Information processing device

Abstract

The process of converting the optimization problem into a predetermined format takes time. [Solution] The information processing device of the present disclosure includes a storage unit that stores corresponding data to which a problem expression and a conversion expression obtained by expanding and organizing the problem expression are associated, and a conversion unit that converts an optimization problem including the problem expression into a pre-set format using the conversion expression based on the corresponding data.

Description

[Technical Field]

[0001] This disclosure relates to an information processing device. [Background technology]

[0002] As a method for solving real-world problems, the energy in combinatorial optimization problems is being converted into the form of an Ising model and then solved. For example, as described in Patent Document 1, the energy of an optimization problem is being formulated in the form of QUBO (Quadratic Unconstrained Binary Optimization), and the problem is being solved by simulated annealing. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2022-67101 [Overview of the project] [Problems that the invention aims to solve]

[0004] However, solving optimization problems requires converting them into formats such as QUBO, and as the problem size increases, the conversion process becomes time-consuming.

[0005] Therefore, one of the purposes of this disclosure is to solve the aforementioned problem of the time required to convert the optimization problem into a predetermined form. [Means for solving the problem]

[0006] An information processing device, which is one form of this disclosure, A storage unit that stores corresponding data where a problem expression and a transformed expression obtained by expanding and rearranging the said problem expression are associated, A conversion unit that converts the optimization problem, including the problem expression, into a pre-set format using the conversion formula based on the aforementioned corresponding data, Equipped with, This is the structure it takes. Furthermore, the information processing method, which is one form of this disclosure, Based on correspondence data that associates a stored problem expression with a transformation expression obtained by expanding and rearranging the problem expression, the optimization problem including the problem expression is transformed into a pre-set format using the transformation expression. This is the structure it takes. Furthermore, one form of this disclosure is a program, In an information processing device, Based on correspondence data that associates a stored problem expression with a transformation expression obtained by expanding and rearranging the problem expression, the optimization problem including the problem expression is transformed into a pre-set format using the transformation expression. To execute the process This is the structure it takes. [Effects of the Invention]

[0007] By being configured as described above, this disclosure can reduce the time required to convert an optimization problem into a predetermined form. [Brief explanation of the drawing]

[0008] [Figure 1] This is a block diagram showing an example of the configuration of the information processing device related to this disclosure. [Figure 2] This flowchart shows an example of processing operations performed by the information processing device related to this disclosure. [Figure 3] This figure shows an example of data related to this disclosure. [Figure 4] This figure shows an example of data related to this disclosure. [Figure 5] This figure shows an example of data related to this disclosure. [Figure 6] This block diagram shows an example of the hardware configuration of the information processing device related to this disclosure. [Figure 7] It is a block diagram showing an example of the configuration of an information processing apparatus according to the present disclosure. [Figure 8] It is a flowchart showing an example of a processing operation by the information processing apparatus according to the present disclosure.

Embodiment for Carrying Out the Invention

[0009] <First Embodiment> The first embodiment of the present disclosure will be described with reference to the drawings. Note that the drawings may be relevant to any of the embodiments.

[0010] The information processing apparatus of the present disclosure is used, as an example, to convert a combinatorial optimization problem with preset constraint conditions into a formulated model. In particular, in this embodiment, an example will be described in which the combinatorial optimization problem is converted into a QUBO (Quadratic Unconstrained Binary Optimization) model.

[0011] The combinatorial optimization problem with constraint conditions is a problem in which an objective function and constraint conditions are set, and a solution that minimizes the objective function while satisfying the constraint conditions is sought. And the combinatorial optimization problem with constraint conditions can be converted into a QUBO model as shown in Equation 1 and Equation 2. At this time, the combinatorial optimization problem with constraint conditions can express the energy value E of the optimization problem using the objective function terms (the first term and the second term) and the constraint condition terms (the third term and the fourth term) as shown in Equation 1, and as shown in Equation 2, these can be combined into one model.

Equation

Equation

[0012] s in the above-described equations i , s j is the spin s i , sj is a variable representing the state, and is expressed as "0" or "1". Here, i and j are the identification numbers of the spin s. Also, Q in the above Equation 2 ij is the weight parameter set corresponding to each combination of spins s i , s j and is called the QUBO matrix.

