JP7040505B2 - Arithmetic logic units, arithmetic systems, operational methods, and computer programs - Google Patents

Description

The present invention relates to arithmetic units, arithmetic systems, arithmetic methods, and computer programs.

A method for solving an optimization problem is known (see, for example, Patent Document 1). Patent Documents 1 and 2 disclose a technique for converting design variables in order to solve an optimization problem. Patent Documents 3 to 7 and Non-Patent Document 1 disclose techniques related to optimal control. Patent Documents 8 and 9 disclose techniques related to quantization.

Special Table 2019-512134 Gazette Japanese Patent Publication No. 2019-512779 JP-A-2017-84343 Japanese Unexamined Patent Publication No. 2015-93655 Japanese Unexamined Patent Publication No. 2014-96091 Japanese Unexamined Patent Publication No. 2005-38397 Japanese Unexamined Patent Publication No. 2004-280792 Special Table 2003-532149 Gazette Japanese Unexamined Patent Publication No. 2016-213683

Yang Wang, Stephen Boyd, "Fast Model Predictive Control Using Online Optimization", IEEE Transactions on Control Systems Technology, 30 June 2009, Volume 18, Issue 2, March 2010, Pages 267-278

However, in the methods described in Patent Documents 1, 2, 7, and 8, there is room for improvement in the speed of solving the optimization problem. The techniques described in Patent Documents 3 to 6 and Non-Patent Document 1 cannot be applied to a system that allows only a finite number of inputs.

The present invention has been made to solve the above-mentioned problems, and an object of the present invention is to provide a technique for solving an optimization problem at high speed and with high accuracy while allowing a finite number of inputs.

The present invention has been made to solve the above-mentioned problems, and can be realized as the following forms. A conversion unit that converts a design variable that is a discrete value at each time into a design variable of a binary integer programming problem, which is an arithmetic device and is a design variable of a secondary programming problem whose parameters change with time. A transmitter that sends the design variables converted by the converter to the Zing machine, and a receiver that receives an approximate solution of a binary integer programming problem calculated by the Rising machine from the design variables transmitted by the transmitter. The evaluation function of the quadratic programming problem is time-series. An arithmetic unit that is a function of the optimal dynamic quantization problem of a signal. In addition, the present invention can also be realized in the following forms.

(1) According to one embodiment of the present invention, an arithmetic unit is provided. This arithmetic unit is a design variable of a quadratic programming problem whose parameters change with time, and has a conversion unit that converts a design variable that is a discrete value at each time into a design variable of a binary integer programming problem, and the above. A transmitter that sends the design variables converted by the converter to the Zing machine, and a receiver that receives an approximate solution of a binary integer programming problem calculated by the Rising machine from the design variables transmitted by the transmitter. It is provided with an inverse conversion unit that reversely converts the approximate solution of the integer programming problem received by the receiving unit into the approximate solution of the quadratic programming problem.

According to this configuration, the discrete value design variables that the Ising machine does not allow are converted into the design variables of the binary integer programming problem that the Ising machine allows. The Ising machine can calculate an approximate solution of the evaluation function in a binary integer programming problem using the converted design variables transmitted by the transmitter. The approximate solution calculated by the Ising machine is received by the receiving unit. The received approximate solution is inversely converted by the inverse transformant into an approximate solution of the quadratic programming problem before conversion by the transformant. Therefore, in this configuration, by converting the design variables that the Ising machine does not allow into the design variables that the Ising machine allows, it is possible to calculate an approximate solution of the optimum value at high speed and with high accuracy using the Ising machine.

(2) In the arithmetic unit of the above embodiment, the conversion unit, the transmission unit, the reception unit, and the inverse conversion unit repeatedly execute the conversion, the transmission, the reception, and the inverse conversion, and the conversion unit. May calculate the parameters of the secondary planning problem at the current time by using the approximate solution of the secondary planning problem that was inversely transformed by the inverse conversion unit one time ago.
According to this configuration, after calculating an approximate solution using the Ising machine, the approximate solution is repeatedly calculated using the approximate solution after an arbitrary processing unit time. As a result, the approximate solution after that is continuously calculated for the input at a certain time.

