WO2020224544A1 - 选址方法、装置及计算机可读存储介质 - Google Patents

选址方法、装置及计算机可读存储介质 Download PDF

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Publication number
WO2020224544A1
WO2020224544A1 PCT/CN2020/088376 CN2020088376W WO2020224544A1 WO 2020224544 A1 WO2020224544 A1 WO 2020224544A1 CN 2020088376 W CN2020088376 W CN 2020088376W WO 2020224544 A1 WO2020224544 A1 WO 2020224544A1
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site
candidate
sites
served
candidate site
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PCT/CN2020/088376
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English (en)
French (fr)
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陈娟
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华为技术有限公司
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/18—Network design, e.g. design based on topological or interconnect aspects of utility systems, piping, heating ventilation air conditioning [HVAC] or cabling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0637—Strategic management or analysis, e.g. setting a goal or target of an organisation; Planning actions based on goals; Analysis or evaluation of effectiveness of goals
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
    • G06Q50/08—Construction
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W16/00—Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
    • H04W16/18—Network planning tools

Definitions

  • This application relates to the field of information processing technology, in particular to an address selection method, device and computer-readable storage medium.
  • the objective function when selecting the location of the service station, can be determined based on multiple candidate site sites and site construction conditions. After that, the decision variables can be determined based on the factors affecting the objective function, and then the constraints can be determined based on the decision variables and site construction conditions. condition. Determine the integer linear programming model according to the above determined objective function, decision variables and constraint conditions. After that, the integer linear programming model can be solved by the branch and bound method or the cutting plane method, so as to determine the obtained from the multiple candidate sites The address of the service station.
  • the present application provides a location selection method, device, and computer-readable storage medium, which can be used to solve the problem that the location selection result cannot be obtained in a limited time when the number of candidate sites involved in the location selection problem in the related technology is large.
  • the technical solution is as follows:
  • a location selection method includes: preprocessing an integer linear programming model to obtain a linear programming model.
  • the integer linear programming model is based on multiple candidate sites and multiple objects to be served.
  • a model established with multiple site establishment conditions, and the value of the decision variable output by the integer linear programming model is an integer value, and the value of the decision variable output by the linear programming model includes an integer value and a decimal value;
  • the parameter values of the multiple parameters of the linear programming model are input to the linear programming model;
  • the first location selection result and the second location selection result are determined according to the integer value in the value of the decision variable output by the linear programming model, and the first location selection result
  • a site selection result includes a plurality of selected site sites, the second site selection result includes a plurality of unselected site sites, and the plurality of selected site sites refers to the plurality of candidate site sites selected for construction The site address of the service station; and the selected site is determined from the remaining candidate site sites excluding the first site selection result and the second site selection result from the plurality of candidate site sites
  • a part of the site selection result can be obtained by solving the linear programming model obtained by the conversion first, and then, according to this part of the site selection result, the previous site selection problem based on multiple candidate sites can be reduced in dimension, and then the reduced dimension can be solved.
  • the location problem so that even if the number of candidate sites is large, the method provided in this application can quickly obtain the location results in a limited time, which solves the problem of directly using branch and bound method or cutting plane method in related technologies.
  • the location result cannot be obtained in a limited time.
  • the integer linear programming model includes an intermediate variable and a constraint condition
  • the intermediate variable is used to indicate whether the object to be served is served
  • the constraint condition includes a first integer set and a second integer set
  • the first The set of integers includes allowable values of the decision variables
  • the second set of integers includes allowable values of the intermediate variables.
  • the process of preprocessing the integer linear programming model to obtain the linear programming model may be: converting the first integer set to a first value range, and converting the second integer set to a second value range.
  • Value range to obtain the linear programming model the first value range refers to a continuous value range that includes the integer values in the first integer set
  • the second value range refers to that includes the first integer value The continuous range of integer values in a two-integer set.
  • the integer linear programming model further includes a first parameter used to indicate the number of service station types to be selected when establishing a station on each candidate site.
  • a first parameter used to indicate the number of service station types to be selected when establishing a station on each candidate site.
  • the K service station types to be selected are converted into K different candidate station addresses at the same location, where K is the first parameter.
  • the constraint condition further includes a first constraint, the first constraint includes a first candidate site set, the first candidate site set includes at least one candidate site pair, and each candidate site pair includes The distance between the two candidate sites of is less than the first threshold; accordingly, after converting the first integer set into a first value range, and the second integer set into a second value range, It is also possible to convert the first candidate site set to a second candidate site set, the second candidate site set includes at least two candidate sites, and any two of the at least two candidate sites The distances between the candidate sites are all less than the first threshold.
  • the decimal solution included in the solution result finally output by the linear programming model can be reduced. Since the decimal value in the solution result of the linear programming model does not meet the value requirements of the integer linear programming variables, it cannot be used to judge whether the candidate site is selected. Therefore, this process reduces the final output of the linear programming model in the solution result The included decimal value is equivalent to reducing the number of useless solutions.
  • the implementation process of determining the selected site from the remaining candidate sites except the first site selection result and the second site selection result among the plurality of candidate site sites may be: Sites included in the first site selection result among the multiple candidate site sites, sites included in the second site selection result, and sites that cannot be constructed at the same time as the selected site included in the first site selection result
  • the site address is deleted; the target to be served served by the site included in the first site selection result among the plurality of target to be served is deleted; according to the remaining candidate site addresses after the deletion and the remaining target to be served after the deletion To determine the selected site among the candidate site sites remaining after the deletion.
  • the sites included in the first site selection result and the second site selection result from the multiple candidate site sites can be deleted, and sites that cannot be constructed at the same time as the selected site site Address, delete the multiple objects to be served by the selected site to reduce the original location problem, and then continue to solve the location problem obtained by the dimensionality reduction, which will not only reduce the location
  • the complexity of the site can be shortened.
  • the realization process of determining the selected site among the candidate site addresses remaining after the deletion may be: according to the remaining candidate sites after the deletion
  • the candidate site and the remaining to-be-served objects after the deletion determine a graph-based site selection graph, the graph-based site selection graph includes a plurality of nodes, and each node is used to indicate one of the candidate sites remaining after the deletion
  • a candidate site, in the multiple nodes, two candidate sites that cannot be established at the same time have a connection between the two corresponding nodes; according to the graph theory site selection graph, determine the remaining candidate sites after deletion Of the selected site. That is, in the embodiment of the present application, the location problem after dimensionality reduction can be solved by the graph theory algorithm, so as to obtain the final location result.
  • each node of the plurality of nodes corresponds to a first weight and a second weight
  • the first weight refers to the deletion of the service station after the service station is constructed on the candidate site indicated by the corresponding node.
  • the second weight refers to the cost of building a service station on the candidate site indicated by the corresponding node; on this basis, the deletion is determined according to the graph theory site selection graph
  • the implementation process of the selected site site among the remaining candidate site sites may be: selecting a target node from the multiple nodes according to the first weight and the second weight corresponding to each node; judging whether to select the target node The indicated candidate site is determined to be the selected site; if the candidate site indicated by the target node is determined to be the selected site, then the selected site determined among the candidate sites remaining after deletion And the site address that cannot be established at the same time as the determined selected site address is deleted, and the to-be-served objects served by the determined selected site address among the remaining to-be-served
  • the realization process of determining whether to determine the candidate site indicated by the target node as the selected site may be: determining the first site selection problem according to the target node and the graph theoretical site selection graph; The first location problem is divided into L layers by a dynamic programming algorithm, where L is less than the maximum number of layers allowed to be divided into the first location problem; the operation results of multiple sub-problems obtained by the segmentation are determined, according to the The operation result of a plurality of sub-problems determines the operation result of the first location problem; according to the operation result of the first location problem, it is judged whether to use the candidate site indicated by the target node as the selected site.
  • the first location problem can be divided into L layers by a dynamic programming algorithm, and then the calculation result of the first location problem can be determined by the calculation results of multiple sub-problems obtained by the division. In this way, the calculation can be guaranteed. At the same time as the accuracy of the result, the amount of calculation is reduced.
  • a location selection method includes: determining a graph-theoretic location map based on multiple candidate site sites, multiple objects to be served, and multiple site-building conditions. It includes multiple nodes, and each node is used to indicate one of the multiple candidate site addresses, and two of the multiple nodes that cannot be established at the same time have a connection between two corresponding candidate sites ; Determine the selected site of the multiple candidate site sites according to the graph theory site selection map.
  • the graph theory site selection map can be determined based on multiple candidate site sites, multiple objects to be served, and multiple site construction conditions, and then use the dynamics described above Planning algorithm or dynamic planning algorithm combined with greedy algorithm to determine the location result. In this way, the inaccuracy of site selection through manual experience is avoided when the integer linear programming model cannot be established.
  • each node of the plurality of nodes corresponds to a first weight and a second weight
  • the first weight refers to the construction of a service station on the candidate site indicated by the corresponding node to the plurality of nodes.
  • the service capability of the object to be served, the second weight refers to the site construction cost of building a service station on the candidate site indicated by the corresponding node; on this basis, the multiple candidates are determined according to the graph theory site selection graph
  • the implementation process of the selected site site in the site site may be: selecting a target node from the multiple nodes according to the first weight and the second weight corresponding to each node; determining whether to select the candidate indicated by the target node The site address is determined as the selected site; if the candidate site indicated by the target node is determined to be the selected site, then the selected site determined from the multiple candidate site addresses and the determined site If the selected site address cannot be constructed at the same time, delete the site to be served, and delete the to-be-served object served by the determined selected site among the multiple
  • the realization process of determining whether to determine the candidate site indicated by the target node as the selected site may be: determining the first site selection problem according to the target node and the graph theoretical site selection graph; The first location problem is divided into L layers by a dynamic programming algorithm, where L is less than the maximum number of layers allowed to be divided into the first location problem; the operation results of multiple sub-problems obtained by the segmentation are determined, according to the The operation result of a plurality of sub-problems determines the operation result of the first location problem; according to the operation result of the first location problem, it is determined whether the candidate site indicated by the target node is determined as the selected site.
  • an address selection device is provided, and the address selection device has the function of realizing the behavior of the address selection method in the first aspect or the second aspect.
  • the address selection device includes at least one module, and the at least one module is used to implement the address selection method provided in the first aspect or the second aspect.
  • an address selection device in a fourth aspect, includes a processor and a memory, and the memory is used to store and support the address selection device to perform the address selection provided in the first or second aspect.
  • the program of the method, and the data used to realize the address selection method provided in the first aspect or the second aspect are stored.
  • the processor is configured to execute a program stored in the memory.
  • the operating device of the storage device may further include a communication bus, which is used to establish a connection between the processor and the memory.
  • a computer-readable storage medium stores instructions that, when run on a computer, cause the computer to execute the address selection described in the first or second aspect. method.
  • a computer program product containing instructions which when run on a computer, causes the computer to execute the address selection method described in the first or second aspect.
  • the integer linear programming model can be converted into a linear programming model for solving, so as to obtain the first site selection result and the second site selection result. After that, the first site selection result and the second site selection result can be determined among multiple candidate sites. 2. The selected site among the remaining candidate sites beyond the site selection result. That is, this application can first obtain a part of the site selection result by solving the linear programming model obtained by the conversion, and then, according to this part of the site selection result, reduce the dimensionality of the previous site selection problem based on multiple candidate sites, and then solve the dimensionality reduction.
  • the method provided in this application can quickly obtain the site selection results in a limited time, which solves the direct use of branch and bound method or cutting plane method in related technologies
  • the location result cannot be obtained in a finite time.
  • Fig. 1 is a schematic structural diagram of a computer device for site selection provided by an embodiment of the present application
  • FIG. 2 is a flowchart of a location selection method provided by an embodiment of the present application.
  • Fig. 3 is an example of a graph theory site selection diagram provided by an embodiment of the present application.
  • FIG. 4 is a flowchart of determining selected site sites among candidate site sites remaining after deletion according to a graph theory site selection diagram provided by an embodiment of the present application;
  • FIG. 5 is a flowchart of another location selection method provided by an embodiment of the present application.
  • FIG. 6 is a schematic structural diagram of an address selection device provided by an embodiment of the present application.
  • Fig. 7 is a schematic structural diagram of another address selection device provided by an embodiment of the present application.
  • the location of the service station is the top priority.
  • the location of the service station is the top priority.
  • how to select the location of each 5G base station in the 5G communication network will directly affect the number of users covered by the 5G communication network and the quality of service of the 5G communication network.
  • a business is planning a store network
  • how to choose the location of a store to maximize the number of users covered by the store and the lowest construction cost or operating cost of the store will directly affect the profitability of the store.
  • the embodiment of this application provides a location selection method, which can be applied to the planning process of various service networks such as communication networks, power distribution networks, store networks, logistics networks, etc., to realize service stations Site selection.
  • Fig. 1 is a schematic structural diagram of a computer device for site selection provided by an embodiment of the present application.
  • the computer device includes at least one processor 101, a communication bus 102, a memory 103, and at least one communication interface 104.
  • the processor 101 may be a general-purpose central processing unit (Central Processing Unit, CPU), a microprocessor, an application-specific integrated circuit (ASIC), or one or more programs for controlling the execution of the program of this application. integrated circuit.
  • CPU Central Processing Unit
  • ASIC application-specific integrated circuit
  • the communication bus 102 may include a path for transferring information between the aforementioned components.
  • the memory 103 can be a read-only memory (ROM) or other types of static storage devices that can store static information and instructions, random access memory (RAM), or other types that can store information and instructions.
  • the type of dynamic storage device can also be Electrically Erasable Programmable Read-Only Memory (EEPROM), Compact Disc Read-Only Memory (CD-ROM) or other CD-ROM storage, Storage (including compact discs, laser discs, optical discs, digital versatile discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or can be used to carry or store desired program codes in the form of instructions or data structures and can be used by Any other medium accessed by the computer, but not limited to this.
  • the memory 103 may exist independently and is connected to the processor 101 through the communication bus 102.
  • the memory 103 may also be integrated with the processor 101.
  • the communication interface 104 uses any device such as a transceiver to communicate with other devices or communication networks, such as Ethernet, radio access network (RAN), wireless local area networks (Wireless Local Area Networks, WLAN), etc.
  • RAN radio access network
  • WLAN Wireless Local Area Networks
  • the processor 101 may include one or more CPUs, such as CPU0 and CPU1 shown in FIG. 1.
  • a computer device may include multiple processors, such as the processor 101 and the processor 105 shown in FIG. 1.
  • processors can be a single-CPU (single-CPU) processor or a multi-core (multi-CPU) processor.
  • the processor here may refer to one or more devices, circuits, and/or processing cores for processing data (for example, computer program instructions).
  • the computer device may further include an output device 106 and an input device 107.
  • the output device 106 communicates with the processor 101 and can display information in a variety of ways.
  • the output device 106 may be a liquid crystal display (LCD), a light emitting diode (LED) display device, a cathode ray tube (CRT) display device, or a projector (projector) Wait.
  • the input device 107 communicates with the processor 101 and can receive user input in a variety of ways.
  • the input device 107 may be a mouse, a keyboard, a touch screen device, or a sensor device.
  • the aforementioned computer equipment may be a general-purpose computer equipment or a special-purpose computer equipment.
  • the computer device may be a desktop computer, a portable computer, a network server, a PDA (Personal Digital Assistant, PDA), a mobile phone, a tablet computer, a wireless terminal device, a communication device, or an embedded device.
  • PDA Personal Digital Assistant
  • the embodiment of the present invention does not limit the type of computer equipment.
  • the memory 103 is used to store the program code 108 that executes the following steps 201-204 in the embodiment of the present application, and the processor 101 controls the execution.
  • the processor 101 is configured to execute the program code 108 stored in the memory 103.
  • the program code 108 may include one or more software modules.
  • an integer linear programming model is usually established based on multiple candidate sites and site construction conditions. After the integer linear programming model is established, the branch and bound method or the cutting plane method can be used to solve the integer linear programming. Model to get the site selection results.
  • the integer linear programming model refers to the linear programming problem in which the value of the decision variable is an integer value.
  • an integer linear programming model may include an objective function and constraint conditions, where the objective function refers to a function designed according to the objective to be optimized and the variables that affect the objective.
  • the cost of building a service station can be used as the target to be optimized, and the objective function can be designed according to the variables that affect the cost of building the site.
  • the objective function can be a function used to minimize the cost of building the site .
  • constraints refer to other constraints that must be met in the process of solving the objective function.
  • the constraint condition of the integer linear programming model includes the constraint condition about the decision variable, and the constraint condition is used to constrain the value of the decision variable to an integer.
  • the optimal solution of the linear programming model corresponding to the integer linear programming model can be solved first, where the optimal solution includes the optimal selection of the decision variables. Value and optimal objective function value. After determining the optimal solution, the optimal objective function value can be taken as the upper bound of the objective function value in the integer linear programming model, and the function value corresponding to any feasible solution of the objective function in the integer linear programming model can be taken as The lower bound of the function value of the objective function.
  • the optimal value of the decision variable in the optimal solution is taken as an integer solution of the integer linear programming model, and the optimal value of the decision variable included in the optimal solution
  • the optimal value divides the feasible solution interval of the decision variables of the integer linear programming model into two parts.
  • the optimal value of the decision variable in the optimal solution is not an integer value, it means that the optimal value of the decision variable is not the solution of the integer linear programming model.
  • the integer linear programming model can be The feasible solution interval of the decision variable is divided into two parts.
  • the integer linear programming model After dividing the feasible solution region of the decision variable of the integer linear programming model into two parts, the integer linear programming model is converted into two integer linear programming models according to the two feasible solution regions obtained by the division and the upper and lower bounds of the objective function determined above Plan the sub-models, and use the aforementioned method to solve the two integer linear programming sub-models, and obtain the optimal solution of the linear programming model corresponding to each sub-model. After that, the upper and lower bounds of the function value of the objective function are determined again according to the optimal objective function value included in the optimal solution.
  • the branch of the sub-model will be pruned, that is, the sub-model will not be re-executed later deal with. If the optimal objective function value in the optimal solution of a certain sub-model is greater than the lower bound of the objective function value, the branch is continued on the basis of the sub-model. By analogy, through continuous branching, until the optimal objective function value in the final optimal solution is equal to the lower bound of the objective function value determined last time, the optimal objective function value at this time and the corresponding decision variable The optimal value of is used as the final solution result of the integer linear programming model.
  • the following uses an example to illustrate the process of solving the integer linear programming model by the above-mentioned branch and bound method.