[0013] Then, the above-mentioned combinatorial optimization problem with constraints can obtain the optimal solution by solving for the spin that minimizes the energy E using a method called simulated annealing (quasi-quantum annealing). At this time, the state of the spin s flips from 0 to 1, or from 1 to 0, to transition the solution and search. In simulated annealing, when evaluating the neighboring solution during the search for the solution, if the evaluation value of the neighboring solution is good (small), it will always transition, but even if the evaluation value of the neighboring solution is bad (large), it can transition probabilistically. This probability is determined by the inverse temperature, which is the reciprocal of the value of the temperature parameter, so the search for the solution is performed while increasing or decreasing the inverse temperature.

[0014] Here, the QUBO matrix represented by Q in the above Equation 2 ij is obtained as the coefficient matrix of each variable in the equation converted to the QUBO form by expanding and arranging the equation of the optimization problem. For example, when the equation before conversion of the optimization problem is the problem expression shown in the following Equation 3, it can be expanded and arranged as shown in Equation 4. Then, as shown in Figure 3, a 3×3 QUBO matrix, which is the coefficient matrix of each variable in Equation 4, can be obtained. Since x is a binary variable, x 2 = x, resulting in a QUBO matrix as shown in Figure 3.

Equation

Equation

[0015] On the other hand, as mentioned above, computational processing is required to expand and organize the optimization problem and convert it into QUBO format, and as the size of the optimization problem increases, the amount of computation increases and the processing time increases. For this reason, the information processing device in this disclosure is configured as follows in order to suppress the amount of computation and processing time when converting the optimization problem into a QUBO format model.

[0016] In the following, we will mainly explain the case where a constrained optimization problem is formulated as an unconstrained optimization problem, as described above. However, this method is also applicable when dealing with constrained optimization problems as they are, and can be applied to other optimization problems such as constrained linear programming problems. Furthermore, in the following, we will mainly illustrate the case where the optimization problem is converted to QUBO form, but the spin s mentioned above will not be used. i ,s j However, this is also applicable when converting to the Ising model format, which is represented by "-1" or "1".

[0017] An example of the configuration and operation of the information processing device in this embodiment will be described in detail. Figure 1 shows an example of the configuration of the information processing device, and Figure 2 shows an example of the operation of the information processing device. The information processing device consists of one or more information processing devices equipped with an arithmetic unit and a storage device. As shown in Figure 1, the information processing device includes a division unit 11, a conversion pattern determination unit 12, a conversion / coefficient matrix generation unit 13, an equation expansion unit 14, an equation simplification unit 15, a coefficient matrix generation unit 16, and an integration unit 17. The functions of the division unit 11, the conversion pattern determination unit 12, the conversion / coefficient matrix generation unit 13, the equation expansion unit 14, the equation simplification unit 15, the coefficient matrix generation unit 16, and the integration unit 17 can be realized by the arithmetic unit executing a program for realizing each function stored in the storage device. The information processing device 10 also includes a conversion pattern storage unit 18 realized in the storage device.

[0018] The conversion pattern storage unit 18 (storage unit) stores conversion patterns consisting of corresponding data, which are associated with a problem expression and a conversion expression obtained by expanding and rearranging the problem expression. The problem expression is an expression included in an optimization problem and is a patterned expression. For example, the problem expression is an expression that has been patterned, such as equation 1, as shown in equation 5 below, which is "(sum of multiple variables without coefficients - constant) squared". Then, by expanding and rearranging the problem expression in equation 5, it can be transformed into the conversion expression shown in equation 6. In this way, the corresponding data that is considered a conversion pattern is composed of the problem expression and the conversion expression being associated with each other. Note that equations 5 and 6 show the problem expression when it is expressed as a mathematical expression and when it is expressed as a program, respectively.

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[0019] Note that the above-described transformation pattern is just one example, and any problem expression and transformation formula may be associated with each other. Another example of a transformation pattern is shown in Figure 4. In Figure 4, each row shows the transformation pattern in which the problem expression and transformation formula are associated with the case of a constrained optimization problem and the case of an unconstrained optimization problem.

[0020] Furthermore, the conversion patterns may be stored in the conversion pattern storage unit 18 in advance, or they may be added to the conversion pattern storage unit 18 later, as will be described later. For example, as will be described later, correspondence data that associates a problem expression included in an optimization problem input to the information processing device with a conversion expression obtained by expanding and organizing such problem expression by the expression expansion unit 14 and the expression organization unit 15 may be stored in the conversion pattern storage unit 18 as a conversion pattern.

