Information processing apparatus

Abstract

This information processing device separates a parameter group included in the objective function of a QUBO problem generated from a combinatorial optimization problem into first parameters for which the value is determined on the basis of a constraint condition and second parameters other than the first parameters, and acquires a solution to a correction QUBO problem for which the second parameters are set to 0. The information processing device also separates the second parameters into third parameters that are the object of estimation and fourth parameters that are not the object of estimation, on the basis of the solution to the correction QUBO problem. The information processing device also estimates the value of the third parameters using decision-making history data relating to the combinatorial optimization problem.

Description

Technical Field

[0001] The present invention relates to an information processing apparatus, an information processing method, and a recording medium that convert a combinatorial optimization problem into a QUBO problem and perform calculations.

Background Art

[0002] Patent Document 1 discloses a method for converting a combinatorial optimization problem into a Quadratic Unconstrained Binary Optimization (QUBO) problem and performing calculations.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] Many combinatorial optimization problems can be formulated as integer programming problems with constraints. Therefore, when converting a combinatorial optimization problem into a QUBO problem and performing calculations, a method of incorporating the constraint conditions into the objective function and replacing it with an optimization problem without constraints is used. Here, if the coefficients in the objective function are not set to appropriate values, a highly accurate solution cannot be obtained. Inverse Ising, which infers the parameters of a model based on given decision history data, is known. However, a huge amount of calculation and data are required to estimate all of the parameter coefficients in the objective function using Inverse Ising. The present invention aims to provide an information processing apparatus that solves the above-described problems.

Means for Solving the Problems

[0005] An information processing apparatus according to one aspect of the present invention Divide the group of parameters included in the objective function of the QUBO problem generated from the combinatorial optimization problem into a first parameter whose value is determined based on the constraint conditions and a second parameter other than that, and a modified QUBO problem solving means for obtaining a solution to the modified QUBO problem in which the second parameter is set to 0, A dividing means for dividing the second parameter into a third parameter to be estimated and a fourth parameter not to be estimated based on the solution of the modified QUBO problem, An estimating means for estimating the value of the third parameter using the decision-making history data related to the combinatorial optimization problem, It is configured to include.

[0006] In addition, the information processing method according to another aspect of the present invention is Divide the group of parameters included in the objective function of the QUBO problem generated from the combinatorial optimization problem into a first parameter whose value is determined based on the constraint conditions and a second parameter other than that, Obtain a solution to the modified QUBO problem in which the second parameter is set to 0, Based on the solution of the modified QUBO problem, divide the second parameter into a third parameter to be estimated and a fourth parameter not to be estimated, Estimate the value of the third parameter using the decision-making history data related to the combinatorial optimization problem, It is configured as described above.

[0007] In addition, a computer-readable recording medium according to another aspect of the present invention is To the computer, A process of dividing the group of parameters included in the objective function of the QUBO problem generated from the combinatorial optimization problem into a first parameter whose value is determined based on the constraint conditions and a second parameter other than that, A process of obtaining a solution to the modified QUBO problem in which the second parameter is set to 0, A process of dividing the second parameter into a third parameter to be estimated and a fourth parameter not to be estimated based on the solution of the modified QUBO problem, A process of estimating the value of the third parameter using decision history data related to the combinatorial optimization problem, and is configured to record a program for causing the process to be performed.

Advantages of the Invention

[0008] According to the present invention, parameters of an objective function of a QUBO problem can be easily determined.

Brief Description of the Drawings

[0009]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Modes for Carrying Out the Invention

[0010] Next, embodiments of the present invention will be described in detail with reference to the drawings. [First Embodiment] First, for ease of understanding, problems assumed in the embodiments of the present invention will be described in detail.

[0011] Many combinatorial optimization problems can be formulated as constrained integer programming problems. Therefore, when converting a combinatorial optimization problem into a QUBO problem for calculation, a method is used that incorporates the constraint conditions into the objective function and replaces it with an optimization problem without constraint conditions. The objective function incorporating the constraint conditions is expressed, for example, by Equation (1) in Figure 4. In Equation (1), the first and second terms correspond to the objective function in the narrow sense, and the third term corresponds to the constraint conditions.

