Station installation design system, station installation design device, station installation design method, and program

Abstract

Provided is a station installation design system in which base stations are appropriately arranged in an entire wireless area and a calculation amount can be suppressed as compared to an overall search. Specifically provided is a station installation design system that designs an installation location for a base station for constructing a wireless area, wherein: the installation state of the base station is represented by two values for each candidate point for the installation location of the base station; a plurality of candidates for the installation state of the base station with respect to all of the candidate points are prepared; the candidates for the installation state of the base station are evaluated as a minimization problem in which a terminal non-coverage rate and a base station installation number are set as objective functions; a multipurpose genetic algorithm is used to add the processes of selection, crossover, and mutation and advance a generation change; candidates for a plurality of station installation design results, which are Pareto optimal solutions, are calculated; and one or more station installation design results can be selected from among the candidates for the plurality of station installation design results in accordance with a requirement.

Description

Station placement design system, station placement design device, station placement design method, and program

[0001] The present invention relates to a station placement design system, a station placement design device, a station placement design method, and a program.

[0002] There are station location design systems that design the installation locations of wireless base stations to build wireless coverage areas. Station location design is a combinatorial optimization problem, and various methods have been proposed as methods for solving combinatorial optimization problems. For example, evolutionary algorithms have been proposed as population-based metaheuristic optimization algorithms that are inspired by evolutionary mechanisms such as reproduction, mutation, genetic recombination, natural selection, and survival of the fittest (see, for example, Non-Patent Document 1).

[0003] In addition, in multi-objective optimization problems, when each objective function has a trade-off relationship, it is difficult to obtain a single solution. Therefore, the concept of Pareto optimal solutions has been introduced instead of the concept of optimal solutions (see, for example, Non-Patent Document 2).

[0004] Shota Yagami and Susumu Kuwashima, "Evolutionary Algorithms," Intelligent Systems Design Laboratory, 152nd Monthly Presentation, April 2014. Tomoyuki Hiroyasu, Mitsunori Miki, Shinya Watanabe, Takeshi Sakoda, and Jiro Kamiura, "Comparison of Methods in Multi-Objective Genetic Algorithms," Doshisha University Faculty of Science and Engineering Research Report, Vol. 43, No. 1, pp. 41-52.

[0005] In conventional station placement design methods, base stations are selected one by one from among the base station placement candidates using a greedy algorithm, which means that the placement of base stations is not always appropriate for the entire wireless area. As a solution to this problem, a method that performs an exhaustive search to find the optimal base station placement location from among the base station placement candidates can be considered, but this method has the problem of increasing the amount of calculation required as the number of base station placement candidates increases.

[0006] The embodiments of the present invention have been made in view of the above-mentioned problems, and provide a station placement design system that can appropriately place base stations in the entire wireless area and reduce the amount of calculation compared to a full search.

[0007] In order to solve the above problems, a station placement design system according to an embodiment of the present invention is a station placement design system that designs the installation positions of base stations for constructing a wireless area, and expresses the installation state of the base station as a binary value for each candidate point for the installation position of the base station, prepares a plurality of candidate installation states for the base station for all candidate points, evaluates the candidate installation states of the base station as a minimization problem in which the uncovered rate of terminals and the number of installed base stations are set as objective functions, and uses a multi-objective genetic algorithm to perform selection, crossover, and mutation processes to proceed with generational change, calculates a plurality of candidate station placement design results that are Pareto optimal solutions, and is able to select one or more station placement design results from the plurality of candidate station placement design results according to requirements.

[0008] According to an embodiment of the present invention, it is possible to provide a station placement design system that can appropriately place base stations in the entire wireless area and reduce the amount of calculation compared to a full search.

[0009] FIG. 1 is a diagram showing an example of the configuration of a station placement design system according to the present embodiment; FIG. 2 is a flowchart showing an example of station placement design processing according to the present embodiment; FIG. 3 is a diagram showing an image of a design target area according to the present embodiment; FIG. 4 is a diagram for explaining ranking; FIG. 5 is a diagram for explaining tournament selection; FIG. 6 is a diagram for explaining uniform crossover; and FIG. 7 is a diagram for explaining Pareto optimal solutions. FIG. 1 shows an example of a result display screen according to the present embodiment; FIG. 2 is a diagram showing an example of a result display screen according to the present embodiment; and FIG. 3 is a diagram showing an example of the hardware configuration of a computer according to the present embodiment.

