JP6365064B2 - Population generation program, population generation method, and population generation apparatus - Google Patents

Description

  The present invention relates to a population generation program and the like.

  In recent years, agent simulation has been used in various public fields such as city planning, transportation, energy, disaster prevention, etc., due to improved computer performance. For example, by using agent simulation, it is possible to know the population breakdown that is optimal for population transition and city maintenance.

  Here, when using the agent simulation in the field as described above, it is desirable to provide the simulator with actually measured data of initial conditions that are realistic. However, it is difficult to obtain the actual measurement data from the viewpoint of survey cost and privacy.

  For this reason, there is a conventional technique in which instead of obtaining actual measurement data, a small number of samples are obtained from a target population, and kernel density estimation is used to approximately reconstruct the entire population from a small number of samples. In this kernel density estimation, an optimum value of a parameter called a bandwidth matrix is searched, and a complex distribution is reproduced using the searched parameter.

Dorin Comaniciu `` An Algorithm for Data-Driven Bandwidth Selection '' IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL.25, NO.2, FEBRUARY 2003

  However, the above-described conventional technique has a problem that the amount of calculation for calculating the population increases.

  The above kernel density estimation can express a complex distribution when the dimension to be handled is low, but in the case of a high dimension, the amount of calculation until the optimum value of the bandwidth matrix is calculated becomes large.

  In one aspect, an object of the present invention is to provide a population generation program, a population generation method, and a population generation device capable of preventing a large amount of calculation and reconstructing a population from a small number of samples. .

  In the first plan, the computer executes the following processing. A computer is caused to execute a process of specifying neighboring points existing in the vicinity of the points for a plurality of points included in the sample set. The computer is caused to select a point included in the sample set and a neighboring point corresponding to the point, and execute a process of generating a new point based on the selected point and a distribution of neighboring points. The computer is caused to execute a process of adding the generated new point to the population.

  According to one embodiment of the present invention, it is possible to prevent a calculation amount from increasing and to reconstruct a population from a small number of samples.

FIG. 1 is a functional block diagram illustrating the configuration of the population generation apparatus according to the present embodiment. FIG. 2 is a diagram illustrating an example of a data structure of the sample set information. FIG. 3 is a diagram illustrating an example of a data structure of k neighborhood information. FIG. 4 is a diagram illustrating an example of the data structure of the whitened sample set. FIG. 5 is a diagram for explaining the process of specifying the neighboring points. FIG. 6 is a diagram for explaining the processing of the generation unit. FIG. 7 is a diagram illustrating an example of a data structure of the population set information. FIG. 8 is a flowchart illustrating the processing procedure of the population generation apparatus according to the present embodiment. FIG. 9 is a diagram illustrating an example of another process in which the generation unit generates a new point. FIG. 10 is a diagram illustrating an example of a computer that executes a population generation program.

  Hereinafter, embodiments of a population generation program, a population generation method, and a population generation device disclosed in the present application will be described in detail with reference to the drawings. Note that the present invention is not limited to the embodiments.

  An example of the population generation apparatus according to the present embodiment will be described. FIG. 1 is a functional block diagram illustrating the configuration of the population generation apparatus according to the present embodiment. As illustrated in FIG. 1, the population generation apparatus 100 includes a communication unit 110, an input unit 120, a display unit 130, a storage unit 140, and a control unit 150.

  The communication unit 110 is a processing unit that performs data communication with other devices via a network. For example, the communication unit 110 corresponds to a communication device or the like. For example, the communication unit 110 outputs the received parameter information 141 and sample set information 142 to the control unit 150 when receiving parameter information 141 and sample set information 142 described later from another apparatus.

  The input unit 120 is an input device that inputs various types of information to the population generation device 100. For example, the input unit 120 corresponds to a keyboard, a mouse, a touch panel, or the like. For example, the user may input the parameter information 141 and the sample set information 142 by operating the input unit 120.

  The display unit 130 is a display device that displays various data output from the control unit 150. For example, the display unit 130 corresponds to a liquid crystal display, a touch panel, or the like.

  The storage unit 140 includes parameter information 141, sample set information 142, k neighborhood information 143, and population information 144. The storage unit 140 corresponds to a storage device such as a semiconductor memory element such as a random access memory (RAM), a read only memory (ROM), and a flash memory.