  • the integer linear programming model is converted to obtain two integer linear programming sub-models, as follows:
  • the function value range of the objective function is obtained as follows: 0 ⁇ Z ⁇ 349. Since the optimal objective function values in the optimal solutions corresponding to sub-models (1) and (2) are both greater than the lower bound of the objective function's function value, and not greater than the upper bound of the objective function's function value, the sub-model (1) ) And (2) branch again according to the aforementioned method, thereby obtaining two sub-models corresponding to sub-model (1) and two sub-models corresponding to sub-model (2). By analogy, details are not repeated in the embodiments of the present application.
  • the integer linear programming problem needs to be divided into sub-problems, and then the sub-problems are continuously divided layer by layer. This is applicable to small-scale planning problems when the number of candidate sites involved in the site selection scenario is small, but for large-scale site selection problems when the number of candidate sites involved is large, it is difficult to achieve a limited time. Solve to get the site selection result.
  • the embodiment of the present application provides a location selection method.
  • this location selection method a part of the location results can be obtained by first solving the linear programming model converted from the integer linear programming model, and then according to this part The site selection result reduces the dimensionality of the previous site selection problem based on multiple candidate sites. After that, the graph theory algorithm is used to solve the dimensionality reduction site selection problem.
  • this application provides The method can also quickly obtain the site selection results in a limited time, and solves the problem that the site selection results cannot be obtained in a limited time when the branch and bound method or the cutting plane method is directly used in the related technology to solve the integer linear programming model.
  • Fig. 2 is a flow chart of a location selection method provided by an embodiment of the present application. The method can be applied to a computer device. As shown in Fig. 2, the method includes the following steps:
  • Step 201 Perform preprocessing on the integer linear programming model to obtain a linear programming model, which is a model established based on multiple candidate site locations, multiple objects to be served, and multiple site construction conditions.
  • multiple candidate site sites refer to sites to be selected, and the site selection method provided in this application is used to select the site where the service station is to be built from the multiple candidate site sites.
  • the multiple candidate site sites can be obtained through computer simulation based on geographic information data such as topography, topography, and distribution of existing service stations in the area where the service network to be planned is located.
  • the multiple candidate site locations may also be determined according to some specific locations that already exist in the service network to be planned. For example, when selecting a site for a 5G base station, the location of an existing 4G base station can be used as a candidate site.
  • Multiple objects to be served refer to objects waiting to be served by the service station in the area where the service network to be planned is located.
  • the multiple objects to be served may be multiple users, or multiple locations obtained by rasterizing the area where the service network to be planned is located.
  • multiple site establishment conditions refer to the restriction conditions to be met in the site selection process determined according to the service requirements of the service network to be planned.
  • the multiple site establishment conditions may include: any two candidate sites whose distance is less than the first threshold cannot be constructed at the same time, the total cost of site construction is less than the second threshold, the construction of one type of service station on a candidate site, and the After selecting the site to build the service station, the number of objects to be served shall not be less than the third threshold and so on.
  • the embodiment of this application does not limit the site establishment conditions.
  • the optimization target before performing this step, can be determined according to the service requirements of the service network to be planned.
  • the optimization goal can include the number of service objects served when the site is built according to the selected site, the area of the area served when the site is built according to the selected site, or the quality of service when the site is built according to the selected site , According to the selected site site to build the site cost, etc.
  • the optimization target may be one or multiple.
  • an objective function can be established according to the optimization target, multiple candidate sites and/or multiple objects to be served.
  • the optimization goal is the service quality of the service object when the site is built according to the selected site
  • the objective function established based on the optimization goal, multiple candidate site locations and multiple objects to be served can be used to make the service station serve The function of maximizing the number of objects to be served.
  • the objective function determined based on the optimization target, multiple candidate site locations, and multiple objects to be served can be a function that minimizes the cost of building a site .
  • the objective function determined according to the optimization target can represent some of the multiple site building conditions.
  • the multiple Among the site-building conditions the site-building conditions that overlap with the site-building conditions represented by the objective function are removed, and constraints are established based on the remaining site-building conditions, multiple candidate sites, and multiple objects to be served, so as to obtain the objective function and constraint conditions.
  • the integer linear programming model since the allowable value of the variable of the integer linear programming model is an integer value, the constraint condition of the integer linear programming model may also include a condition for restricting the allowable value of the variable in the model to an integer.
  • the optimization goal is based on the service quality of the objects to be served when the selected site is constructed.
  • Multiple site construction conditions include that any two candidate sites whose distance is less than the first threshold cannot be constructed at the same time. If the cost is less than the second threshold, and one type of service station is built on a candidate site, the integer linear programming model established based on the optimization goal, multiple candidate sites, multiple objects to be served, and multiple site conditions is as follows:
  • N refers to the number of objects to be served
  • w i refers to the service weight coefficient of object i among multiple objects to be served.
  • y i is an intermediate variable used to indicate whether the object to be served is included in the object to be served.
  • the value of y i is 0 or 1. When the value of y i is 0, it means that the object to be served does not include the object to be served i, that is, the object to be served i is not served; when the value of y i is When the value is 1, it means that the objects to be served include object i to be served, that is, object i to be served is served.
  • K refers to the number of service station types to be selected when building a station on each candidate site.
  • the service station type can be the same as K One of the types.
  • M refers to the number of candidate sites, r i, j, k are used to indicate whether the k-th type of service station built on candidate site j serves the object to be served i, x j, k are decision variables, used Indicate whether to build the k-th type of service station on the candidate site j , where the value of x j,k is 0 or 1.
  • the value of x j,k is 1, it means that the candidate site j is Select the site, and the type of service station built on the candidate site is the k-th type.
  • c j,k refers to the cost of constructing the k-th type of service station on the candidate site j
  • C refers to the second threshold
  • V refers to the set of candidate site pairs, where V includes multiple candidate site pairs, The distance between the two candidate sites included in each candidate site pair is less than the first threshold.
  • variable value in the integer linear programming model is an integer value
  • it can be realized by the two conditions of x j,k ⁇ 0,1 ⁇ and y i ⁇ 0,1 ⁇ in the constraint condition.
  • the service weight coefficient w i may be determined according to the distance between the object i to be served and the candidate site.
  • the reciprocal of the distance between the object i to be served and the candidate site may be used as the service weight coefficient.
  • the service weight coefficient may be determined according to the number of users contained in each grid. The embodiment of the application does not limit the service weight coefficient here.
  • the optimization goal is to build a site based on the site construction cost of the selected site.
  • Multiple site construction conditions include that any two candidate sites whose distances are less than the first threshold cannot be constructed at the same time, and one site can be constructed on one candidate site.
  • the type of service station, the service quality of the service object to be served after the service station is established at the selected station site is not less than the third threshold, then the establishment is established based on the optimization goal, multiple candidate site locations, multiple objects to be served, and multiple site conditions
  • the integer linear programming model is as follows:
  • W refers to the third threshold.
  • the relevant meanings of the remaining parameters in the above objective function and constraint conditions can be referred to the foregoing related descriptions, which are not repeated in the embodiments of the present application.
  • the integer linear programming model can be preprocessed to obtain the linear programming model.
  • the linear programming model is easier to solve and the technology in the industry is relatively mature. Therefore, in the embodiments of the present application, some relaxation methods can be used to perform certain preprocessing on the integer linear programming model, thereby reducing It is converted into a linear programming model.
  • the constraint conditions of the integer linear programming model include conditions that allow the variables in the constraint model to be integers.
  • the allowable values of variables in the linear programming model can be integer values or decimal values. Based on this, when the integer linear programming model is preprocessed to obtain the linear programming model, the condition that the integer linear programming model is allowed to be an integer for the constraint variable can be relaxed first.
  • the constraint conditions of the integer linear programming model may include a first set of integers for constraining decision variables to be integer values, and
  • the value of the intermediate variable is the second integer set of integer values.
  • the first integer set can be converted into a first value range
  • the second integer set can be converted into a second value range, wherein the first value range and the second value range are both continuous
  • the first value range includes all integers in the first integer set
  • the second value range includes all integers in the second integer set.
  • the embodiment of the present application can convert the discrete value range of the variable in the integer linear programming model into a continuous value range.
  • the minimum value in the integer set can be used as the lower limit of the converted value range
  • the maximum value in the integer set can be used as the converted value The upper limit of the range.
  • the first integer set used to constrain the allowable values of decision variables and the second integer set used to constrain the allowable values of intermediate variables are both ⁇ 0,1 ⁇ , that is, the allowable values of decision variables and intermediate variables are 0 or 1.
  • the continuous value range converted from the discrete value range of the above-mentioned decision variable and intermediate variable is [0,1].
  • the integer linear programming model may include a first parameter, and for the convenience of subsequent description, the first parameter is represented by K.
  • the first parameter is used to indicate the number of service station types to be selected when building a station on each candidate site. In other words, when building a service station on any candidate site, there will be K candidate service station types for selection. In addition, considering that one type of service station is usually required to be built on a station site, one type can be selected from K candidate service station types for station construction. Based on this, when the first parameter is included in the integer linear programming model, the K service station types to be selected when the station is built on each candidate site can be converted into K different candidate sites at the same location.
  • the two integer linear programming models provided above are still taken as examples for explanation. Convert the K service station types to be selected when constructing stations on each candidate site in the integer linear programming model into K different candidate sites at the same location. In this way, since there are originally M candidate sites, therefore, After conversion, (M*K) candidate sites can be obtained. In this way, for the first integer linear programming model, all constraints related to the first parameter can be converted according to the above method. among them, This condition can be converted to This condition can be converted to This condition can be deleted, This condition can be converted into ⁇ x j + ⁇ x j ' ⁇ 1 ( j, j') ⁇ V.
  • the objective function and the constraint conditions related to the first parameter conditions can also be transformed, which is not repeated here in the embodiment of the application.
  • the integer linear programming model may also include a first constraint, and the first constraint includes the first constraint.
  • the candidate site set, the first candidate site set includes at least one candidate site pair, the distance between the two candidate sites included in each candidate site pair is less than the first threshold, and each candidate site pair is in Only one of the two candidate sites can be used as a condition for the site to be selected.
  • the first constraint can limit the distance between any two selected sites to not be less than the first threshold. Based on this, in the embodiment of the present application, this constraint in the integer linear programming model can also be relaxed.
  • the first candidate site set in the first constraint may be converted into the second candidate site set.
  • the second candidate site set includes at least two candidate sites, and the distance between any two candidate sites in the at least two candidate site sites is less than the first threshold. That is, when the first constraint includes the first candidate site set, the first constraint can restrict each candidate site pair in the first candidate site set to have one candidate site as the selected site. , But there is no restriction between candidate sites belonging to different candidate site pairs. In this way, when there are multiple candidate site pairs included in the first candidate site set, there may be multiple candidate site pairs belonging to different candidate site pairs that can be used as selected site sites.
  • the first constraint after the conversion can restrict at least two candidate sites in the second candidate site set to have one candidate site as the selected site, that is Yes, no matter how many candidate sites are in the second candidate site set, subject to the restriction of the first constraint, there will be at most one candidate site in the second candidate site as the selected site.
  • the two integer linear programming models provided above are still taken as examples for illustration.
  • the constraints in the The constraint of (j,j') ⁇ V is the first constraint.
  • V is the first candidate site set
  • (j,j') is a candidate site pair
  • the first candidate site set V is converted to the second candidate site set U, because the second candidate site set is There will be at most one candidate site that can be used as the selected site. Therefore, the first constraint Can be converted to
  • the first candidate site set when the first candidate site set is not converted, according to the first constraint, when solving the linear programming model, only two candidate sites in a candidate site pair are required to satisfy This condition is sufficient. Therefore, assuming that the values of the decision variables corresponding to the two candidate sites in a candidate site pair are both 0.5, then the two candidate site sites meet the above conditions. Therefore, the two candidate site sites The value of the decision variable corresponding to the candidate site will be output as part of the solution result, that is, the two decimal values will be output. And if the first candidate site set is converted to the second candidate site set, the decision variables corresponding to all candidate sites in the second candidate site set need to satisfy This condition.
  • the decision variables corresponding to the three candidate sites in the second candidate site set is 0.5
  • the decision variables corresponding to the three candidate sites in the second candidate site set The above conditions cannot be met, at this time, these three decimal values will not be output as part of the solution result of the linear programming model. It can be seen that by converting the first candidate site set to the second candidate site set, the decimal value included in the final output of the linear programming model can be reduced. Since the decimal value in the solution result of the linear programming model does not meet the value requirements of the integer linear programming variables, it cannot be used to judge whether the candidate site is selected. Therefore, this process reduces the final output of the linear programming model in the solution result The included decimal value is equivalent to reducing the number of useless solutions.
  • the integer linear programming model can be preprocessed to obtain the linear programming model.
  • the allowable values of the variables of the integer linear programming model can be processed first by the above method.
  • the integer linear programming model also includes the first parameter and the first constraint, the first parameter and the first constraint can also be continued by the method provided above Any one of them is processed. Of course, all of them can also be processed, which is not limited in the embodiment of the present application.
  • U is the second candidate site set.
  • Step 202 Input parameter values of multiple parameters of the linear programming model into the linear programming model.
  • the objective function and constraint conditions include not only intermediate variables and decision variables, but also multiple parameters. Based on this, after preprocessing the integer linear programming model to obtain the linear programming model, the parameter values of the multiple parameters can be input, so that the linear programming model can be subsequently solved to obtain the location selection result.
  • the parameter values of the multiple parameters may include coverage relationship data between multiple candidate sites and multiple objects to be served, weight data of each object to be served in the multiple objects to be served, and the parameter value of the first parameter And the construction cost of each service station.
  • the coverage relationship data between multiple candidate sites and multiple objects to be served may be determined in advance through a certain system simulation tool or determined through data mining technology, and the coverage relationship data may mainly include instructions When constructing a service station on any candidate site, data on whether the multiple objects to be served are served. For example, if there are currently 10 candidate site sites and 100 to-be-served objects, the coverage relationship data may include information indicating whether each of the 100 to-be-served objects is For the data to be served, when the service station is built on the candidate site 2, the data of whether each of the 100 service objects is served or not, and so on.
  • the input coverage relationship data between multiple candidate sites and multiple objects to be served can be used as parameter values of parameters r i, j
  • the entered weight data of each of the multiple to-be-served objects can be used as the parameter value of w i
  • the entered parameter value of the first parameter can be used as the parameter value of parameter K
  • the entered construction of each service station The cost can be used as the parameter value of c j .
  • Step 203 Determine the first location result and the second location result according to the integer value in the value of the decision variable output by the linear programming model.
  • the linear programming model can be solved to obtain the solution result.
  • the solution result includes the value of the decision variable.
  • the solution result can also include the values of intermediate variables.
  • the value of the variable of the linear programming model can be an integer value or a decimal value
  • the value of the variable of the integer linear programming model is required to be an integer value
  • the result that the decision variable is an integer value can be approximated as the solution result of the integer linear programming model, that is, it can be used as the location selection result.
  • the result that the remaining decision variables are decimal values does not satisfy the value conditions of the variables of the integer linear programming model, so it cannot be used as the solution result of the corresponding integer linear programming model.
  • the first location result and the second location result can be determined according to the result that the decision variable in the solution result is an integer value.
  • the result that the decision variable in the solution result is an integer value can be filtered out.
  • the first location result is determined according to the result of the value of the decision variable in the filtered result as the first value, where the first value is used to indicate that the candidate site corresponding to the decision variable is the selected site Numerical value.
  • each decision variable can be used to indicate whether a candidate site can be used as the selected site
  • the value of the decision variable is the first value
  • the site included in the first site selection result is the site that can be used as the selected site among the determined candidate site sites.
  • the value of the decision variable in the remaining result is an integer value, but it is not the first value, it can be determined that the candidate site represented by the decision variable in the remaining result will not be It is regarded as the selected site, that is, the candidate site represented by the decision variable in the remaining results is the unselected site.
  • the corresponding candidate site address can be obtained according to the decision variables in the remaining results, and the obtained site address can be used as the second site selection result.
  • the site included in the second site selection result is the site that is not selected among the multiple candidate site sites.
  • the integer value in the solution result of the linear programming model can be approximated as the solution result of the integer linear programming model, there may still be a certain error between the two.
  • it can also be judged whether the candidate site corresponding to each selected decision variable Is the candidate site included in the first candidate site set. For any one of the selected decision variables, if the candidate site corresponding to the decision variable is neither the first candidate site set nor the candidate site included in the second candidate site set, the candidate site corresponding to the decision variable can be The site address is the selected site site, and the determined multiple selected site sites are used as the first site selection result.
  • the candidate site corresponding to the decision variable is a candidate site included in the first candidate site set or the second candidate site set
  • the candidate site corresponding to the decision variable may be regarded as a non-selected site.
  • the candidate site corresponding to these results can also be regarded as the unselected site, and the determined multiple unselected sites are regarded as the second choice. Address results.
  • the decision variable can be filtered from the solution result
  • the value of is an integer value result.
  • the result of the intermediate variable value of an integer value can also be filtered from the solution result.
  • the determined unselected site and unserved object to be served shall be the second location result.
  • the value of the intermediate variable is the second value, it means that the object to be served represented by the intermediate variable is served.
  • step 204 can be used to determine which of the candidate sites represented by this part of the decision variable with a decimal value can be used as the selected site.
  • Step 204 Determine the selected site from the remaining candidate sites except the first site selection result and the second site selection result from the multiple candidate site sites.
  • the site included in the first site selection result and the site included in the second site selection result from the multiple candidate site sites And delete the sites that cannot be built at the same time as the selected site included in the first site selection result; delete the to-be-served objects served by the site included in the first site selection result among multiple to-be-served objects; delete according to the deletion After the remaining candidate site addresses and the remaining to-be-served objects after deletion, determine the selected site among the remaining candidate site addresses after deletion.
  • the first site selection result includes the selected site site
  • the second site selection result includes the unselected site site, that is, the multiple candidate site sites are included in the first site selection.
  • the site addresses in the site results and the second site selection results can already be clearly determined whether to be selected. Therefore, the site sites included in the first site selection result and the second site selection result can be deleted from multiple candidate site sites. .
  • other candidate site sites may also include those in the first site selection result. The site site cannot be constructed at the same time. Since the site site in the first site selection result has been determined to be selected, these candidate sites that cannot be constructed at the same time as the site site in the first site selection result will obviously not be selected Therefore, this part of the candidate site can also be deleted to obtain the remaining candidate site.