[0010] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. The embodiment described below is merely an example, and the embodiment to which the present invention is applied is not limited to the following embodiment.

[0011] <Configuration Example of Station Placement Design System> Fig. 1 is a diagram showing a configuration example of a station placement design system according to this embodiment. The station placement design system 1 is a system that performs station placement design, which designs appropriate installation positions of wireless base stations for constructing a wireless area, based on input design conditions. In the example of Fig. 1, the station placement design system 1 includes a station placement design device 100 and a terminal device 110 that can communicate with the station placement design device 100.

[0012] The station placement design device 100 is an information processing device having a computer configuration, or a system including multiple computers. The station placement design device 100 realizes each functional configuration shown in Fig. 1 by, for example, a computer included in the station placement design device 100 executing a program stored in a storage medium. In the example of Fig. 1, the station placement design device 100 has each functional configuration such as a communication unit 101, an input / output unit 102, a station placement design unit 103, and a storage unit 104. Note that at least a portion of each of the above functional configurations may be realized by hardware.

[0013] The communication unit 101 executes a communication process for communicating with other devices such as the terminal device 110. For example, the communication unit 101 transmits and receives data to and from the terminal device 110 via a communication network such as a wide area network (WAN) and / or a local area network (LAN).

[0014] The input / output unit 102 performs, for example, input processing to accept input of design conditions and the like from the terminal device 110, and output processing to output a result display screen that displays the station placement design results by the station placement design device 100 to the terminal device 110.

[0015] The station location design unit 103 executes station location design processing to design appropriate installation positions of wireless base stations for establishing a wireless area based on the input design conditions.

[0016] The storage unit 104 stores, for example, the design conditions received by the input / output unit 102, the station placement design results designed by the station placement design unit 103, and various data used during the station placement design.

[0017] (Processing Overview) Because there are limits to the range of radio waves from a wireless base station (hereinafter referred to as a base station) and the number of terminals that a single base station can accommodate, if there are not enough base stations installed, the area coverage and terminal accommodation will be insufficient. On the other hand, if there are too many base stations installed, the cost of the base stations themselves, as well as installation and operation costs, will increase, resulting in inefficiency. Therefore, it is important to design base stations so that the necessary number of base stations can be installed in appropriate locations.

[0018] In conventional base station placement design methods, base stations are selected and placed one by one from among candidate base station locations, for example, using a greedy algorithm. (Reference: Toshiro Nakahira, Daisuke Murayama, Satoshi Takatani, Kenichi Kawamura, and Takatsune Moriyama, "Multi-Wireless Area Design Method Based on Communication Capacity and Base Station Cost," IEICE Techniques, IEICE General Conference, B-5-97, March 2022.) However, this method may not be able to optimally place base stations across the entire wireless area. To address this issue, a comprehensive search for the optimal base station location from among the candidate locations is considered, but this method poses the problem of increased computational complexity as the number of candidate base station locations increases.

[0019] Furthermore, in radio station location design, there is generally a trade-off between the number of base stations and the coverage rate. Therefore, when actually installing base stations, the relationship between the number of base stations and the coverage rate must be clarified, and then considerations must be made regarding how many base stations to install, or to what extent the coverage rate should be compromised and the number of base stations to be installed should be reduced, taking into account costs. Furthermore, even after a radio station location design has been completed, the requirements may change. However, conventional technologies derive a single radio station location design that achieves a certain coverage rate. Therefore, when attempting to derive multiple design result candidates for different numbers of base stations, it is necessary to change parameters and re-derive the design multiple times.

[0020] Therefore, the station location design system 1 according to this embodiment expresses the installation status of a base station for each candidate point for the installation location of the base station as a binary value such as [0, 1], and regards the installation status of the base station for all candidate points as genes. For example, 0 indicates that a base station is not installed at the candidate point, and 1 indicates that a base station is installed at the candidate point. In this way, the station location design system 1 prepares multiple candidate installation statuses for all candidate points. The station location design system 1 also evaluates the candidate installation statuses of the base station as a minimization problem in which the uncovered rate of terminals and the number of installed base stations are set as objective functions, respectively. Furthermore, the station location design system 1 uses a multi-objective genetic algorithm to perform selection, crossover, and mutation processes to advance generational changes, calculate multiple candidate station location design results that are Pareto-optimal solutions, and enable the user to select one or more station location design results from among them according to requirements.