  The parameter information 141 includes “neighbor size k”, “output size l”, and “number of extraction points m”. The neighborhood size k is a parameter for designating the size when the k neighborhood of a certain point in the sample set information 142 is obtained. The output size l is a parameter that specifies the number of points to be included in the population information 144. The “number of extraction points m” is a parameter that specifies the number of points to be extracted when the points included in the sample set information 142 and the points near the points are extracted and given to the crossing kernel described later.

  The sample set information 142 is a sample corresponding to information on some points in the information on points included in the population. FIG. 2 is a diagram illustrating an example of a data structure of the sample set information.

In the example shown in FIG. 2, the horizontal axis is an axis corresponding to the attribute “household age”, and the vertical axis is an axis corresponding to the attribute “household annual income”. Further, the points x _{1 to} x ₁₅ are arranged corresponding to the values of the attributes. In the example shown in FIG. 2, for convenience of explanation, two axes corresponding to two types of attributes are shown, but this sample set information 142 has axes corresponding to two or more types of attributes. Each point x _{1 to} x ₁₅ of the sample set information 142 is represented by an n-dimensional vector when there are n types of attributes.

  The k-neighbor information 143 is information indicating a relationship between a point of the sample set information 142 and a neighboring point existing in the vicinity of this point. FIG. 3 is a diagram illustrating an example of a data structure of k neighborhood information. As shown in FIG. 3, the k neighborhood information 143 associates points with neighborhood points. The number of neighboring points is the number specified by the neighborhood size k.

  The population information 144 is population information generated based on the sample set information 142. The process for generating the population information 144 will be described later.

  The control unit 150 includes an acquisition unit 151, a whitening processing unit 152, a specifying unit 153, a generation unit 154, and an inverse whitening processing unit 155. The control unit 150 corresponds to an integrated device such as an application specific integrated circuit (ASIC) or a field programmable gate array (FPGA). The control unit 150 corresponds to an electronic circuit such as a CPU (Central Processing Unit) or an MPU (Micro Processing Unit).

  The acquisition unit 151 acquires parameter information 141 and sample set information 142 from the communication unit 110 or the input unit 120. The acquisition unit 151 registers the parameter information 141 and the sample set information 142 in the storage unit 140.

  The whitening processing unit 152 is a processing unit that performs whitening processing on the sample set information 142. The whitening processing unit 152 outputs the sample set information 142 that has been subjected to whitening processing to the specifying unit 153. In the following description, the sample set information 142 that has been subjected to the whitening process is referred to as a whitened sample set.

  Here, an example of the whitening process will be described. The whitening processing unit 152 adjusts the position of each point in the sample set information 142 so that the average vector of the entire points included in the sample set information 142 becomes 0 and the covariance matrix of the entire points becomes a unit matrix. To do.

  An example of processing in which the whitening processing unit 152 sets the average vector of points included in the sample set information 142 to 0 will be described. The whitening processing unit 152 calculates the average vector of the points included in the sample set information 142, and subtracts the average vector value from the vector value of each point, thereby calculating the average vector of the points included in the sample set information 142. Set to 0.

  An example of processing in which the whitening processing unit 152 performs adjustment so that the covariance matrix of points included in the sample set information 142 becomes a unit matrix will be described. The whitening processing unit 152 performs, for each point of the sample set information 142, processing for enlarging or reducing the interval between the points, and processing for rotating the position of each point around the origin. The vector value is updated, and the covariance matrix is calculated based on the updated vector value of each point. The whitening processing unit 152 calculates an interval between each point and a rotation amount in which the covariance matrix is a unit matrix.

  The whitening processing unit 152 performs processing that sets the average vector of points included in the sample set information 142 described above to 0 and processing that uses a covariance matrix as a unit matrix, thereby satisfying Equation (1). Specify the quantization matrix “T”. In Expression (1), “S” indicates a sample matrix in which vector values of points included in the sample set information 142 are arranged, and “E [TS]” indicates an average vector of the whitened sample matrix TS. “Cov [TS]” indicates a covariance matrix of the whitened sample matrix TS, and “I” indicates a unit matrix.