(3) In the arithmetic unit of the above aspect, the evaluation function of the secondary planning problem may be a function of the optimum control problem of the control system that allows only input of discrete values.
According to this configuration, the evaluation function of the optimal control problem that allows only the input of discrete values can be solved at high speed and with high accuracy by using the Ising machine that does not allow the input of discrete values.

(4) In the arithmetic unit of the above aspect, the evaluation function of the secondary planning problem may be a function of the optimum dynamic quantization problem of the time series signal.
According to this configuration, it is possible to solve the optimum dynamic quantization problem at high speed and with high accuracy by converting the time series signal into the design variables of the binary integer programming problem and using the Ising machine.

(5) In the arithmetic unit of the above aspect, the integer programming problem may be a 0-1 variable programming problem.
According to this configuration, versatility can be improved by using a generally widely used 0-1 variable programming problem as a binary integer programming problem.

It should be noted that the present invention can be realized in various aspects, for example, an arithmetic unit, an analysis apparatus, an arithmetic system including a singing machine, an apparatus and system including these, an arithmetic method, an analysis method, and the like. It can be realized in the form of a computer program for executing a system or a method, a server device for distributing the computer program, a non-temporary storage medium for storing the computer program, or the like.

It is a block diagram of the arithmetic system including the arithmetic unit as the embodiment of this invention. It is a flowchart of the calculation method of this embodiment. It is explanatory drawing which shows the effect of Example 1. FIG. It is explanatory drawing which shows the effect of Example 1. FIG. It is explanatory drawing which shows the effect of Example 1. FIG. It is explanatory drawing which shows the effect of Example 2. FIG. It is explanatory drawing which shows the effect of Example 2. FIG.

<Embodiment>
FIG. 1 is a block diagram of an arithmetic system 100 including an arithmetic unit 2 as an embodiment of the present invention. The arithmetic system 100 converts the design variables of the quadratic programming problem into the design variables of the binary integer programming problem that can be evaluated by the singing machine 3. Further, the arithmetic system 100 inversely transforms the approximate solution in the binary integer programming problem calculated by the Ising machine 3 into the approximate solution in the quadratic programming problem.

As shown in FIG. 1, the arithmetic system 100 is an arithmetic unit that calculates an approximate solution of a secondary planning problem by transmitting and receiving a design variable and an approximate solution to the Ising machine 3 capable of evaluating the Ising model and the Ising machine 3. 2 and. The Ising machine 3 and the arithmetic unit 2 are connected by, for example, a LAN (Local Area Network) or the Internet, and can communicate with each other.

The Ising machine 3 is a computer specialized in solving combinatorial optimization problems, and can calculate an approximate solution of a binary integer programming problem at high speed by using a special model called the Ising model. The Ising model used by the Ising machine 3 is a model that expresses macro (whole) behavior when a huge number of micro elements interact with each other and a forcing force is applied to each micro element. Micro elements in the Ising model are also called spins and take binary values such as 0-1 and ± 1. Therefore, the Ising machine 3 has a feature that the approximate solution of the binary integer programming problem can be calculated at high speed, but the approximate solution cannot be calculated from the evaluation function of the quadratic programming problem. Hereinafter, the Ising machine 3 of the present embodiment will be described by way of example in a case where only the Ising model represented as the “0-1 variable planning problem” is allowed. However, as described above, the Ising machine 3 may be configured to allow only the Ising model represented, for example, as a "± 1 variable planning problem".

The arithmetic unit 2 is a so-called personal computer (PC). As shown in FIG. 1, the arithmetic unit 2 includes an input unit 20 that receives input from a user or the like, a CPU (Central Processing Unit) 10 that executes various programs, a ROM (Read Only Memory) 50, and a RAM (Random). Access Memory) 60, a communication unit (transmitter, receiver) 30 that sends and receives information to and from the Zing machine 3, a storage unit 40 that stores various information, and an output unit 70 that outputs various data as images and sounds. , Is equipped.