[0012] In the first and second terms, x i is a binary variable that takes a value of 0 or 1. Also, i, j, and N are natural numbers. Also, N corresponds to the number of each variable in the combinatorial optimization problem. Also, Q ij and h i are the parameters (coefficients) of the quadratic term and the linear term, respectively. Also, Q is an N×N matrix and h is a vector. Using the spin variable s i =±1, since x i =(s i +1) / 2 can be expressed, the objective function is equivalent to the Ising model.

[0013] In the third term, c l (g l (x)-d l ) 2 corresponds to the constraint conditions in the original combinatorial optimization problem. That is, the constraint conditions in the original combinatorial optimization problem are g l (x)=d l . Also, c l is a weight coefficient that is generally set to a large value (for example, 100). K is a natural number and corresponds to the number of constraint conditions. The third term is a term that increases in the case of a combination that does not satisfy the constraint conditions. Thereby, when the constraint conditions in the original combinatorial optimization problem are not satisfied, it is possible to increase the value of the objective function so that it is not adopted as a solution.

[0014] Here, if the parameters Q ij and h i in the objective function are not set to appropriate values, a highly accurate solution cannot be obtained.

[0015] Inverse Ising, which infers the parameters of a model based on given decision history data, is known. However, to estimate all of the parameters Q ij and h i in the objective function using Inverse Ising requires enormous calculations and data and is extremely difficult.

[0016] This embodiment aims to provide an information processing apparatus that solves the above-described problems.

[0017] FIG. 1 is a block diagram of an information processing apparatus 10 according to a first embodiment of the present invention. The information processing apparatus 10 is an apparatus that converts a combinatorial optimization problem into a QUBO problem and performs calculations. Referring to FIG. 1, the information processing apparatus 10 includes a machine I / F (interface) unit 11, a communication I / F unit 12, an operation input unit 13, a screen display unit 14, a storage unit 15, and an arithmetic processing unit 16.

[0018] The machine I / F unit 11 is connected to an annealing machine 17 by wire or wirelessly and performs data transmission and reception between the annealing machine 17 and the arithmetic processing unit 16. The annealing machine 17 is an apparatus that probabilistically obtains values of binary variables that minimize or maximize the objective function of an Ising model having binary variables as arguments. The annealing machine 17 may be configured by a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), an FPGA (Field-Programmable Gate Array) in addition to a quantum annealing machine or a quantum computer.

[0019] The communication I / F unit 12 is composed of a data communication circuit and performs data communication with an external device (not shown) by wire or wirelessly. The operation input unit 13 is composed of an operation input device such as a keyboard or a mouse, detects an operator's operation, and outputs it to the arithmetic processing unit 16. The screen display unit 14 is composed of a screen display device such as an LCD (Liquid Crystal Display), and displays various information on the screen according to an instruction from the arithmetic processing unit 16.

[0020] The storage unit 15 is composed of a storage device such as a hard disk or a memory, and stores processing information and a program 151 necessary for various processes in the arithmetic processing unit 16. The program 151 is a program that realizes various processing units when read and executed by the arithmetic processing unit 16, and is pre-read from an external device (not shown) or a recording medium via a data input / output function such as the communication I / F unit 12 and stored in the storage unit 15. The main processing information stored in the storage unit 15 includes data 152, an objective function 153, and a combination 154.

[0021] The data 152 is past decision-making history data of an expert regarding a combinatorial optimization problem. For example, when the information processing apparatus 10 solves a shift scheduling problem using the annealing machine 17, an optimal solution determined by an expert based on their knowledge and experience for a similar shift scheduling problem in the past is stored as the data 152. Note that the decision-making history is not limited to that of an expert. Here, the decision-making history refers to a set of combinations of information (also referred to as state data) and solutions (also referred to as action data) regarding the problem to be solved.

[0022] The objective function 153 is an objective function of a QUBO problem generated from a combinatorial optimization problem. The objective function 153 is represented by, for example, Equation (1) in FIG. 4.

[0023] The combination 154 is a combination obtained by solving a combinatorial optimization problem using the annealing machine 17.

[0024] The arithmetic processing unit 16 has one or more processors such as an MPU (Micro Processing Unit) and its peripheral circuits, and by reading and executing the program 151 from the storage unit 15, it causes the above hardware and the program 151 to cooperate to realize various processing units. The main processing units realized by the arithmetic processing unit 16 include a QUBO problem generation unit 161 and a QUBO problem solving unit 162.

