Information processing device, information processing system, program, and isin model creation assistance method

Abstract

Provided is an information processing device that provides support for the creation of an Isin model for solving an optimal solution search problem for a composite material provided with a mixing restriction condition by an annealing optimizer, the information processing device comprising: an input receiving unit that receives an input from the annealing optimizer; an input unit configured to receive an objective function in which characteristics of a composite material corresponding to the mixing are formulated, and input of a mixing restriction condition; and a data creation unit configured so as to create an Isin model for an optimal solution for mixing that satisfies a constraint condition formula in which a mixing constraint condition is formulated and that optimizes the solution characteristics of the annealing-type optimizer, the amount ri of the substance i being represented by bits among the substances mixed with the composite material, and the amount ri being represented by bits among the substances mixed with the composite material. The composite material is characterized in that the material i is contained in the composite material, and whether the material i is contained in the composite material is also represented as a bit, the constraint condition formula includes conditions satisfying the following formula (1) and formula (2), and the constraint condition formula is formulated so that when at least one of formula (1) and formula (2) is not satisfied, the optimal solution of the mixture is not calculated.

Description

Technical Field

[0001] This disclosure relates to information processing apparatus, information processing system, program, and method for supporting the creation of Isin models. Background Technology

[0002] There is currently a technique that can rapidly calculate stable combinations of A-sites, B-sites, and anion sites in perovskite crystal structures, even with large combinations, by performing a basis state search based on the Ising model or QUBO (Quadratic Unconstrained Binary Optimization). (See, for example, Patent Document 1).

[0003] <Prior art documents>

[0004] <Non-Patent Literature>

[0005] Patent Document 1: Japanese Patent Application Publication No. 2021-033768 Summary of the Invention

[0006] <The problem to be solved in this invention>

[0007] For example, there exist optimal solution retrieval problems, such as searching for the composition of composite materials with the best properties, and selecting the best combination from various mixed combinations. Annealed optimizers can solve the formulaic optimal solution retrieval problem using the Ising model.

[0008] Furthermore, when searching for the composition of composite materials with optimal properties and selecting the best combination from various mixtures, mixing constraints are often set. For example, when there is a group of materials with poor compatibility, conditions related to the group of materials are applied as mixing constraints. In the Ising model, mixing constraints can be set as limiting conditions.

[0009] The constraints (penalty functions) in the Ising model serve to prevent the selection of mixed combinations that do not satisfy the mixed constraints, thus serving as the optimal combination. However, the constraints need to be expressed by formulas of the Ising type (constraint terms), but expressing mixed constraints by constraint terms is not easy.

[0010] The purpose of this disclosure is to provide an information processing apparatus, an information processing system, a program, and a method for supporting the creation of Ising models for retrieving optimal solutions to composite materials with mixed constraints, which are solved by annealed optimizers.

[0011] <Methods for solving problems>

[0012] This disclosure includes the structures described below.

[0013] [1] An information processing apparatus that provides support for the creation of an Ising model for solving an optimal solution retrieval problem of composite materials with mixed constraints by an annealing-type optimizer, the information processing apparatus being characterized in that it comprises:

[0014] The input receiving unit is configured to receive an objective function formulating the properties of the composite material corresponding to the mixing, and the input of the mixing constraints; and

[0015] The data production department is configured to produce an Ising model that enables the annealed optimizer to solve for the mixed constraints, which are then formulated to satisfy the mixed constraints, and for the characteristics to become the optimal solution of the mixture.

[0016] In the substance mixed with the composite material, the amount r of substance i is... i The value is represented by bits, and whether substance i is included in the composite material is also represented by bits.

[0017] The constraint condition includes conditions that satisfy equations (1) and (2).

[0018] [Number 1]

[0019]

[0020] The q A0 This is an auxiliary variable that is "0" when substance A is included in the composite material and "1" when substance A is not included in the composite material.

[0021] The q B0 This is an auxiliary variable that is "0" when substance B is included in the composite material and "1" when substance B is not included in the composite material.

[0022] The m B This is to represent the amount r of substance B mixed in the composite material. B Number of bits required

[0023] The q Bj It is either a "0" or a "1" in the binary representation of the mixture of substance B.

[0024] The constraint condition is formulated such that the optimal solution of the mixture is not calculated if at least one of the equations (1) and (2) is not satisfied.

[0025] [2] The information processing apparatus according to [1] is characterized in that,

[0026] The constraint condition also includes conditions that satisfy the following equations (3) and (4).

[0027] [Number 2]

[0028]

[0029] The q A0 It is an auxiliary variable that is "0" when material A is included in the composite material and "1" when material A is not included in the composite material.

[0030] The q B0 This is an auxiliary variable that is "0" when material B is included in the composite material and "1" when material B is not included in the composite material.

[0031] The m A This is to represent the amount r of substance A mixed in the composite material. A Number of bits required

[0032] The q Aj It is the number "0" or "1" in the binary representation of the mixture of material A.

[0033] The constraint is formulated as follows: if at least one of equations (3) and (4) is not satisfied, the optimal solution of the mixture cannot be calculated.

[0034] [3] The information processing apparatus according to [1] or [2] is characterized in that,

[0035] The amount r of substance i in the composite material is such that, when the condition related to the amount of substance i in the composite material is set to a continuous number, the amount r of substance i is... i In equation (5) below, the bit representation is used, and whether the substance i is included in the composite material is also represented by bits.

[0036] [Number 3]

[0037]

[0038] The q ij It is the number "0" or "1" in the binary representation of the mixture of substance i.

[0039] The C j These are the coefficients of the binary representation of the mixture of substance i.

[0040] C1 is the amount of the smallest unit of the mixture.

[0041] The m i Is to become C m <M i, MAX The largest natural number,

[0042] The M i, MAX The amount of substance i, r i The maximum amount.

[0043] [4] The information processing apparatus according to any one of [1] to [3] is characterized in that,

[0044] The amount r of substance i in the composite material is such that, when the condition relating to the amount of substance i in the composite material is set as a discrete number, the amount r of substance i is... i The value is represented by bits, and whether the substance i is included in the composite material is also represented by bits.

[0045] [5] The information processing apparatus according to any one of [1] to [4] is characterized in that,

[0046] Equations (1) and (2) represent the mixing constraint condition where substance B is not used when substance A is used.

[0047] [6] The information processing apparatus according to [2] is characterized in that,

[0048] Equations (3) and (4) represent the mixing constraints under which substance A is not used when substance B is used.

[0049] [7] An information processing system comprising an annealed optimizer and an information processing device, the information processing device providing support for the creation of an Ising model for solving an optimal solution retrieval problem of composite materials with mixed constraints by an annealed optimizer, the information processing system being characterized in that it comprises:

[0050] The input receiving unit is configured to receive an objective function formulating the properties of the composite material corresponding to the mixing, and the input of the mixing constraints; and

[0051] The data production department is configured to produce an Ising model that enables the annealed optimizer to solve for the mixed constraints, which are then formulated to satisfy the mixed constraints, and for the characteristics to become the optimal solution of the mixture.