The input unit 20 of this embodiment is composed of a keyboard and a mouse. The input information received by the input unit 20 is transmitted to the CPU 10. The CPU 10 expands the computer program stored in the ROM 50 into the RAM 60 and executes it. As a result, the CPU 10 functions as a conversion unit 11 and an inverse conversion unit 12. The functions of the conversion unit 11 and the inverse conversion unit 12 will be described later.

The communication unit 30 transmits the design variables converted by the conversion unit 11 to the Ising machine 3 by wireless communication. Further, the communication unit 30 receives an approximate solution of the 0-1 variable planning problem calculated by the Ising machine 3. The storage unit 40 is composed of a hard disk drive (HDD: Hard Disk Drive) or the like. The storage unit 40 stores various types of information according to the input information received by the input unit 20 and the control information from the CPU 10. The output unit 70 of the present embodiment is composed of a monitor capable of displaying an image and a speaker capable of outputting audio. The output unit 70 outputs various outputs according to the control information from the CPU 10. For example, the output unit 70 displays an approximate solution of the quadratic programming problem calculated by the inverse conversion unit 12 on the monitor as an image.

The conversion unit 11 converts the design variables of the secondary planning problem input by the input unit 20 or stored in the storage unit 40 into the design variables of the 0-1 variable planning problem. The design variable of the quadratic programming problem is a variable whose parameters change with time, and is a variable that takes a discrete value at each time. That is, since the quadratic programming problem input to the conversion unit 11 is a problem that the Ising machine 3 cannot solve, the conversion unit 11 converts the quadratic programming problem into an Ising model. On the other hand, the inverse conversion unit 12 converts the approximate solution of the 0-1 variable planning problem calculated by the Ising machine 3 received by the communication unit 30 into the approximate solution of the secondary planning problem before the conversion unit 11 converts it. And reverse conversion.

In the following, a method of converting a quadratic programming problem into a 0-1 variable programming problem will be described. First, in order to obtain an approximate solution to the quadratic programming problem, consider a problem that minimizes the evaluation function H of the following relational expression (1). It is assumed that u in the following relational expression (1) is a matrix and is an element (u ∈ U) of a finite set consisting of M vectors. In this case, the set U is expressed by the following relational expression (2).

The conversion unit 11 converts the design variables of the secondary planning problem into the design variables of the 0-1 variable planning problem allowed by the Ising model. The conversion unit 11 assumes that for the set U represented by the relational expression (2), "M (the number of elements of the set U) satisfies" M = 2 ^L "using a natural number L having a certain value". In this case, u _i is expressed as the following relational expression (3) for any i.

b _{j, l} ∈ {0,1} (j = 1, ..., m, l = 1, ..., L) is a binary variable that takes either 0 or 1 value, and K _j (j = 1, ..., M) are scaling parameters. The above relational expression (3) means that each element of the set U can be represented by a binary encoder using L bits.

The above relational expression (3) can be regarded as a linear map from {0,1} mL to the set U, and when expressed in a matrix, it is expressed as the following relational expression (4).

Here, the above relational expression (1) can be expressed as the following relational expression (5). In addition, a part of the above relational expression (5) was replaced with the following relational expression (6). The following relational expression (5) in this case is a quadratic programming problem with 0-1 variables. Here, the Ising model allowed by the Ising machine 3 is expressed by the following relational expression (7).

Σ _i in the above relational expression (7) is a variable called a qubit and satisfies σ _i ∈ {-1, + 1}. J _ij is an interaction parameter, and _hi is a parameter called a magnetic field. The above relational expression (7) can be expressed as a matrix as in the following relational expression (8).