  • the first site selection result includes a part of the selected site sites determined from a plurality of candidate site sites, and this part of the selected site sites will serve some of the multiple to-be-served objects. In other words, this part of the selected site will correspond to some of the objects to be served. Based on this, in order not to repeatedly serve the objects that have been served, the part of the objects that have been served among the multiple objects to be served can be deleted, so as to obtain the remaining objects to be served.
  • the first location selection result it is possible to determine which of the multiple objects to be served are the objects that have been served. It should be noted that, according to the introduction of step 203, it can be known that the served object may or may not be included in the first site selection result. In this case, according to the difference in the content contained in the first site selection result, different methods can be used to determine which of the multiple to-be-served objects are already served objects.
  • the selected site included in the first site selection result can be used to determine the location in the first site selection through computer simulation.
  • a site is built on the selected site included in the address result, which of the multiple to-be-served objects will be served, that is, the multiple to-be-served objects are determined.
  • the served object can be directly obtained from the first site selection result, and the obtained served object is determined as The objects served when the service station is built on the site included in the first site selection result, that is, the objects that have been served among the plurality of objects to be served.
  • the second site selection result may include not only sites that are not selected, but also objects that are not served.
  • the number of candidate sites and the number of objects to be served will both decrease. Since the number of candidate sites and the number of objects to be served is reduced, when continuing to determine the selected site from the remaining candidate sites based on the remaining objects to be served, it is equivalent to reducing the dimensionality of the previous site selection problem
  • the site selection problem is solved. In this way, compared to obtaining the selected site directly by solving the integer linear programming model, it not only reduces the difficulty of site selection, but also shortens the time required for site selection.
  • the graph theory site selection map can be determined according to the remaining candidate station locations and the remaining service objects.
  • the graph theory site selection graph includes multiple nodes, and each node is used to indicate one of the candidate sites remaining after deletion, and two of the multiple nodes correspond to two candidate sites that cannot be constructed at the same time. There is a connection between each node; the selected site among the candidate sites remaining after deletion is determined according to the site selection graph of graph theory.
  • each candidate site site can be used as a node, and any two candidate site sites that cannot be built at the same time correspond to There is an edge between two nodes.
  • the two candidate site sites that cannot be established at the same time may refer to two candidate site sites whose distance between each other is less than the first threshold.
  • it may also be a candidate site determined based on other business requirements that cannot be built at the same time.
  • each node can also correspond to a first weight and a second weight.
  • the first weight refers to the service capability for the remaining objects to be served after the service station is built on the candidate site indicated by the corresponding node.
  • the so-called service capability of the service object can refer to the total number of objects to be served covered, or the quality of service of the object to be served, etc.
  • the service weight coefficient of the object to be served can be used to characterize the service of the object to be served ability.
  • the service weight coefficient corresponding to each object to be served is used to characterize the service capability of the object to be served.
  • the sum of the service weight coefficients corresponding to the objects to be served when the site is built is the first weight.
  • the second weight refers to the cost of building a service station on the candidate site indicated by the corresponding node.
  • Fig. 3 is an example of a graph-theoretic site selection diagram shown in an embodiment of the present application.
  • node V 1 is used to characterize candidate site 1
  • node V 2 is used to characterize candidate site 2, and so on.
  • there are connecting edges between node V 1 and nodes V 2 , V 5 and V 6 indicating that candidate site 1 and candidate site 2 cannot be constructed at the same time, and candidate site 1 and candidate site 5 cannot be constructed at the same time.
  • Site 1 and candidate site 6 cannot be built at the same time. For the other two nodes with connected edges, it has the same meaning.
  • each node corresponds to the first weights W i and C i , where W i refers to the sum of the service weight coefficients corresponding to the remaining objects to be served when the station is built on the candidate site i indicated by the i-th node, C i refers to the cost of building a site on the candidate site i.
  • the steps shown in FIG. 4 can be used to determine the selected site site among the candidate site sites remaining after deletion according to the graph theory site selection map.
  • the first weight is used to indicate the service capability of the remaining objects to be served
  • the second weight refers to the cost of building a site at the corresponding site.
  • the ratio between the first weight and the second weight corresponding to each node can be determined. The larger the ratio, the higher the cost-effectiveness of building a site at the site indicated by the corresponding node, that is, the more the corresponding node is more in line with the business. demand.
  • the node with the largest ratio between the corresponding first weight and the second weight is selected from the multiple nodes as the target node, and the node is the node that best meets the business requirements among the multiple nodes.
  • the first location problem can be determined according to the target node and the graph theory location graph, and the first location problem is divided into L layers through the dynamic programming algorithm.
  • L is less than the first location problem allowed to be divided Maximum number of layers; determine the operation result of multiple sub-problems obtained by segmentation, determine the operation result of the first location problem according to the operation results of multiple sub-questions; determine whether to select the candidate indicated by the target node according to the operation result of the first location problem
  • the site address is used as the selected site site.
  • the first location problem can be determined according to the target node, the graph theory site selection graph, and the target to be optimized determined when the integer linear programming model is established or the objective function of the integer linear programming model.
  • the first location problem is to determine whether the target node is the selected site.
  • the optimal solution for solving the first site selection problem is the optimal solution when determining the site indicated by the target node as the selected site and the solution when not as the selected site. value.
  • the first integer linear programming model For example, taking the first integer linear programming model provided above as an example, according to its objective function, it can be seen that the goal it wants to achieve is to maximize the service capacity of the service object. In addition, according to the site construction conditions, it requires that the cost of site construction is not Greater than the second threshold. In other words, the first integer linear programming model requires that the service capacity of the service object be maximized under the premise that the cost of building a site does not exceed the second threshold.
  • the optimal solution of the first location problem is opt(G,C)
  • the optimal solution Refers to the optimal solution of the corresponding location problem after assuming that the site indicated by the target node is selected, Refers to the graph theory site selection graph updated after assuming that the site location indicated by the target node is selected, Refers to the optimal solution of the corresponding location problem after assuming that the site indicated by the target node is not selected, Refers to the graph theory location map updated after assuming that the site address indicated by the target node is not selected. It can be seen that after the optimal solution of the above two hypothetical problems is determined, the optimal solution of the first location problem can be obtained. In other words, the optimal solution of the first location problem can be determined by dividing the first location problem into two sub-problems and solving the optimal solutions of the two sub-problems.
  • the candidate site indicated by the target node is selected, and based on this assumption, the target node in the graph theory location selection graph is deleted. Since the candidate site indicated by the node connected to the target node cannot be constructed at the same time as the site indicated by the target node, it is assumed that the site address indicated by the target node can be used as the selected site. The candidate site addresses indicated by nodes with connected nodes will not be regarded as the selected site sites, so these nodes can be deleted. In addition, since the site address indicated by the target node will be used as the selected site site, when a site is built at the site indicated by the target node, some of the remaining service objects will be served.
  • the weight of the object to be served by the site indicated by the target node contained in the first weight corresponding to each node in the remaining nodes can also be subtracted to obtain a new graph On the site selection map.
  • a new location problem can be determined based on the new graph theory site selection map. At this time, this new location problem is actually the location problem under the assumption that the site indicated by the target node is selected.
  • the candidate site indicated by the target node is not selected. Since the site address indicated by the target node is not selected, the candidate site indicated by other nodes that have an edge with the target node may still be selected. Therefore, the target node can be connected to the candidate site. The connecting edges between other nodes and the target node are deleted, and a new graph theory location graph is obtained. According to this graph theory, a new location problem can also be determined. At this time, this new location problem is actually the location problem under the assumption that the site address indicated by the target node is not selected.
  • the first location problem can be divided into one level, and two new sub-problems can be obtained. These two sub-problems can be solved, and the optimal solution of the two sub-problems can be determined to obtain the first The optimal solution to the location problem.
  • the new graph theory site selection graph does not include child nodes or the total site construction cost is zero.
  • the solution result of each sub-problem according to the inverse process of the segmentation process, according to the solution results of the multiple sub-problems at the bottom, the solution results of the sub-problems in each layer are determined layer by layer, until the first location problem is finally obtained To the optimal solution.
  • the site address indicated by the target node may be used as the selected site address.
  • the site address indicated by the target node can be regarded as the site not selected .
  • a node when performing the second-level segmentation, when a node is selected from the graph theoretic location graph corresponding to each sub-problem, it can be selected according to the target node, or according to the first weight of the node.
  • you when selecting according to the target borrowing point, you can select a node that has an edge with the target node, or select a node that includes the target node to be served from the target node.
  • the node with the largest first weight can be selected.
  • the number of layers to which the first location problem is segmented under the segment cut-off condition is taken as the maximum number of layers allowed to be segmented for the first location problem. If the first location problem is divided according to the maximum number of layers allowed to be divided, the amount of calculation may be relatively large. Based on this, in order to reduce the amount of calculation, it is also possible to stop after L layer segmentation, where L is less than the maximum number of layers allowed to be segmented in the first location problem. In this way, after the L-level segmentation is performed and the 2 L sub-problems are obtained, the greedy algorithm can be used to solve the 2 L sub-problems.
  • the optimal solution of the first location problem can be determined in the reverse direction according to the inverse process of segmentation, and then the target node indicated by the target node can be determined according to the optimal solution of the first location problem. Whether the candidate site is selected.
  • step 2043 can be performed next. If it is determined that the candidate site indicated by the target node cannot be used as the selected site, then the next step can be performed Step 2044.
  • the candidate site indicated by the target node may be deleted from the remaining candidate site addresses.
  • this part of The site addresses that cannot be built at the same time are also deleted.
  • the service station will serve some of the remaining objects to be served. Therefore, this part of the objects served by the site address indicated by the target node can be deleted from the remaining objects to be served.
  • the candidate site indicated by the target node may be deleted from the remaining candidate sites. Since the candidate site indicated by the target node is not selected, other candidate sites that cannot be built at the same time as the candidate site indicated by the target node may still be selected. Therefore, there is no need for this part of the candidate site Address to delete. In addition, since the candidate site indicated by the target node is not selected, the site indicated by the target node will not be able to serve any objects to be served. Therefore, the remaining objects to be served do not need to be updated. .
  • step 2043 After deleting the candidate site indicated by the target node among the remaining candidate site sites through step 2043 and the candidate site that cannot be established at the same time as the candidate site indicated by the target node, or, through step 2044, After deleting the candidate site indicated by the target node among the candidate site addresses, it can be determined whether there are remaining candidate site addresses after deleting again. If there are still remaining candidate site addresses, step 2046 may continue to determine the selected site among the remaining candidate site addresses. Of course, if there are no remaining candidate sites after deleting again, it can be explained that for all candidate sites, it has been determined whether they can be selected as sites. At this point, you can use all the selected site sites previously determined as the final site selection results and end the operation.
  • step 2046 If there are remaining candidate site addresses after deleting again, update the graph theory site selection map according to the remaining candidate sites after deleting again, and return to step 2041.
  • the remaining candidate site addresses are deleted through step 2043, and the remaining objects to be served are deleted, then in this step, the remaining candidate site addresses after deletion again and after deletion again can be used in this step.
  • the remaining objects to be served re-determine the graph theory location map, and use the re-determined graph theory location map to update the previous graph theory location map. After that, you can return to step 2041 and continue to update according to the method described above.
  • the site selection map of the latter graph theory will determine the site site selected from the remaining candidate site sites after deletion again.
  • the remaining candidate site addresses are deleted through step 2044, since the remaining to-be-served objects have not changed, it can be based on the remaining candidate site addresses after deletion again and the remaining to-be-served addresses that have not changed.
  • the subject re-determines the graph theory location graph and uses the re-determined graph theory location graph to update the previous graph theory location graph. After that, it can return to step 2041 and continue to use the aforementioned method according to the updated graph theory.
  • Location map to determine the selected site from the remaining candidate sites after deletion again.
  • the integer linear programming model is converted into a linear programming model for solving to obtain the first site selection result and the second site selection result.
  • the first site selection result and the second site selection result are removed from the multiple candidate sites.
  • the selected site is determined among the remaining candidate site sites other than the site sites included in the second site selection result. That is, this application can first obtain a part of the site selection result by solving the linear programming model obtained by the conversion, and then, according to this part of the site selection result, reduce the dimensionality of the previous site selection problem based on multiple candidate sites, and then solve the dimensionality reduction.
  • the site selection problem In this way, when the number of candidate sites is large, the method provided by this application can not only reduce the difficulty of site selection, but also shorten the time spent in site selection.
  • the location of the business hall is selected.
  • the objects to be served are users on each grid after rasterizing the location area.
  • the business hall There is only one type.
  • the target to be optimized is the number of users covered by the business hall.
  • the site construction conditions include: two candidate sites with a distance of less than 150 meters cannot be built at the same time, and the number of selected sites is not more than 300.
  • the integer linear programming model is established as follows:
  • w i refers to the service weight coefficient of the object i among the objects to be served.
  • w i is equal to the ratio of the number of users on the grid i to the total number of users.
  • V is the first candidate site set, including 1380 candidate site pairs, and the distance between two candidate sites in each candidate site pair is less than 150 meters.
  • U is the second candidate site set, wherein the distance between any two candidate sites in the second candidate site set is less than 150 meters.
  • Table 2 lists the user coverage ratio of the site selection results and the time spent in site selection when the site selection of the business hall is determined by the above-mentioned location method, the greedy algorithm in related technologies, and the genetic algorithm.
  • the user coverage ratio is 94.4%, which is very close to the upper limit of the optimal solution, and it takes only 500 seconds.
  • the greedy algorithm is used for a short time, the user coverage ratio is only 78.3%, which is far less than the upper limit of the optimal solution, and the site selection effect is poor.
  • the user coverage ratio is lower than the user coverage ratio of the embodiment of the present application, and it takes a long time. It can be seen that the site selection method provided in this application achieves a better coverage capability while ensuring a shorter time consumption.
  • the foregoing embodiment mainly introduces the conversion of the integer linear programming model to the linear programming model for solving, so as to obtain the first location result and the second location result, and then divide the first location result and the second location result from the multiple candidate sites.
  • the site selection result includes the implementation process of determining the selected site site among the remaining candidate site sites except the site site.
  • an integer linear programming model may not be established based on multiple candidate site sites, multiple objects to be served, and multiple site building conditions.
  • the site construction conditions include constraints on the coverage capacity of each service station, since the coverage capacity of each service station affects each other, the restriction conditions cannot be established based on the site construction conditions, and therefore, the corresponding Planning model.
  • the site selection method shown in Figure 5 can be used to determine the site to be selected from multiple candidate sites. As shown in Figure 5, the method includes the following steps:
  • Step 501 According to multiple candidate sites, multiple to-be-served objects, and multiple site building conditions, determine a graph-based site selection graph.
  • the graph-based site selection graph includes multiple nodes, and each node is used to indicate multiple candidate sites One of the candidate sites in the multiple nodes, the two candidate sites that cannot be established at the same time in multiple nodes have a connection between the two corresponding nodes.
  • the graph theory location map is determined based on all the candidate sites and the objects to be served, while the foregoing embodiment is aimed at removing the first location results and the second location selection. After the result, the remaining candidate sites and the remaining to-be-served objects are determined by graph theory site selection.
  • each node can also correspond to a first weight and a second weight.
  • the method for determining the first weight and the second weight can refer to the relevant introduction in the foregoing embodiment.
  • Step 502 Determine the selected site among multiple candidate sites according to the graph theory site selection map.
  • the graph theory site selection map can be determined based on multiple candidate site sites, multiple objects to be served, and multiple site construction conditions, and then pass The dynamic programming algorithm introduced above or the dynamic programming algorithm combined with the greedy algorithm to determine the location result. That is, the embodiment of the present application provides a solution to the location problem that cannot establish an integer linear programming model.
  • an address selection device 600 which includes:
  • the processing module 601 is configured to execute step 201 in the foregoing embodiment
  • the input module 602 is configured to execute step 202 in the foregoing embodiment
  • the first determining module 603 is configured to execute step 203 in the foregoing embodiment
  • the second determining module 604 is configured to execute step 204 in the foregoing embodiment.
  • the integer linear programming model includes intermediate variables and constraint conditions.
  • the intermediate variables are used to indicate whether the object to be served is served.
  • the constraint conditions include a first integer set and a second integer set.
  • the first integer set includes the allowable selection of decision variables.
  • Value, the second set of integers includes the allowable values of intermediate variables;
  • the processing module 601 is specifically used for:
  • the first value range refers to the continuous selection of integer values in the first integer set
  • the value range refers to a continuous value range that includes the integer values in the second integer set.
  • the integer linear programming model further includes a first parameter, where the first parameter is used to indicate the number of service station types to be selected when establishing a station on each candidate site;
  • the processing module 601 is also specifically used for:
  • K service station types to be selected when the station is built on each candidate site are converted into K different candidate sites at the same location, and K is the first parameter.
  • the constraint condition further includes a first constraint, the first constraint includes a first candidate site set, the first candidate site set includes at least one candidate site pair, and each candidate site pair includes two candidate sites The distance between is less than the first threshold;
  • the processing module 601 is also specifically used for:
  • the second candidate site set includes at least two candidate sites, and the distance between any two candidate sites in the at least two candidate sites is equal Less than the first threshold.
  • the second determining module 604 includes:
  • the deleting unit is used to combine the sites included in the first site selection result, sites included in the second site selection result, and sites that cannot be constructed at the same time as the selected site included in the first site selection result among the multiple candidate site sites Address to delete;
  • the unit is also used to delete the object to be served served by the site included in the first location result among the multiple objects to be served;
  • the determining unit is used for determining the selected site among the candidate site addresses remaining after the deletion according to the candidate site addresses remaining after the deletion and the remaining service objects after the deletion.
  • the determining unit includes:
  • the first determining subunit is used to determine the graph theory site selection graph based on the candidate site sites remaining after deletion and the objects to be served after deletion.
  • the graph theory site selection graph includes multiple nodes, and each node is used to indicate the deletion One candidate site among the remaining candidate site sites, and two nodes corresponding to the two candidate site sites that cannot be built at the same time among multiple nodes have a connection edge;
  • the second determining subunit is used to determine the selected site among the candidate sites remaining after deletion according to the graph theory site selection map.
  • each node in the plurality of nodes corresponds to a first weight and a second weight
  • the first weight refers to the value of the remaining objects to be served after the service station is constructed on the candidate site indicated by the corresponding node.