[0052] In the substance mixed with the composite material, the amount r of substance i is... i The value is represented by bits, and whether substance i is included in the composite material is also represented by bits.

[0053] The constraint condition includes conditions that satisfy equations (1) and (2).

[0054] [Number 4]

[0055]

[0056] The q A0 This is an auxiliary variable that is "0" when substance A is included in the composite material and "1" when substance A is not included in the composite material.

[0057] The q B0 This is an auxiliary variable that is "0" when substance B is included in the composite material and "1" when substance B is not included in the composite material.

[0058] The m B This is to represent the amount r of substance B mixed in the composite material. B Number of bits required

[0059] The q Bj It is either a "0" or a "1" in the binary representation of the mixture of substance B.

[0060] The constraint condition is formulated such that the optimal solution of the mixture is not calculated if at least one of the equations (1) and (2) is not satisfied.

[0061] [8] A program, characterized in that,

[0062] The program enables the execution of an information processing device that supports the creation of the Ising model for retrieving optimal solutions to composite materials with mixed constraints, using an annealed optimizer:

[0063] The steps of accepting the objective function, which is a formula for the properties of the composite material corresponding to the mixing, and the input of the mixing constraints; and

[0064] The steps of constructing an Ising model for solving the formulated constraint expressions that satisfy the mixed constraints by the annealed optimizer, and for obtaining the optimal solution of the mixture where the characteristics are optimal.

[0065] In the substance mixed with the composite material, the amount r of substance i is... i The value is represented by bits, and whether substance i is included in the composite material is also represented by bits.

[0066] The constraint condition includes conditions that satisfy equations (1) and (2).

[0067] [Number 5]

[0068]

[0069] The q A0 This is an auxiliary variable that is "0" when substance A is included in the composite material and "1" when substance A is not included in the composite material.

[0070] The q B0 This is an auxiliary variable that is "0" when substance B is included in the composite material and "1" when substance B is not included in the composite material.

[0071] The m B This is to represent the amount r of substance B mixed in the composite material. B Number of bits required

[0072] The q Bj It is either a "0" or a "1" in the binary representation of the mixture of substance B.

[0073] The constraint condition is formulated such that the optimal solution of the mixture is not calculated if at least one of the equations (1) and (2) is not satisfied.

[0074] [9] A method for supporting the creation of Ising models for an information processing device, the information processing device providing support for the creation of Ising models for retrieving optimal solutions to composite materials with mixed constraints by an annealed optimizer, the method being characterized by performing the following processing:

[0075] The objective function, which is a formula for the properties of the composite material corresponding to the mixture, and the inputs of the mixing constraints are accepted; and

[0076] An Ising model is constructed to enable the annealed optimizer to solve the mixed constraints, which are then formalized into a formula, and to obtain the optimal solution for the mixed constraints, where the characteristic is optimal.

[0077] In the substance mixed with the composite material, the amount r of substance i is... i The value is represented by bits, and whether substance i is included in the composite material is also represented by bits.

[0078] The constraint condition includes conditions that satisfy equations (1) and (2).

[0079] [Number 6]

[0080]

[0081] The q A0 This is an auxiliary variable that is "0" when substance A is included in the composite material and "1" when substance A is not included in the composite material.

[0082] The q B0 This is an auxiliary variable that is "0" when substance B is included in the composite material and "1" when substance B is not included in the composite material.

[0083] The m B This is to represent the amount r of substance B mixed in the composite material. B Number of bits required

[0084] The q Bj It is either a "0" or a "1" in the binary representation of the mixture of substance B.

[0085] The constraint condition is formalized so that the optimal solution of the mixture is not calculated if at least one of the equations (1) and (2) is not satisfied.

[0086]

[10] An information processing apparatus that provides support for the creation of an Ising model for solving an optimal solution retrieval problem of composite materials with mixed constraints by an annealing-type optimizer, the information processing apparatus being characterized by comprising:

[0087] The input receiving unit is configured to receive an objective function formulating the properties of the composite material corresponding to the mixing, and the input of the mixing constraints; and

[0088] The data production department is configured to produce an Ising model that enables the annealed optimizer to solve for the mixed constraints, which are then formulated to satisfy the mixed constraints, and for the characteristics to become the optimal solution of the mixture.

[0089] In the substance mixed with the composite material, the amount r of substance i is... i The value is represented by bits, and whether substance i is included in the composite material is also represented by bits.

[0090] The constraint conditions include the conditions that satisfy equations (6), (7), and (8).

[0091] [Number 7]

[0092]

[0093] The q i0 This is an auxiliary variable that is "0" when substance i is included in the composite material and "1" when substance i is not included in the composite material.

[0094] The m i This is to represent the amount r of substance i mixed in the composite material. i Number of bits required

[0095] The q ij It is the number "0" or "1" in the binary representation of the mixture of substance i.

[0096] N is the number of substances i that meet the constraint conditions through equation (8).

[0097] The constraint condition is formulated such that the optimal solution of the mixture is not calculated if at least one of the equations (6), (7) and (8) is not satisfied.

[0098] <The Effects of the Invention>

[0099] The purpose of this disclosure is to provide an information processing apparatus, an information processing system, a program, and a method for supporting the creation of Ising models for retrieving optimal solutions to composite materials with mixed constraints, which are solved by annealed optimizers. Attached Figure Description

[0100] Figure 1 This is a structural diagram of an example of the information processing system of this embodiment.

[0101] Figure 2 This is a hardware structure diagram of an example of the computer described in this embodiment.

[0102] Figure 3 This is an illustration of an example of mixed constraints.

[0103] Figure 4 This is an illustration of an example of mixed constraints.

[0104] Figure 5 This is a structural diagram of an example of the information processing system of this embodiment.

[0105] Figure 6 This is a diagram illustrating an example of bit representation of matter.

[0106] Figure 7A This is a diagram illustrating a specific example of the bit representation of "substance 1".

[0107] Figure 7B This is a diagram illustrating a specific example of the bit representation of "substance 1".

[0108] Figure 7C This is a diagram illustrating a specific example of the bit representation of "substance 1".

[0109] Figure 8 This is a diagram illustrating an example of how matter is represented by bits.

[0110] Figure 9 This is a diagram illustrating an example of the bit representation of the composition of a composite material.

[0111] Figure 10A This is an illustration of an example of the constraints shown in equations (12) and (13).

[0112] Figure 10B This is an illustration of an example of the constraints shown in equations (12) and (13).

[0113] Figure 11A This is an illustration of an example of the constraints shown in equations (14) and (15).

[0114] Figure 11B This is an illustration of an example of the constraints shown in equations (14) and (15).

[0115] Figure 12A The figure shows an example of the use of the constraints shown in equations (14) and (15).

[0116] Figure 12B The figure shows an example of the use of the constraints shown in equations (14) and (15).

[0117] Figure 12C The figure shows an example of the use of the constraints shown in equations (14) and (15).

[0118] Figure 12D The figure shows an example of the use of the constraints shown in equations (14) and (15).

[0119] Figure 13A This is a diagram illustrating examples of the use of the constraints shown in equations (14) and (15), as well as equations (16) and (17).