[0025] The QUBO problem generation unit 161 converts a combinatorial optimization problem into a QUBO problem.

[0026] The QUBO problem solving unit 162 uses the annealing machine 17 to solve the QUBO problem generated by the QUBO problem generation unit 161. The QUBO problem solving unit 162 includes an objective function calculation unit 1621 and a combination calculation unit 1622.

[0027] The objective function calculation unit 1621 calculates the objective function 153 of the QUBO problem generated by the QUBO problem generation unit 161. The objective function calculation unit 1621 includes a modified QUBO problem solving unit 16211, a division unit 16212, and an estimation unit 16213.

[0028] The modified QUBO problem solving unit 16211 divides the parameters Q ij and h i included in the objective function 153 into a first parameter whose value is determined based on the constraint conditions and a second parameter other than that. Further, the modified QUBO problem solving unit 16211 obtains a solution to the modified QUBO problem in which the second parameter is set to 0.

[0029] The division unit 16212 divides the second parameter into a third parameter that needs to be estimated and a fourth parameter that does not need to be estimated and whose value may be a predetermined value (for example, a small value such as 0 or 1) based on the solution to the modified QUBO problem obtained by the modified QUBO problem solving unit 16211. That is, the division unit 16212 divides the second parameter into a third parameter that is the estimation target and a fourth parameter that is not the estimation target.

[0030] The estimation unit 16213 estimates the value of the third parameter using the data 152.

[0031] The combination calculation unit 1622 calculates a combination 154 that minimizes the objective function calculated by the objective function calculation unit 1621 using the annealing machine 17.

[0032] Next, the operation of the information processing apparatus 10 will be described.

[0033] FIG. 2 is a flowchart showing an example of the operation of the information processing apparatus 10. Referring to FIG. 2, first, the QUBO problem generation unit 161 inputs a combinatorial optimization problem from an operator through the operation input unit 13 or from an external device through the communication I / F unit 12, and generates a QUBO problem by converting this combinatorial optimization problem into a QUBO problem (step S1).

[0034] Next, the QUBO problem solving unit 162 uses the annealing machine 17 to solve the QUBO problem generated by the QUBO problem generation unit 161, thereby obtaining a solution to the QUBO problem (step S2). The QUBO problem solving unit 162 stores the solution to the QUBO problem in the storage unit 15 as a combination 154. Further, the QUBO problem solving unit 162 displays the combination 154 on the display screen of the display unit 14 and / or outputs it to an external device through the communication I / F unit 12.

[0035] In obtaining the solution to the QUBO problem in step S2 above, the following processing is performed. First, the objective function calculation unit 1621 calculates the objective function 153 of the QUBO problem generated by the QUBO problem generation unit 161 (step S3). Next, the combination calculation unit 1622 calculates a combination 154 that minimizes the calculated objective function 153 using the annealing machine 17 (step S4).

[0036] In calculating the objective function 153 in step S3 above, the following processing is performed. First, the modified QUBO problem solving unit 16211 is the parameter Q included in the objective function 153 ij and hi is divided into a first parameter whose value is determined based on constraint conditions and a second parameter other than the first parameter, and a solution to the modified QUBO problem with the second parameter set to 0 is obtained (step S5). Next, the division unit 16212 divides the second parameter into a third parameter that is the estimation target and a fourth parameter that is not the estimation target and whose value may be set to a predetermined value based on the solution to the modified QUBO problem obtained by the modified QUBO problem solving unit 16211 (step S6). Next, the estimation unit 16213 estimates the value of the third parameter using the data 152 (step S7).

[0037] Subsequently, each part will be described in more detail.

[0038] Now, consider the constrained optimization problem represented by Equation (2) in FIG. 4. When such a constrained optimization problem is given, the QUBO problem generation unit 161 converts it into the objective function of the QUBO problem represented by Equation (3) in FIG. 4. That is, the constraint conditions are incorporated into the objective function and replaced with an optimization problem under unconstrained conditions. In Equation (3), the coefficient c l in Equation (1) is set to 100, but it is not limited to 100 and may be a large value. The method for determining the value of the coefficient c l of the quadratic equation representing the constraint conditions is arbitrary. At this point, the values of the parameters Q ij and h i are undetermined.