  • Service capability refers to the cost of building a service station on the candidate site indicated by the corresponding node;
  • the second determining subunit is specifically used for:
  • the candidate site indicated by the target node is determined to be the selected site, delete the determined selected site from the remaining candidate sites after deletion and the site that cannot be built at the same time as the determined selected site, and delete After deleting, the remaining service objects determined to be served by the selected site are deleted, and the graph theory site selection map is updated according to the remaining candidate site addresses after the deletion and the remaining service objects after the deletion again, and return According to the first weight and the second weight corresponding to each node, the step of selecting the target node from multiple nodes until there is no remaining candidate site after deletion again.
  • the second determining subunit is specifically used for:
  • the first location problem is divided into L layers through the dynamic programming algorithm, and L is less than the maximum number of layers allowed to be divided in the first location problem;
  • the embodiment of the present application can first obtain a part of the site selection result by solving the linear programming model obtained by the conversion, and then, according to this part of the site selection result, reduce the dimensionality of the previous site selection problem based on multiple candidate sites, and then solve the problem. Site selection after maintenance. In this way, when the number of candidate sites is large, the method provided by this application can not only reduce the difficulty of site selection, but also shorten the time spent in site selection.
  • an embodiment of the present application provides an address selection device 700, and the device 700 includes:
  • the first determining module 701 is configured to execute step 501 in the foregoing embodiment
  • the second determining module 702 is configured to execute step 502 in the foregoing embodiment.
  • each node of the multiple nodes corresponds to a first weight and a second weight
  • the first weight refers to the service capability of multiple objects to be served after the service station is built on the candidate site indicated by the corresponding node
  • the second weight refers to the cost of building a service station on the candidate site indicated by the corresponding node
  • the second determining module includes:
  • the selection unit is used to select a target node from multiple nodes according to the first weight and the second weight corresponding to each node;
  • a judging unit for judging whether to determine the candidate site indicated by the target node as the selected site
  • the trigger unit is used to determine the candidate site indicated by the target node as the selected site, then determine the selected site from the multiple candidate sites and the site that cannot be constructed at the same time as the determined selected site Delete, delete the to-be-served objects served by the selected site location determined among multiple to-be-served objects, and update the graph theory site selection map according to the remaining candidate site addresses after the deletion and the remaining to-be-served objects after the deletion to trigger the selection
  • the unit selects the target node from multiple nodes according to the first weight and the second weight corresponding to each node, until there is no remaining candidate site after deletion.
  • the judging unit is specifically used for:
  • the first location problem is divided into L layers through the dynamic programming algorithm, and L is less than the maximum number of layers allowed to be divided in the first location problem;
  • the graph theory site selection map can be determined based on multiple candidate site sites, multiple objects to be served, and multiple site construction conditions, and then pass The dynamic programming algorithm introduced above or the dynamic programming algorithm combined with the greedy algorithm to determine the location result. That is, the embodiment of the present application provides a solution to the location problem that cannot establish an integer linear programming model.
  • the address selection device provided in the above embodiment performs address selection, only the division of the above-mentioned functional modules is used as an example. In actual applications, the above-mentioned functions can be allocated by different functional modules as required. The internal structure of the device is divided into different functional modules to complete all or part of the functions described above.
  • the address selection device provided in the foregoing embodiment and the address selection method embodiment belong to the same concept, and the specific implementation process is detailed in the method embodiment, and details are not repeated here.
  • the computer program product includes one or more computer instructions.
  • the computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices.
  • the computer instructions may be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions may be transmitted from a website, computer, server, or data center.
  • the computer-readable storage medium may be any available medium that can be accessed by a computer or a data storage device such as a server or a data center integrated with one or more available media.
  • the usable medium may be a magnetic medium (for example: floppy disk, hard disk, tape), optical medium (for example: Digital Versatile Disc (DVD)), or semiconductor medium (for example: Solid State Disk (SSD) )Wait.

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Abstract

一种选址方法及装置，属于信息处理技术领域。该方法将整数线性规划模型转换为线性规划模型进行求解，以得到第一选址结果和第二选址结果（203），之后，从多个候选站址中除第一选址结果和第二选址结果包括的站址之外的剩余候选站址中确定被选站址（204）。该方法可以首先通过求解转化得到的线性规划模型得到一部分选址结果，之后，根据这部分选址结果对之前基于多个候选站址的选址问题进行降维，进而求解降维后的选址问题。这样，当候选站址的数量较大时，通过该方法不仅可以降低选址的难度，而且可以缩短选址所耗费的时间。

Description

选址方法、装置及计算机可读存储介质
本申请要求于2019年5月6日提交的申请号为201910373187.2、申请名称为“选址方法、装置及计算机可读存储介质”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
技术领域
本申请涉及信息处理技术领域，特别涉及一种选址方法、装置及计算机可读存储介质。
背景技术
当前，随着服务技术的发展，诸如无线通信网络、配电网络等服务网络的规划变得越来越重要。其中，服务站的选址问题是服务网络规划中的关键问题。
相关技术中，在进行服务站的选址时，可以根据多个候选站址以及建站条件确定目标函数，之后，可以根据影响该目标函数的因素确定决策变量，进而根据决策变量和建站条件确定约束条件。根据上述确定的目标函数、决策变量和约束条件确定整数线性规划模型，之后，可以利用分支定界法或割平面法对该整数线性规划模型进行求解，从而从该多个候选站址中确定得到服务站的站址。
然而，当采用分支定界法或割平面法对整数线性规划模型进行求解时，若上述多个候选站址的数量较大，则在有限的时间内很难求解得到选址结果。
发明内容
本申请提供了一种选址方法、装置及计算机可读存储介质，可以用于解决相关技术中选址问题涉及的候选站址数量较大时，无法在有限时间内得到选址结果的问题。所述技术方案如下：
第一方面，提供了一种选址方法，所述方法包括：对整数线性规划模型进行预处理，得到线性规划模型，所述整数线性规划模型是根据多个候选站址、多个待服务对象和多个建站条件建立的模型，且所述整数线性规划模型输出的决策变量的取值为整数值，所述线性规划模型输出的决策变量的取值包括整数值和小数值；将所述整数线性规划模型的多个参数的参数值输入所述线性规划模型；根据所述线性规划模型输出的决策变量的取值中的整数值确定第一选址结果和第二选址结果，所述第一选址结果包括多个被选站址，所述第二选址结果包括多个不被选站址，所述多个被选站址是指所述多个候选站址中被选作建设服务站的站址；从所述多个候选站址中除所述第一选址结果和所述第二选址结果之外的剩余候选站址中确定被选站址。
本申请实施例可以首先通过求解转化得到的线性规划模型得到一部分选址结果，之后，根据这部分选址结果对之前基于多个候选站址的选址问题进行降维，进而求解降维后的选址问题，这样，即使候选站址的数量较大，通过本申请提供的方法也可以在有限的时间内快速得到选址结果，解决了相关技术中直接采用分支定界法或割平面法求解整数线性规划模型时， 无法在有限时间内得到选址结果的问题。
可选地，所述整数线性规划模型包括中间变量和约束条件，所述中间变量用于指示待服务对象是否被服务，所述约束条件包括第一整数集和第二整数集，所述第一整数集包括所述决策变量的允许取值，所述第二整数集包括所述中间变量的允许取值。相应地，所述对整数线性规划模型进行预处理，得到线性规划模型的实现过程可以为：将所述第一整数集转换为第一取值范围，将所述第二整数集转换为第二取值范围，得到所述线性规划模型，所述第一取值范围是指包含所述第一整数集内的整数值的连续取值范围，所述第二取值范围是指包含所述第二整数集内的整数值的连续取值范围。
可选地，所述整数线性规划模型还包括第一参数，所述第一参数用于指示在每个候选站址上建站时待选服务站类型的数量。在此基础上，在将所述第一整数集转换为第一取值范围，将所述第二整数集转换为第二取值范围之后，还可以将在每个候选站址上建站时的K个待选服务站类型转换为在相同位置上的K个不同候选站址，所述K为所述第一参数。
可选地，所述约束条件还包括第一约束，所述第一约束包括第一候选站址集合，所述第一候选站址集合包括至少一个候选站址对，每个候选站址对包括的两个候选站址之间的距离小于第一阈值；相应地，在将所述第一整数集转换为第一取值范围，将所述第二整数集转换为第二取值范围之后，还可以将所述第一候选站址集合转换为第二候选站址集合，所述第二候选站址集合包括至少两个候选站址，且所述至少两个候选站址中的任意两个候选站址之间的距离均小于所述第一阈值。
通过将第一候选站址集合转换为第二候选站址集合，可以减少线性规划模型最终输出的求解结果中包括的小数解。由于线性规划模型的求解结果中的小数值不满足整数线性规划的变量的取值要求，不能用来判断候选站址是否被选，因此，通过这一处理减少线性规划模型最终输出的求解结果中包括的小数值，相当于减少了无用解的数量。
可选地，从所述多个候选站址中除所述第一选址结果和所述第二选址结果之外的剩余候选站址中确定被选站址的实现过程可以为：将所述多个候选站址中所述第一选址结果包括的站址、所述第二选址结果包括的站址以及与所述第一选址结果中包括的被选站址不能同时建站的站址进行删除；将所述多个待服务对象中所述第一选址结果包括的站址所服务的待服务对象进行删除；根据删除后剩余的候选站址和删除后剩余的待服务对象，确定所述删除后剩余的候选站址中的被选站址。
在得到第一选址结果和第二选址结果之后，可以通过删除多个候选站址中第一选址结果和第二选址结果包括的站址、与被选站址不能同时建站的站址，删除多个待服务对象中被选站址所服务的待服务对象来对原选址问题进行降维，之后，对降维得到的选址问题继续进行求解，这样，不仅可以降低选址的复杂度，而且可以缩短选址的时间。
可选地，根据删除后剩余的候选站址和删除后剩余的待服务对象，确定所述删除后剩余的候选站址中的被选站址的实现过程可以为：根据所述删除后剩余的候选站址和所述删除后剩余的待服务对象确定图论选址图，所述图论选址图中包括多个节点，每个节点用于指示所述删除后剩余的候选站址中的一个候选站址，所述多个节点中两个不能同时建站的候选站址对应的两个节点之间具有连边；根据所述图论选址图确定所述删除后剩余的候选站址中的被选站址。也即，在本申请实施例中，可以通过图论算法来对降维后的选址问题进行求解，从而得到最终的选址结果。