[0120] Figure 13B This is a diagram illustrating examples of the use of the constraints shown in equations (14) and (15), as well as equations (16) and (17).

[0121] Figure 14 This is a flowchart illustrating an example of the processing sequence of the information processing system of this embodiment.

[0122] Figure 15 This is a diagram illustrating an example of the use of the constraint conditions shown in equation (18).

[0123] Figure 16 This is a diagram illustrating an example of the use of the constraint conditions shown in equation (18). Detailed Implementation

[0124] The embodiments of the present invention will now be described in detail. However, the present invention is not limited to the following embodiments.

[0125] <System Structure>

[0126] Figure 1 This is a structural diagram of an example of the information processing system of this embodiment. Figure 1The information processing system 1 shown includes an annealed optimizer 10 and an information processing device 12. The annealed optimizer 10 and the information processing device 12 are connected via a communication network 18, such as a local area network (LAN) or the Internet, in a manner that enables data communication.

[0127] The annealing-type optimizer 10 is an example of a device that uses the Ising model to solve the optimal solution retrieval problem (optimization problem). An optimization problem is the problem of finding the solution that minimizes or maximizes the objective function among solutions that satisfy constraints. In an optimization problem, the desired solution is represented by decision variables. The objective function is a function of the value to be minimized or maximized, represented by the decision variables. The constraints are a table of relationships representing the requirements that must be satisfied, represented by the decision variables.

[0128] Furthermore, combinatorial optimization problems are optimization problems with combinatorial structures. A combinatorial optimization problem is to find the combination of decision variables that minimizes or maximizes the objective function from a set of decisions that satisfy constraints.

[0129] The annealing optimizer 10 can be implemented using a quantum computer with quantum annealing or using an Ising machine (annealing machine) that implements quantum annealing using digital circuits such as FPGA (Field Programmable Gate Array) or GPU (Graphics Processing Unit). The annealing optimizer 10 can also be implemented using, for example, a digital annealer (trademarked) as an example of an Ising machine.

[0130] The annealed optimizer 10 solves optimization problems reduced to the Ising model by observing the convergence of the Ising model. Furthermore, the Ising model can also be represented using QUBO. Through variable transformation, the energy function of the Ising model and the cost function of QUBO are equivalent.

[0131] The Ising model is a statistical mechanical model representing the behavior of magnetic materials. The Ising model possesses the property of updating the spin state through the interaction between the spins of a magnetic material in a way that minimizes energy (Hamiltonian function), ultimately minimizing the energy. The annealing-type optimizer 10 reduces the optimization problem to the Ising model, finding the state with the minimum energy and using that state as the optimal solution to the optimization problem.

[0132] The information processing device 12 is a user-operated device such as a PC, tablet terminal, or smartphone. For users who wish to solve optimization problems using the annealed optimizer 10, the information processing device 12 provides support for creating an Ising model for solving the optimization problem using the annealed optimizer 10, as described later.

[0133] Furthermore, the information processing device 12 generates input information for the annealing optimizer 10 to solve the optimization problem, based on the user's operation. The input information to the annealing optimizer 10 includes the objective function and constraints written in Ising form, as described later.

[0134] By inputting the input information for the annealing optimizer 10 into the annealing optimizer 10, the user can solve the optimization problem that is reduced to the Ising model.

[0135] In this way, the information processing device 12 provides support to the user to generate the Ising model for solving the optimization problem by the annealing optimizer 10. Furthermore, the information processing device 12 receives the optimal solution to the optimization problem solved by the annealing optimizer 10 and displays the optimal solution on a display device, etc., in a manner that allows the user to confirm the output.

[0136] in addition, Figure 1 The information processing system 1 shown is one example. It can also be accessed and utilized by a user terminal (not shown) connected to the information processing device 12 via a communication network 18.

[0137] Alternatively, the annealed optimizer 10 can also be implemented as a cloud computing service. For example, the annealed optimizer 10 can also be implemented by calling an API (Application Programming Interface) via a communication network 18.

[0138] Furthermore, the annealed optimizer 10 is not limited to being implemented as a cloud computing service; it can also be implemented through local deployment or operated by other companies. The annealed optimizer 10 can also be implemented using multiple computers.

[0139] Furthermore, in the way users access and utilize the information processing device 12, the information processing device 12 can be implemented as a cloud computing service, can be implemented through local deployment, can be a service operated by other companies, or can be implemented through multiple computers. Figure 1 The information processing system 1 shown undoubtedly has various system structure examples depending on its use and purpose.

[0140] <Hardware Structure>

[0141] Figure 1 Information processing device 12, for example, via Figure 2 The hardware structure shown is implemented by the computer 500.

[0142] Figure 2 This is a hardware structure diagram of an example of the computer described in this embodiment. Figure 2The computer 500 includes an input device 501, a display device 502, an external I / F 503, RAM 504, ROM 505, CPU 506, communication I / F 507, and HDD 508, which are connected to each other via bus B. Furthermore, the input device 501 and the display device 502 can also be connected together.

[0143] Input device 501 includes touch panels, operation keys or buttons, keyboards or mice, etc., used by users to input various signals. Display device 502 consists of a liquid crystal or organic EL display for showing images, and speakers for outputting sound or other audio data. Communication I / F 507 is an interface for data communication between computer 500 and computer 500.

[0144] The HDD508 is an example of a non-volatile storage device for storing programs and data. The stored programs and data include the basic software OS that controls the computer 500 as a whole, and application programs that provide various functions on the OS. Alternatively, the computer 500 may use a drive device that uses flash memory as the storage medium (such as a solid-state drive: SSD, etc.) instead of the HDD508.

[0145] External I / F 503 is an interface to external devices. External devices include recording media 503a, etc. Thus, computer 500 can read and / or write to recording media 503a via external I / F 503. Recording media 503a includes floppy disks, CDs, DVDs, SD memory cards, USB storage devices, etc.

[0146] ROM 505 is an example of a non-volatile semiconductor memory (storage device) that can retain programs and data even when the power is cut off. ROM 505 stores programs and data such as BIOS, OS settings, and network settings that are executed when the computer 500 starts up. RAM 504 is an example of a volatile semiconductor memory (storage device) that temporarily stores programs and data.

[0147] CPU 506 is an arithmetic device that reads programs and data from storage devices such as ROM 505 or HDD 508 into RAM 504 and performs processing, thereby realizing the overall control and functions of computer 500. The information processing device 12 of this embodiment can realize the various functions described later. Here, the description of the hardware structure of the annealing-type optimizer 10 is omitted.

[0148] <Example of a problem to solve an optimization problem>

[0149] The following example illustrates how to solve an optimization problem by taking the composition of a composite material with optimal properties as an example of a composite material composition subject to mixed constraints.

[0150] For example, in this embodiment, using Figure 3 The mixed constraints are shown. Figure 3 This is an illustrative diagram illustrating an example of mixed constraints. Composite materials are composed of multiple material groups. Figure 3 An example of a composite material consisting of “material group 1” and “material group 2” is shown. Figure 3 Examples are shown where mixing constraints exist in each group of materials that constitute the composite material.