[0021] Next, we will explain the processing functions of the information processing device. As an example, the entire formulation of an optimization problem, such as equation 3 above or equation 7 below, is input to the information processing device.

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[0022] The division unit 11 receives the input optimization problem and divides it into problem expressions of predetermined units (step S1 in Figure 2). At this time, the division unit 11 divides it into problem expressions of units that can be represented by monomials or polynomials, for example, those registered as conversion patterns. For example, the optimization problem shown in equation 3 cannot be divided any further and is treated as a problem expression as is. For example, the optimization problem shown in equation 7 is divided into a problem expression representing the sum described in the first part and a problem expression representing the square described in the second part. The division unit 11 then inputs the optimization problem, now divided into problem expressions, into the conversion pattern determination unit 12. The division unit 11 is not limited to dividing the optimization problem with only one division pattern, but may also divide it with multiple division patterns, that is, multiple division patterns with different division points, and input the optimization problem, now divided into problem expressions for each division pattern, into the conversion pattern determination unit 12. Then, processing is performed for each of the divided problem expressions (step S2 in Figure 2).

[0023] The transformation pattern determination unit 12 (determination unit) performs a pattern determination to determine whether the problem expression included in the optimization problem, that is, the divided problem expression, is included in the transformation patterns stored in the transformation pattern storage unit 18 (step S3 in Figure 2). For example, the squared problem expression in equation 3 and equation 7 above is registered as a problem expression in a transformation pattern, so it is determined to be a transformation pattern (Yes in step S3 in Figure 2). The transformation pattern determination unit 12 then inputs the problem expression determined to be a transformation pattern into the transformation / coefficient matrix generation unit 13. On the other hand, if the problem expression is not registered as a problem expression in a transformation pattern, the transformation pattern determination unit 12 determines that it is not a transformation pattern (No in step S3 in Figure 2) and inputs such a problem expression into the equation expansion unit 14. The transformation pattern determination unit 12 performs a pattern determination on all problem expressions included in the optimization problem at once.

[0024] The transformation / coefficient matrix generation unit 13 (transformation unit) transforms a problem expression determined to be a transformation pattern into a transformation expression based on the transformation patterns stored in the transformation pattern storage unit 18. For example, the squared problem expression in equation 3 and equation 7 is transformed into the transformation expression shown in equation 6, according to the transformation pattern consisting of the corresponding data between equation 5 and equation 6 described above. The transformation / coefficient matrix generation unit 13 then generates a coefficient matrix for each variable in the transformed transformation expression (step S4 in Figure 2). For example, the squared problem expression in equation 3 and equation 7 is transformed into the 3x3 coefficient matrix shown in Figure 3 based on the transformation expression in equation 6. Note that the transformation / coefficient matrix generation unit 13 may only transform into a transformation expression. In other words, the transformation / coefficient matrix generation unit 13 may transform the problem expression into the form of a transformation expression, or into the form of a coefficient matrix.

[0025] On the other hand, problem expressions that are determined not to be conversion patterns are processed by the expression expansion unit 14, the expression simplification unit 15, and the coefficient matrix generation unit 16 (conversion unit). The expression expansion unit 14 expands the problem expression that is determined not to be a conversion pattern (step S5 in Figure 2), and the expression simplification unit 15 simplifies the expanded problem expression and converts it into a conversion expression (step S6 in Figure 2). Then, the coefficient matrix generation unit 16 generates the coefficient matrix for each variable in the conversion expression obtained by expanding and simplifying the problem expression (step S7 in Figure 2). The expression expansion unit 14 and the expression simplification unit 15 may store the corresponding data between the problem expression before expansion and simplification and the conversion expression after expansion and simplification as a new conversion pattern in the conversion pattern storage unit 18.