  E [TS] = 0, Cov [TS] = I (1)

  For example, the whitening processing unit 152 multiplies the vector of each point included in the sample set information 142 by the whitening matrix T, thereby updating the value of the vector of each point to generate a whitened sample set. The whitening processing unit 152 outputs information on the generated whitened sample set to the specifying unit 153 and the generating unit 154. Further, the whitening processing unit 152 outputs information on the whitening matrix T to the inverse whitening processing unit 155.

FIG. 4 is a diagram illustrating an example of the data structure of the whitened sample set. In the example illustrated in FIG. 4, the horizontal axis is an axis corresponding to the first principal component A ₁ (generally different from the household head age) output from the whitening processing unit 152, and the vertical axis is the second principal component A. ₂ (generally different from the household annual income). The whitening unit 152 by being processed whitened, the position of each point _x 1 _{~x 15} shown in FIG. 2 is moved to the position of each point _x 1 _{~x 15} shown in FIG.

  The specifying unit 153 is a processing unit that specifies, for each point in the whitened sample set, neighboring points that exist in the vicinity of the point. The specifying unit 153 registers the relationship between the point and the neighboring point corresponding to this point in the k neighborhood information 143. The identifying unit 153 associates the number of neighboring points with the neighborhood size k of the parameter information 141.

  An example of processing of the specifying unit 153 will be described. FIG. 5 is a diagram for explaining the process of specifying the neighboring points. The specifying unit 153 calculates the Eugrid distance from each point for each point. Each arrow in FIG. 5 indicates the Eugrid distance. The identifying unit 153 sets the points from the closest Eugrid distance to the reference point to the k-th point as the vicinity points of the reference point. The kth corresponds to the neighborhood size k.

For example, the reference point and the point _{x 1,} sequentially point near the Euclidean distance is short between the point _{x 1, x 2, x 3} , x 4, x 5, and,. The neighborhood size k is set to “3”. In this case, the specifying unit 153 sets the neighborhood points of the point x ₁ to “x ₂ , x ₃ , x ₄ ”, and registers the relationship between the points and the neighborhood points in the k neighborhood information 143. The identifying unit 153 identifies neighboring points for the other points x _{2 to} x _{15 in} the same manner and registers them in the k neighboring information 143.

  Returning to the description of FIG. The generation unit 154 is a processing unit that selects a point included in the whitened sample set and a neighboring point corresponding to this point, and generates a new point based on the selected point and the distribution of the neighboring point. The generation unit 154 adds the newly generated points to the population information 144 and repeats the above processing until the number of points included in the population information 144 reaches the output size l. The generation unit 154 outputs the population information 144 to which the newly generated points are added to the inverse whitening processing unit 155.

  Here, an example of a process in which the generation unit 154 generates a new point will be described. The generation unit 154 uniformly selects a point x from a plurality of points included in the whitened sample set. Further, the generation unit 154 performs non-restoration extraction uniformly and randomly from neighboring points corresponding to the point x that is uniformly and randomly selected. The generation unit 154 sets the number of points and neighboring points to be the same as the number of extraction points m.

For example, a case where the generation unit 154 selects one point uniformly and randomly from a plurality of points x _{1 to} x ₁₅ included in the whitened sample set and selects the point x ₁ will be described. Generator 154, refers to the k-nearest neighbor information 143, identifies a neighboring point corresponding to the point _{x 1.} The generation unit 154 uniformly and non-restoratively extracts “number of extracted points m−1” points from the specified neighboring points.

  In the following description, a point extracted uniformly and randomly from the whitened sample set and a non-restored and extracted point uniformly from the vicinity of this point will be referred to as extracted points as appropriate. The generation unit 154 extracts points so that the number of extraction points is the same as the extraction point number m.

The generation unit 154 gives the extracted point to the crossing kernel and generates a new point y. FIG. 6 is a diagram for explaining the processing of the generation unit. In the example shown in FIG. 6, the points extracted uniformly randomly from whitened sample set as _{x 13,} to the neighboring point identified on the basis of this point _{x 13} a point _{x 4, x 6, x 12} , x 14 . Points x ₁₂ and x ₁₄ are points that have been non-restored and extracted uniformly and randomly from the neighboring points. The generation unit 154 gives the extraction points x ₁₂ , x ₁₃ , and x ₁₄ to the crossing kernel, and generates a new point y ₁ . The generation unit 154 adds the point y ₁ to the population information 144. The generation unit 154 repeatedly executes a process of generating new points until the size of the population information 144 reaches the output size l.