可选地，所述多个节点中的每个节点对应有第一权重和第二权重，所述第一权重是指在相应节点所指示的候选站址上建设服务站后对所述删除后剩余的待服务对象的服务能力，所述第二权重是指在相应节点所指示的候选站址上建设服务站的建站成本；在此基础上，根据所述图论选址图确定所述删除后剩余的候选站址中的被选站址的实现过程可以为：根据每个节点对应的第一权重和第二权重，从所述多个节点中选择目标节点；判断是否将所述目标节点所指示的候选站址确定为被选站址；如果将所述目标节点所指示的候选站址确定为被选站址，则将所述删除后剩余的候选站址中确定的被选站址以及与确定的被选站址不能同时建站的站址删除，将所述删除后剩余的待服务对象中确定的被选站址所服务的待服务对象删除，根据再次删除后剩余的候选站址和再次删除后剩余的待服务对象对所述图论选址图进行更新，返回根据每个节点对应的第一权重和第二权重，从所述多个节点中选择目标节点的步骤，直到再次删除后不存在剩余的候选站址时为止。
可选地，判断是否将所述目标节点所指示的候选站址确定为被选站址的实现过程可以为：根据所述目标节点和所述图论选址图，确定第一选址问题；通过动态规划算法将所述第一选址问题进行L层分割，所述L小于所述第一选址问题允许被分割的最大层数；确定分割得到的多个子问题的运算结果，根据所述多个子问题的运算结果确定所述第一选址问题的运算结果；根据所述第一选址问题的运算结果判断是否将所述目标节点所指示的候选站址作为被选站址。
在本申请实施例中，可以通过动态规划算法对第一选址问题划分L层，进而通过划分得到的多个子问题的运算结果来确定第一选址问题的运算结果，这样，可以在保证运算结果的准确性的同时，减少计算量。
第二方面，提供了一种选址方法，所述方法包括：根据多个候选站址、多个待服务对象和多个建站条件，确定图论选址图，所述图论选址图中包括多个节点，每个节点用于指示所述多个候选站址中的一个候选站址，所述多个节点中两个不能同时建站的候选站址对应的两个节点之间具有连边；根据所述图论选址图确定所述多个候选站址中的被选站址。
在本申请实施例中，当根据建站条件无法建立整数线性规划模型时，可以根据多个候选站址、多个待服务对象和多个建站条件确定图论选址图，再通过前述介绍的动态规划算法或者是动态规划算法结合贪婪算法来确定选址结果。这样，避免了在无法建立整数线性规划模型时，通过人工经验进行选址的不准确性。
可选地，所述多个节点中的每个节点对应有第一权重和第二权重，所述第一权重是指在相应节点所指示的候选站址上建设服务站后对所述多个待服务对象的服务能力，所述第二权重是指在相应节点所指示的候选站址上建设服务站的建站成本；在此基础上，根据所述图论选址图确定所述多个候选站址中的被选站址的实现过程可以为：根据每个节点对应的第一权重和第二权重，从所述多个节点中选择目标节点；判断是否将所述目标节点所指示的候选站址确定为被选站址；如果将所述目标节点所指示的候选站址确定为被选站址，则将所述多个候选站址中确定的被选站址以及与所述确定的被选站址不能同时建站的站址删除，将所述多个待服务对象中所述确定的被选站址所服务的待服务对象删除，根据删除后剩余的候选站址和删除后剩余的待服务对象对所述图论选址图进行更新，返回所述根据每个节点对应的第一权重和第二权重，从所述多个节点中选择目标节点的步骤，直到删除后不存在剩余的候选站 址时为止。
可选地，判断是否将所述目标节点所指示的候选站址确定为被选站址的实现过程可以为：根据所述目标节点和所述图论选址图，确定第一选址问题；通过动态规划算法将所述第一选址问题进行L层分割，所述L小于所述第一选址问题允许被分割的最大层数；确定分割得到的多个子问题的运算结果，根据所述多个子问题的运算结果确定所述第一选址问题的运算结果；根据所述第一选址问题的运算结果判断是否将所述目标节点所指示的候选站址确定为被选站址。
第三方面，提供了一种选址装置，所述选址装置具有实现上述第一方面或第二方面中选址方法行为的功能。所述选址装置包括至少一个模块，该至少一个模块用于实现上述第一方面或第二方面所提供的选址方法。
第四方面，提供了一种选址装置，所述选址装置的结构中包括处理器和存储器，所述存储器用于存储支持选址装置执行上述第一方面或第二方面所提供的选址方法的程序，以及存储用于实现上述第一方面或第二方面所提供的选址方法所涉及的数据。所述处理器被配置为用于执行所述存储器中存储的程序。所述存储设备的操作装置还可以包括通信总线，该通信总线用于该处理器与存储器之间建立连接。
第五方面，提供了一种计算机可读存储介质，所述计算机可读存储介质中存储有指令，当其在计算机上运行时，使得计算机执行上述第一方面或第二方面所述的选址方法。
第六方面，提供了一种包含指令的计算机程序产品，当其在计算机上运行时，使得计算机执行上述第一方面或第二方面所述的选址方法。
上述第三方面、第四方面、第五方面和第六方面所获得的技术效果与第一方面和第二方面中对应的技术手段获得的技术效果近似，在这里不再赘述。
本申请提供的技术方案带来的有益效果至少包括：
本申请实施例可以将整数线性规划模型转换为线性规划模型进行求解，以得到第一选址结果和第二选址结果，之后，再确定多个候选站址中除第一选址结果和第二选址结果之外的剩余候选站址中的被选站址。也即，本申请可以首先通过求解转化得到的线性规划模型得到一部分选址结果，之后，根据这部分选址结果对之前基于多个候选站址的选址问题进行降维，进而求解降维后的选址问题，这样，即使候选站址的数量较大，通过本申请提供的方法也可以在有限的时间内快速得到选址结果，解决了相关技术中直接采用分支定界法或割平面法求解整数线性规划模型时，无法在有限时间内得到选址结果的问题。
附图说明
图1是本申请实施例提供的用于选址的计算机设备的结构示意图；
图2是本申请实施例提供的一种选址方法流程图；
图3是本申请实施例提供的一种图论选址图的示例；
图4是本申请实施例提供的根据图论选址图确定删除后剩余的候选站址中的被选站址的流程图；
图5是本申请实施例提供的另一种选址方法流程图；
图6是本申请实施例提供的一种选址装置结构示意图；
图7是本申请实施例提供的另一种选址装置结构示意图。
具体实施方式
为使本申请的目的、技术方案和优点更加清楚，下面将结合附图对本申请实施方式作进一步地详细描述。
在本申请实施例进行详细的解释说明之前，先对本申请实施例涉及的应用场景予以介绍。
当前，随着各种服务技术的发展，为了满足用户需求，各种服务网络的规划变得越来越重要。其中，在进行网络规划时，服务站的选址问题是重中之重。例如，在进行5G通信网络的规划时，如何选取5G通信网络中各个5G基站的位置，将直接影响5G通信网络覆盖的用户数以及5G通信网络的服务质量。再例如，当商家在进行商铺网络规划时，如何选取商铺的位置，以使商铺覆盖的用户数最大化且商铺的建设成本或运营成本最低，将直接影响到商家的效益。基于此，本申请实施例中提供了一种选址方法，该选址方法可以应用于诸如通信网络、配电网络、商铺网络、物流网络等各种服务网络的规划过程中，以实现服务站的选址。
图1是本申请实施例提供的一种用于选址的计算机设备的结构示意图。参见图1，该计算机设备包括至少一个处理器101，通信总线102，存储器103以及至少一个通信接口104。
处理器101可以是一个通用中央处理器(Central Processing Unit，CPU)，微处理器，特定应用集成电路(application-specific integrated circuit，ASIC)，或一个或多个用于控制本申请方案程序执行的集成电路。
通信总线102可包括一通路，在上述组件之间传送信息。
存储器103可以是只读存储器(read-only memory，ROM)或可存储静态信息和指令的其它类型的静态存储设备，随机存取存储器(random access memory，RAM))或者可存储信息和指令的其它类型的动态存储设备，也可以是电可擦可编程只读存储器(Electrically Erasable Programmable Read-Only Memory，EEPROM)、只读光盘(Compact Disc Read-Only Memory，CD-ROM)或其它光盘存储、光碟存储(包括压缩光碟、激光碟、光碟、数字通用光碟、蓝光光碟等)、磁盘存储介质或者其它磁存储设备、或者能够用于携带或存储具有指令或数据结构形式的期望的程序代码并能够由计算机存取的任何其它介质，但不限于此。存储器103可以是独立存在，通过通信总线102与处理器101相连接。存储器103也可以和处理器101集成在一起。
通信接口104，使用任何收发器一类的装置，用于与其它设备或通信网络通信，如以太网，无线接入网(RAN)，无线局域网(Wireless Local Area Networks，WLAN)等。
在具体实现中，作为一种实施例，处理器101可以包括一个或多个CPU，例如图1中所示的CPU0和CPU1。
在具体实现中，作为一种实施例，计算机设备可以包括多个处理器，例如图1中所示的 处理器101和处理器105。这些处理器中的每一个可以是一个单核(single-CPU)处理器，也可以是一个多核(multi-CPU)处理器。这里的处理器可以指一个或多个设备、电路、和/或用于处理数据(例如计算机程序指令)的处理核。
在具体实现中，作为一种实施例，计算机设备还可以包括输出设备106和输入设备107。输出设备106和处理器101通信，可以以多种方式来显示信息。例如，输出设备106可以是液晶显示器(liquid crystal display，LCD),发光二级管(light emitting diode，LED)显示设备，阴极射线管(cathode ray tube，CRT)显示设备，或投影仪(projector)等。输入设备107和处理器101通信，可以以多种方式接收用户的输入。例如，输入设备107可以是鼠标、键盘、触摸屏设备或传感设备等。
上述的计算机设备可以是一个通用计算机设备或者是一个专用计算机设备。在具体实现中，计算机设备可以是台式机、便携式电脑、网络服务器、掌上电脑(Personal Digital Assistant，PDA)、移动手机、平板电脑、无线终端设备、通信设备或者嵌入式设备。本发明实施例不限定计算机设备的类型。
其中，存储器103用于存储执行本申请实施例中下述步骤201-204的程序代码108，并由处理器101来控制执行。处理器101用于执行存储器103中存储的程序代码108。程序代码108中可以包括一个或多个软件模块。
目前，在进行服务站选址时，通常根据多个候选站址以及建站条件建立整数线性规划模型，在建立整数线性规划模型之后，可以采用分支定界法或割平面法来求解该整数线性规划模型，从而得到选址结果。其中，整数线性规划模型是指决策变量的取值为整数值的线性规划问题。通常，整数线性规划模型可以包括目标函数和约束条件，其中，目标函数是指根据待优化的目标和影响该目标的变量所设计的函数。例如，在选址问题中，可以将服务站的建站成本作为待优化目标，并根据影响建站成本的变量设计得到目标函数，此时，该目标函数可以是用于表示该建站成本最小化的函数。另外，约束条件是指在求解目标函数的过程中所要满足的其他限制条件。例如，在整数线性规划模型的约束条件中包括关于决策变量的约束条件，该约束条件用于约束决策变量的取值为整数。
需要说明的是，当采用分支定界法来求解整数线性规划模型时，首先可以求解整数线性规划模型对应的线性规划模型的最优解，其中，该最优解中包括决策变量的最优取值和最优目标函数值。在确定最优解之后，可以将最优目标函数值作为整数线性规划模型中的目标函数的函数值的上界，并将该整数线性规划模型中的目标函数的任意可行解对应的函数值作为该目标函数的函数值的下界。之后，若最优解中的决策变量的最优值为整数值，则将该决策变量的最优值作为该整数线性规划模型的一个整数解，并根据最优解中包括的决策变量的最优取值将整数线性规划模型的决策变量的可行解区间划分为两部分。当然若最优解中的决策变量的最优值不为整数值，则说明该决策变量的最优值并非该整数线性规划模型的解，此时，可以根据上述的方法将该整数线性规划模型的决策变量的可行解区间划分为两部分。在将整数线性规划模型的决策变量的可行解区域划分为两部分之后，根据划分得到的两个可行解区域和前述确定的目标函数的上界和下界将整数线性规划模型转换为两个整数线性规划子模型，并采用前述方法对这两个整数线性规划子模型进行求解，得到每个子模型对应的线性规划模型的最优解。之后，重新根据最优解中包括的最优目标函数值确定目标函数的函数值的上界 和下界。其中，若某个子模型的最优解中的最优目标函数值小于目标函数的函数值的下界，则将该子模型这一分支进行剪枝，也即后续不再对这一子模型再进行处理。若某个子模型的最优解中的最优目标函数值大于目标函数的函数值的下界，则继续在该子模型的基础上进行分支。由此类推，通过不断分支，直到最终确定的最优解中的最优目标函数值等于前一次确定的目标函数的函数值的下界为止，将此时的最优目标函数值、对应的决策变量的最优取值作为该整数线性规划模型的最终求解结果。
下面以一个示例来对上述的分支定界法求解整数线性规划模型的过程进行说明。
假设整数线性规划模型如下：
目标函数：max Z＝40x 1+90x 2；
约束条件：9x 1+7x 2≤56；7x 1+20x 2≤70；x 1≥0；x 2≥0；x 1和x 2均为整数。
首先，可以不考虑约束条件中的整数限制，将该整数线性规划模型作为线性规划模型进行求解，从而得到最优解：x 1＝4.8029，x 2＝1.8168，Z＝355.8779。此时，可以将Z＝356作为目标函数的函数值的上界，另外，根据x 1≥0和x 2≥0可知，x 1＝x 2＝0也是该目标函数的一组可行解，将x 1＝x 2＝0时的目标函数值Z＝0作为该目标函数的函数值的下界。
在本示例中，决策变量有两个，可以任选其中一个决策变量进行分支。假设选取x 1，根据x 1＝4.8029可以将x 1的可行解的区间划分为两部分，分别为x 1≥5和x 1≤4。
根据上述确定的目标函数的上界和下界、划分得到的x 1两部分可行解区间，对整数线性规划模型进行转换，得到两个整数线性规划子模型，分别如下：
(1)、目标函数：max Z＝40x 1+90x 2；
约束条件：9x 1+7x 2≤56；7x 1+20x 2≤70；0≤x 1≤4；x 2≥0；x 1和x 2均为整数。
(2)目标函数：max Z＝40x 1+90x 2；
约束条件：9x 1+7x 2≤56；7x 1+20x 2≤70；x 1≥5；x 2≥0；x 1和x 2均为整数。
在得到上述两个整数线性规划子模型之后，对于每一个子模型，均参照前述对整数线性规划模型的处理过程，求解每个子模型对应的线性规划模型，分别得到子模型(1)对应的线性规划模型的最优解为：x 1＝4，x 2＝2.1，Z＝349。子模型(2)对应的线性规划模型的最优解为：x 1＝5，x 2＝1.57，Z＝341.4。其中，由于两个最优解中最优目标函数值的最大值为349，所以将目标函数的函数值的上界更新为349。另外，由于另一个最优解中的决策变量的取值不符合整数条件，因此，保持目标函数的函数值的下界不变，也即，仍为0。这样，重新得到目标函数的函数值范围为：0≤Z≤349。由于子模型(1)和(2)对应的最优解中的最优目标函数值均大于目标函数的函数值下界，且不大于目标函数的函数值的上界，因此，将子模型(1)和(2)再次根据前述方法进行分支，从而得到子模型(1)对应的两个子模型，子模型(2)对应的两个子模型。以此类推，本申请实施例不再赘述。
由此可见，在通过分支定界法对整数线性规划模型进行求解时，需要将整数线性规划问题划分为子问题，再将子问题不断的一层一层继续划分。这对于选址场景下涉及的候选站址数量较少时的小规模的规划问题可以适用，但是对于涉及的候选站址数量较大时的大规模选址问题，则很难在有限的时间内求解得到选址结果。
同样的，根据割平面法求解整数线性规划模型也存在同样的问题。基于此，本申请实施例提供了一种选址方法，在该种选址方法中，可以首先通过求解由整数线性规划模型转化得到的线性规划模型来得到一部分选址结果，之后，根据这部分选址结果对之前基于多个候选 站址的选址问题进行降维，之后，通过图论算法来求解降维后的选址问题，这样，即使候选站址的数量较大，通过本申请提供的方法也可以在有限的时间内快速得到选址结果，解决了相关技术中直接采用分支定界法或割平面法求解整数线性规划模型时，无法在有限时间内得到选址结果的问题。
接下来结合附图2对本申请实施例提供的选址方法进行详细的解释说明。
图2是本申请实施例提供的一种选址方法的流程图，该方法可以应用于计算机设备中，如图2所示，该方法包括以下步骤：
步骤201：对整数线性规划模型进行预处理，得到线性规划模型，该整数线性规划模型是根据多个候选站址、多个待服务对象和多个建站条件建立的模型。
其中，多个候选站址是指待选的站址，本申请提供的选址方法即用于从该多个候选站址中选择出要建设服务站的站址。需要说明的是，该多个候选站址可以根据所要规划的服务网络所在的区域内的地形、地貌、已有服务站的分布情况等地理信息数据，通过计算机模拟得到。或者，在一种可能的实现方式中，该多个候选站址也可以根据所要规划的服务网络内的已经存在的一些特定位置确定得到。例如，在进行5G基站的选址时，可以将现有的4G基站的位置作为候选站址。
多个待服务对象是指所要规划的服务网络所在的区域内等待服务站服务的对象。其中，该多个待服务对象可以是多个用户，也可以是将所要规划的服务网络所在的区域进行栅格化后得到的多个位置。
另外，多个建站条件是指根据待规划的服务网络的业务需求确定的选址过程中所要满足的限制条件。例如，该多个建站条件可以包括：任意两个距离小于第一阈值的候选站址上不能同时建站、建站总成本小于第二阈值、一个候选站址上建设一种类型的服务站、在被选站址建设服务站后所服务的待服务对象的数量不小于第三阈值等等。本申请实施例不对建站条件进行限定。
在本申请实施例中，在执行本步骤之前，首先可以根据待规划的服务网络的业务需求确定优化目标。其中，优化目标可以包括根据被选站址进行建站时所服务的待服务对象的数量、根据被选站址进行建站时所服务的区域的面积，或者根据被选站址进行建站时的服务质量、根据被选站址进行建站时的建站成本等。需要说明的是，在本申请实施例中，优化目标可以为一个，也可以为多个。
在确定优化目标之后，可以根据该优化目标以及多个候选站址和/或多个待服务对象建立目标函数。例如，当优化目标为根据被选站址进行建站时对待服务对象的服务质量时，根据该优化目标、多个候选站址和多个待服务对象建立的目标函数即可以为使服务站所服务的待服务对象的数量最大化的函数。再例如，当优化目标为根据被选站址进行建站时的建站成本时，则根据该优化目标、多个候选站址和多个待服务对象确定的目标函数可以是使建站成本最小化的函数。
由上述示例可以看出，在一些可能的情况中，根据优化目标确定的目标函数就可以表征多个建站条件中的某些建站条件，在这种情况下，在确定目标函数之后，可以将多个建站条件中与目标函数所表征的建站条件重复的建站条件去除，并根据剩余的建站条件、多个候选站址和多个待服务对象来建立约束条件，从而得到包含有目标函数和约束条件的整数线性规 划模型。其中，由于整数线性规划模型的变量的允许取值为整数值，因此，在整数线性规划模型的约束条件中还可以包括用于限制模型中的变量的允许取值为整数的条件。
示例性地，假设优化目标为根据被选站址进行建站时所服务的待服务对象的服务质量，多个建站条件包括任意两个距离小于第一阈值的候选站址上不能同时建站、建站总成本小于第二阈值、一个候选站址上建设一种类型的服务站，则根据该优化目标、多个候选站址、多个待服务对象和多个建站条件建立的整数线性规划模型如下：
目标函数：
Figure PCTCN2020088376-appb-000001
约束条件：
Figure PCTCN2020088376-appb-000002
(j,j')∈V，x j,k∈{0,1}，y i∈{0,1}；