[0021] As a result, the station placement design system 1 according to this embodiment can obtain a globally optimal solution in station placement design (less likely to fall into a local solution) than the greedy method, and can significantly reduce the amount of calculation compared to a full search. Furthermore, the station placement design system 1 according to this embodiment calculates multiple station placement design result candidates that are Pareto optimal solutions, making it possible to select a radio station placement design result that meets the requirements from among them.

[0022] As described above, according to this embodiment, it is possible to provide a station placement design system 1 that can appropriately place base stations in the entire wireless area and reduce the amount of calculation compared to a full search.

[0023] The configuration of the station placement design system 1 shown in Fig. 1 is an example. For example, the functions of the station placement design device 100 may be distributed among multiple information processing devices. At least a part of the processing performed by the station placement design unit 103 may be realized by a cloud service or a program executed by a virtual machine on the cloud. Furthermore, the station placement design device 100 may input design conditions and display a screen showing the results of the station placement design without using the terminal device 110.

[0024] <Processing Flow> Next, the processing flow of the station placement design method according to this embodiment will be described.

[0025] 2 is a flowchart showing an example of the station placement design process according to this embodiment. This process shows a specific example of the station placement design process executed by the station placement design system 1 described with reference to FIG.

[0026] In step S201, the station placement design unit 103 sets a design target area. As an example, the station placement design unit 103 sets the design target area 300 indoors where a plurality of shielding objects 301 are arranged, as shown in Fig. 3. The design target area 300 set by the station placement design unit 103 has three-dimensional coordinates based on, for example, three-dimensional CAD data or three-dimensional data acquired by a three-dimensional sensor.

[0027] In step S202, the station location design unit 103 places multiple evaluation points (hereinafter referred to as terminals 302) for evaluating wireless quality such as received power within the set design target area 300, for example, as shown in FIG. 3. The station location design unit 103 also places multiple candidate points 303, which are candidates for base station installation locations, within the design target area 300, for example, as shown in FIG. 3. Furthermore, the station location design unit 103 calculates the received power that each terminal 302 receives from the base station installed at each candidate point 303. For example, the station location design unit 103 uses a known radio wave propagation simulation technique such as ray tracing to calculate the received power that each terminal 302 receives when a base station is installed at each candidate point 303.

[0028] In step S203, the station placement design unit 103 generates an initial population. For example, the station placement design unit 103 randomly generates multiple station placement design patterns. The station placement design unit 103 also expresses whether or not to place a base station at a candidate point 303 as [0, 1], regards the installation status of the base station for each candidate point 303 as a gene, and executes the processes from step S204 onwards.

[0029] In step S204, the station placement design unit 103 evaluates and ranks the generated station placement design patterns (hereinafter referred to as populations) using the uncovered rate of terminals and the number of installed base stations as objective functions.

[0030] For example, the first objective function f １ is the number of base stations installed, and the second objective function f ２ is set as the uncovered rate of the terminal, and a minimization problem is set to simultaneously minimize the first objective function f1 and the second objective function f2. This minimization problem can be expressed by the following equations (1) to (3).

[0031]

[0032] subject to

[0033] Equations (1) and (2) are the objective functions to be simultaneously minimized, and equation (3) is the constraint. Also, i is the terminal ∀i∈I, j is the base station ∀j∈J, n is the station placement design plan ∀n∈N, r ｉｊ is the received power that terminal i receives from base station j, and p ｉ，ｎ is the maximum received power, p ｔ is the target received power, z ｉ，ｎ is the degree of achievement of the target received power. The number of base stations to be installed is, for example, the number of base stations to be installed in the design area 300. The terminal uncoverage rate is, for example, a value indicating the proportion of terminals 302 that have not reached the target received power among the multiple terminals 302 set in the design area 300. Note that the terminal uncoverage rate (hereinafter referred to as the uncoverage rate) may also be the area uncoverage rate, etc.

[0034] For example, the station placement design unit 103 evaluates and ranks the population using two objective functions shown in equations (1) and (2) as a multi-objective optimization problem such as the well-known NSGA-II (Non-dominated Sorting Genetic Algorithms-II).

[0035] 4 is a diagram for explaining ranking. For example, the station placement design unit 103 searches for an individual group that is not dominated by any other individual from among the individuals, and sets this as an individual group 401 with rank 1. Next, the station placement design unit 103 searches for an individual group that is not dominated by any other individual from among the individuals, and sets this as an individual group 402 with rank 2. The station placement design unit 103 ranks the individuals by repeatedly performing the same process until there are no more individuals to evaluate.