[0026] The integration unit 17 (transformation unit) adds the coefficient matrix generated by the transformation / coefficient matrix generation unit 13 and the coefficient matrix generated by processing in the equation expansion unit 14, equation simplification unit 15, and coefficient matrix generation unit 16 (step S8 in Figure 2). Then, by performing the above processing for each divided problem expression, all coefficient matrices are integrated to generate a single coefficient matrix (steps S2 to S9 in Figure 2 are repeated). For example, if one optimization problem is divided into multiple problem expressions, the problem expressions corresponding to the transformation pattern are converted into coefficient matrices in the transformation / coefficient matrix generation unit 13, and the problem expressions that do not correspond to the transformation pattern are converted into coefficient matrices in the equation expansion unit 14, equation simplification unit 15, and coefficient matrix generation unit 16, and these coefficient matrices are integrated to form a single coefficient matrix. The integration unit 17 then outputs the integrated coefficient matrix as a model matrix used to solve the optimization problem, for example, a QUBO matrix. In this case, the integration unit 17 may output the coefficient matrix generated by the transformation / coefficient matrix generation unit 13 if that is the only coefficient matrix available, or it may output the coefficient matrix generated by the coefficient matrix generation unit 16 if that is the only coefficient matrix available.

[0027] The integration unit 17 may also integrate the transformed equation obtained by the transformation / coefficient matrix generation unit 13 from the transformed equation obtained by the equation expansion unit 14 and the equation simplification unit 15 from the transformed equation obtained by the expanded and simplified equations of the problem expression. The integration unit 17 may then output the integrated transformed equation as a model to be used in solving the optimization problem.

[0028] As described above, in this disclosure, conversion patterns consisting of correspondence data between problem expressions and conversion formulas are registered in advance, and problem expressions included in optimization problems are converted into conversion formulas according to the conversion patterns. This makes it possible to reduce the time required to convert optimization problems into a predetermined format such as QUBO format.

[0029] Furthermore, this disclosure divides the optimization problem into problem expressions and simultaneously determines whether the divided problem expressions correspond to a transformation pattern. This further reduces the time required to convert the optimization problem into a predetermined format.

[0030] Furthermore, in this disclosure, if the problem expression does not correspond to a conversion pattern, the problem expression is expanded and rearranged to convert it into a conversion expression, and the correspondence data between the problem expression before conversion and the conversion expression after conversion is registered as a new conversion pattern. This reduces the time required to convert the optimization problem to be later converted into a predetermined format.

[0031] While the above examples primarily illustrate the transformation of problem expressions for unconstrained problems, this disclosure is also applicable to constrained problems if they are registered as transformation patterns as shown in Figure 4. Furthermore, even if a constrained problem is not registered as a transformation pattern as shown in Figure 4, it can still be applied to constrained problems by creating a pattern for constrained problems that are equivalent to unconstrained problems. For example, the constrained problem shown in equation 8 is equivalent to the unconstrained problem shown in equation 9, so by creating a pattern for "addition of variables without coefficients = constant," it is possible to handle constrained problems as well.

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[0032] <Second Embodiment> Next, a second embodiment of this disclosure will be described with reference to the drawings. The drawings may be relevant to either embodiment.

[0033] The information processing device in this embodiment has the same configuration as Embodiment 1 described above. In addition, the information processing device has the following configuration. The following will mainly describe the configuration that differs from the above.

[0034] The conversion pattern determination unit 12 (assignment unit) of the information processing device in this embodiment has the function of calculating and assigning sequential indices (sequential numbers) to the indices (numbers) of variables used in the problem expression of an optimization problem. For example, as shown in Figure 5(5-1), in the case of a one-dimensional index y[i] or a two-dimensional index x[i][j], sequential indices q0 to q5 are calculated and assigned as shown in Figure 5(5-2). Specifically, the conversion pattern determination unit 12 calculates sequential indices as follows, as an example. For the 1-dimensional case: first element + i Example: y[1]=q4+1=q5 For 2D: stride + i * stride + j Example: x[1][0]=q0+1*2+0=q2

[0035] Furthermore, the transformation pattern determination unit 12 may perform the calculation and assignment of serial indices for variables together when determining the transformation pattern as described above. This reduces the duplication of the variable index calculation process. For example, in the example in Figure 5, the number of calculations can be reduced to the number of variables x and y. As a result, the time required to transform the optimization problem into a predetermined format can be shortened. However, the calculation and assignment of serial indices for variables as described above is not necessarily limited to being performed when determining the transformation pattern, but may be performed at any time before the transformation of the problem expression.

[0036] <Third Embodiment> Next, a third embodiment of the present disclosure will be described. The problem-solving device in this embodiment includes a problem-solving unit that solves an optimization problem using the coefficient matrix output as described above. That is, the problem-solving device solves an optimization problem using the simulated annealing method, for example, using a QUBO model as shown in Equation 2, which is the QUBO matrix that is the output coefficient matrix. However, the problem-solving device is not limited to solving for the QUBO model, but may also solve for models using other types of coefficient matrices output from the information processing device.