其中，N是指待服务对象的数量，w i是指多个待服务对象中的待服务对象i的服务权重系数。y i是中间变量，用于指示被服务的对象中是否包括待服务对象i。其中，y i的取值为0或1，当y i的取值为0时，表示被服务的对象中不包括待服务对象i，也即待服务对象i未被服务；当y i的取值为1时，表示被服务的对象中包括待服务对象i，也即待服务对象i被服务。K是指在每个候选站址上建站时待选服务站类型的数量，也即是，存在K个服务站类型，在一个站址上建设服务站时，该服务站的类型可以该K个类型中的一个。M是指候选站址的数量，r i,j,k用于指示在候选站址j上建设的第k个类型的服务站是否服务待服务对象i，x j,k是决策变量，用于指示是否在候选站址j上建设第k个类型的服务站，其中，x j,k的取值为0或1，当x j,k的取值为1时，表示候选站址j为被选站址，且在候选站址上建设的服务站的类型为第k个类型。当x j,k的取值为0时，表示不在候选站址j上建设第k个类型。c j,k是指在候选站址j上建设第k个类型的服务站的成本，C是指第二阈值，V是指候选站址对集合，其中，V包括多个候选站址对，每个候选站址对包括的两个候选站址之间的距离小于第一阈值。
另外，对于整数线性规划模型中的变量取值为整数值的约束，可以通过约束条件中x j,k∈{0,1}，y i∈{0,1}这两个条件来实现。
需要说明的是，服务权重系数w i可以是根据待服务对象i与候选站址之间距离确定得到。示例性地，可以将待服务对象i与候选站址之间的距离的倒数作为服务权重系数。或者，当待服务对象是将某个区域进行栅格化后每个栅格的位置时，该服务权重系数可以根据每个栅格内包含的用户数量来确定。本申请实施例在此不对服务权重系数做限定。
示例性地，假设优化目标为根据被选站址进行建站时的建站成本，多个建站条件包括任意两个距离小于第一阈值的候选站址上不能同时建站、一个候选站址上建设一种类型的服务站、在被选站址建设服务站后对待服务对象的服务质量不小于第三阈值，则根据该优化目标、多个候选站址、多个待服务对象和多个建站条件建立的整数线性规划模型如下：
目标函数：
Figure PCTCN2020088376-appb-000003
约束条件：
Figure PCTCN2020088376-appb-000004
x j，k∈{0，1}，y i∈{0，1}；
其中，W是指第三阈值。另外，上述目标函数和约束条件中其余参数的相关含义可以参 考前述相关说明，本申请实施例在此不再赘述。
在建立整数线性规划模型之后，可以对该整数线性规划模型进行预处理，从而得到线性规划模型。由于与整数线性规划模型相比，线性规划模型的求解更容易且业界技术比较成熟，因此，在本申请实施例中，可以通过一些松弛方法来对整数线性规划模型进行一定的预处理，从而将其转换为线性规划模型。
由前文中的介绍可知，整数线性规划模型的约束条件中包括用于约束模型中的变量的允许取值为整数的条件。而线性规划模型中变量的允许取值可以为整数值也可以为小数值。基于此，在对整数线性规划模型进行预处理，以得到线性规划模型时，可以首先对整数线性规划模型中用于约束变量的允许取值为整数的条件进行松弛。
示例性地，当整数线性规划模型中包括中间变量和决策变量时，该整数线性规划模型的约束条件中可以包括用于约束决策变量的取值为整数值的第一整数集，以及用于约束中间变量的取值为整数值的第二整数集。在这种情况下，可以将第一整数集转换为第一取值范围，将第二整数集转换为第二取值范围，其中，第一取值范围和第二取值范围均为连续的取值范围，且第一取值范围包含有第一整数集内的所有整数，第二取值范围包含有第二整数集内的所有整数。也就是说，本申请实施例可以将整数线性规划模型中的变量的离散的取值范围转换为连续的取值范围。
需要说明的是，在转换的过程中，对于每个整数集，可以将该整数集中的最小值作为转换后的取值范围的下限值，将该整数集中的最大值作为转换后的取值范围的上限值。
例如，以前述所示出的两个整数线性规划为例，其中，用于约束决策变量的允许取值的第一整数集和用于约束中间变量的允许取值的第二整数集均为{0,1}，也即，决策变量和中间变量的允许取值为0或1。在这种情况下，可以将0作为转换后的取值范围的下限值，将1作为转换后的取值范围的上限值。由此可见，根据上述决策变量和中间变量的离散的取值范围转换得到的连续的取值范围为[0,1]。
在对整数线性规划模型中变量的允许取值进行转换之后，还可以对整数线性规划模型中的其他参数进行松弛。
示例性地，整数线性规划模型中可以包括第一参数，为了后续便于说明，将该第一参数用K来表示。该第一参数用于指示在每个候选站址上建站时待选服务站类型的数量。也就是说，在任一个候选站址上建设服务站时，将有K个待选服务站类型供选择。并且，考虑到通常一个站址上要求建设一个类型的服务站，因此，可以从K个待选服务站类型选择一个类型进行建站。基于此，当整数线性规划模型中包含有第一参数时，可以将在每个候选站址上建站时的K个待选服务站类型转换为在相同位置上的K个不同候选站址。
例如，仍以前述提供的两种整数线性规划模型为例来进行说明。将整数线性规划模型中在每个候选站址上建站时的K个待选服务站类型转换为在相同位置上的K个不同候选站址，这样，由于原本有M个候选站址，因此，通过转换后可以得到有(M*K)个候选站址。这样，对于第一个整数线性规划模型，约束条件中涉及到第一参数的条件均可以按照上述方法进行转换。其中，
Figure PCTCN2020088376-appb-000005
这一条件可以转换为
Figure PCTCN2020088376-appb-000006
这一条件可以转换为
Figure PCTCN2020088376-appb-000007
这一条件可以删除，
Figure PCTCN2020088376-appb-000008
这一条件可以转换为∑x j+∑x j'≤1(j,j')∈V。
同理，对于第二整数线性规划模型，目标函数和约束条件中涉及到第一参数的条件也均可以进行转换，本申请实施例在此不再赘述。
可选地，由前文对建站条件以及整数线性规划模型的约束条件的介绍可知，考虑到建站成本、业务需求等因素，整数线性规划模型中还可以包括第一约束，该第一约束包括第一候选站址集合，第一候选站址集合中包括至少一个候选站址对，每个候选站址对包括的两个候选站址之间的距离小于第一阈值，且每个候选站址对中的两个候选站址中仅有一个候选站址可作为被选站址的条件。由此可见，通过第一约束可以限制任意两个被选站址之间的距离不小于第一阈值。基于此，在本申请实施例中，还可以对整数线性规划模型中的这一约束进行松弛。示例性地，可以将第一约束中的第一候选站址集合转换为第二候选站址集合。其中，该第二候选站址集合中包括至少两个候选站址，且至少两个候选站址中的任意两个候选站址之间的距离均小于第一阈值。也即是，当第一约束中包括第一候选站址集合时，通过第一约束可以限制第一候选站址集合中的每个候选站址对中可以有一个候选站址作为被选站址，但是属于不同的候选站址对的候选站址之间并无限制。这样，当第一候选站址集合中包括的候选站址对有多个时，可能有属于不同候选站址对的多个候选站址可以作为被选站址。而将第一候选站址集合转换为第二候选站址集合之后，由于第二候选站址集合中不包括候选站址对，而是包括至少两个候选站址，且任意两个候选站址之间的距离均小于第一阈值，因此，通过转换后的第一约束可以限制第二候选站址集合中的至少两个候选站址中可以有一个候选站址作为被选站址，也即是，无论第二候选站址集合中有多少个候选站址，通过第一约束的限制，第二候选站址中将最多有一个候选站址可以作为被选站址。
仍以前述提供的两个整数线性规划模型为例来进行示例说明。在前述两个整数线性规划模型中，约束条件中的
Figure PCTCN2020088376-appb-000009
(j,j')∈V这一约束即是第一约束。其中，V为第一候选站址集合，(j,j')为一个候选站址对，将第一候选站址集合V转换为第二候选站址集合U，由于第二候选站址集合中将最多有一个候选站址可以作为被选站址，因此，第一约束中的
Figure PCTCN2020088376-appb-000010
可以被转换为
Figure PCTCN2020088376-appb-000011
需要说明的是，在未对第一候选站址集合进行转换时，根据第一约束，在求解线性规划模型时，由于仅仅需要一个候选站址对中的两个候选站址满足
Figure PCTCN2020088376-appb-000012
这一条件即可，因此，假设一个候选站址对中的两个候选站址对应的决策变量的取值均为0.5，则这两个候选站址是满足上述条件的，因此，这两个候选站址对应的决策变量的取值将被作为求解结果的一部分输出，也即，这两个小数值将被输出。而如果将第一候选站址集合转换为第二候选站址集合，由于第二候选站址集合中所有候选站址对应的决策变量需满足
Figure PCTCN2020088376-appb-000013
这一条件。因此，假设此时第二候选站址集合中有三个候选站址对应的决策变量的取值均为0.5，则根据上述条件，第二候选站址集合中这三个候选站址对应的决策变量无法满足上述条件，此时，这三个小数值将均无法作为线性规划模型的求解结果的一部分输出。由此可见，通过将第一候选站址集合转换为第二候选站址集合，可以减少线性规划模型最终输出的求解结果中包括的小数值。由于线性规划模型的求解结果中的小数值不满足整数线性规划的变量的取值要求，不能用来判断候选站址是否被选，因此，通过这一处理减少线性规划模型最终输出的求解结果中包括的小数值，相当于减少了无用解的数量。
通过上述提供的预处理方法，可以对整数线性规划模型进行预处理，从而得到线性规划 模型。需要说明的是，在对整数线性规划模型进行预处理时，首先可以通过上述方法对整数线性规划模型的变量的允许取值进行处理。在对整数线性规划模型的变量的允许取值进行处理之后，如果该整数线性规划模型中还包括第一参数和第一约束，则还可以通过上述提供的方法继续对第一参数和第一约束中的任一个进行处理。当然，也可以对其全部进行处理，本申请实施例对此不作限定。
以前述提供的两个整数线性规划模型为例，当依次对该整数线性规划模型的变量的允许取值、第一参数和第一约束进行处理之后，得到的线性规划模型分别如下：
(1)、目标函数：
Figure PCTCN2020088376-appb-000014
约束条件：
Figure PCTCN2020088376-appb-000015
0≤x j≤1，0≤y i≤1；
其中，U为第二候选站址集合。
(2)、目标函数：
Figure PCTCN2020088376-appb-000016
约束条件：
Figure PCTCN2020088376-appb-000017
0≤x j≤1，0≤y i≤1。
步骤202：将线性规划模型的多个参数的参数值输入该线性规划模型。
在根据多个候选站址和多个待服务对象建立的整数线性规划模型中，目标函数和约束条件不仅包括中间变量和决策变量，还包括多个参数。基于此，在对整数线性规划模型进行预处理得到线性规划模型之后，可以输入该多个参数的参数值，以便后续对该线性规划模型进行求解，以得到选址结果。
其中，该多个参数的参数值可以包括多个候选站址和多个待服务对象之间的覆盖关系数据、多个待服务对象中每个待服务对象的权重数据、第一参数的参数值以及建设每个服务站的建站成本等。
需要说明的是，多个候选站址和多个待服务对象之间的覆盖关系数据可以是预先通过一定系统仿真工具确定或者通过数据挖掘技术确定得到，且该覆盖关系数据主要可以包括用于指示在任一候选站址上建设服务站时，该多个待服务对象是否被服务的数据。例如，当前有10个候选站址和100个待服务对象，则该覆盖关系数据中可以包括用于指示在候选站址1上建设服务站时，100个待服务对象中每个待服务对象是否被服务的数据，在候选站址2上建设服务站时，100个带服务对象中的每个待服务对象是否被服务的数据，以此类推。
以步骤201中介绍的两个整数线性规划模型转换得到线性规划模型为例，输入的多个候选站址和多个待服务对象之间的覆盖关系数据即可以作为参数r i,j的参数值，输入的多个待服务对象中每个待服务对象的权重数据可以作为w i的参数值，输入的第一参数的参数值可以作为参数K的参数值，输入的建设每个服务站的建站成本则可以作为c j的参数值。
步骤203：根据线性规划模型输出的决策变量的取值中的整数值确定第一选址结果和第二选址结果。
在将多个参数的参数值输入值线性规划模型之后，可以对该线性规划模型进行求解，从而得到求解结果。其中，该求解结果包括决策变量的取值。除此之外，该求解结果中还可以包括中间变量的取值。
需要说明的是，由于线性规划模型的变量的取值可以为整数值也可以为小数值，而整数线性规划模型的变量的取值要求为整数值，因此，在得到线性规划模型的求解结果之后，该求解结果中决策变量为整数值的结果即可以近似的作为整数线性规划模型的求解结果，也即，可以作为选址结果。而剩余决策变量为小数值的结果由于不满足整数线性规划模型的变量的取值条件，所以不可以作为对应的整数线性规划模型的求解结果。基于此，在得到线性规划模型的求解结果后，可以根据该求解结果中决策变量为整数值的结果确定第一选址结果和第二选址结果。
示例性地，当求解结果中包括决策变量的取值，不包括中间变量的取值时，可以将该求解结果中决策变量为整数值的结果筛选出来。之后，根据筛选出来的结果中决策变量的取值为第一数值的结果确定第一选址结果，其中，第一数值是指用于指示决策变量所对应的候选站址为被选站址的数值。
需要说明的是，由于每个决策变量的取值均可以用于指示一个候选站址是否可以作为被选站址，当决策变量的取值为第一数值时，即可以确定该决策变量所代表的候选站址可以作为被选站址。基于此，可以从筛选出来的决策变量的取值为整数值的结果中获取决策变量的取值为第一数值的结果，并获取这部分结果中的所有决策变量对应的候选站址，从而得到第一选址结果。此时，第一选址结果中包括的站址即为确定的该多个候选站址中可以作为被选站址的站址。
对于筛选出来的结果中剩余的结果，由于剩余结果中的决策变量的取值虽然为整数值，但是不为第一数值，因此，可以确定剩余结果中的决策变量所代表的候选站址将不被作为被选站址，也即，剩余结果中的决策变量代表的候选站址为不被选的站址。基于此，可以根据剩余结果中的决策变量获取对应的候选站址，并将获取到的站址作为第二选址结果。此时，第二选址结果中包括的站址即为多个候选站址中不被选的站址。
可选地，虽然线性规划模型的求解结果中的整数值可以近似的作为整数线性规划模型的求解结果，但是二者之间可能还是存在一定的误差。基于此，为了提高选址结果的最优性，在将线性规划模型的求解结果中决策变量为第一数值的结果筛选出来之后，还可以判断每个筛选出来的决策变量对应的候选站址是否为第一候选站址集合中包括的候选站址。对于任一个筛选出来的决策变量，若该决策变量对应的候选站址不为第一候选站址集合也不为第二候选站址集合包括的候选站址，则可以将该决策变量对应的候选站址作为被选站址，将确定的多个被选站址作为第一选址结果。若该决策变量对应的候选站址为第一候选站址集合或第二候选站址集合包括的候选站址，则可以将该决策变量对应的候选站址作为不被选站址。另外，对于求解结果中决策变量为整数值但不为第一数值的结果，这些结果对应的候选站址也可以作为不被选站址，将确定的多个不被选站址作为第二选址结果。
可选地，当求解结果中不仅包括决策变量的取值，还包括用于指示每个待服务对象是否被服务的中间变量的取值时，一方面，可以从该求解结果中筛选出决策变量的取值为整数值得结果，另一方面，还可以从该求解结果中筛选出中间变量的取值为整数值的结果。之后，可以根据筛选出来的结果中决策变量的取值为第一数值的结果确定被选站址，并根据筛选出来的结果中中间变量的取值为第二数值的结果确定被服务的待服务对象。之后，将确定的被选站址和被服务的待服务对象作为第一选址结果。根据筛选出来的结果中决策变量的取值不为第一数值的结果确定不被选的站址，并根据筛选出来的结果中中间变量的取值不为第二数 值的结果确定不被服务的待服务对象，将确定的不被选站址和不被服务的待服务对象作为第二选址结果。其中，当中间变量的取值为第二数值时，表示中间变量所代表的待服务对象被服务。
通过将整数线性规划模型转换为线性规划模型，并对线性规划模型进行求解，可以初步判断出多个候选站址中的一部分站址是否可以作为被选站址。而对于线性规划模型输出的决策变量的取值为小数值的结果，则无法根据小数值判断对应的决策变量所代表的候选站址是否可以作为被选站址。基于此，接下来可以通过步骤204对来判断这部分取值为小数值的决策变量所代表的候选站址中哪些站址可以作为被选站址。
步骤204：从多个候选站址中除第一选址结果和第二选址结果之外的剩余候选站址中确定被选站址。
在通过线性规划模型的求解结果确定出第一选址结果和第二选址结果之后，可以将多个候选站址中第一选址结果包括的站址、第二选址结果包括的站址以及与第一选址结果中包括的被选站址不能同时建站的站址进行删除；将多个待服务对象中第一选址结果包括的站址所服务的待服务对象进行删除；根据删除后剩余的候选站址和删除后剩余的待服务对象，确定删除后剩余的候选站址中的被选站址。
需要说明的是，由前文所述可知，第一选址结果中包括被选站址，第二选址结果中包括不被选站址，也即，多个候选站址中包括在第一选址结果和第二选址结果中的站址已经可以明确确定是否被选，因此，可以首先将多个候选站址中包括在第一选址结果和第二选址结果中的站址进行删除。除此之外，根据建站条件，多个候选站址中除第一选址结果和第二选址结果包括的站址之外的其他候选站址中还可能包括与第一选址结果中的站址不能同时建站的站址，由于第一选址结果中的站址已经确定被选，因此，这些不能与第一选址结果中的站址同时建站的候选站址显然将无法作为被选站址，因此，可以将这部分候选站址也进行删除，从而得到剩余候选站址。
另外，第一选址结果包含了从多个候选站址中确定出来的一部分被选站址，这部分被选站址将会对多个待服务对象中的部分待服务对象进行服务。换句话说，这部分被选站址将会对应的服务多个待服务对象中的部分对象。基于此，为了这些已经被服务的对象不被重复服务，可以将多个待服务对象中已经被服务的这部分对象删除，从而得到剩余的待服务对象。
其中，在删除多个待服务对象中已经被服务的对象之前，首先可以根据第一选址结果来确定多个待服务对象中哪些对象是已经被服务的对象。需要说明的是，根据步骤203的介绍可知，第一选址结果中可能包含有被服务对象，也可能不包含。在这种情况下，根据第一选址结果包含内容的不同，可以通过不同方式来确定多个待服务对象中的哪些待服务对象为已经被服务的对象。
示例性地，如果第一选址结果中包含有被选站址，不包含有被服务对象，则可以根据第一选址结果中包含的被选站址，通过计算机模拟来确定在第一选址结果包含的被选站址上建站时，多个待服务对象中的哪些待服务对象将被服务，也即确定多个待服务对象中的被服务对象。
可选地，如果第一选址结果中不仅包含有被选站址，还包含有被服务对象，则可以直接从第一选址结果中获取被服务对象，并将获取的被服务对象确定为在第一选址结果包括的站址上建设服务站时所服务的对象，也即，该多个待服务对象中已经被服务的对象。
可选地，在一种可能的情况中，如前文所述，第二选址结果中不仅可以包含有不被选站址，还可以包含有不被服务的对象，在这种情况下，可以直接从第二选址结果中获取不被服务的对象，这些不被服务的对象即可以直接作为多个待服务对象中除被服务对象之外的剩余服务对象。也即是，不必再执行从多个待服务对象中删除第一选址结果包括的站址所服务的待服务对象的步骤，而是可以直接从第二选址结果获取剩余的待服务对象。
在通过上述处理后，候选站址的数量和待服务对象的数量均会减少。由于候选站址和待服务对象的数量减少，因此，当接下来继续根据剩余的待服务对象从剩余的候选站址中确定被选站址时，相当于是对之前的选址问题进行降维后的选址问题进行求解。这样，相对于直接通过求解整数线性规划模型来得到被选站址，不仅降低了选址的难度，而且可以缩短选址所需的时间。
在确定剩余的候选站址和剩余的待服务对象之后，可以根据剩余的候选站址和剩余的待服务对象确定图论选址图。其中，该图论选址图中包括多个节点，每个节点用于指示删除后剩余的候选站址中的一个候选站址，多个节点中两个不能同时建站的候选站址对应的两个节点之间具有连边；根据图论选址图确定删除后剩余的候选站址中的被选站址。
需要说明的是，在根据剩余的候选站址和剩余的待服务对象确定图论选址图时，每个候选站址可以作为一个节点，且任意两个不能同时建站的候选站址所对应的两个节点之间具有连边。其中，不能同时建站的两个候选站址可以是指彼此之间的距离小于第一阈值的两个候选站址。当然，也可能是根据其他业务需求确定的不能同时建站的候选站址。