[0151] Figure 3 The mixing constraints include the mixture number, continuous / discrete composition, and quantity. The mixture number is a condition related to the number of substances contained in the material group that are mixed into the composite material; this condition sets the minimum and maximum mixture number. Continuous / discrete composition is a condition related to the quantity of substances mixed into the composite material; this condition sets whether the quantity of substances mixed in the composite material is continuous or discrete.

[0152] A quantity is a condition relating to the amount of substance mixed into a composite material, which sets the amount of substance mixed into the composite material. When the amount of substance mixed into the composite material is a continuous number, a minimum quantity and a maximum quantity are set for the quantity. When the amount of substance mixed into the composite material is a discrete number, the quantity is set for its amount of substance.

[0153] For example, Figure 3 The mixing constraint condition indicates that "Material Group 1" contains five substances, "Material 1" to "Material 5", and that one to three of these substances are mixed into the composite material. Furthermore, Figure 3 The mixing constraint condition indicates that "Material Group 2" contains three types of "Material 6" to "Material 8", and mixes more than two types of "Material 6" to "Material 8" into the composite material.

[0154] Furthermore, in this embodiment, the following is utilized: Figure 4 The mixed constraints are shown. Figure 4 This is an illustration of an example of mixed constraints. Figure 4 Is with Figure 3 The example shown illustrates a condition related to the combination of substances within a given group. When combinations of substances with poor compatibility exist, combinations of substances that should be avoided are defined. For example... Figure 4 As shown, the combination of substances to be avoided can be set as follows: Figure 3 The combination of "Matter 1" and "Matter 4" can be set within the same matter group, or it can be like... Figure 3 They are set in different matter groups, like "Matter 1" and "Matter 6".

[0155] The problem with this embodiment is that it satisfies... Figure 3 and Figure 4 The mixing constraints are considered, and the optimal solution is obtained by mixing the optimal substances with the properties of the composite material.

[0156] <Functional Structure>

[0157] The structure of the information processing system 1 in this embodiment is described below. Figure 5 This is a structural diagram of an example of the information processing system of this embodiment. Additionally, Figure 5 The structural diagram has appropriately omitted parts that are not needed in the description of this embodiment.

[0158] Figure 5 The annealing-type optimizer 10 shown includes a call receiving unit 20 and an optimal solution calculation unit 22. The information processing device 12 includes an input receiving unit 30, a transformation unit 32, a data production unit 34, a display unit 36, a material information storage unit 50, and a constraint-based information storage unit 52.

[0159] The input receiving unit 30 is an input interface that accepts user operations. The input receiving unit 30 receives input from the user containing information needed for the annealing-type optimizer 10 to solve the combined optimization problem. For example, the input receiving unit 30 accepts an objective function that formulates the properties of the composite material corresponding to the mixing of materials.

[0160] The objective function is a formulaic function representing the properties of the composite material corresponding to the mixing of substances. The smaller the value, the closer the manufactured product is to the properties desired by the user. For example, the user might desire high performance or low cost. Furthermore, for example, the input receiving unit 30 receives, for example... Figure 3 and Figure 4 The input of the mixed constraints shown.

[0161] Transformation unit 32 transforms the mixed constraints into constraint expressions. A constraint expression is an Ising-type formula that formalizes the mixed constraints. The constraint expression is formulated such that it becomes "0" when the mixed constraints are satisfied and a larger value when the mixed constraints are not satisfied.

[0162] For example, the constraint condition is formulated in such a way that, for each group of substances constituting the composite material, at least one of the conditions related to the number of mixtures of substances contained in the group of substances into the composite material and the condition related to the amount of substances mixed into the composite material is not satisfied.

[0163] The constraints of the equation type shown in equation (6) and the constraints of the inequality type shown in equation (7) can be expressed by the formula of the Ising type.

[0164] [Number 8]

[0165]

[0166] C i K: Real number

[0167] X i : 0 or 1

[0168] d i l: real number

[0169] X i : 0 or 1

[0170] The data production unit 34 generates, for example, the Ising model E shown in equation (8), which is used by the annealing optimizer 10 to solve the objective function and the constraint condition equation.

[0171] E=E1+E2･･･(8)

[0172] E1 is the objective function written in Ising form. E2 is the constraint expression written in Ising form. E2 is the number corresponding to the mixed constraint number, which is included as one or more terms (restriction terms) in the Ising model E.

[0173] In addition, E1 and E2 are formulas of the Ising type, therefore, as shown in the following formula (9), they can be expressed in the QUBO type.

[0174] [Number 9]

[0175]

[0176] X i : 0 or 1 J ij h i Real numbers

[0177] The data generation unit 34 generates input information in the form of data usable by the annealing optimizer 10 according to the above formula (8), and sends it to the annealing optimizer 10. The display unit 36 ​​displays the optimal solution received from the annealing optimizer 10 on the display device 502 for user confirmation. The optimal solution displayed on the display device 502 is displayed as information that is easy for the user to understand, such as information about the composition of the composite material.

[0178] The material information storage unit 50 stores the properties (performance, cost, etc.) of the substances included in the material group. For example, the properties of a composite material can be represented by the sum of the values ​​of the properties of the substances mixed in the composite material multiplied by the mixing ratio.

[0179] The call receiving unit 20 of the annealed optimizer 10 accepts calls from the information processing device 12 and receives input information from the information processing device 12 for the annealed optimizer 10 generated according to the above formula (8).

[0180] The optimal solution calculation unit 22 obtains the {x} that minimizes the Ising model E based on the input information received by the call receiving unit 20. i}. Obtain the {x} that minimizes the Ising model E. i That is, it is equivalent to obtaining the composition of the composite material that satisfies the mixed constraint condition represented by E2 and the objective function represented by E1 becomes the minimum.

[0181] The optimal solution calculation unit 22 can calculate the constraint equation that satisfies the mixed constraint conditions after they have been formalized, and the composite material properties become the optimal mixture of substances, which is taken as the optimal solution. The call receiving unit 20 sends the optimal solution calculated by the optimal solution calculation unit 22 to the information processing device 12.

[0182] in addition, Figure 5 The structure is one example. The information processing system 1 of this embodiment can take into account various structures. In addition, in this embodiment, an example of the input receiving unit 30 accepting mixed constraint inputs has been described, but it can also accept formulaic constraint inputs.

[0183] <Bit Representation of Matter>

[0184] To represent mixed constraints using the Ising model, a bit representation of the amounts of each substance is required. For example, the bit representation of a substance uses... Figure 6 The bit representation is shown.

[0185] Figure 6 This is a diagram illustrating an example of the bit representation of matter. Regarding matter, in equation (10), the amount r of matter i is... i Represented in bits, and based on the auxiliary variable q of substance i i0 Whether substance i is included in the composite material is also represented by a bit.

[0186] [Number 10]

[0187]

[0188] q ij It is the number "0" or "1" in the binary representation of the mixture of substance i. C j It is bit q in the binary representation of the mixture of substance i. ij The coefficient. C0 is a significant figure for the amount of substance in the mixture. m i Is to become C m <M i, MAXThe largest natural number. M i、MAX The amount of substance i, r i The maximum value of M. i、MIN The amount of substance i, r i The minimum quantity.