An example of the crossing kernel used by the generation unit 154 will be described. The crossover kernel is defined by equation (2). In Expression (2), Expression (5) represents an average vector of extraction points and is defined by Expression (3). In equation (1), ε _i is defined by equation (4). ε _i is a random number according to a Gaussian distribution “N (0, 1 / m)” having an average “0” and a standard deviation “1 / m”, as shown in Expression (4). “M” shown in the equations (2) to (4) corresponds to the number of extraction points m.

  The generation unit 154 outputs the population information 144 having the output size l to the inverse whitening processing unit 155.

The inverse whitening processing unit 155 is a processing unit that performs the inverse whitening processing by multiplying the vector of each point included in the population information 144 by the inverse matrix “T ⁻¹ ” of the whitening matrix T. . The reverse whitening processing unit 155 performs reverse whitening on the whitened population information 144 to generate population set information 144 having original attribute values. The inverse whitening processing unit 155 registers the generated population set information 144 in the storage unit 140.

FIG. 7 is a diagram illustrating an example of a data structure of the population set information. In the example illustrated in FIG. 7, the horizontal axis is an axis corresponding to the attribute “household type age”, and the vertical axis is an axis corresponding to the attribute “household annual income”. As described above, the generator 154, the point of the population information 144 has been increased to output size l, from a small number of samples x ₁ ~x ₁₅ shown in FIG. 2, the reconstructed entire population .

  Next, a processing procedure of the population generation apparatus 100 according to the present embodiment will be described. FIG. 8 is a flowchart illustrating the processing procedure of the population generation apparatus according to the present embodiment. As illustrated in FIG. 8, the acquisition unit 151 of the population generation device 100 acquires the neighborhood size k (step S101). The acquisition unit 151 acquires the output size l (step S102). The acquisition unit 151 acquires the extraction point m (step S103). The acquisition unit 151 registers each acquired parameter in the parameter information 141.

  The whitening processing unit 152 of the population generation device 100 acquires the sample set information 142 (Step S104), and executes a whitening process on the sample set information 142 (Step S105).

  The specifying unit 153 of the population generation apparatus 100 calculates the k neighborhood of each point of the whitened sample set (step S106). In step S <b> 106, the specifying unit 153 specifies a neighboring point that exists in the vicinity of the point for each point of the whitened sample set, and registers the specifying result in the k-neighbor information 143.

Generator 154 of the population generator 100, the point _{x 1} from whitening sample set is selected uniformly randomly (step S107). As an example in step S107, the selected point on the uniform random, and the point x _1.

The generation unit 154 of the population generation apparatus 100 performs non-restoration extraction of points x ₂ ,..., X _m uniformly and randomly from the vicinity of k of the point x ₁ (step S108). The generation unit 154 gives the extraction points x ₁ ,... X _m to the crossing kernel, and generates one point y (step S109). The extraction points x ₁ ,..., X _{m in} step S109 are an example.

  The generation unit 154 adds y to the population information 144 (Step S110). The generation unit 154 determines whether the size of the population information 144 is l (step S111). If the size of the whitening population is not l (No at Step S111), the generation unit 154 proceeds to Step S107.

  On the other hand, when the size of the population information 144 is 1 (Yes at Step S111), the inverse whitening processing unit 155 of the population generation apparatus 100 performs the whitening process on the population information 144 to obtain the population information. Generate (step S112). The inverse whitening processing unit 155 outputs the population information 144 (step S113).

  Next, the effect of the population generation apparatus 100 according to the present embodiment will be described. The specifying unit 153 of the population generating apparatus 100 specifies neighboring points that exist in the vicinity of the points for a plurality of points included in the sample set subjected to the whitening process. The generation unit 154 of the population generation apparatus 100 selects a point included in the sample set subjected to whitening processing and a neighboring point corresponding to this point, and creates a new point based on the selected point and the distribution of the neighboring point. And add the generated points to the population. For this reason, according to the population generation apparatus 100 according to the present embodiment, it is possible to prevent a calculation amount from increasing and to construct a population from a small number of samples.