除此之外，每个节点还可以对应有第一权重和第二权重。其中，第一权重是指在相应节点所指示的候选站址上建设服务站后对剩余的待服务对象的服务能力。所谓对待服务对象的服务能力，可以是指覆盖的待服务对象的总数量，也可以是指对待服务对象的服务质量等，并且，可以通过待服务对象的服务权重系数来表征对待服务对象的服务能力。例如，在前述提供的两个整数线性规划模型中，均是通过每个待服务对象对应的服务权重系数来表征对相应待服务对象的服务能力，在这种情况下，即可以将在相应站址上建站时待服务对象对应的服务权重系数的总和作为第一权重。另外，第二权重是指在相应节点所指示的候选站址上建设服务站的建站成本。
图3是本申请实施例中示出的一种图论选址图的示例。如图3中所示，节点V 1用于表征候选站址1，节点V 2用于表征候选站址2，以此类推。其中节点V 1和节点V 2、V 5和V 6之间具有连边，说明候选站址1和候选站址2不能同时建站，候选站址1和候选站址5不能同时建站，候选站址1和候选站址6也不能同时建站。对于其他具有连边的两个节点，具有同样的含义。另外，每个节点对应有第一权重W i和C i，其中，W i是指在第i个节点所指示的候选站址i上建站时，剩余的待服务对象对应的服务权重系数总和，C i则是指在候选站址i上建站时的建站成本。
在确定图论选址图之后，可以通过图4所示的步骤来根据该图论选址图确定删除后剩余的候选站址中的被选站址。
2041：根据每个节点对应的第一权重和第二权重，从多个节点中选择目标节点。
其中，如前所述，第一权重用于指示对剩余待服务对象的服务能力，第二权重是指在相应站址上建站时的建站成本。考虑到建站成本越低，对剩余待服务对象的服务能力越高，则越符合业务需求。因此，在从多个节点中选择目标节点时，可以根据上述原则从多个节点中 选择最符合业务需求的节点。基于此，可以确定每个节点对应的第一权重和第二权重之间的比值，比值越大，则说明在相应节点所指示的站址上建站的性价比越高，即相应节点的越符合业务需求。从多个节点中选择对应的第一权重和第二权重之间的比值最大的节点作为目标节点，该节点即为多个节点中最符合业务需求的节点。
2042：判断是否将目标节点所指示的候选站址确定为被选站址。
在确定目标节点之后，可以根据目标节点和图论选址图，确定第一选址问题，通过动态规划算法将第一选址问题进行L层分割，L小于第一选址问题允许被分割的最大层数；确定分割得到的多个子问题的运算结果，根据多个子问题的运算结果确定第一选址问题的运算结果；根据第一选址问题的运算结果判断是否将目标节点所指示的候选站址作为被选站址。
其中，在确定目标节点之后，根据目标节点、图论选址图以及在建立整数线性规划模型时所确定的待优化目标或者是整数线性规划模型的目标函数，可以确定第一选址问题，该第一选址问题是用于确定目标节点是否作为被选站址的问题。在这种情况下，求解第一选址问题的最优解也即是在确定目标节点所指示的站址作为被选站址时的解和不作为被选站址时的解中的最优值。
例如，以前述提供的第一个整数线性规划模型为例，根据其目标函数可知，其所要达到的目标是使对待服务对象的服务能力最大化，另外，根据建站条件可知，其要求建站成本不大于第二阈值。换句话说，第一个整数线性规划模型要求在建站成本不超过第二阈值的前提下，对待服务对象的服务能力最大化。在此基础上，根据图论选址图，可以确定第一选址问题为S＝(G,C)，其中G是指当前的图论选址图，C是指第二阈值。假设该第一选址问题的最优解为opt(G,C)，则该最优解
Figure PCTCN2020088376-appb-000018
Figure PCTCN2020088376-appb-000019
是指假设目标节点所指示的站址被选之后对应的选址问题的最优解，
Figure PCTCN2020088376-appb-000020
是指假设目标节点所指示的站址被选之后更新的图论选址图，
Figure PCTCN2020088376-appb-000021
是指假设目标节点所指示的站址不被选之后对应的选址问题的最优解，
Figure PCTCN2020088376-appb-000022
是指假设目标节点所指示的站址不被选之后更新的图论选址图。由此可见，当上述两个假设问题的最优解确定之后，即可以得到第一选址问题的最优解。换句话说，第一选址问题的最优解可以通过将第一选址问题分为两个子问题，求解这两个子问题的最优解来确定得到。
基于上述描述，在确定第一选址问题之后，首先可以假设目标节点所指示的候选站址被选，基于该假设，将图论选址图中的目标节点删除。由于与目标节点具有连边的节点所指示的候选站址不能与目标节点所指示的站址同时建站，因此，在假设目标节点所指示的站址可以作为被选站址的情况下，与目标节点具有连边的节点所指示的候选站址将不会被作为被选站址，因此可以将这些节点删除。另外，由于目标节点所指示的站址将作为被选站址，因此，在该目标节点所指示的站址建站时将会对剩余服务对象中的部分服务对象进行服务。基于此，在删除节点之后，还可以将剩余节点中每个节点所对应的第一权重中包含的被目标节点所指示的站址所服务的待服务对象的权重减去，从而得到新的图论选址图。根据得到的新的图论选址图可以确定得到一个新的选址问题。此时，这个新的选址问题实际上就是在假设目标节点所指示的站址被选的情况下的选址问题。
之后，假设目标节点所指示的候选站址不被选。由于目标节点所指示的站址不被选，因此，与该目标节点具有连边的其他节点所指示的候选站址将还存在被选的可能，因此，可以将与该目标节点具有连边的其他节点与该目标节点之间的连边删除，从而得到新的图论选址 图。根据该图论选址图同样可以确定一个新的选址问题。此时，这个新的选址问题实际上就是在假设目标节点所指示的站址不被选的情况下的选址问题。
由此可见，通过上述方法可以将第一选址问题进行一层划分，得到两个新的子问题，对这两个子问题进行求解，根据这两个子问题的最优解即可以确定得到第一选址问题的最优解。而在求解这两个子问题时，对于每个子问题，可以从每个子问题对应的图论选址图中选择一个节点，并参照前述根据目标节点对第一选址问题的划分方法，根据选择的节点，对这两个子问题分别再次进行划分，得到四个子问题，从而完成第二层的划分。以此类推，直到假设某个节点指示的候选站址被选之后，新的图论选址图中不包括子节点或者是总的建站成本为0为止。对最终分割得到的多个子问题进行求解。根据每个子问题的求解结果，按照与分割过程相逆的过程，根据最底层的多个子问题的求解结果，逐层确定每一层中的子问题的求解结果，直到最终得到第一选址问题的最优解为止。当第一选址问题的最优解等于目标节点所指示的站址被选所对应的子问题的最优解时，则可以将该目标节点所指示的站址作为被选站址。当第一选址问题的最优解等于目标节点所指示的站址不被选所对应的子问题的最优解时，则可以将该目标节点所指示的站址作为不被选的站址。
需要说明的是，在进行第二层分割时，当从每个子问题对应的图论选址图中选择一个节点时，可以根据目标节点来选择，也可以根据节点的第一权重来选择。其中，当根据目标借点来选择时，可以选择与目标节点具有连边的节点，或者选择所服务的待服务对象中包含有目标节点所服务的待服务对象的节点。当根据节点的第一权重来选择时，则可以选择第一权重最大的节点。同理，在进行后续每一层的分割时，在从某个子问题对应的图论选址图中选择节点时，也同样可以参考上述介绍的方法，根据该子问题所对应的节点来选择节点，或者根据剩余节点的第一权重来选择，本申请实施例在此不再赘述。
需要说明的是，在通过上述方法对第一选址问题进行分割时，将上述分割截止条件下的第一选址问题被分割的层数作为第一选址问题允许被分割的最大层数。若将第一选址问题按照允许被分割的最大层数进行分割，计算量可能较大。基于此，为了减少计算量，也可以进行L层分割之后即停止，其中，L小于该第一选址问题允许被分割的最大层数。这样，在进行L层分割，得到2 L个子问题之后，可以采用贪婪算法来对2 L个子问题进行求解。在得到这些子问题的求解结果之后，同样可以按照分割的逆过程，逆向向上确定得到第一选址问题的最优解，进而根据第一选址问题的最优解确定该目标节点所指示的候选站址是否被选。
若通过上述方法确定目标节点所指示的候选站址可以作为被选站址，则接下来可以执行步骤2043，若确定目标节点所指示的候选站址不能作为被选站址，则接下来可以执行步骤2044。
2043：如果将目标节点所指示的候选站址确定为被选站址，则将删除后剩余的候选站址中确定的被选站址以及与确定的被选站址不能同时建站的站址删除，将删除后剩余的待服务对象中确定的被选站址所服务的待服务对象删除。
在将目标节点所指示的候选站址确定为被选站址之后，可以将该目标节点所指示的候选站址从之前剩余的候选站址中删除。另外，对于剩余的候选站址中不能与该目标节点所指示的候选站址同时建站的站址，由于已经确定该目标节点所指示的候选站址为被选站址，因此，可以将这部分不能与其同时建站的站址也删除。除此之外，由于在目标节点所指示的站址上建设服务站之后，该服务站将会对剩余的待服务对象中部分对象进行服务。因此，可以将这 部分由该目标节点所指示的站址所服务的对象从剩余的待服务对象中删除。
2044：如果将目标节点所指示的候选站址确定为不被选站址，则将删除后剩余的候选站址中确定的不被选站址进行删除。
在将目标节点所指示的候选站址确定为不被选站址之后，可以将该目标节点所指示的候选站址从剩余的候选站址中删除。由于该目标节点所指示的候选站址不被选，所以，与该目标节点所指示的候选站址不能同时建站的其他候选站址还存在被选的可能，因此，不需要对这部分候选站址进行删除。另外，由于该目标节点所指示的候选站址不被选，因此，该目标节点所指示的站址将无法对任何待服务对象进行服务，因此，之前的剩余的待服务对象也不需要进行更新。
2045：判断再次删除后是否还存在剩余的候选站址。
在通过步骤2043对剩余的候选站址中目标节点所指示的候选站址、以及与目标节点所指示的候选站址不能同时建站的候选站址进行删除之后，或者，在通过步骤2044对剩余的候选站址中目标节点所指示的候选站址进行删除之后，可以判断再次删除后是否还存在剩余的候选站址。如果还存在剩余的候选站址，则接下来可以继续通过步骤2046来确定剩余的候选站址中的被选站址。当然，如果再次删除后不存在剩余的候选站址，则可以说明对于所有的候选站址，均已确定出其是否可以作为被选站址。此时，可以将之前确定的所有被选站址作为最终的选址结果，并结束操作。
2046：若再次删除后还存在剩余的候选站址，则根据再次删除后剩余的候选站址对图论选址图进行更新，并返回步骤2041。
如果再次删除后还存在剩余的候选站址，则可以继续从再次删除后剩余的候选站址中确定被选站址。
需要说明的是，当通过步骤2043对剩余的候选站址进行了删除，并对剩余的待服务对象进行了删除，则在本步骤中，可以根据再次删除后剩余的候选站址和再次删除后剩余的待服务对象重新确定图论选址图，并利用重新确定的图论选址图对之前的图论选址图进行更新，之后，可以返回步骤2041，继续通过前述介绍的方法根据该更新后的图论选址图，从再次删除后剩余的候选站址中确定被选站址。
可选地，如果通过步骤2044对剩余的候选站址进行了删除，由于剩余的待服务对象并没有发生变化，因此，可以根据再次删除后剩余的候选站址和未发生变化的剩余的待服务对象重新确定图论选址图，并利用重新确定的图论选址图对之前的图论选址图进行更新，之后，可以返回步骤2041，继续通过前述介绍的方法根据该更新后的图论选址图，从再次删除后剩余的候选站址中确定被选站址。
在本申请实施例中，将整数线性规划模型转换为线性规划模型进行求解，以得到第一选址结果和第二选址结果，之后，从多个候选站址中除第一选址结果和第二选址结果包括的站址之外的剩余候选站址中确定被选站址。也即，本申请可以首先通过求解转化得到的线性规划模型得到一部分选址结果，之后，根据这部分选址结果对之前基于多个候选站址的选址问题进行降维，进而求解降维后的选址问题。这样，当候选站址的数量较大时，通过本申请提供的方法不仅可以降低选址的难度，而且可以缩短选址所耗费的时间。
接下来是本申请实施例提供的根据上述介绍的选址方法进行选址的一个示例。在该示例 中，对商家营业厅进行选址。其中，待服务对象是对选址区域进行栅格化后的每个栅格上的用户，在该示例中，待服务对象的数量N＝2895，候选站址的数量M＝1181，且营业厅类型只有一个。根据商家营业厅的业务需求，待优化目标是营业厅覆盖的用户数量，建站条件包括：距离小于150米的两个候选站址不能同时建站，被选站址的数量不大于300。根据上述建站条件、多个候选站址和多个待服务对象建立整数线性规划模型如下：
目标函数：
Figure PCTCN2020088376-appb-000023
约束条件：
Figure PCTCN2020088376-appb-000024
x j+x j',≤1，(j,j')∈V，
Figure PCTCN2020088376-appb-000025
x j∈{0,1}，y i∈{0,1}。
其中，w i是指多个待服务对象中的待服务对象i的服务权重系数，在该示例中，w i等于栅格i上的用户数占总用户数的比例。V为第一候选站址集合，包括1380个候选站址对，每个候选站址对中的两个候选站址之间的距离小于150米。
通过对上述整数线性规划模型中的变量的允许取值以及第一候选站址集合进行处理，来实现对整数线性规划模型的预处理，从而得到如下的线性规划模型：
目标函数：
Figure PCTCN2020088376-appb-000026
约束条件：
Figure PCTCN2020088376-appb-000027
0≤x j≤1，0≤y i≤1。
其中，U为第二候选站址集合，其中，该第二候选站址集合中任意两个候选站址之间的距离均小于150米。
将前述的w i、N、M以及r i,j等参数的参数值输入该线性规划模型，对该线性规划模型进行求解，得到的求解结果如表1中所示。
表1
最优目标函数值 x j＝1的个数 x j＝0的个数 0<x j<1的个数 x j总个数
0.951 149 467 565 1181
由上表可知，通过求解该线性规划模型，可以得到149个被选站址和467个不被选站址。接下来可以从剩余的565个候选站址再次确定被选站址。也即，将原问题中从1181个候选站址中选择被选站址降维到从565个候选站址中确定被选站址，降维52％。
之后，对于这565个候选站址，可以将其中与确定的149个被选站址不能同时建站的候选站址删除，将确定的149个被选站址所覆盖的待服务对象删除，从而得到剩余的候选站址和剩余的待服务对象。之后，可以根据剩余的候选站址和剩余的待服务对象，通过前述步骤204中介绍的方法，建立图论选址图，并预设对第一选址问题分割层数L＝5，以此来确定剩余候选站址中的被选站址。
表2列出了通过上述选址方法、相关技术中的贪婪算法、遗传算法等方法确定营业厅站址时，得到的选址结果的用户覆盖比例和选址所耗费时间。
表2
性能 本申请实施例 贪婪算法 遗传算法 最优解上限
用户覆盖比例 94.4％ 78.3％ 89％ 95.1％
耗费时间(s) 500 10 613  
如表2中所示，采用本申请实施例提供的选址方法确定的选址结果，用户覆盖比例为 94.4％，极为接近最优解上限，并且，耗费时间只有500秒。而采用贪婪算法，虽然耗费时间较短，但是，用户覆盖比例仅为78.3％，远远小于最优解上限，选址效果较差。采用遗传算法，用户覆盖比例低于本申请实施例的用户覆盖比例，且耗费时间也较长。由此可见，本申请提供的选址方法在保证耗费时间较短的同时，达到了更好的覆盖能力。
上述实施例主要介绍了将整数线性规划模型转换为线性规划模型进行求解，以得到第一选址结果和第二选址结果，进而从多个候选站址中除第一选址结果和第二选址结果包括的站址之外的剩余候选站址中确定被选站址的实现过程。可选地，在有些情况下，可能根据多个候选站址、多个待服务对象和多个建站条件无法建立整数线性规划模型。例如，当建站条件中包含有对每个服务站的覆盖容量的约束时，由于各个服务站的覆盖容量之间彼此有影响，因此，根据该建站条件无法建立约束条件，因此，无法建立得到对应的规划模型。在这种情况下，则可以通过图5所示的选址方法来从多个候选站址中确定被选站址。如图5所示，该方法包括以下步骤：
步骤501：根据多个候选站址、多个待服务对象和多个建站条件，确定图论选址图，该图论选址图中包括多个节点，每个节点用于指示多个候选站址中的一个候选站址，多个节点中两个不能同时建站的候选站址对应的两个节点之间具有连边。
本步骤的实现方式可以参考前述实施例中的步骤204中根据剩余候选站址和剩余的待服务对象确定图论选址图的实现方式。其中，与前述实施例不同的是，本实施例中是根据所有的候选站址和待服务对象来确定图论选址图，而前述实施例是针对去除第一选址结果和第二选址结果之后剩余的候选站址以及剩余的待服务对象确定图论选址图。
另外，每个节点同样可以对应有第一权重和第二权重。其中，第一权重和第二权重的确定方式可以参考前述实施例中的相关介绍。
步骤502：根据图论选址图确定多个候选站址中的被选站址。
本步骤的实现方式可以参考前述实施例中的步骤2041-2047中介绍的相关方法，本申请实施例在此不再赘述。
综上可知，在本申请实施例中，当根据建站条件无法建立整数线性规划模型时，可以根据多个候选站址、多个待服务对象和多个建站条件确定图论选址图，再通过前述介绍的动态规划算法或者是动态规划算法结合贪婪算法来确定选址结果。也即，本申请实施例提供了用于解决无法建立整数线性规划模型的选址问题的解决方法。
接下来对本申请实施例提供的选址装置进行介绍。
参见图6，本申请实施例提供了一种选址装置600，该装置600包括：
处理模块601，用于执行前述实施例中的步骤201；
输入模块602，用于执行前述实施例中的步骤202；
第一确定模块603，用于执行前述实施例中的步骤203；
第二确定模块604，用于执行前述实施例中的步骤204。
可选地，整数线性规划模型包括中间变量和约束条件，中间变量用于指示待服务对象是否被服务，约束条件包括第一整数集和第二整数集，第一整数集包括决策变量的允许取值，第二整数集包括中间变量的允许取值；
处理模块601具体用于：
将第一整数集转换为第一取值范围，将第二整数集转换为第二取值范围，得到线性规划模型，第一取值范围是指包含第一整数集内的整数值的连续取值范围，第二取值范围是指包含第二整数集内的整数值的连续取值范围。
可选地，整数线性规划模型还包括第一参数，第一参数用于指示在每个候选站址上建站时待选服务站类型的数量；
处理模块601具体还用于：
将在每个候选站址上建站时的K个待选服务站类型转换为在相同位置上的K个不同候选站址，K为第一参数。
可选地，约束条件还包括第一约束，第一约束包括第一候选站址集合，第一候选站址集合包括至少一个候选站址对，每个候选站址对包括的两个候选站址之间的距离小于第一阈值；
处理模块601具体还用于：
将第一候选站址集合转换为第二候选站址集合，第二候选站址集合包括至少两个候选站址，且至少两个候选站址中的任意两个候选站址之间的距离均小于第一阈值。
可选地，第二确定模块604包括：
删除单元，用于将多个候选站址中第一选址结果包括的站址、第二选址结果包括的站址以及与第一选址结果中包括的被选站址不能同时建站的站址进行删除；
单元，还用于将多个待服务对象中第一选址结果包括的站址所服务的待服务对象进行删除；
确定单元，用于根据删除后剩余的候选站址和删除后剩余的待服务对象，确定删除后剩余的候选站址中的被选站址。
可选地，确定单元，包括：
第一确定子单元，用于根据删除后剩余的候选站址和删除后剩余的待服务对象确定图论选址图，图论选址图中包括多个节点，每个节点用于指示删除后剩余的候选站址中的一个候选站址，多个节点中两个不能同时建站的候选站址对应的两个节点之间具有连边；
第二确定子单元，用于根据图论选址图确定删除后剩余的候选站址中的被选站址。
可选地，多个节点中的每个节点对应有第一权重和第二权重，第一权重是指在相应节点所指示的候选站址上建设服务站后对删除后剩余的待服务对象的服务能力，第二权重是指在相应节点所指示的候选站址上建设服务站的建站成本；
第二确定子单元具体用于：
根据每个节点对应的第一权重和第二权重，从多个节点中选择目标节点；
判断是否将目标节点所指示的候选站址确定为被选站址；