[0189] Auxiliary variable q i0 In the amount of substance i r i It becomes "0" when it is not 0 (the composite material contains substance i), and the amount r of substance i is... i It becomes "1" when it is 0 (the composite material does not contain substance i).

[0190] For example, the bit representation of "Substance 1" with one significant digit after the decimal point and a quantity of "2 to 10" is as follows: Figures 7A to 7C As shown. Figures 7A to 7C This is a diagram illustrating a specific example of the bit representation of "substance 1".

[0191] The maximum quantity M of "substance 1" i、MAX The value is "10". Therefore, C is made to... m <M i, MAX The largest natural number m i The value is "7". We need to ensure the number of bits for "Substance 1", plus the number representing the auxiliary variable n. i0 The auxiliary bits total 8 bits.

[0192] For example, when the amount of "substance 1" is "4.2", since the composite material contains "substance 1", the value of the auxiliary bit is "0". The bit values ​​"j=1~7" used to represent the amount of "substance 1" "4.2", the bit "j=2" representing the amount of "0.2", the bit "j=4" representing the amount of "0.8", and the bit "j=6" representing the amount of "3.2" become "1".

[0193] Additionally, for example, the bit representation of matter can also be... Figure 8 The bit representation is shown. Figure 8 This is a diagram illustrating an example of the bit representation of matter. The amount r of matter i. i In equation (11), the bit representation is used, and the auxiliary variable n of substance i is used. i0 Whether a composite material contains substance i is also represented by a bit.

[0194] [Number 11]

[0195]

[0196] When the amount of substance is "M" i,1 M i,2 、･･･、M i, L In the case of discrete numbers, the amount r of substance ii M represents i, L The bits are represented by bits, and based on the auxiliary variable n of substance i... i0 Whether a composite material contains substance i is also represented by a bit.

[0197] By utilizing the bits described above to represent the amount of each substance, the composition of the composite material can be as follows: Figure 9 The bit representation is shown. Figure 9 This is a diagram illustrating an example of the bit representation of the composition of a composite material.

[0198] Figure 9 Examples of substances constituting a composite material, namely "Substance 1" to "Substance 5", are shown. "Substance 1", "Substance 2", and "Substance 5" are examples of substances whose quantities are set as continuous numbers. "Substance 3" and "Substance 4" are examples of substances whose quantities are set as discrete numbers.

[0199] The number of bits required to ensure the quantities of "Substance 1" through "Substance 5" depends, as described above, on whether the amounts of substances mixed in the composite material are set as continuous or discrete, and the quantities of the substances. q1j through q5j are bit representations of the quantities of "Substance 1" through "Substance 5". For example, if the smallest unit of quantity is 0.1 and the maximum quantity of "Substance 1" is "30", the quantity of "Substance 1" can be represented by bits q11 through q19. Furthermore, the quantities of the three "Substance 3" with discrete values ​​of "3", "5", and "10" can be represented by bits q31 through q33.

[0200] When using the annealed optimizer 10, the bit representation can be represented by the one-dimensional vector representation {x} shown in equation (9). i By concatenating the bit representations of all the substances contained in the composite material group, {x} can be represented by a one-dimensional vector as shown in equation (9). i The composition of composite materials is represented by}.

[0201] <Constraints>

[0202] In this embodiment, in the composition of a composite material consisting of multiple material groups, the following constraints are set when solving an optimization problem to find the optimal mixture of materials that best represents the properties of the composite material.

[0203] Constraint 1

[0204] In this embodiment, constraints are set for each substance i as shown in equations (12) and (13).

[0205] [Number 12]

[0206]

[0207] If the amount of substance i is set as a continuous number, then m contained in equations (12) and (13) i Is to become C m <M i, MAX The largest natural number. If the quantity of substance i is set as a discrete number, m contained in equations (12) and (13) i r represents the amount of substance i. i The number of discrete numbers. Therefore, m i +1 means ensuring that the auxiliary variable q is included in the appended values. i0 The number of bits of substance i after the auxiliary bits.

[0208] The inequality constraint in equation (12) is to address the auxiliary variable q on the left side. i0 When the value is "1", the second term on the left is determined to be "0", and the auxiliary variable q on the left is also considered. i0 When the value is "0", the second term on the left is determined to be "1~m". i "The constraints of "

[0209] The inequality constraint in equation (13) is to address the auxiliary variable q on the left side. i0 When the value is "0", the second term on the determination side is not "0", which is a constraint condition. The constraints of the inequalities in equations (12) and (13) are to make the auxiliary variable q of substance i... i0 Comply with r i When >0, q is satisfied. i0 =0, in r i When =0, q satisfies i0 =1 constraint.

[0210] Figure 10A and Figure 10B This is an illustration of an example of the constraints of equations (12) and (13). Figure 10A and Figure 10B Examples of calculations for equations (12) and (13) for "substance 1" are shown. In "substance 1" with quantities of "2 to 10", m i Become "7".

[0211] When using "Substance 1", such as Figure 10A As shown in the table, the constraint is satisfied if the bit arrangement representing the amount of mixture of "substance 1" contains a bit "1". Conversely, the constraint is violated if the bit arrangement representing the amount of mixture of "substance 1" does not contain a bit "1" when using "substance 1".

[0212] When "Substance 1" is not used, such as Figure 10BAs shown in the table, the constraint is satisfied if the bit "1" is not included in the bit arrangement representing the amount of mixture of "Substance 1". Conversely, the constraint is violated if the bit "1" is included in the bit arrangement representing the amount of mixture of "Substance 1" when "Substance 1" is not used.

[0213] Furthermore, since the constraints shown in equations (12) and (13) are set for each substance i, if there are 20 substances i, then 20 × 2 = 40 constraints are set. Constraint 1 is the auxiliary variable q. i0 The constraints.

[0214] Constraint 2

[0215] In this embodiment, when there is a combination of substances with poor compatibility, the constraints shown in equations (14) and (15) are set for each combination of substances that are to be avoided. Here, an example of a combination of substances A and B with poor compatibility will be explained. Equations (14) and (15) represent the constraints of not using substance B when using substance A.

[0216] [Number 13]

[0217]

[0218] If the substance B is a continuous quantity, then the m contained in equations (14) and (15) b Is to become C m <M i, MAX The largest natural number. If the quantity of substance B is set as a discrete number, the m contained in equations (14) and (15) B r represents the amount of substance B. i The number of discrete numbers. Therefore, mB+1 represents ensuring that the auxiliary variable q is used for additional representation. B0 The number of bits of substance B after the auxiliary bits.

[0219] The inequality constraint in equation (14) is for the auxiliary variable q on the left side. A0 When it is "1", the second term on the left is determined to be "0~m". B ", the auxiliary variable q on the left A0 The constraint condition for determining that the second term on the left is "0" when it is "0".

[0220] The inequality constraint in equation (15) is to address the auxiliary variable q on the left side. A0 The condition that the second term on the left side is allowed to be "0" is determined when the value is "1". Furthermore, for the constraints of the inequalities in equations (14) and (15), it is necessary to set an auxiliary variable q for substance i. i0 In r i When >0, it is qi0 =0, in r i =0 is q i0 =1 constraint.