The variable b ∈ {0,1} shown in the above relational expression (5) of the quadratic programming problem of the 0-1 variable and the variable σ ∈ {-1, + 1} shown in the above relational expression (7) of the Ising model. By utilizing the fact that there is a relationship of the following relational expression (9) with and, the following relational expression (10) is obtained from the above relational expression (5).
σ = 2b-1 ... (9)

The relational expression (10) is an Ising model like the relational expression (8). In this way, the conversion unit 11 transforms the quadratic programming problem into a 0-1 variable planning problem allowed by the Ising model. The communication unit 30 transmits the Ising model represented by the above relational expression (10) converted by the conversion unit 11 to the Ising machine 3. The Ising machine 3 calculates a variable σ _opt ∈ {-1, + 1} ^mL of the Ising model that minimizes the above relational expression (10).

The communication unit 30 receives the variable σ _opt transmitted from the Ising machine 3. The inverse conversion unit 12 inversely converts the variable σ _opt received by the communication unit 30 into a variable of {0,1} as in the following relational expression (11). The inverse transformation unit 12 restores the variable {0,1} represented by the following relational expression (11) to a discrete input as shown by the following relational expression (12).
b _opt = 2σ _opt -1 _mL … (11)
u _opt = Eb _opt … (12)

In the following, an example of the discrete-time linear system represented by the following relational expression (13) as the optimum control problem of the control system will be described.

In the above relational expression (13), t ∈ N represents a discrete time. For n, m, l ∈ N (set of natural elements), x (t) ∈ R ⁿ (n-dimensional real space) represents a state, and u (t) ∈ U ⊂ R ^m represents a control input. , A (t) ∈ R ^l represents a known signal and y (t) ∈ R ^l represents an output. Further, A ∈ R ⁿ × ⁿ , B1 ∈ R ⁿ × ^m , B2 ∈ R ^m × ^l , C ∈ R ^l × ^m , D ∈ R ^l × ^m are known constant matrices representing the dynamic characteristics of the system. .. The control system represented by the above relational expression (13) is assumed to be completely controllable and fully observable. Further, it is assumed that the set U is a finite set represented by the above relational expression (2). In the control system represented by the above relational expression (13), the input u (t) at each time takes only the elements of the set U, which is different from the normal control system. Next, in order to control the above relational expression (13), the evaluation function H represented by the following relational expression (14) is designed.

Q ∈ R ^l × ^l and R ∈ R ^m × ^m in the above relational expression (14) are definite-value symmetric matrices called weight matrices and are design parameters. Further, N ∈ N is a design parameter called a prediction step. The optimal control problem is the input string u (t) represented by the following relational expression (15) from the time t to the time (t + N-1) when the state x (t) at the time t is observed. , The problem is to find the following relational expression (16) that minimizes the evaluation function such as the above relational expression (14). Note that UN in the following relational expression (16) represents a Cartesian product set of ^U.

In the optimal control problem, by defining the augmented matrix represented by the following relational expression (17), a quadratic form expression represented by the following relational expression (18) can be obtained.

Here, the assumption that it is represented by the relational expression (3) is added again to the set U defined by the relational expression (2), and the following relational expression (3) is added to the relational expression (3). 19) Define the augmented matrix.

At this time, the evaluation function H of the optimal control problem can be expressed as the following relational expression (20). Using the following relational expression (20), the Ising model of the optimal control problem is as shown in the following relational expression (21). That is, the evaluation function H of the optimal control problem is reduced to the Ising model.

In the following, as an example of the optimum dynamic quantization problem of a time series signal, the problem of quantizing the audio signal {a (t)}, t ∈ N, a (t) ∈ R will be described. Let the quantized signal be {u (t)}, t ∈ N, u (t) ∈ R, and at each time t ∈ N, a set U = {u _i | u consisting of M pre-fixed elements. It is assumed that u (t) ∈ U is satisfied for _i ∈ R, i = 1, ..., M}. When quantizing {a (t)} to {u (t)}, it is preferable that the quantization error | {a (t)}-{u (t)} | is small, and this is expressed as an evaluation function. , Is expressed as the following relational expression (22). In order to minimize the following relational expression (22), the following relational expression (23) may be selected as u (t) at each time t ∈ N.