如果将目标节点所指示的候选站址确定为被选站址，则将删除后剩余的候选站址中确定的被选站址以及与确定的被选站址不能同时建站的站址删除，将删除后剩余的待服务对象中确定的被选站址所服务的待服务对象删除，根据再次删除后剩余的候选站址和再次删除后剩余的待服务对象对图论选址图进行更新，返回根据每个节点对应的第一权重和第二权重，从多个节点中选择目标节点的步骤，直到再次删除后不存在剩余的候选站址时为止。
可选地，第二确定子单元具体用于：
根据目标节点和图论选址图，确定第一选址问题；
通过动态规划算法将第一选址问题进行L层分割，L小于第一选址问题允许被分割的最大层数；
确定分割得到的多个子问题的运算结果，根据多个子问题的运算结果确定第一选址问题的运算结果；
根据第一选址问题的运算结果判断是否将目标节点所指示的候选站址作为被选站址。
综上，本申请实施例可以首先通过求解转化得到的线性规划模型得到一部分选址结果，之后，根据这部分选址结果对之前基于多个候选站址的选址问题进行降维，进而求解降维后的选址问题。这样，当候选站址的数量较大时，通过本申请提供的方法不仅可以降低选址的难度，而且可以缩短选址所耗费的时间。
参见图7，本申请实施例提供了一种选址装置700，该装置700包括：
第一确定模块701，用于执行前述实施例中的步骤501；
第二确定模块702，用于执行前述实施例中的步骤502。
可选地，多个节点中的每个节点对应有第一权重和第二权重，第一权重是指在相应节点所指示的候选站址上建设服务站后对多个待服务对象的服务能力，第二权重是指在相应节点所指示的候选站址上建设服务站的建站成本；
第二确定模块，包括：
选择单元，用于根据每个节点对应的第一权重和第二权重，从多个节点中选择目标节点；
判断单元，用于判断是否将目标节点所指示的候选站址确定为被选站址；
触发单元，用于如果将目标节点所指示的候选站址确定为被选站址，则将多个候选站址中确定的被选站址以及与确定的被选站址不能同时建站的站址删除，将多个待服务对象中确定的被选站址所服务的待服务对象删除，根据删除后剩余的候选站址和删除后剩余的待服务对象对图论选址图进行更新，触发选择单元根据每个节点对应的第一权重和第二权重，从多个节点中选择目标节点，直到删除后不存在剩余的候选站址时为止。
可选地，判断单元具体用于：
根据目标节点和图论选址图，确定第一选址问题；
通过动态规划算法将第一选址问题进行L层分割，L小于第一选址问题允许被分割的最大层数；
确定分割得到的多个子问题的运算结果，根据多个子问题的运算结果确定第一选址问题的运算结果；
根据第一选址问题的运算结果判断是否将目标节点所指示的候选站址确定为被选站址。
综上可知，在本申请实施例中，当根据建站条件无法建立整数线性规划模型时，可以根据多个候选站址、多个待服务对象和多个建站条件确定图论选址图，再通过前述介绍的动态规划算法或者是动态规划算法结合贪婪算法来确定选址结果。也即，本申请实施例提供了用于解决无法建立整数线性规划模型的选址问题的解决方法。
需要说明的是：上述实施例提供的选址装置在进行选址时，仅以上述各功能模块的划分进行举例说明，实际应用中，可以根据需要而将上述功能分配由不同的功能模块完成，即将设备的内部结构划分成不同的功能模块，以完成以上描述的全部或者部分功能。另外，上述实施例提供的选址装置与选址方法实施例属于同一构思，其具体实现过程详见方法实施例， 这里不再赘述。
在上述实施例中，可以全部或部分地通过软件、硬件、固件或者其任意结合来实现。当使用软件实现时，可以全部或部分地以计算机程序产品的形式实现。所述计算机程序产品包括一个或多个计算机指令。在计算机上加载和执行所述计算机指令时，全部或部分地产生按照本申请实施例所述的流程或功能。所述计算机可以是通用计算机、专用计算机、计算机网络、或者其他可编程装置。所述计算机指令可以存储在计算机可读存储介质中，或者从一个计算机可读存储介质向另一个计算机可读存储介质传输，例如，所述计算机指令可以从一个网站站点、计算机、服务器或数据中心通过有线(例如：同轴电缆、光纤、数据用户线(Digital Subscriber Line，DSL))或无线(例如：红外、无线、微波等)方式向另一个网站站点、计算机、服务器或数据中心进行传输。所述计算机可读存储介质可以是计算机能够存取的任何可用介质或者是包含一个或多个可用介质集成的服务器、数据中心等数据存储设备。所述可用介质可以是磁性介质(例如：软盘、硬盘、磁带)、光介质(例如：数字通用光盘(Digital Versatile Disc，DVD))、或者半导体介质(例如：固态硬盘(Solid State Disk，SSD))等。
本领域普通技术人员可以理解实现上述实施例的全部或部分步骤可以通过硬件来完成，也可以通过程序来指令相关的硬件完成，所述的程序可以存储于一种计算机可读存储介质中，上述提到的存储介质可以是只读存储器，磁盘或光盘等。
以上所述为本申请提供的实施例，并不用以限制本申请，凡在本申请的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本申请的保护范围之内。

Claims (26)

  1. 一种选址方法，其特征在于，所述方法包括：
    对整数线性规划模型进行预处理，得到线性规划模型，所述整数线性规划模型是根据多个候选站址、多个待服务对象和多个建站条件建立的模型，且所述整数线性规划模型输出的决策变量的取值为整数值，所述线性规划模型输出的决策变量的取值包括整数值和小数值；
    将所述整数线性规划模型的多个参数的参数值输入所述线性规划模型；
    根据所述线性规划模型输出的决策变量的取值中的整数值确定第一选址结果和第二选址结果，所述第一选址结果包括多个被选站址，所述第二选址结果包括多个不被选站址，所述多个被选站址是指所述多个候选站址中被选作建设服务站的站址；
    从所述多个候选站址中除所述第一选址结果和所述第二选址结果之外的剩余候选站址中确定被选站址。
  2. 如权利要求1所述的方法，其特征在于，所述整数线性规划模型包括中间变量和约束条件，所述中间变量用于指示待服务对象是否被服务，所述约束条件包括第一整数集和第二整数集，所述第一整数集包括所述决策变量的允许取值，所述第二整数集包括所述中间变量的允许取值；
    所述对整数线性规划模型进行预处理，得到线性规划模型，包括：
    将所述第一整数集转换为第一取值范围，将所述第二整数集转换为第二取值范围，得到所述线性规划模型，所述第一取值范围是指包含所述第一整数集内的整数值的连续取值范围，所述第二取值范围是指包含所述第二整数集内的整数值的连续取值范围。
  3. 如权利要求2所述的方法，其特征在于，所述整数线性规划模型还包括第一参数，所述第一参数用于指示在每个候选站址上建站时待选服务站类型的数量；
    所述将所述第一整数集转换为第一取值范围，将所述第二整数集转换为第二取值范围之后，还包括：
    将在每个候选站址上建站时的K个待选服务站类型转换为在相同位置上的K个不同候选站址，所述K为所述第一参数。
  4. 如权利要求2或3所述的方法，其特征在于，所述约束条件还包括第一约束，所述第一约束包括第一候选站址集合，所述第一候选站址集合包括至少一个候选站址对，每个候选站址对包括的两个候选站址之间的距离小于第一阈值；
    所述将所述第一整数集转换为第一取值范围，将所述第二整数集转换为第二取值范围之后，还包括：
    将所述第一候选站址集合转换为第二候选站址集合，所述第二候选站址集合包括至少两个候选站址，且所述至少两个候选站址中的任意两个候选站址之间的距离均小于所述第一阈值。
  5. 如权利要求1-4任一所述的方法，其特征在于，所述从所述多个候选站址中除所述第一选址结果和所述第二选址结果之外的剩余候选站址中确定被选站址，包括：
    将所述多个候选站址中所述第一选址结果包括的站址、所述第二选址结果包括的站址以及与所述第一选址结果中包括的被选站址不能同时建站的站址进行删除；
    将所述多个待服务对象中所述第一选址结果包括的站址所服务的待服务对象进行删除；
    根据删除后剩余的候选站址和删除后剩余的待服务对象，确定所述删除后剩余的候选站址中的被选站址。
  6. 如权利要求5所述的方法，其特征在于，所述根据删除后剩余的候选站址和删除后剩余的待服务对象，确定所述删除后剩余的候选站址中的被选站址，包括：
    根据所述删除后剩余的候选站址和所述删除后剩余的待服务对象确定图论选址图，所述图论选址图中包括多个节点，每个节点用于指示所述删除后剩余的候选站址中的一个候选站址，所述多个节点中两个不能同时建站的候选站址对应的两个节点之间具有连边；
    根据所述图论选址图确定所述删除后剩余的候选站址中的被选站址。
  7. 如权利要求6所述的方法，其特征在于，所述多个节点中的每个节点对应有第一权重和第二权重，所述第一权重是指在相应节点所指示的候选站址上建设服务站后对所述删除后剩余的待服务对象的服务能力，所述第二权重是指在相应节点所指示的候选站址上建设服务站的建站成本；
    所述根据所述图论选址图确定所述删除后剩余的候选站址中的被选站址，包括：
    根据每个节点对应的第一权重和第二权重，从所述多个节点中选择目标节点；
    判断是否将所述目标节点所指示的候选站址确定为被选站址；
    如果将所述目标节点所指示的候选站址确定为被选站址，则将所述删除后剩余的候选站址中确定的被选站址以及与确定的被选站址不能同时建站的站址删除，将所述删除后剩余的待服务对象中确定的被选站址所服务的待服务对象删除，根据再次删除后剩余的候选站址和再次删除后剩余的待服务对象对所述图论选址图进行更新，返回根据每个节点对应的第一权重和第二权重，从所述多个节点中选择目标节点的步骤，直到再次删除后不存在剩余的候选站址时为止。
  8. 如权利要求7所述的方法，其特征在于，所述判断是否将所述目标节点所指示的候选站址确定为被选站址，包括：
    根据所述目标节点和所述图论选址图，确定第一选址问题；
    通过动态规划算法将所述第一选址问题进行L层分割，所述L小于所述第一选址问题允许被分割的最大层数；
    确定分割得到的多个子问题的运算结果，根据所述多个子问题的运算结果确定所述第一选址问题的运算结果；
    根据所述第一选址问题的运算结果判断是否将所述目标节点所指示的候选站址作为被选站址。
  9. 一种选址方法，其特征在于，所述方法包括：
    根据多个候选站址、多个待服务对象和多个建站条件，确定图论选址图，所述图论选址图中包括多个节点，每个节点用于指示所述多个候选站址中的一个候选站址，所述多个节点中两个不能同时建站的候选站址对应的两个节点之间具有连边；
    根据所述图论选址图确定所述多个候选站址中的被选站址。
  10. 如权利要求9所述的方法，其特征在于，所述多个节点中的每个节点对应有第一权重和第二权重，所述第一权重是指在相应节点所指示的候选站址上建设服务站后对所述多个待服务对象的服务能力，所述第二权重是指在相应节点所指示的候选站址上建设服务站的建站成本；
    所述根据所述图论选址图确定所述多个候选站址中的被选站址，包括：
    根据每个节点对应的第一权重和第二权重，从所述多个节点中选择目标节点；
    判断是否将所述目标节点所指示的候选站址确定为被选站址；
    如果将所述目标节点所指示的候选站址确定为被选站址，则将所述多个候选站址中确定的被选站址以及与所述确定的被选站址不能同时建站的站址删除，将所述多个待服务对象中所述确定的被选站址所服务的待服务对象删除，根据删除后剩余的候选站址和删除后剩余的待服务对象对所述图论选址图进行更新，返回所述根据每个节点对应的第一权重和第二权重，从所述多个节点中选择目标节点的步骤，直到删除后不存在剩余的候选站址时为止。
  11. 如权利要求10所述的方法，其特征在于，所述判断是否将所述目标节点所指示的候选站址确定为被选站址，包括：
    根据所述目标节点和所述图论选址图，确定第一选址问题；
    通过动态规划算法将所述第一选址问题进行L层分割，所述L小于所述第一选址问题允许被分割的最大层数；
    确定分割得到的多个子问题的运算结果，根据所述多个子问题的运算结果确定所述第一选址问题的运算结果；
    根据所述第一选址问题的运算结果判断是否将所述目标节点所指示的候选站址确定为被选站址。
  12. 一种选址装置，其特征在于，所述装置包括：
    处理模块，用于对整数线性规划模型进行预处理，得到线性规划模型，所述整数线性规划模型是根据多个候选站址、多个待服务对象和多个建站条件建立的模型，且所述整数线性规划模型输出的决策变量的取值为整数值，所述线性规划模型输出的决策变量的取值包括整数值和小数值；
    输入模块，用于将所述整数线性规划模型的多个参数的参数值输入所述线性规划模型；
    第一确定模块，用于根据所述线性规划模型输出的决策变量的取值中的整数值确定第一选址结果和第二选址结果，所述第一选址结果包括多个被选站址，所述第二选址结果包括多个不被选站址，所述多个被选站址是指所述多个候选站址中被选作建设服务站的站址；
    第二确定模块，用于从所述多个候选站址中除所述第一选址结果和所述第二选址结果之 外的剩余候选站址中确定被选站址。
  13. 如权利要求12所述的装置，其特征在于，所述整数线性规划模型包括中间变量和约束条件，所述中间变量用于指示待服务对象是否被服务，所述约束条件包括第一整数集和第二整数集，所述第一整数集包括所述决策变量的允许取值，所述第二整数集包括所述中间变量的允许取值；
    所述处理模块具体用于：
    将所述第一整数集转换为第一取值范围，将所述第二整数集转换为第二取值范围，得到所述线性规划模型，所述第一取值范围是指包含所述第一整数集内的整数值的连续取值范围，所述第二取值范围是指包含所述第二整数集内的整数值的连续取值范围。
  14. 如权利要求13所述的装置，其特征在于，所述整数线性规划模型还包括第一参数，所述第一参数用于指示在每个候选站址上建站时待选服务站类型的数量；
    所述处理模块具体还用于：
    将在每个候选站址上建站时的K个待选服务站类型转换为在相同位置上的K个不同候选站址，所述K为所述第一参数。
  15. 如权利要求13或14所述的装置，其特征在于，所述约束条件还包括第一约束，所述第一约束包括第一候选站址集合，所述第一候选站址集合包括至少一个候选站址对，每个候选站址对包括的两个候选站址之间的距离小于第一阈值；
    所述处理模块具体还用于：
    将所述第一候选站址集合转换为第二候选站址集合，所述第二候选站址集合包括至少两个候选站址，且所述至少两个候选站址中的任意两个候选站址之间的距离均小于所述第一阈值。
  16. 如权利要求12-15任一所述的装置，其特征在于，所述第二确定模块包括：
    删除单元，用于将所述多个候选站址中所述第一选址结果包括的站址、所述第二选址结果包括的站址以及与所述第一选址结果中包括的被选站址不能同时建站的站址进行删除；
    所述单元，还用于将所述多个待服务对象中所述第一选址结果包括的站址所服务的待服务对象进行删除；
    确定单元，用于根据删除后剩余的候选站址和删除后剩余的待服务对象，确定所述删除后剩余的候选站址中的被选站址。
  17. 如权利要求16所述的装置，其特征在于，所述确定单元，包括：
    第一确定子单元，用于根据所述删除后剩余的候选站址和所述删除后剩余的待服务对象确定图论选址图，所述图论选址图中包括多个节点，每个节点用于指示所述删除后剩余的候选站址中的一个候选站址，所述多个节点中两个不能同时建站的候选站址对应的两个节点之间具有连边；
    第二确定子单元，用于根据所述图论选址图确定所述删除后剩余的候选站址中的被选站 址。
  18. 如权利要求17所述的装置，其特征在于，所述多个节点中的每个节点对应有第一权重和第二权重，所述第一权重是指在相应节点所指示的候选站址上建设服务站后对所述删除后剩余的待服务对象的服务能力，所述第二权重是指在相应节点所指示的候选站址上建设服务站的建站成本；
    所述第二确定子单元具体用于：
    根据每个节点对应的第一权重和第二权重，从所述多个节点中选择目标节点；
    判断是否将所述目标节点所指示的候选站址确定为被选站址；
    如果将所述目标节点所指示的候选站址确定为被选站址，则将所述删除后剩余的候选站址中确定的被选站址以及与确定的被选站址不能同时建站的站址删除，将所述删除后剩余的待服务对象中确定的被选站址所服务的待服务对象删除，根据再次删除后剩余的候选站址和再次删除后剩余的待服务对象对所述图论选址图进行更新，返回根据每个节点对应的第一权重和第二权重，从所述多个节点中选择目标节点的步骤，直到再次删除后不存在剩余的候选站址时为止。
  19. 如权利要求18所述的装置，其特征在于，所述第二确定子单元具体用于：
    根据所述目标节点和所述图论选址图，确定第一选址问题；
    通过动态规划算法将所述第一选址问题进行L层分割，所述L小于所述第一选址问题允许被分割的最大层数；
    确定分割得到的多个子问题的运算结果，根据所述多个子问题的运算结果确定所述第一选址问题的运算结果；
    根据所述第一选址问题的运算结果判断是否将所述目标节点所指示的候选站址作为被选站址。
  20. 一种选址装置，其特征在于，所述装置包括：
    第一确定模块，用于根据多个候选站址、多个待服务对象和多个建站条件，确定图论选址图，所述图论选址图中包括多个节点，每个节点用于指示所述多个候选站址中的一个候选站址，所述多个节点中两个不能同时建站的候选站址对应的两个节点之间具有连边；
    第二确定模块，用于根据所述图论选址图确定所述多个候选站址中的被选站址。
  21. 如权利要求20所述的装置，其特征在于，所述多个节点中的每个节点对应有第一权重和第二权重，所述第一权重是指在相应节点所指示的候选站址上建设服务站后对所述多个待服务对象的服务能力，所述第二权重是指在相应节点所指示的候选站址上建设服务站的建站成本；
    所述第二确定模块，包括：
    选择单元，用于根据每个节点对应的第一权重和第二权重，从所述多个节点中选择目标节点；
    判断单元，用于判断是否将所述目标节点所指示的候选站址确定为被选站址；
    触发单元，用于如果将所述目标节点所指示的候选站址确定为被选站址，则将所述多个候选站址中确定的被选站址以及与所述确定的被选站址不能同时建站的站址删除，将所述多个待服务对象中所述确定的被选站址所服务的待服务对象删除，根据删除后剩余的候选站址和删除后剩余的待服务对象对所述图论选址图进行更新，触发所述选择单元根据每个节点对应的第一权重和第二权重，从所述多个节点中选择目标节点，直到删除后不存在剩余的候选站址时为止。
  22. 如权利要求21所述的装置，其特征在于，所述判断单元具体用于：
    根据所述目标节点和所述图论选址图，确定第一选址问题；
    通过动态规划算法将所述第一选址问题进行L层分割，所述L小于所述第一选址问题允许被分割的最大层数；
    确定分割得到的多个子问题的运算结果，根据所述多个子问题的运算结果确定所述第一选址问题的运算结果；
    根据所述第一选址问题的运算结果判断是否将所述目标节点所指示的候选站址确定为被选站址。
  23. 一种计算机系统，其特征在于，所述计算机系统包括处理器和存储器；
    所述存储器用于存储支持所述装置执行权利要求1-8任一项所述的方法的程序，以及存储用于实现权利要求1-8任一项所述的方法所涉及的数据；
    所述处理器被配置为用于执行所述存储器中存储的程序。
  24. 一种计算机系统，其特征在于，所述计算机系统包括处理器和存储器；
    所述存储器用于存储支持所述装置执行权利要求9-11任一项所述的方法的程序，以及存储用于实现权利要求9-11任一项所述的方法所涉及的数据；
    所述处理器被配置为用于执行所述存储器中存储的程序。
  25. 一种计算机可读存储介质，其特征在于，包括指令，所述指令在计算机上运行时，使得计算机执行权利要求1-8任一项所述的方法。
  26. 一种计算机可读存储介质，其特征在于，包括指令，所述指令在计算机上运行时，使得计算机执行权利要求9-11任一项所述的方法。
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