corresponding initial merge R+ tree; S327: The unmerged candidate target nodes in the initial round of candidate target nodes and the root nodes in the initial round of merged R+ trees whose target user number is less than the maximum service capacity are merged as the candidate target nodes for the next round, until the number of root nodes in the merged R+ trees whose target user number is less than the maximum service capacity after multiple rounds of merging is less than 2, and the merging is completed to obtain all the merged R+ trees generated in the final round; S328: Construct an R+ forest based on all the generated independent R+ trees and all the merged R+ trees generated in the final round.

8. The multi-objective joint site selection method for urban public service facilities with a hierarchical structure according to claim 7 is characterized in that: The spherical distance between the candidate addresses corresponding to the two nodes to be merged is calculated based on the radian values ​​of the longitude and latitude of the geographical locations of the candidate addresses corresponding to any two nodes to be merged, and the expression is: ； in, Indicates Candidate addresses and Candidate addresses The spherical distance between Indicates candidate address The latitude in radians of the geographical location; Indicates candidate address The arc value of longitude of the geographical location; Indicates candidate address The latitude in radians of the geographical location; Indicates candidate address The arc value of longitude of the geographical location; Represents the radius of the Earth.

9. The multi-objective joint site selection method for urban public service facilities with a hierarchical structure according to claim 4 is characterized in that: The candidate address corresponding to the target node with a larger new popularity among the two target nodes to be selected, its new popularity, its new user set, its new travel trajectory set corresponding to its new user set, its maximum service capacity and its construction cost, as the candidate address of the first merged node in the initial round, its popularity, its target user set, its travel trajectory set corresponding to its target user, its maximum service capacity and its construction cost, include: The two target nodes in the target node pair with the highest merge function value in the initial round of target node pair set are and , whose merged user set is ; Based on the merged user collection , get the candidate address The new popularity ,include: If the first The user belongs to the candidate address hash map set and the first user exists in the user hash map set. User and The attraction value between candidate addresses, that is, , and , then the Users and its corresponding attraction value are added to the The candidate data set of candidate addresses and thus joined All users in and their corresponding attractiveness values; based on And join All users in and their corresponding attractiveness values ​​are constructed A new candidate data set of candidate addresses ;in, Indicates that the user hash map set exists The element is User and The attractiveness value of the candidate addresses; Jordi The number of users in the new candidate data set Less than or equal to its maximum service capacity ,Right now , , then the The sum of all attractiveness values ​​in the new candidate data set of candidate addresses is taken as the first The new popularity of candidate addresses is expressed as: ； in, Indicates Candidate addresses The new popularity of Indicates Candidate addresses New candidate data set The sum of all attraction values ​​in ; Represents the maximum service capacity set of the candidate addresses used; at the same time, based on the All users in the new candidate data set of candidate addresses are constructed New user set of candidate addresses ,Right now ; Jordi The number of users in the new candidate data set Greater than its maximum service capacity ,Right now , then for All the attractiveness values ​​in the new candidate data set of candidate addresses are sorted in descending order, and the previous The sum of the attraction values ​​is taken as the The new popularity of candidate addresses is expressed as: ； in, express Before the accumulation The sum of the attraction values; express Index of medium attractiveness value; Indicates the value of the maximum service capacity; at the same time, based on the previous The user corresponding to the attractiveness value is constructed New user set of candidate addresses , ; Based on the new user set , and obtain the corresponding new travel trajectory set; Based on the merged user collection , get the candidate address The new popularity ; like , then the target node to be selected Corresponding candidate address and its new popularity, the new user set and new travel trajectory set corresponding to its new popularity, its maximum service capacity, and its construction cost, as the candidate address corresponding to the first merged node in the initial round and its popularity, its target user set, the travel trajectory set corresponding to its target user, its maximum service capacity, and its construction cost; like , then the target node to be selected Corresponding candidate address and its new popularity, the new user set and new travel trajectory set corresponding to its new popularity, its maximum service capacity, and its construction cost, as the candidate address corresponding to the first merged node in the initial round and its popularity, its target user set, the travel trajectory set corresponding to its target user, its maximum service capacity, and its construction cost.

10. The multi-objective joint site selection method for urban public service facilities with a hierarchical structure according to claim 1 is characterized in that: The method aligns all R+ trees in the R+ forest to obtain each level after alignment; After marking each level of alignment, the index of each level is obtained, including: Align the root nodes of all R+ trees in the R+ forest to the same level, record it as the root node level, and label it as , which is the index layer ; Align the child nodes of the root nodes of all R+ trees in the R+ forest to the level below the root node level and mark them as , which is the index layer ; Align all the grandchild nodes of the root node in the R+ forest to the next level below the root node level and mark them as , which is the index layer ; This process continues in this way until all leaf nodes in all R+ trees are aligned and the hierarchical annotations are completed.

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