[0036] In step S205, the station placement design unit 103 saves the elites. For example, the station placement design unit 103 stores the top ranked individuals in the storage unit 104 or the like to pass them on to the next generation. This ensures that the optimal solution is always updated in the correct direction. In addition, the station placement design unit 103 executes the processes of steps S206 to S208 in parallel with the process of step S205.

[0037] In step S206, the station placement design unit 103 performs a selection operation on the population. For example, the station placement design unit 103 performs a tournament selection to select a top-ranked station from a randomly selected population. Note that the tournament selection is an example of a selection operation performed by the station placement design unit 103.

[0038] FIG. 5 is a diagram for explaining tournament selection. As an illustrative example, assume that there are six populations, (A) to (F), as shown in FIG. 5. For example, when individuals (A), (B), and (C) are randomly selected from populations (A) to (F), the station placement design unit 103 selects the individual (A) with the highest score. Similarly, when individuals (C), (E), and (F) are randomly selected from populations (A) to (F), the station placement design unit 103 selects the individual (C) with the highest score. By performing such a selection operation, the station placement design unit 103 can diversify solutions and reduce the risk of falling into a local solution.

[0039] In step S206, the station placement design unit 103 performs a crossover operation on the population. For example, the station placement design unit 103 performs uniform crossover, which randomly replaces all genes. Note that uniform crossover is an example of a crossover operation performed by the station placement design unit 103.

[0040] 6 is a diagram for explaining uniform crossover. As an illustrative example, when there are (parent A) and (parent B) as shown in FIG. 6, the station placement design unit 103 randomly swaps (parent A) and (parent B) to generate (child A) and (child B). By such crossover processing, the station placement design unit 103 can diversify the solutions.

[0041] In step S208, the station placement design unit 103 performs a mutation operation on the population, which significantly changes the individuals with a certain probability. This allows the station placement design unit 103 to reduce the risk of falling into a local solution.

[0042] In step S209, the station placement design unit 103 forms a next generation population. Also in step S209, the station placement design unit 103 determines whether the number of generations has reached a predetermined number G (e.g., 200). If the number of generations has not reached the predetermined number G, the station placement design unit 103 returns the process to step S204 and executes the same process again. On the other hand, if the number of generations has reached the predetermined number G, the station placement design unit 103 ends the process of FIG. 2.

[0043] 2, the station placement design system 1 can calculate multiple station placement design result candidates that are Pareto optimal solutions. Here, the Pareto optimal solution is an optimal solution that takes into account trade-offs with respect to multiple objective functions (here, a first objective function f1: the number of installed base stations, and a second objective function f2: the uncovered rate).

[0044] FIG. 7 is a diagram for explaining the Pareto optimal solution. This diagram shows the Pareto optimal solution when there are two objective functions (f １ , f ２ ) is shown. In multi-objective optimization, it is not possible to determine a single optimal solution, so as shown in Figure 7, a set of feasible solutions is found that cannot be improved without worsening the values ​​of other objective functions. This solution is called the Pareto optimal solution. Finding the Pareto optimal solution has the advantage of making it easier to find a compromise.

[0045] The Pareto optimal solution is also called the Pareto solution. There is not just one Pareto optimal solution, but multiple Pareto optimal solutions. The curve that is the set of these Pareto optimal solutions is called the Pareto front.

[0046] The processing of steps S204 to S210 in FIG. 2 is an example of processing in which a multi-objective genetic algorithm is used to perform selection, crossover, and mutation processes to advance generational change, and calculate multiple candidate station placement design results that are Pareto-optimal solutions.

[0047] (Example of Result Display Screen) Fig. 8 is a diagram (1) showing an example of a result display screen output by the station placement design system 1. In the example of Fig. 8, the station placement design system 1 displays a first objective function f １ : Number of base stations installed, horizontal axis is the second objective function f ２ : As the uncovered rate, a plurality of Pareto optimal solutions 801 obtained by the process of FIG. 2 are displayed on the graph 800 as black circles (or dots).

[0048] The station placement design system 1 may display the design results for each generation on the graph 800 as circles (or dots) of other colors as a status during design derivation (optimization progress status).

[0049] Preferably, the station location design system 1 displays, as a design result, an installation position of a base station 901 in the design target area 300, as shown in Fig. 9, based on a Pareto optimal solution 801 selected by a user's mouse operation 803 or the like. Note that the station location design system 1 may display multiple design results such as those shown in Fig. 9, based on multiple Pareto optimal solutions 801 selected by a user's mouse operation 803 or the like.