[0039] Next, the modified QUBO problem solving unit 16211 divides all the parameters Q ij and h i of the objective function given by Equation (3) into a first parameter whose value is determined based on constraint conditions and a second parameter other than the first parameter. Here, since the first-order parameter h i of x is easy to estimate, it may always be classified as the second parameter for later speculation. Therefore, substantially, the modified QUBO problem solving unit 16211 is the second-order parameter Q of x ijis divided into a first parameter whose value is determined based on the constraint conditions and a second parameter other than that. In the case of Equation (3), based on the third to eighth terms corresponding to the constraint conditions, the modified QUBO problem solving unit 16211 determines the parameter Q ij among the parameters Q 12 , Q 23 , Q 34 , Q 45 , Q 56 , Q 16 as the first parameter whose value is determined based on the constraint conditions, and the others as the second parameter. The reason is that the quadratic terms (i≠j) appearing in the third to eighth terms corresponding to the constraint conditions are x1x2, x2x3, x3x4, x4x5, x5x6, x1x6. Also, the values of the parameters Q 12 , Q 23 , Q 34 , Q 45 , Q 56 , Q 16 can be, for example, 100. The method for determining the value of the first parameter corresponding to the constraint conditions is arbitrary.

[0040] Next, the modified QUBO problem solving unit 16211 obtains the solution of the modified QUBO problem in which all the parameters classified as the second parameter among the parameters Q ij and h i in the objective function given by Equation (3) are set to 0. The solution of this modified QUBO problem is all combinations that satisfy the constraint conditions of the original constrained optimization problem.

[0041] One method for obtaining the solution of the modified QUBO problem is to formulate the modified QUBO problem and actually perform the optimization calculation. The modified QUBO problem solving unit 16211 may perform the calculation using the annealing machine 17 when actually calculating the modified QUBO problem. Note that the solution of the modified QUBO problem can also be obtained as the solution of the MaxCut problem.

[0042] Another method for obtaining a solution to the modified QUBO problem is to use the past decision-making history data of experts regarding the original constrained optimization problem. That is, among the constrained optimization problems, there exists an optimal combination determined by experts leveraging their own experience as history data. In the case of this embodiment, such history data is stored in the storage unit 15 as data 152. The modified QUBO problem solution unit 16211 acquires, as the solution to the modified QUBO problem, a combination that satisfies the constraint conditions from the data 152 corresponding to the original constrained optimization problem.

[0043] Next, the division unit 16212 divides the second parameter into a third parameter that is the estimation target and a fourth parameter that is not the estimation target and whose value may be set to a predetermined value based on the solution to the modified QUBO problem obtained by the modified QUBO problem solution unit 16211. Hereinafter, this division method will be described in detail.

[0044] When representing binary variables as nodes and the parameter Q ij of the objective function as the weight (edge weight) assigned to the edge between node i and node j, a part of the objective function can be represented as a graph as shown in FIG. 3 for example. However, the parameter h i cannot be represented. In FIG. 3, the parameters Q 12 , Q 23 , Q 34 , Q 45 , Q 56 , Q 16 corresponding edges correspond to the constraint conditions of the objective function shown in Equation (3) of FIG. 4. Due to these constraint conditions, nodes x1, x3, x5 and nodes x2, x4, x6 will always take values with opposite signs when applied to the Ising model. That is, in the QUBO model, when the values of nodes x1, x3, x5 are 1, the values of nodes x2, x4, x6 are 0, or when the values of nodes x1, x3, x5 are 0, the values of nodes x2, x4, x6 are 1. At this time, the parameters Q 13 , Q 14 , Q 15 , Q 24 , Q 25 , Q 26 , Q35 , Q 36 , Q 46 The edge weights indicated by the dashed lines corresponding to them do not need to be accurately estimated because they are values that do not affect the relationship (distribution) of the possible values of the nodes x1, x2, x3, x4, x5, x6 at both ends of those edges, or values that have only a negligibly small effect. Therefore, parameter Q 13 , Q 14 , Q 15 , Q 24 , Q 25 , Q 26 , Q 35 , Q 36 , Q 46 becomes the fourth parameter that does not need to be accurately estimated. For example, parameter Q 13 , Q 14 , Q 15 , Q 24 , Q 25 , Q 26 , Q 35 , Q 36 , Q 46 can be set to 0, which obviously has no effect. However, the value of parameter Q 13 , Q 14 , Q 15 , Q 24 , Q 25 , Q 26 , Q 35 , Q 36 , Q 46 is not limited to 0. As long as the values of these parameters are sufficiently small compared to the large coefficient associated with the constraint condition (100 in the example of Equation (3)), they can be 1 or the like.