  For example, the generation unit 145 of the population generation apparatus 100 according to the present embodiment gives a point included in the sample set and a neighboring point corresponding to this point to the crossing kernel shown in Expression (1), and adds a new point. Generate. This crossing kernel is for generating a new point based on, for example, Expression (1), and there is no step of calculating an optimum bandwidth matrix as in the conventional kernel density estimation. Therefore, a population set having a high-dimensional complex distribution can be generated without increasing the amount of calculation.

  Further, the population generation apparatus 100 according to the present embodiment generates the population information 144 of the output size l based on the sample set information 142 having a small number of points. For this reason, it is possible to acquire information close to actual measurement data that is difficult to obtain from the viewpoint of survey cost and privacy, and it can be used for various agent simulations.

  Incidentally, the generation unit 154 of the population generation apparatus 100 according to the present embodiment generates a new point by giving a point included in the sample set and a neighboring point corresponding to this point to the crossing kernel. The process of generating is not limited to this. The generation unit 154 may assign a probability density function having statistical moments up to the n-th order of neighboring points of the sample set point to generate a new point according to the assigned probability density function.

FIG. 9 is a diagram illustrating an example of other processing in which the generation unit 154 generates a new point. For convenience of explanation, a point included in the sample set into a one-dimensional, the points of the sample collection and x ₁ ~x _4. The generation unit 154 specifies a Gaussian distribution of points x ₁ , x ₂ , x ₃ , x ₄ included in the sample set. The Gaussian distribution of x ₁ where the Gaussian distribution 10a, the Gaussian distribution of the _{x 2} where the Gaussian distribution 10b, and Gaussian distribution of _{x 3} where the Gaussian distribution 10c, and Gaussian 10d Gaussian distribution of _{x 4.} The generation unit 154 specifies the probability distribution 20 obtained by averaging the Gaussian distributions 10a to 10d. The generation unit 154 generates a new point y according to the probability distribution 20. In this way, the generation unit 154 may generate a new point using a probability density function other than the crossover kernel.

  Next, an example of a computer that executes a population generation program that realizes the same function as the population generation apparatus 100 shown in the above embodiment will be described. FIG. 10 is a diagram illustrating an example of a computer that executes a population generation program.

  As illustrated in FIG. 10, the computer 200 includes a CPU 201 that executes various arithmetic processes, an input device 202 that receives data input from a user, and a display 203. The computer 200 includes a reading device 204 that reads a program and the like from a storage medium, and an interface device 205 that exchanges data with other computers via a network. The computer 200 also includes a RAM 206 that temporarily stores various information and a hard disk device 207. The devices 201 to 207 are connected to the bus 208.

  The hard disk device 207 has a specific program 207a and a generation program 207b. The CPU 201 reads the specific program 207 a and the generation program 207 b and develops them in the RAM 206. The specific program 207a functions as a specific process 206a. The generation program 207b functions as a generation process 206b.

  For example, the specifying process 206 a corresponds to the specifying unit 153. The generation process 206 b corresponds to the generation unit 154.

  Note that the specific program 207a and the generation program 207b are not necessarily stored in the hard disk device 207 from the beginning. For example, each program is stored in a “portable physical medium” such as a flexible disk (FD), a CD-ROM, a DVD disk, a magneto-optical disk, and an IC card inserted into the computer 200. Then, the computer 200 may read and execute the specific program 207a and the generation program 207b.

  The following supplementary notes are further disclosed with respect to the embodiments including the above examples.

(Supplementary note 1)
For a plurality of points associated with the values for each principal component included in the sample set, identify neighboring points that exist in the vicinity of each point,
By selecting a point included in the sample set and a neighboring point corresponding to the point, and assigning the selected point and the neighboring point to a predetermined probability density function, the value and probability of each principal component that can be taken by the new point Is generated, a new point is generated based on the generated distribution,
A population generation program characterized by executing a process of adding a generated new point to a population.

(Additional remark 2) The process which produces | generates the said new point selects the point contained in the said sample set, and the neighboring point corresponding to the said point, calculates the average vector of the selected point and a neighboring point, and selected point The population generation program according to appendix 1, wherein the new point is generated based on each vector of neighboring points, the average vector, and a value according to a predetermined Gaussian distribution.

(Additional remark 3) The process which produces | generates the said new point selects the point contained in the said sample set which has less than a predetermined number of points, and the neighboring point corresponding to the said point, and selects the distribution of the selected point and the neighboring point. The population generation program according to appendix 1 or 2, wherein a population having a predetermined number or more points is generated by repeatedly executing a process of generating new points based on the above.