[0037] Furthermore, the information processing device described in Embodiments 1 and 2 may also have a function to perform a solution using the coefficient matrix described above. In other words, the information processing device described in Embodiments 1 and 2 may convert the optimization problem into a coefficient matrix and then perform a solution using such a coefficient matrix.

[0038] <Fourth Embodiment> Next, a fourth embodiment of this disclosure will be described with reference to the drawings. This embodiment shows an outline of the information processing device, etc., described in the embodiments described above. Note that the drawings may be relevant to any of the embodiments.

[0039] First, the hardware configuration of the information processing device 100 in this disclosure will be described. The information processing device 100 is composed of a general information processing device, and as an example, it is equipped with the following hardware configuration as shown in Figure 6. ·CPU(Central Processing Unit)101(Arithmetic unit) ROM (Read Only Memory) 102 (Storage Device) • RAM (Random Access Memory) 103 (Storage Device) • Program group 104 loaded into RAM 103 • Storage device 105 for storing the program group 104 • Drive device 106 for reading and writing to external storage medium 110 of the information processing device. • Communication interface 107 connecting to a communication network 111 outside the information processing device. • Input / output interface 108 for data input and output. • Bus 109 connecting each component

[0040] Figure 6 shows an example of the hardware configuration of the information processing device 100, and the hardware configuration of the information processing device is not limited to the case described above. For example, the information processing device may consist of only a part of the configuration described above, such as not having a drive device 106. In addition, the information processing device may use a GPU (Graphic Processing Unit), DSP (Digital Signal Processor), MPU (Micro Processing Unit), FPU (Floating point number Processing Unit), PPU (Physics Processing Unit), TPU (Tensor Processing Unit), quantum processor, microcontroller, or a combination thereof instead of the CPU described above.

[0041] The information processing device 100 can be equipped with the storage unit 121 and conversion unit 122 shown in Figure 7 by having the CPU 101 acquire the program group 104 and execute it. The program group 104 is, for example, stored in advance in a storage device 105 or ROM 102, and the CPU 101 loads it into RAM 103 and executes it as needed. The program group 104 may also be supplied to the CPU 101 via a communication network 111, or it may be stored in advance in a storage medium 110, and the drive device 106 reads the program and supplies it to the CPU 101. However, the storage unit 121 and conversion unit 122 described above may be constructed with dedicated electronic circuits to realize such means.

[0042] The memory unit 121 stores correspondence data in which the problem expression and the transformed expression obtained by expanding and rearranging the problem expression are associated. Then, the transformation unit 122 transforms the optimization problem, including the problem expression, into a pre-set format using the transformation expression based on the correspondence data (step S101 in Figure 8).

[0043] In the above configuration, the information processing device 100 first stores correspondence data in which a pre-set problem expression and a converted expression obtained by pre-expanding and organizing the problem expression are associated. The conversion unit 122 then checks whether the problem expression included in the optimization problem is stored as correspondence data, and if it is stored, converts the problem expression into a converted expression based on the correspondence data. This reduces the processing required to expand and organize the problem expression included in the optimization problem. As a result, the time required to convert the optimization problem into a predetermined format can be shortened.

[0044] Furthermore, at least one of the functions of the storage unit 121 and the conversion unit 122 described above may be performed on an information processing device installed and connected to any location on the network, that is, it may be performed using so-called cloud computing.

[0045] Furthermore, the aforementioned programs can be stored and supplied to a computer using various types of non-transitory computer-readable media. Non-transitory computer-readable media include various types of tangible storage media. Examples of non-transitory computer-readable media include magnetic recording media (e.g., flexible disks, magnetic tapes, hard disk drives), magneto-optical recording media (e.g., magneto-optical disks), CD-ROMs (Read Only Memory), CD-Rs, CD-R / Ws, and semiconductor memory (e.g., mask ROMs, PROMs (Programmable ROMs), EPROMs (Erasable PROMs), flash ROMs, and RAMs (Random Access Memory)). Programs may also be supplied to a computer using various types of transient computer-readable media. Examples of transient computer-readable media include electrical signals, optical signals, and electromagnetic waves. Transitory computer-readable media can be supplied to a computer via wired communication channels such as electric wires and optical fibers, or via wireless communication channels.