[0045] Here, consider the combinations of the possible values of the nodes at both ends of the edge to which the edge weight Q 13 , Q 14 , Q 15 , Q 24 , Q 25 , Q 26 , Q 35 , Q 36 , Q 46 is assigned. For example, for edge weight Q 13The nodes x1 and x3 at both ends of the assigned edge have a combination of (0, 0) or (1, 1), and other combinations are not possible as long as the constraint conditions are satisfied. Also, the edge weight Q 14 The nodes x1 and x4 at both ends of the assigned edge have a combination of (0, 1) or (1, 0), and other combinations are not possible as long as the constraint conditions are satisfied. In this way, the nodes at both ends of the edge with the edge weight assigned that does not need to be estimated always tend to have the same value or always different values as long as the constraint conditions are satisfied. The division unit 16212 utilizes this tendency to divide the second parameter into a third parameter that needs to be estimated and a fourth parameter that does not need to be estimated based on the solution of the modified QUBO problem. Specifically, the division unit 16212 sets the edge weight where the nodes at both ends of the edge are "the same value for all solutions of the modified QUBO problem" or "different values for all solutions of the modified QUBO problem" as the fourth parameter that does not need to be estimated, and the rest as the third parameter that needs to be estimated.

[0046] In the case of the objective function represented by Equation (3) in FIG. 4, at least some of the parameters Q ij could become the fourth parameter that does not need to be estimated. However, depending on the constraint conditions, there may be a case where there is no fourth parameter in the parameters Q ij Even in that case, the number of parameters that need to be estimated is reduced by the number of the first parameters determined from the constraint conditions.

[0047] Next, the estimation unit 16213 estimates the value of the third parameter using the data 152. That is, at this point, the parameter Q in Equation (3) in FIG. 4 ij is divided into the first parameter with a large value derived from the constraint conditions, the fourth parameter with a value of 0 that does not need to be accurately estimated, and the undetermined third parameter. Also, the parameter h in Equation (3) in FIG. 4 iIt is also classified into a third parameter whose value is undetermined. The estimation unit 16213 estimates the values of these undetermined third parameters using the data 152. The estimation unit 16213 is ij and h i do not need to estimate all of them, and only a part of them needs to be estimated, so the amount of calculation and data required for this is significantly reduced. The estimation unit 16213 estimates the value of the third parameter using inverse indexing.

[0048] Generally, for M sets of data sets D = {(s1 m ,…, s N m )} m=1,…,M from the indexing model Σ i≠j A ij s i s j + Σ i b i s i The equations for estimating the parameters A and b can be described as minimizing the function f(A, b; D) as in Equation (4) of FIG. 4. That is, A and b that minimize f(A, b; D) are the estimated parameter values. For example, in the method based on pseudo-likelihood, the function f(A, b; D) is represented by, for example, Equation (5) of FIG. 4. However, the function f(A, b; D) is not limited to Equation (5). For the calculation of Equation (4), ordinary continuous optimization such as the conjugate gradient method can be applied. The estimation unit 16213 estimates the value of the third parameter using the data 152 corresponding to the M sets of data sets D after converting the first term and the second term of Equation (3) in FIG. 4 into an indexing model. As a result, all the values of the parameters Q ij and h i are determined. That is, the objective function of the QUBO problem is determined.

[0049] Next, the combination calculation unit 1622 calculates a combination 154 that minimizes the above-determined objective function using the annealing machine 17. Since the method of solving the QUBO problem using the annealing machine 17 is well known, a detailed description thereof is omitted.