The ultimate goal of quantizing speech is to reduce the amount of data while maintaining the naturalness of human hearing. It is known that human auditory characteristics are characterized by a filter called a perceptual filter (PF). Reducing the quantization error after passing through this filter is a better method of quantization. Although several perceptual filters have been known so far, in this embodiment, a linear time-invariant filter represented by the following relational expression (24) is used. If the quantization error after passing through the perceptual filter PF represented by the following relational expression (24) is defined again, it is expressed by the following relational expression (25), and the evaluation function H corresponding to the following relational expression (25) has the following relation. It is expressed as the equation (26).

When the perceptual filter PF and the audio signal {a (t)} are given, the state-space representation of the above relational expression (25) gives the following relational expression (27). Next, considering the correspondence between the relational expression (26) and the relational expression (13) in the discrete time linear system, the following relational expression (28) is derived. Further, considering the correspondence between the evaluation function H of the relational expression (26) and the relational expression (14) in the discrete time linear system, the following relational expression (29) is derived.

As described above, the problem of performing quantization that minimizes the above relational expression (26) is the optimal control problem introduced in the discrete time linear system under the correspondence of the above relational expressions (27) to (29). It will be returned. That is, the evaluation function H of the time-series quantization problem is reduced to the Ising model.

FIG. 2 is a flowchart of the calculation method of the present embodiment. As shown in FIG. 2, in the calculation flowchart of the present embodiment (hereinafter, also simply referred to as “calculation flow”), first, a quadratic programming problem to be solved by input of the input unit 20 or the like is input to the calculation device 2. (Step S1). The conversion unit 11 performs a conversion process of converting the input design variable of the quadratic programming problem into the design variable of the 0-1 variable planning problem (step S2). As described in the above relational expressions (1) to (10), the conversion unit 11 converts the quadratic programming problem into an Ising model allowed by the Ising machine 3. The communication unit 30 performs a transmission step of transmitting the design variables converted by the conversion unit 11 to the Ising machine 3 (step S3). The communication unit 30 transmits the Ising model converted by the conversion unit 11 to the Ising machine 3.

The Ising machine 3 calculates the Ising model transmitted by the communication unit 30 (step S4). As explained in the above relational expressions (12) to (20), the Ising machine 3 sets the variable σ _opt ∈ {-1, + 1} ^mL of the Ising model that minimizes the evaluation function H in the 0-1 variable planning problem. calculate. After that, the communication unit 30 performs a receiving step of receiving the variable σ _opt ∈ {-1, + 1} ^mL as an approximate solution of the 0-1 variable planning problem calculated by the Ising machine 3 (step S5). The inverse conversion unit 12 performs an inverse conversion step of inversely converting the approximate solution of the 0-1 variable planning problem received by the communication unit 30 into the approximate solution of the secondary planning problem before the conversion unit 11 converts. Step S6). The inverse transformation unit 12 restores the variable σ _opt ∈ {-1, + 1} ^mL of the Ising model to a discrete input using the above relational expressions (11) and (12). After that, the calculation flow ends. The arithmetic unit 2 repeatedly executes each process of steps S2, S3, S5, and S6. The conversion unit 11 calculates each parameter in the quadratic programming problem at the current time by using the approximate value of the quadratic programming problem that was inversely converted by the inverse conversion unit 12 one before an arbitrary processing time. The processes of steps S2, S3, S5, and S6 are the conversion of the design variable by the conversion unit 11, the transmission of the converted design variable by the communication unit 30, and the 0-1 variable planning problem transmitted from the zing machine 3. It includes the reception of the approximate solution and the inverse conversion of the received approximate solution by the inverse transformor into the approximate solution of the quadratic design problem.