[0046] Although the present disclosure has been described above with reference to embodiments, the present disclosure is not limited to the embodiments described above. Various modifications to the structure and details of the present disclosure are possible, as can be understood by those skilled in the art within the scope of the present disclosure. Furthermore, each of the embodiments described above can be combined with other embodiments as appropriate.

[0047] <Note> Some or all of the above embodiments may also be described as follows. The general configuration of the information processing apparatus, information processing method, and program in this disclosure is described below. However, this disclosure is not limited to the configuration described in the following notes. Furthermore, some or all of the configurations and functions described in Appendices 2 to 7, which are dependent on Appendice 1 below, may also be dependent on Appendices 8 and 10 in the same way as Appendices 2 to 7. Moreover, not limited to Appendices 1, 8, and 10, some or all of the configurations and functions described as appendices may also be dependent on similar hardware, software, various recording means for recording software, or systems, without departing from the embodiments described above. (Note 1) A storage unit that stores corresponding data where a problem expression and a transformed expression obtained by expanding and rearranging the said problem expression are associated, A conversion unit that converts the optimization problem, including the problem expression, into a pre-set format using the conversion formula based on the aforementioned corresponding data, Equipped with an information processing device. (Note 2) The information processing device described in Appendix 1, The system includes a determination unit that determines whether the problem expression included in the optimization problem is included in the corresponding data. The conversion unit, if it is determined that the problem expression of the optimization problem is included in the corresponding data, converts the problem expression of the optimization problem based on the corresponding data, and if it is determined that the problem expression of the optimization problem is not included in the corresponding data, expands and rearranges the problem expression of the optimization problem and converts it. Information processing device. (Note 3) The information processing device described in Appendix 2, The system includes a division unit that divides the optimization problem into predetermined units of the problem expression, The determination unit determines, for each of the divided problem expressions, whether or not the problem expression is included in the corresponding data. The conversion unit, for each of the divided problem expressions, converts the problem expression based on the corresponding data if it is determined to be included in the corresponding data, expands and rearranges the problem expression and converts it if it is determined not to be included in the corresponding data, and then integrates each of the converted problem expressions to convert the optimization problem. Information processing device. (Note 4) The information processing device described in Appendix 2, The conversion unit expands and rearranges the problem expression of the optimization problem and associates the resulting expression with the problem expression before conversion as the conversion expression, and stores the corresponding data, which is the association between the problem expression and the conversion expression, in the storage unit. Information processing device. (Note 5) The information processing device described in Appendix 1, Prior to the aforementioned transformation, the system includes an assignment unit that calculates and assigns sequential indices to the variables used in the optimization problem based on the problem expression of the optimization problem. Information processing device. (Note 6) The information processing device described in Appendix 1, The transformation unit converts the optimization problem into a matrix consisting of the coefficients of the variables in the transformed equation. Information processing device. (Note 7) The information processing device described in Appendix 6, The system includes a solution unit that solves the optimization problem using the aforementioned matrix. Information processing device. (Note 8) Based on correspondence data that associates a stored problem expression with a transformation expression obtained by expanding and rearranging the problem expression, the optimization problem including the problem expression is transformed into a pre-set format using the transformation expression. Information processing methods. (Note 9) The information processing method described in Appendix 8, Determine whether the problem expression included in the optimization problem is included in the corresponding data. If it is determined that the data is included in the aforementioned corresponding data, the problem expression of the optimization problem is transformed based on the aforementioned corresponding data; if it is determined that the data is not included in the aforementioned corresponding data, the problem expression of the optimization problem is expanded and rearranged and then transformed. Information processing methods. (Note 9.1) The information processing method described in Appendix 9, The optimization problem is divided into the problem expression of a predetermined unit, For each of the divided problem expressions, it is determined whether or not that problem expression is included in the corresponding data. For each of the divided problem expressions, if it is determined that it is included in the corresponding data, the problem expression is transformed based on the corresponding data; if it is determined that it is not included in the corresponding data, the problem expression is expanded and rearranged and transformed; and the transformed problem expressions are integrated to transform the optimization problem. Information processing methods. (Appendix 9.2) The information processing method described in Appendix 9, The problem expression of the optimization problem is expanded and rearranged to obtain a transformed expression, which is then associated with the original problem expression as the transformed expression, and the corresponding data of the problem expression and the transformed expression is stored. Information processing methods. (Appendix 9.3) The information processing method described in Appendix 8, Before the transformation, based on the problem expression of the optimization problem, a sequential index of the variables used in the optimization problem is calculated and assigned. Information processing methods. (Appendix 9.4) The information processing method described in Appendix 8, The optimization problem is transformed into a matrix consisting of the coefficients of the variables in the transformed equation. Information processing methods. (Note 9.5) The information processing method described in Appendix 9.4, The optimization problem is solved using the aforementioned matrix. Information processing methods. (Note 10) In an information processing device, Based on correspondence data that associates a stored problem expression with a transformation expression obtained by expanding and rearranging the problem expression, the optimization problem including the problem expression is transformed into a pre-set format using the transformation expression. A program that executes a process. [Explanation of symbols]