[0050] As described above, in the present embodiment, the objective function calculation unit 1621 first determines all parameters Q ij and h i into a first parameter whose value is determined based on the constraint conditions and a second parameter other than that. Next, the objective function calculation unit 1621 obtains a solution to the modified QUBO problem with the second parameter set to 0. Next, the objective function calculation unit 1621 divides the second parameter into a third parameter to be estimated and a fourth parameter not to be estimated based on the solution to the modified QUBO problem. Next, the objective function calculation unit 1621 estimates the value of the third parameter using the data 152 which is decision history data regarding the combinatorial optimization problem. Therefore, according to the present embodiment, it is not necessary to estimate all of the parameters Q ij and h i , and only a part of them needs to be estimated. As a result, the parameters of the objective function of the QUBO problem can be easily determined.

[0051] The present embodiment is applicable when converting an arbitrary type of combinatorial optimization problem into a QUBO problem for calculation. Hereinafter, the present embodiment will be further described by taking a simple shift scheduling problem as an example.

[0052] Now, assume that work schedules for four people A, B, C, and D are made for seven days. At this time, consider as a constraint condition that one of the employees A or B must work on each workday. Assume that a schedule that also takes into account the compatibility of the people working on the same day is a better schedule, and consider determining the objective function (defining what is better) in the schedule problem at this time from past work data (data determined by a skilled person considering the constraint conditions and compatibility). Let the variable representing whether person A works on the nth day be x A,n , and define it similarly for B to E. When this is formulated as a QUBO, it becomes as shown in Equation (6) of FIG. 4. The constraint condition "one of the employees A or B must work on each workday" can be described as "x A,n +x A,n =1 for n = 1, ···, 7", and for example, 100(x A,n +xA,n -1) 2 Since it can be expressed as Q AB,n = 100 etc. The remaining Q AC,n , Q AD,n , Q BC,n , Q BD,n , Q CD,n corresponds to a parameter that reflects compatibility and is estimated from past work data.

[0053] The first embodiment of the present invention described above can be variously additionally modified. For example, the QUBO problem generation unit 161, the objective function calculation unit 1621, the division unit 16212, the estimation unit 16213, and the combination calculation unit 1622 may be distributed among a plurality of different computers. Further, the data 152 may be stored in a distributed manner in a plurality of memories, in addition to being centrally stored in the local memory or remote memory of the computer.

[0054] [Second Embodiment] Next, a second embodiment of the present invention will be described with reference to FIG. 5. FIG. 5 is a block diagram of the information processing apparatus 20 in the present embodiment.

[0055] Referring to FIG. 5, the information processing apparatus 20 according to the present embodiment includes a modified QUBO problem solving unit 21, a division unit 22, and an estimation unit 23.

[0056] The modified QUBO problem solving unit 21 divides a group of parameters included in the objective function of the QUBO problem generated from the combinatorial optimization problem into a first parameter whose value is determined based on the constraint conditions and a second parameter other than that, and is configured to obtain a solution to the modified QUBO problem in which the second parameter is set to 0. The modified QUBO problem solving unit 21 can be configured in the same manner as, for example, the modified QUBO problem solving unit 16211 in FIG. 1, but is not limited thereto.

[0057] The splitting unit 22 is configured to divide the second parameter into a third parameter to be estimated and a fourth parameter not to be estimated based on the solution of the modified QUBO problem obtained by the modified QUBO problem solving unit 21. The splitting unit 22 can be configured in the same manner as, for example, the splitting unit 16212 in FIG. 1, but is not limited thereto.

[0058] The estimation unit 16213 is configured to estimate the value of the third parameter using the decision history data regarding the combinatorial optimization problem. The estimation unit 16213 can be configured in the same manner as, for example, the estimation unit 16213 in FIG. 1, but is not limited thereto.

[0059] The information processing apparatus 20 configured as described above operates as follows. That is, the modified QUBO problem solving unit 21 divides the parameter group included in the objective function of the QUBO problem generated from the combinatorial optimization problem into a first parameter whose value is determined based on the constraint conditions and a second parameter other than that, and obtains a solution of the modified QUBO problem in which the second parameter is set to 0. Next, the splitting unit 22 divides the second parameter into a third parameter to be estimated and a fourth parameter not to be estimated based on the solution of the modified QUBO problem obtained by the modified QUBO problem solving unit 21. Next, the estimation unit 16213 estimates the value of the third parameter using the decision history data regarding the combinatorial optimization problem.