Each figure from FIG. 3 to FIG. 5 is an explanatory diagram showing the effect of the first embodiment. 3 and 4 show the calculation method (Quantum Annealing) as the first embodiment using the singing machine 3 of the present embodiment, the interior-point method (Interior-Point Method) and the simulated annealing method (Simulated Annealing) as comparative examples. ) And the effect when control is performed for the control system of a certain optimum control problem are shown. The effect shown in FIG. 3 is the time transition of the input variable with respect to the input string (FIG. 3). The effect shown in FIG. 4 is the time transition of the state variable with respect to the state (FIG. 4). In Example 1 and Example 2 described later, 2000Q manufactured by D-Wave Canada was used as the Ising machine 3.

In FIG. 3, the solid line curve C _{QA showing} the time transition of the input variable of the first embodiment, the one-dot chain line curve C _{IPM showing} the time transition of the input variable of the internal point method, and the time transition of the input variable of the annealed method are shown. The curve _CSA representing is shown. As shown in FIG. 3, it can be seen that the curve C _QA of Example 1 _achieves better control performance than the other two curves C _IPM and CS A.

In FIG. 4, a solid line L _QA showing the time transition of the state variable of Example 1, a polygonal line L _IPM of the alternate long and short dash line showing the time transition of the state variable of the internal point method, and the time transition of the state variable of the annealed method are shown. A polygonal line L _QA representing is shown. As shown in FIG. 4, it can be seen that the polygonal line L _QA of the present embodiment achieves better control performance than the other two polygonal lines L _IPM and L _SA .

In FIG. 5, the time required for the first embodiment to be executed and the time required for the interior point method and the simulated annealing method of the comparative example to be executed are shown in the table TA. The time required for the first embodiment shown in FIG. 5 is the time excluding the data communication time between the arithmetic unit 2 and the Ising machine 3. Therefore, in the table TA of FIG. 5, Example 1 is compared in parallel with the other two methods. As shown in FIG. 5, in the first embodiment, 1.9 × 10 ⁻² seconds is required as the total time (QA (Computation Time)) including the conversion of the design variable and the inverse conversion. Of these, the time required for annealing (QA (Annealing Time)) is 2.0 × 10 ^-3 seconds. That is, the time required for Example 1 to be executed is longer than 1.1 × 10 ⁻² seconds of the interior point method and longer than 2.7 × 10 ^-1 of the simulated annealing method. Example 1 takes about 72% (1.9 × 10 ⁻² / (1.1 × 10 ⁻² )) more time than the interior point method, but is performed as shown in FIGS. 3 and 4. The time transition of the input variable and the state variable of Example 1 is improved as compared with the interior point method.

6 and 7 are explanatory views showing the effect of the second embodiment. In FIGS. 6 and 7, the calculation method of Example 2 (QA) and the exact solution method (exact) and simulated annealing method (SA) by full search as comparative examples are used to quantize speech. The effect when a control signal is input is shown. The effects shown in FIG. 6 are the respective evaluations calculated by the three methods. FIG. 6 shows a boxplot BP _QA showing the evaluation value of Example 2, a boxplot BP _SA showing the evaluation value of simulated annealing, and a boxplot BP _ex showing the evaluation value of the exact solution method. ing. In the example shown in FIG. 7, the evaluation value of Example 2 achieves 1.25 times better quantization than simulated annealing.

The effect shown in FIG. 7 is the time required when the three methods are performed. FIG. 7 is a bar graph showing the time required for various methods to be executed. The common logarithm is adopted as the horizontal axis in FIG. 7. In the second embodiment shown in FIG. 7, the data communication time between the arithmetic unit 2 and the Ising machine 3 is excluded as in the first embodiment. FIG. 7 shows the total time (QA (Computation Time)) including the conversion and the inverse conversion of the design variable, and the time required for annealing (QA (Annealing Time)). The total time (QA (Computation Time)) of Example 2 is about 2.08 times the time of simulated annealing and about 0.001 times the time of the exact solution method. Comparing only the time required for annealing, the time required for Example 2 is about 0.005 times that of simulated annealing and about 2.3 × 10 ^-6 times that of the exact solution method.