[0050] The result display screens shown in FIGS. 8 and 9 may be created by the station placement design device 100, or may be created and displayed by the terminal device 110 based on data acquired from the station placement design device 100.

[0051] (Application Example) In the above embodiment, the number of installed base stations is used as the objective function in the station placement design, but this is not limiting. For example, when designing a combination of multiple base stations with different equipment costs, objective function 1 can be defined as minimizing the total equipment cost, making it possible to derive a station placement design result for a mixture of multiple models.

[0052] In the above embodiment, the received signal strength at each installed terminal 302 is used as the criterion, but other criteria such as the signal-to-interference and noise ratio, the throughput, etc. may also be used. In this case, the station placement design system 1 can calculate estimated values ​​of the signal-to-interference and noise ratio, the throughput, etc. based on the received signal strength.

[0053] <Hardware Configuration> (Hardware Configuration of Station Placement Design Device) The station placement design device 100 and the terminal device 110 according to this embodiment have, for example, the hardware configuration of a computer 1000 as shown in Fig. 10. Alternatively, the station placement design device 100 is realized by a plurality of computers 1000.

[0054] 10 is a diagram showing an example of the hardware configuration of a computer according to this embodiment. In the example of Fig. 10, a computer 1000 includes a processor 1001, a memory 1002, a storage device 1003, a communication device 1004, an input device 1005, an output device 1006, and a bus B.

[0055] The processor 1001 is, for example, an arithmetic unit such as a CPU (Central Processing Unit) that executes predetermined programs to realize various functions. The memory 1002 is a storage medium readable by the computer 1000 and includes, for example, a RAM (Random Access Memory) and a ROM (Read Only Memory). The storage device 1003 is a computer-readable storage medium and may include, for example, a HDD (Hard Disk Drive), an SSD (Solid State Drive), various optical disks, and magneto-optical disks.

[0056] The communication device 1004 includes one or more pieces of hardware (communication devices) for communicating with other devices via a wireless or wired network. The input device 1005 is an input device (e.g., a keyboard, a mouse, a microphone, a switch, a button, a sensor, etc.) that receives input from the outside. The output device 1006 is an output device (e.g., a display, a speaker, an LED lamp, etc.) that outputs to the outside. Note that the input device 1005 and the output device 1006 may be integrated into one device (e.g., an input / output device such as a touch panel display).

[0057] The bus B is commonly connected to the above components and transmits, for example, address signals, data signals, and various control signals. The processor 1001 is not limited to a CPU, and may be, for example, a DSP (Digital Signal Processor), a PLD (Programmable Logic Device), or an FPGA (Field Programmable Gate Array).

[0058] (Supplementary Note) The station location design device 100 in this embodiment is not limited to being realized by a dedicated device, but may also be realized by a general-purpose computer. In this case, a program for realizing this function may be recorded on a computer-readable recording medium, and the program recorded on this recording medium may be read into a computer system and executed to realize the function. Note that the term "computer system" here includes hardware such as an OS and peripheral devices.

[0059] Furthermore, "computer-readable recording media" includes various storage devices such as portable media such as flexible disks, optical magnetic disks, ROMs, and CD-ROMs, as well as hard disks built into computer systems. Furthermore, "computer-readable recording media" may also include devices that dynamically store programs for a short period of time, such as communication lines when transmitting programs via networks such as the Internet or communication lines such as telephone lines, and devices that store programs for a certain period of time, such as volatile memory within computer systems that serve as servers or clients in such cases.

[0060] Furthermore, the above program may be one that realizes part of the above-mentioned functions, or may be one that can realize the above-mentioned functions in combination with a program already recorded in a computer system, or may be one that is realized using hardware such as a PLD (Programmable Logic Device) or FPGA (Field Programmable Gate Array).

[0061] <Effects of the embodiment> According to the present embodiment, it is possible to provide a station placement design system that can appropriately place base stations in the entire wireless area and reduce the amount of calculation compared to a full search.

[0062] For example, the station placement design system 1 according to this embodiment can obtain a globally optimal solution (less likely to fall into a local solution) than the greedy method, and can significantly reduce the amount of calculation compared to a full search. Furthermore, the station placement design system 1 according to this embodiment can calculate multiple station placement design result candidates that are Pareto optimal solutions, and can select a radio station placement design result that meets the requirements from among them.