[0060] According to the information processing apparatus 20 configured and operating as described above, the parameters of the objective function of the QUBO problem can be easily determined. The reason is that the number of parameters that the estimation unit 23 has to estimate is reduced.

[0061] Although the present invention has been described with reference to the above embodiments, the present invention is not limited to the above-described embodiments. Various changes that can be understood by those skilled in the art can be made to the configuration and details of the present invention within the scope of the present invention.

Industrial Applicability

[0062] The present invention can be used when estimating parameters of an objective function when converting a combinatorial optimization problem such as a shift scheduling problem into a QUBO problem for calculation from past decision-making history data of an expert.

[0063] Some or all of the above embodiments may be described as follows in the appended claims, but are not limited thereto. [Appended Claim 1] Dividing a group of parameters included in an objective function of a QUBO (quadratic unconstrained binary optimization) problem generated from a combinatorial optimization problem into a first parameter whose value is determined based on a constraint condition and a second parameter other than that, and obtaining a solution of a modified QUBO problem in which the second parameter is set to 0, a modified QUBO problem solving means; A dividing means for dividing the second parameter into a third parameter to be estimated and a fourth parameter not to be estimated based on the solution of the modified QUBO problem; An estimating means for estimating the value of the third parameter using decision-making history data regarding the combinatorial optimization problem; An information processing apparatus comprising the same. [Appended Claim 2] The modified QUBO problem solving means is configured to formulate the modified QUBO problem and actually perform an optimization calculation to obtain the solution. The information processing apparatus according to Appended Claim 1. [Appended Claim 3] The modified QUBO problem solving means is configured to obtain the solution from past decision-making history data of an expert regarding the combinatorial optimization problem. The information processing apparatus according to Appended Claim 1. [Appended Claim 4] The division means is configured to determine, in a graph in which binary variables are assigned to nodes and parameters are assigned to edge weights between node i and node j, that parameters corresponding to edge weights assigned to edges where the nodes at both ends of the edge have the same value or different values for all solutions of the modified QUBO problem are non-estimation target fourth parameters. The information processing apparatus according to Supplementary Note 2 or 3. [Supplementary Note 5] The estimation means is configured to perform the estimation by reverse annealing. The information processing apparatus according to any one of Supplementary Notes 1 to 4. [Supplementary Note 6] The information processing apparatus further includes combination calculation means for calculating a combination that minimizes the objective function using an annealing machine. The information processing apparatus according to any one of Supplementary Notes 1 to 5. [Supplementary Note 7] A group of parameters included in the objective function of the QUBO problem generated from the combinatorial optimization problem is divided into first parameters whose values are determined based on constraint conditions and second parameters other than those, a solution of the modified QUBO problem with the second parameter set to 0 is obtained, based on the solution of the modified QUBO problem, the second parameter is divided into a third parameter to be estimated and a fourth parameter not to be estimated, the value of the third parameter is estimated using the decision-making history data regarding the combinatorial optimization problem. Information processing method. [Supplementary Note 8] In the acquisition of the solution, the solution is obtained by formulating the modified QUBO problem and performing an optimization calculation. The information processing method according to Supplementary Note 7. [Supplementary Note 9] In the acquisition of the solution, the solution is obtained from the decision-making history data regarding the combinatorial optimization problem. The information processing method according to Supplementary Note 7. [Supplementary Note 10] In the division of the second parameter, in a graph in which binary variables are assigned to nodes and the parameter is an edge weight assigned to an edge between node i and node j, it is determined that the parameter corresponding to the edge weight assigned to an edge whose nodes at both ends of the edge have the same value or different values for all solutions of the modified QUBO problem is a fourth parameter that is not an estimation target. The information processing method according to Appendix 8 or 9. [Appendix 11] Perform the estimation by reverse annealing. The information processing method according to any one of Appendices 7 to 10. [Appendix 12] Furthermore, calculate the combination that minimizes the objective function using an annealing machine. The information processing method according to any one of Appendices 7 to 11. [Appendix 13] On a computer, A process of dividing a group of parameters included in the objective function of a QUBO problem generated from a combinatorial optimization problem into a first parameter whose value is determined based on a constraint condition and a second parameter other than that, A process of obtaining a solution to a modified QUBO problem in which the second parameter is set to 0, A process of dividing the second parameter into a third parameter that is an estimation target and a fourth parameter that is not an estimation target based on the solution to the modified QUBO problem, A process of estimating the value of the third parameter using the decision-making history data regarding the combinatorial optimization problem, A computer-readable recording medium recording a program for causing the above to be performed.