[0048] 10 Information Processing Devices 11 Division 12 Conversion pattern determination unit 13 Transformation and Coefficient Matrix Generation Unit 14 Formula expansion part 15 Type arrangement section 16. Coefficient Matrix Generation Unit 17. Integration Department 18 Conversion Pattern Storage Unit 100 Information Processing Devices 101 CPU 102 ROM 103 RAM 104 Program Groups 105 Storage device 106 Drive unit 107 Communication Interface 108 Input / Output Interfaces 109 Bus 110 Storage medium 111 Communication Network 121 Storage section 122 Conversion section

Claims

1. A storage unit that stores corresponding data where a problem expression and a transformed expression obtained by expanding and rearranging the said problem expression are associated, A conversion unit that converts the optimization problem, including the problem expression, into a pre-set format using the conversion formula based on the aforementioned corresponding data, Equipped with an information processing device.

2. An information processing apparatus according to claim 1, The system includes a determination unit that determines whether the problem expression included in the optimization problem is included in the corresponding data. The conversion unit, if it is determined that the problem expression of the optimization problem is included in the corresponding data, converts the problem expression of the optimization problem based on the corresponding data, and if it is determined that the problem expression of the optimization problem is not included in the corresponding data, expands and rearranges the problem expression of the optimization problem and converts it. Information processing device.

3. An information processing apparatus according to claim 2, The system includes a division unit that divides the optimization problem into predetermined units of the problem expression, The determination unit determines, for each of the divided problem expressions, whether or not the problem expression is included in the corresponding data. The conversion unit, for each of the divided problem expressions, converts the problem expression based on the corresponding data if it is determined to be included in the corresponding data, expands and rearranges the problem expression and converts it if it is determined not to be included in the corresponding data, and then integrates each of the converted problem expressions to convert the optimization problem. Information processing device.

4. An information processing apparatus according to claim 2, The conversion unit expands and rearranges the problem expression of the optimization problem and associates the resulting expression with the problem expression before conversion as the conversion expression, and stores the corresponding data, which is the association between the problem expression and the conversion expression, in the storage unit. Information processing device.

5. An information processing apparatus according to claim 1, Prior to the aforementioned transformation, the system includes an assignment unit that calculates and assigns sequential indices to the variables used in the optimization problem based on the problem expression of the optimization problem. Information processing device.

6. An information processing apparatus according to claim 1, The transformation unit converts the optimization problem into a matrix consisting of the coefficients of the variables in the transformed equation. Information processing device.

7. An information processing apparatus according to claim 6, The system includes a solution unit that solves the optimization problem using the aforementioned matrix. Information processing device.

8. Based on correspondence data that associates a stored problem expression with a transformation expression obtained by expanding and rearranging the problem expression, the optimization problem including the problem expression is transformed into a pre-set format using the transformation expression. Information processing methods.

9. The information processing method according to claim 8, Determine whether the problem expression included in the optimization problem is included in the corresponding data. If it is determined that the data is included in the aforementioned corresponding data, the problem expression of the optimization problem is transformed based on the aforementioned corresponding data; if it is determined that the data is not included in the aforementioned corresponding data, the problem expression of the optimization problem is expanded and rearranged and then transformed. Information processing methods.

10. In an information processing device, Based on correspondence data that associates a stored problem expression with a transformation expression obtained by expanding and rearranging the problem expression, the optimization problem including the problem expression is transformed into a pre-set format using the transformation expression. A program that executes a process.

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