[0221] Figure 11A and Figure 11B This is an illustration of an example of the constraints shown in equations (14) and (15). Figure 11A The diagram shows calculation examples of equations (14) and (15) for the constraint conditions on substance B when using substance A. In substance B with quantities of "2 to 10", m... b It is "7".

[0222] The constraint that "substance B is not used when substance A is used" is, for example... Figure 11A As shown in the table, the condition is satisfied if the bit arrangement representing the amount of mixture of substance B does not contain a bit "1". Furthermore, the constraint "substance B is not used when substance A is used" is violated if the bit arrangement representing the amount of mixture of substance B contains a bit "1".

[0223] The constraint of "using substance B when substance A is not used" is, for example... Figure 11B As shown in the table, the condition is satisfied if the bit arrangement representing the amount of mixture of substance B contains a bit of "1". The constraint "use substance B when substance A is not used" is violated if the bit arrangement representing the amount of mixture of substance B does not contain a bit of "1".

[0224] Furthermore, for each combination of substances with poor compatibility, the constraints shown in equations (14) and (15) are set. In addition, to satisfy the opposite situation, the constraints shown in equations (16) and (17) are also set for substance A. Equations (16) and (17) represent the constraints of not using substance A when using substance B.

[0225] [Number 14]

[0226]

[0227] If the substance A is a continuous quantity, then the m contained in formulas (16) and (17) a Is to become C m <M i, MAX The largest natural number. If the quantity of substance A is set as a discrete number, mA in equations (16) and (17) represents the quantity r of substance A. i The number of discrete numbers. Therefore, m A +1 means ensuring that the auxiliary variable q is included in the appended values. A0 The number of bits of substance A after the auxiliary bits.

[0228] The constraint of the inequality form of equation (16) is applied to the auxiliary variable q on the left side. B0 When it is "1", the second term on the left is determined to be "0~m". A " and the auxiliary variable q on the left. B0 The constraint condition for determining that the second term on the left is "0" when it is "0".

[0229] The inequality constraint in equation (17) is to address the auxiliary variable q on the left side. B0 When it is "1", the second term on the left is allowed to be "0~m". B The constraints of the determination of "". In addition, the constraints of the inequalities in equations (16) and (17) necessitate setting an auxiliary variable q for substance i. i0 In r i >0 q i0 =0, in r i =0 when q i0 =1 constraint.

[0230] The following provides further examples of this implementation method. Figures 12A-12D This is a diagram illustrating an example of the use of the constraints shown in equations (14) and (15). Furthermore, Figures 12A-12D It shows m B Examples of substance B with the number "7".

[0231] Figure 12A The constraint "when substance A is used, substance B is not used" is due to the auxiliary variable q. A0 =0, auxiliary variable q B0 The bit arrangement representing the amount of substance B mixed with "1" does not contain any "1" bits, thus satisfying the condition.

[0232] Figure 12B The constraint "use substance B when substance A is not used" is due to the auxiliary variable q. A0 =1, auxiliary variable q B0 The bit arrangement representing the amount of substance B as "0" contains bits of "1", thus satisfying the condition.

[0233] Figure 12C The constraint "substance B is not used when substance A is not used" is due to the auxiliary variable q. A0 When the auxiliary variable q is "1", B0 The bit arrangement representing the amount of substance B mixed with "1" does not contain any "1" bits, thus satisfying the condition.

[0234] Figure 12D The constraint "when using substance A, also use substance B" is due to the auxiliary variable q. A0 =0, auxiliary variable qB0 The bit arrangement representing the amount of substance B as "0" contains bits of "1", thus satisfying the condition.

[0235] in addition, Figures 12A-12D An example of setting constraints on substance B is shown. To satisfy the opposite situation, an example of setting the same constraints on substance A will be explained.

[0236] Figures 13A-13B This is a diagram illustrating examples of the use of the constraints shown in equations (14) and (15), and equations (16) and (17). Furthermore, Figures 13A-13B It shows m A and m B Examples are for the number "7".

[0237] Figure 13A The constraint "use substance B when substance A is not used" is due to the auxiliary variable q. A0 =0, auxiliary variable q B0 The bit arrangement representing the amount of substance B mixed with "1" does not contain any "1" bits, thus satisfying the condition.

[0238] Figure 13B The constraint "when substance B is used, substance A is not used" is due to the auxiliary variable q. A0 =1, auxiliary variable q B0 The bit arrangement representing the amount of mixture A as "0" does not contain any "1" bits, thus satisfying the condition.

[0239] As mentioned above, the constraints shown in equations (16) and (17), which are opposite to those shown in equations (14) and (15), also hold.

[0240] According to this embodiment, when there is a combination of substances with poor compatibility, in order to prevent a combination of substances with poor compatibility from being selected as the optimal combination, constraints can be set for each combination of substances that should be avoided. For example, when there is a combination of substances with poor compatibility such as miscibility that leads to non-mixing, and the combination is known in advance, useless exploration can be avoided by setting the constraints as described above.

[0241] Constraint 3

[0242] In this embodiment, when there is a combination of substances with poor compatibility, in addition to setting the constraint conditions as shown in Equation (12) and Equation (13) above for each substance i, the constraint conditions as shown in Equation (18) above are also set for the substance i that is to be constrained.

[0243] [Number 15]

[0244]

[0245] In equation (18), N is the number of substances i that are subject to the constraints set according to equation (18). The left side is the number of unused substances i among the substances i that are subject to the constraints. The inequality constraint in equation (18) is to determine whether the number of unused substances i is greater than "N-1".

[0246] Here, examples will be given of substances A and B that are poorly compatible and which are not used together. Figure 15 This is a diagram illustrating an example of the use of the constraint conditions shown in equation (18). Additionally, in Figure 15 The example shown is where the number of substances i with the set constraints is "2".

[0247] Figure 15 (A) The constraint "use substance B when substance A is not used" is due to the auxiliary variable q. A0 =0, auxiliary variable q B0 The left side is "1", and the right side is also "1", so the condition is satisfied.

[0248] Figure 15 (B) The constraint "use substance B when substance A is not used" is due to the auxiliary variable q. A0 =1, auxiliary variable q B0 The left side is "1" and the value is "0", thus satisfying the condition.

[0249] Figure 15 (C) The constraint "when using substance A, also use substance B" is due to the auxiliary variable q. A0 =1, auxiliary variable q B0 The left side is "1" and the right side is "2", so the condition is satisfied.

[0250] Figure 15 The constraint in (D) that "substance B is used when substance A is used" is due to the auxiliary variable q. A0 =0, auxiliary variable q B0 Since the left side is "0", it does not satisfy equation (18) and violates the constraint.

[0251] Next, examples will be given of substances A, B, and C being a poorly compatible combination and not using substances A, B, and C simultaneously. Figure 16 This is a diagram illustrating an example of the use of the constraint conditions shown in equation (18). In Figure 16 The example shown is where the number of substances i with the set constraints is "3".