Explanation of Signs

[0064] 10 Information processing apparatus 11 Machine I / F unit 12 Communication I / F unit 13 Operation input unit 14 Display unit 15 Storage unit 16 Arithmetic processing unit 17 Annealing Machine 20 Information Processing Device 21 Modified QUBO Problem Solving Unit 22 Division Unit 23 Estimation Unit 151 Program 152 Data 153 Objective Function 154 Combination 161 QUBO Problem Generation Unit 162 QUBO Problem Solving Unit 1621 Objective Function Calculation Unit 1622 Combination Calculation Unit 16211 Modified QUBO Problem Solving Unit 16212 Division Unit 16213 Estimation Unit

Claims

1. A group of parameters included in an objective function of a QUBO (Quadratic Unconstrained Binary Optimization) problem generated from a combinatorial optimization problem is divided into a first parameter whose value is determined based on a constraint condition and a second parameter other than the first parameter, and a modified QUBO problem solving means for obtaining a solution of a modified QUBO problem in which the second parameter is set to 0, a dividing means for dividing the second parameter into a third parameter to be estimated and a fourth parameter not to be estimated based on the solution of the modified QUBO problem, an estimating means for estimating the value of the third parameter using decision history data related to the combinatorial optimization problem, An information processing apparatus comprising:

2. The modified QUBO problem solving means is configured to formulate the modified QUBO problem and obtain the solution by performing an optimization calculation. The information processing apparatus according to claim 1.

3. The modified QUBO problem solving means is configured to obtain the solution from decision history data related to the combinatorial optimization problem. The information processing apparatus according to claim 1.

4. In the dividing means, in a graph in which binary variables are assigned to nodes and parameters are assigned to edge weights assigned to edges between node i and node j, whether the nodes at both ends of the edge have the same value for all solutions of the modified QUBO problem, or The parameter corresponding to the edge weight assigned to an edge that has different values for all solutions of the modified QUBO problem is determined to be a fourth parameter that is not an estimation target. The information processing apparatus according to claim 2 or 3.

5. The estimating means is configured to perform the estimation by inverse indexing. The information processing apparatus according to any one of claims 1 to 4.

6. The information processing apparatus further comprises a combination calculating means for calculating a combination that minimizes the objective function using an annealing machine. The information processing apparatus according to any one of claims 1 to 5.

7. An information processing method by a computer, wherein the computer divides a group of parameters included in an objective function of a QUBO problem generated from a combinatorial optimization problem into a first parameter whose value is determined based on a constraint condition and a second parameter other than the first parameter, the computer obtains a solution of a modified QUBO problem in which the second parameter is set to 0, The computer divides the second parameter into a third parameter to be estimated and a fourth parameter not to be estimated based on the solution to the modified QUBO problem. The computer estimates the value of the third parameter using the decision-making history data related to the combinatorial optimization problem. Information processing method.

8. In the acquisition of the solution, the computer formulates the modified QUBO problem and performs an optimization calculation to acquire the solution. The information processing method according to claim 7.

9. In the acquisition of the solution, the computer acquires the solution from the decision-making history data related to the combinatorial optimization problem. The information processing method according to claim 7.

10. A computer, a process of dividing a parameter group included in an objective function of a QUBO problem generated from a combinatorial optimization problem into a first parameter whose value is determined based on a constraint condition and a second parameter other than the first parameter; a process of acquiring a solution to a modified QUBO problem in which the second parameter is set to 0; a process of dividing the second parameter into a third parameter to be estimated and a fourth parameter not to be estimated based on the solution to the modified QUBO problem; a process of estimating the value of the third parameter using the decision-making history data related to the combinatorial optimization problem; A program for causing the above to be performed.

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