(Appendix 4) A point generation method executed by a computer,
For a plurality of points associated with the values for each principal component included in the sample set, identify neighboring points that exist in the vicinity of each point,
By selecting a point included in the sample set and a neighboring point corresponding to the point, and assigning the selected point and the neighboring point to a predetermined probability density function, the value and probability of each principal component that can be taken by the new point Is generated, a new point is generated based on the generated distribution,
A method of generating a population, characterized by executing a process of adding a generated new point to the population.

(Additional remark 5) The process which produces | generates the said new point selects the point contained in the said sample set, and the neighboring point corresponding to the said point, calculates the average vector of the selected point and a neighboring point, and selected point The population generation method according to appendix 4, wherein the new point is generated based on each vector of neighboring points, the average vector, and a value according to a predetermined Gaussian distribution.

(Additional remark 6) The process which produces | generates the said new point selects the point contained in the said sample set which has less than a predetermined number of points, and the neighboring point corresponding to the said point, and selects the distribution of the selected point and the neighboring point. 6. The population generation method according to appendix 4 or 5, wherein a population having a predetermined number or more points is generated by repeatedly executing a process of generating new points.

(Additional remark 7) About the some point matched with the value for every main component contained in a sample set, the specific part which each specifies the nearby point which exists in the vicinity of each point,
By selecting a point included in the sample set and a neighboring point corresponding to the point, and assigning the selected point and the neighboring point to a predetermined probability density function, the value and probability of each principal component that can be taken by the new point And a generation unit for generating a new point based on the generated distribution, and adding the generated new point to the population.

(Supplementary Note 8) The generation unit selects a point included in the sample set and a neighboring point corresponding to the point, calculates an average vector of the selected point and the neighboring point, and selects each of the selected point and the neighboring point. The population generation apparatus according to appendix 7, wherein the new point is generated based on a vector, the average vector, and a value according to a predetermined Gaussian distribution.

(Supplementary Note 9) The generation unit selects a point included in the sample set having less than a predetermined number of points and a neighboring point corresponding to the point, and generates a new point based on the selected point and the distribution of neighboring points. The population generation apparatus according to appendix 7 or 8, wherein a population having a predetermined number or more points is generated by repeatedly executing a process of generating points.

100 population generation device 153 identification unit 154 generation unit

Claims (5)

On the computer,
For a plurality of points associated with the values for each principal component included in the sample set, identify neighboring points that exist in the vicinity of each point,
By selecting a point included in the sample set and a neighboring point corresponding to the point, and assigning the selected point and the neighboring point to a predetermined probability density function, the value and probability of each principal component that can be taken by the new point Is generated, a new point is generated based on the generated distribution,
A population generation program characterized by executing a process of adding a generated new point to a population.   The process of generating the new point selects a point included in the sample set and a neighboring point corresponding to the point, calculates an average vector of the selected point and the neighboring point, and selects the selected point and the neighboring point. The population generation program according to claim 1, wherein the new point is generated based on each vector, the average vector, and a value according to a predetermined Gaussian distribution.   The process of generating the new point selects a point included in the sample set having less than a predetermined number of points and a neighboring point corresponding to the point, and based on the selected point and the distribution of neighboring points, a new point is created. The population generation program according to claim 1 or 2, wherein a population having a predetermined number or more points is generated by repeatedly executing a process for generating such points. A point generation method executed by a computer,
For a plurality of points associated with the values for each principal component included in the sample set, identify neighboring points that exist in the vicinity of each point,
By selecting a point included in the sample set and a neighboring point corresponding to the point, and assigning the selected point and the neighboring point to a predetermined probability density function, the value and probability of each principal component that can be taken by the new point Is generated, a new point is generated based on the generated distribution,
A method of generating a population, characterized by executing a process of adding a generated new point to the population. For a plurality of points associated with the values for each principal component included in the sample set, a specifying unit that specifies each neighboring point existing in the vicinity of each point;
By selecting a point included in the sample set and a neighboring point corresponding to the point, and assigning the selected point and the neighboring point to a predetermined probability density function, the value and probability of each principal component that can be taken by the new point And a generation unit for generating a new point based on the generated distribution, and adding the generated new point to the population.

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