[0252] Combinations of use and non-use of substances A, B, and C, such as... Figure 16The table shows 8 categories. Auxiliary variable q A0 The value becomes "0" when substance A is used and "1" when it is not used. Auxiliary variable q B0 The variable qC0 becomes "0" when substance B is used and "1" when it is not used.

[0253] The constraint that "substances A, B, and C are not used" is due to the auxiliary variable q. A0 =1, auxiliary variable q B0 =1, auxiliary variable q C0 The left side is "3" and the value is "1", thus satisfying the condition.

[0254] The constraint of "using only substance A" is due to the auxiliary variable q. A0 =0, auxiliary variable q B0 =1, auxiliary variable q C0 The left side is "1" and the right side is "2", so the condition is satisfied.

[0255] The constraint of "using only substance B" is due to the auxiliary variable q. A0 The value is "1", and the auxiliary variable q is "1". B0 =0, auxiliary variable q C0 The left side is "1" and the right side is "2", so the condition is satisfied.

[0256] The constraint of "using only substance C" is due to the auxiliary variable q. A0 =1, auxiliary variable q B0 =1, auxiliary variable q C0 The left side is "2" and the value is "0", thus satisfying the condition.

[0257] The constraint of "using substances B and C" is due to the auxiliary variable q. A0 =1, auxiliary variable q B0 =0, auxiliary variable q C0 The left side is "1" and the left side is "0", so it does not satisfy equation (18) and violates the constraint.

[0258] The constraint of "using only substances A and C" is due to the auxiliary variable q. A0 =0, auxiliary variable q B0 =1, auxiliary variable q C0 The left side is "1" and the left side is "0", so it does not satisfy equation (18) and violates the constraint.

[0259] The constraint of "using substance A and substance B" is due to the auxiliary variable q. A0 =0, auxiliary variable q B0=0, auxiliary variable q C0 If the left side is "1", it does not satisfy equation (18) and violates the constraint.

[0260] The constraint of "using substances A, B, and C" is due to the auxiliary variable q. A0 =0, auxiliary variable q B0 The value is "0", the auxiliary variable qC0 is "0", and the left side is "0", which does not satisfy equation (18) and violates the constraint.

[0261] According to this embodiment, when there is a combination of substances with poor compatibility, constraint conditions can be set to prevent such combinations from being selected as the optimal combination. For example, when there is a combination of substances with poor compatibility such as mutual solubility that result in non-mixing, and the combination is known in advance, useless exploration can be avoided by setting the constraint conditions described above.

[0262] <Processing>

[0263] Figure 14 This is a flowchart illustrating an example of the processing sequence of the information processing system of this embodiment.

[0264] In step S100, the information processing device 12 receives input from the user of the information required for solving the combined optimization problem by the annealing-type optimizer 10. For example, the information processing device 12 receives an input of an objective function formulating the properties of the composite material corresponding to the mixing of materials. Furthermore, the information processing device 12 receives input of mixing constraints.

[0265] In step S102, the information processing device 12 transforms the mixed constraint condition received in step S100 into a constraint condition expression. The information processing device 12 transforms the mixed constraint condition into a constraint condition expression based on the information of the constraint condition expression defined corresponding to the substance i stored in the constraint condition expression information storage unit 52. Alternatively, the user can also perform the process of transforming the mixed constraint condition into a constraint condition expression.

[0266] In step S104, the information processing device 12 generates the Ising model, which is used by the annealing optimizer 10 to solve the problem based on the objective function and the constraint conditions.

[0267] In step S106, the information processing device 12 generates input information in a data format usable by the annealing optimizer 10 based on the generated Ising model, and sends it to the annealing optimizer 10. The input information in the data format usable by the annealing optimizer 10 includes the objective function and constraint expressions. The input information used by the annealing optimizer 10 may be, for example, an electronic file to be sent to the annealing optimizer 10.

[0268] In step S108, the information processing device 12 sends the input information for the annealing-type optimizer 10 to the annealing-type optimizer 10. The annealing-type optimizer 10 calculates the optimal solution (the properties of the composite material become the best mixture of substances) from the solutions that satisfy the constraints (mixed constraints) according to the received input information.

[0269] In step S110, the annealing optimizer 10 sends information representing the calculated optimal solution to the information processing device 12. The information processing device 12 transforms the information (bit information) representing the optimal solution received from the annealing optimizer 10 into user-understandable information such as the material mixture of the composite material, and outputs this information. For example, the information processing device 12 displays the composition (material name) of the composite material of the optimal solution and its quantity.

[0270] The composition of the composite material explored as the optimal solution in this embodiment can be utilized by controlling a composite material generation apparatus, such as an aluminum alloy manufacturing apparatus, to generate the composite material by specifying the substances to be mixed and their amounts. Furthermore, this embodiment can also be used to explore the mixed composition of semiconductor materials, as an example of a composite material. Examples of semiconductor materials include photoresist materials, adhesives, binders, and sealants, which are composite materials comprising multiple resins, additives, and / or fillers.

[0271] As described above, the information processing system 1 according to this embodiment can support the creation of the Ising model for solving the optimization problem of composite materials with mixed constraints by the annealing-type optimizer 10.

[0272] The embodiments described above are as follows; however, it should be understood that various changes in form and detail may be made without departing from the purpose and scope of the claims. The present invention has been described above based on embodiments, but the present invention is not limited to the above embodiments, and various modifications can be made within the scope of the claims. This application claims priority to basic application No. 2023-222639 filed with the Japan Patent Office on December 28, 2023, and basic application No. 2024-033063 filed with the Japan Patent Office on March 5, 2024, and the entire contents of the above basic applications are incorporated herein by reference.

[0273] Symbol Explanation

[0274] 1. Information Processing System

[0275] 10 Annealing-type optimizer

[0276] 12 Information processing devices

[0277] 18. Communication Networks

[0278] 20. Call the receiving department

[0279] 22 Optimal Solution Calculation Department

[0280] 30 Input Receiving Unit

[0281] 32 Transformer

[0282] 34 Data Production Department

[0283] 36 Display Section

[0284] 50. Material Information Storage Department

[0285] 52 Constrained Information Storage Unit

Claims

1. An information processing apparatus that provides support for the creation of an Ising model for finding the optimal solution of a composite material with mixed constraints using an annealing-type optimizer, the information processing apparatus being characterized by comprising: The input receiving unit is configured to receive an objective function that formulates the properties of the composite material corresponding to the mixing, and the input of the mixing constraints. and The data production department is configured to produce an Ising model that enables the annealed optimizer to solve for the mixed constraints, which are then formulated to satisfy the mixed constraints, and for the characteristics to become the optimal solution of the mixture. In the substance mixed with the composite material, the amount r of substance i is... i The value is represented by bits, and whether substance i is included in the composite material is also represented by bits. The constraint condition includes conditions that satisfy equations (1) and (2). [Number 1] The q A0 This is an auxiliary variable that is "0" when substance A is included in the composite material and "1" when substance A is not included in the composite material. The q B0 This is an auxiliary variable that is "0" when substance B is included in the composite material and "1" when substance B is not included in the composite material. The m B This is to represent the amount r of substance B mixed in the composite material. B Number of bits required The q Bj It is the number "0" or "1" in the binary representation of the mixture of substance B. The constraint condition is formulated such that the optimal solution of the mixture is not calculated if at least one of the equations (1) and (2) is not satisfied.