Conventionally, in optimal control problems and quantization problems, when converted as a binary integer programming problem, the number of variables increases, so it is formulated as an integer programming problem that can take integer values larger than binary, and is directly solved. Was there. On the other hand, in the arithmetic unit 2 of the present embodiment, the conversion unit 11 converts the design variables of the quadratic programming problem into the design variables of the 0-1 variable planning problem. The design variable of the quadratic programming problem is a variable whose parameters change with time, and is a variable that takes a discrete value at each time. The inverse conversion unit 12 inversely converts the approximate solution of the 0-1 variable planning problem calculated by the Ising machine 3 received by the communication unit 30 into the approximate solution of the quadratic programming problem. Therefore, in the arithmetic unit 2 of the present embodiment, the Ising machine 3 is converted into the design variables allowed by the Ising machine 3 by converting the design variables not allowed by the Ising machine 3 into the design variables allowed by the Ising machine 3 as shown in FIGS. 3 to 7. It can be used to calculate an approximate solution of the optimum value with high speed and high accuracy.

Further, the arithmetic unit 2 of the present embodiment repeatedly executes each process of steps S2, S3, S5, and S6. The conversion unit 11 calculates each parameter in the quadratic programming problem at the current time by using the approximate value of the quadratic programming problem that was inversely converted by the inverse conversion unit 12 one before an arbitrary processing time. Therefore, in the arithmetic unit 2 of the present embodiment, after the approximate solution using the Ising machine 3 is calculated at one time, the approximate solution is repeatedly calculated using the approximate solution after an arbitrary processing unit time. .. As a result, the arithmetic unit 2 can continuously calculate an approximate solution after the input at a certain time.

Further, in the present embodiment, the evaluation function H of the secondary planning problem input to the arithmetic unit 2 is a function of the optimum control problem of the control system that allows only the input of discrete values. Therefore, in the arithmetic unit 2 of the present embodiment, the design variables are converted by the conversion unit 11 even if the evaluation function of the optimum control problem that allows the input and drinking of discrete values, which is not allowed by the rising machine 3. As a result, the arithmetic unit 2 can calculate the approximate value of the evaluation function at high speed and with high accuracy by using the Ising machine 3.

Further, in the present embodiment, the evaluation function H of the secondary planning problem input to the arithmetic unit 2 is a function of the optimum dynamic quantization problem of the time-series signal that allows only the input of discrete values. Therefore, in the arithmetic unit 2 of the present embodiment, the design variable is converted by the conversion unit 11 even if it is the evaluation function of the maximum quantization problem that allows the input drinking of the discrete value, which is not allowed by the rising machine 3. As a result, the arithmetic unit 2 can calculate the approximate value of the evaluation function at high speed and with high accuracy by using the Ising machine 3.

<Modified example of the embodiment>
The present invention is not limited to the above embodiment, and can be carried out in various embodiments without departing from the gist thereof, and for example, the following modifications are also possible.

In the above embodiment, an example of the arithmetic unit 2 and the arithmetic system 100 including the arithmetic unit 2 has been described, but the configurations of the arithmetic unit 2 and the arithmetic system 100 can be variously modified. For example, the arithmetic unit 2 may not include the input unit 20, the storage unit 40, and the output unit 70. For example, the input unit 20 and the output unit 70 may be provided in the arithmetic system 100 or other systems in a state where various information can be transmitted and received by the communication unit 30. The storage unit 40 may exist on the cloud and transmit / receive various information to / from the arithmetic unit 2 via the communication unit 30. In the above embodiment, 2000Q of D-Wave Canada is cited as an example of the Ising machine 3, but any Ising machine that can evaluate the Ising model may be adopted.

In the above embodiment, the optimum control problem of the control system and the optimum dynamic quantization problem of the time-series signal are dealt with as an example of calculating the approximate value using the rising machine 3, but other optimization problems are dealt with. You may. As such an optimization problem, the design variables of the quadratic programming problem may be discrete values at each time, with the parameters changing with time.