[0063] Summary of Embodiments This specification discloses at least the following station placement design system, station placement design device, station placement design method, and program: (Item 1) A station placement design system that designs installation positions of base stations to build a wireless area, expressing the installation state of the base station for each candidate point of the installation position of the base station as a binary value and preparing multiple candidate installation states of the base station for all the candidate points, evaluating the candidate installation states of the base station as a minimization problem in which the uncovered rate of terminals and the number of installed base stations are set as objective functions, using a multi-objective genetic algorithm to perform selection, crossover, and mutation processes to advance generational change and calculate multiple candidate station placement design results that are Pareto optimal solutions, and capable of selecting one or more station placement design results from the multiple candidate station placement design results according to requirements. (Section 2) A station location design device that designs the installation locations of base stations to construct a wireless area, expressing the installation state of the base station for each candidate point of the installation location of the base station using a binary value, and preparing multiple candidate installation states of the base station for all candidate points, evaluating the candidate installation states of the base station as a minimization problem in which the uncovered rate of terminals and the number of installed base stations are set as objective functions, and using a multi-objective genetic algorithm to perform selection, crossover, and mutation processes to proceed with generational change, calculating multiple candidate station location design results that are Pareto optimal solutions, and being able to select one or more station location design results from the multiple candidate station location design results according to requirements. (Clause 3) A station placement design method in which a computer that designs installation locations of base stations to build a wireless area, expresses the installation state of the base station for each candidate point of the installation location of the base station as a binary value, and prepares a plurality of candidate installation states of the base station for all candidate points, evaluates the candidate installation states of the base station as a minimization problem in which the uncovered rate of terminals and the number of installed base stations are set as objective functions, and proceeds with generational change by adding selection, crossover, and mutation processes using a multi-objective genetic algorithm to calculate a plurality of candidate station placement design results that are Pareto optimal solutions, and is capable of selecting one or more station placement design results from the plurality of candidate station placement design results according to requirements. (Clause 4) A program that causes a computer to execute the station placement design method described in clause 3.

[0064] Although the present embodiment has been described above, the present invention is not limited to such a specific embodiment, and various modifications and changes are possible within the scope of the gist of the present invention described in the claims.

[0065] REFERENCE SIGNS LIST 1 Station placement design system 100 Station placement design device 110 Terminal device 101 Communication unit 102 Input / output unit 103 Station placement design unit 104 Storage unit 303 Candidate point 1000 Computer

Claims

1. A station placement design system for designing the installation positions of base stations for constructing a wireless area, which represents the installation state of the base stations in binary for each candidate point of the installation positions of the base stations, prepares a plurality of candidates for the installation states of the base stations for all candidate points, evaluates the candidates for the installation states of the base stations as a minimization problem with the uncovered rate of terminals and the number of installed base stations as objective functions respectively, advances generation alternation by applying selection, crossover, and mutation processes using a multi-objective genetic algorithm, calculates a plurality of candidate station placement design results that are Pareto optimal solutions, and is a station placement design system capable of selecting one or more station placement design results according to requirements from among the plurality of candidate station placement design results.

2. A station placement design apparatus for designing the installation positions of base stations for constructing a wireless area, which represents the installation state of the base stations in binary for each candidate point of the installation positions of the base stations, prepares a plurality of candidates for the installation states of the base stations for all candidate points, evaluates the candidates for the installation states of the base stations as a minimization problem with the uncovered rate of terminals and the number of installed base stations as objective functions respectively, advances generation alternation by applying selection, crossover, and mutation processes using a multi-objective genetic algorithm, calculates a plurality of candidate station placement design results that are Pareto optimal solutions, and is a station placement design apparatus capable of selecting one or more station placement design results according to requirements from among the plurality of candidate station placement design results.

3. A station placement design method in which a computer for designing the installation positions of base stations for constructing a wireless area represents the installation state of the base stations in binary for each candidate point of the installation positions of the base stations, prepares a plurality of candidates for the installation states of the base stations for all candidate points, evaluates the candidates for the installation states of the base stations as a minimization problem with the uncovered rate of terminals and the number of installed base stations as objective functions respectively, advances generation alternation by applying selection, crossover, and mutation processes using a multi-objective genetic algorithm, calculates a plurality of candidate station placement design results that are Pareto optimal solutions, and is capable of selecting one or more station placement design results according to requirements from among the plurality of candidate station placement design results.

4. A program for causing a computer to execute the station placement design method according to claim 3.

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