2. The information processing device according to claim 1, characterized in that, The constraint condition also includes conditions that satisfy the following equations (3) and (4). [Number 2] The q A0 It is an auxiliary variable that is "0" when material A is included in the composite material and "1" when material A is not included in the composite material. The q B0 This is an auxiliary variable that is "0" when material B is included in the composite material and "1" when material B is not included in the composite material. The m A This is to represent the amount r of substance A mixed in the composite material. A Number of bits required The q Aj It is the number "0" or "1" in the binary representation of the mixture of material A. The constraint is formulated as follows: if at least one of equations (3) and (4) is not satisfied, the optimal solution of the mixture cannot be calculated.

3. The information processing apparatus according to claim 1 or 2, characterized in that... , The amount r of substance i in the composite material is such that, when the condition related to the amount of substance i in the composite material is set to a continuous number, the amount r of substance i is... i In equation (5) below, the bit representation is used, and whether the substance i is included in the composite material is also represented by bits. [Number 3] The q ij It is the number "0" or "1" in the binary representation of the mixture of substance i. The C j These are the coefficients of the binary representation of the mixture of substance i. C1 is the amount of the smallest unit of the mixture. The m i Is to become C m <M i, MAX The largest natural number, The M i, MAX The amount of substance i, r i The maximum amount.

4. The information processing apparatus according to any one of claims 1 to 3, characterized in that, The amount r of substance i in the composite material is such that, when the condition relating to the amount of substance i in the composite material is set as a discrete number, the amount r of substance i is... i The value is represented by bits, and whether the substance i is included in the composite material is also represented by bits.

5. The information processing apparatus according to any one of claims 1 to 4, characterized in that, Equations (1) and (2) represent the mixing constraint condition where substance B is not used when substance A is used.

6. The information processing apparatus according to claim 2, characterized in that, Equations (3) and (4) represent the mixing constraints under which substance A is not used when substance B is used.

7. An information processing system comprising an annealing optimizer and an information processing device, the information processing device providing support for the creation of an Ising model for solving an optimal solution retrieval problem of composite materials with mixed constraints by the annealing optimizer, the information processing system being characterized in that it comprises: The input receiving unit is configured to receive an objective function that formulates the properties of the composite material corresponding to the mixing, and the input of the mixing constraints. and The data production department is configured to produce an Ising model that enables the annealed optimizer to solve for the mixed constraints, which are then formulated to satisfy the mixed constraints, and for the characteristics to become the optimal solution of the mixture. In the substance mixed with the composite material, the amount r of substance i is... i The value is represented by bits, and whether substance i is included in the composite material is also represented by bits. The constraint condition includes conditions that satisfy equations (1) and (2). [Number 4] The q A0 This is an auxiliary variable that is "0" when substance A is included in the composite material and "1" when substance A is not included in the composite material. The q B0 This is an auxiliary variable that is "0" when substance B is included in the composite material and "1" when substance B is not included in the composite material. The m B This is to represent the amount r of substance B mixed in the composite material. B Number of bits required The q Bj It is the number "0" or "1" in the binary representation of the mixture of substance B. The constraint condition is formulated such that the optimal solution of the mixture is not calculated if at least one of the equations (1) and (2) is not satisfied.

8. A program, characterized in that, The program enables the execution of an information processing device that supports the creation of the Ising model for retrieving optimal solutions to composite materials with mixed constraints, using an annealed optimizer: The steps include accepting the objective function, which is a formula for the properties of the composite material corresponding to the mixing, and the input of the mixing constraints; and The steps of constructing an Ising model for solving the formulated constraint expressions that satisfy the mixed constraints by the annealed optimizer, and for obtaining the optimal solution of the mixture where the characteristics are optimal. In the substance mixed with the composite material, the amount r of substance i is... i The value is represented by bits, and whether substance i is included in the composite material is also represented by bits. The constraint condition includes conditions that satisfy equations (1) and (2). [Number 5] The q A0 This is an auxiliary variable that is "0" when substance A is included in the composite material and "1" when substance A is not included in the composite material. The q B0 This is an auxiliary variable that is "0" when substance B is included in the composite material and "1" when substance B is not included in the composite material. The m B This is to represent the amount r of substance B mixed in the composite material. B Number of bits required The q Bj It is the number "0" or "1" in the binary representation of the mixture of substance B. The constraint condition is formulated such that the optimal solution of the mixture is not calculated if at least one of the equations (1) and (2) is not satisfied.

9. A method for supporting the creation of Ising models for an information processing device, the information processing device providing support for creating Ising models for retrieving optimal solutions to composite materials with mixed constraints by an annealed optimizer, the method being characterized by performing the following processing: The objective function, which is a formula for the properties of the composite material corresponding to the mixture, and the inputs of the mixing constraints are accepted; and An Ising model is constructed to enable the annealed optimizer to solve the mixed constraints, which are then formalized into a formula, and to obtain the optimal solution for the mixed constraints, where the characteristic is optimal. In the substance mixed with the composite material, the amount r of substance i is... i The value is represented by bits, and whether substance i is included in the composite material is also represented by bits. The constraint condition includes conditions that satisfy equations (1) and (2). [Number 6] The q A0 This is an auxiliary variable that is "0" when substance A is included in the composite material and "1" when substance A is not included in the composite material. The q B0 This is an auxiliary variable that is "0" when substance B is included in the composite material and "1" when substance B is not included in the composite material. The m B This is to represent the amount r of substance B mixed in the composite material. B Number of bits required The q Bj It is the number "0" or "1" in the binary representation of the mixture of substance B. The constraint condition is formalized so that the optimal solution of the mixture is not calculated if at least one of the equations (1) and (2) is not satisfied.

10. An information processing apparatus that provides support for the creation of an Ising model for solving an optimal solution retrieval problem of composite materials with mixed constraints by an annealing-type optimizer, the information processing apparatus being characterized by comprising: The input receiving unit is configured to receive an objective function that formulates the properties of the composite material corresponding to the mixing, and the input of the mixing constraints. and The data production department is configured to produce an Ising model that enables the annealed optimizer to solve for the mixed constraints, which are then formulated to satisfy the mixed constraints, and for the characteristics to become the optimal solution of the mixture. In the substance mixed with the composite material, the amount r of substance i is... i The value is represented by bits, and whether substance i is included in the composite material is also represented by bits. The constraint conditions include the conditions that satisfy equations (6), (7), and (8). [Number 7] The q i0 This is an auxiliary variable that is "0" when substance i is included in the composite material and "1" when substance i is not included in the composite material. The m i This is to represent the amount r of substance i mixed in the composite material. i Number of bits required The q ij It is the number "0" or "1" in the binary representation of the mixture of substance i. N is the number of substances i that meet the constraint conditions through equation (8). The constraint condition is formulated such that the optimal solution of the mixture is not calculated if at least one of the equations (6), (7) and (8) is not satisfied.

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