Although this embodiment has been described above based on the embodiments and modifications, the embodiments described above are for facilitating the understanding of the present embodiment and do not limit the present embodiment. This aspect may be modified or improved without departing from its spirit and claims, and this aspect includes its equivalent. Further, if the technical feature is not described as essential in the present specification, it may be deleted as appropriate.

2 ... Arithmetic logic unit 3 ... Ising machine 10 ... CPU
11 ... Conversion unit 12 ... Reverse conversion unit 20 ... Input unit 30 ... Communication unit (transmitter, receiver)
40 ... Storage unit 50 ... ROM
60 ... RAM
70 ... Output unit 100 ... Arithmetic system BP _QA , BP _SA , BP _ex ... Box whiskers showing evaluation values C _QA , C _IPM , C _SA ... Curves showing time transition of input variables H ... Evaluation functions L _QA , L _IPM , L _SA ... Line that represents the time transition of the state variable PF ... Perceptual filter TA ... Table U ... Set σ _opt ... Variable

Claims (7)

Arithmetic logic unit
A conversion unit that converts a design variable that is a design variable of a quadratic programming problem whose parameters change with time and is a discrete value at each time into a design variable of a quadratic integer programming problem.
A transmitter that sends the design variables converted by the converter to the Ising machine,
A receiver that receives an approximate solution of a binary integer programming problem calculated by the Ising machine from the design variables transmitted by the transmitter.
An inverse transformant that reversely transforms the approximate solution of the integer programming problem received by the receiver into the approximate solution of the quadratic programming problem.
Equipped with
The evaluation function of the quadratic planning problem is an arithmetic unit which is a function of the optimum dynamic quantization problem of a time series signal . The arithmetic unit according to claim 1.
The conversion unit, the transmission unit, the reception unit, and the inverse conversion unit repeatedly execute the conversion, the transmission, the reception, and the inverse conversion.
The conversion unit is an arithmetic unit that calculates an approximate solution of the quadratic programming problem at the current time by using an approximate solution of the quadratic programming problem that was inversely converted by the inverse conversion unit one time ago. The arithmetic unit according to claim 1 or 2, wherein the arithmetic unit is used.
The evaluation function of the secondary planning problem is an arithmetic unit, which is a function of an optimal control problem of a control system that allows only input of discrete values. The arithmetic unit according to any one of claims 1 to 3 .
The integer programming problem is an arithmetic unit, which is a 0-1 variable programming problem. It ’s an arithmetic system,
The arithmetic unit according to any one of claims 1 to 4 , and the arithmetic unit.
An Ising machine that calculates an approximate solution to the integer programming problem,
A computing system. It ’s a calculation method,
A conversion process that converts a design variable that is a design variable of a quadratic programming problem whose parameters change with time and is a discrete value at each time into a design variable of a quadratic integer programming problem.
The transmission process of sending the converted design variables to the Ising machine,
A receiving process that receives an approximate solution of a binary integer programming problem calculated by the Ising machine from the transmitted design variables, and a receiving process.
An inverse transformation step of inversely converting the received approximate solution of the integer programming problem to the approximate solution of the quadratic programming problem.
Equipped with
The evaluation function of the quadratic planning problem is a function of the optimum dynamic quantization problem of a time series signal, which is an arithmetic method. It ’s a computer program,
A conversion function that converts a design variable that is a design variable of a quadratic programming problem whose parameters change with time and is a discrete value at each time into a design variable of a quadratic integer programming problem.
A transmission function that sends the design variables converted by the conversion function to the Ising machine,
A reception function that receives an approximate solution of a binary integer programming problem calculated by the Ising machine from the design variables transmitted by the transmission function, and a reception function.
An inverse conversion function that reversely converts the approximate solution of the integer programming problem received by the reception function into the approximate solution of the quadratic programming problem, and
Let the computer run
The evaluation function of the secondary planning problem is a computer program which is a function of the optimum dynamic quantization problem of the time series signal .

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