Information processing device, information processing system, program, and information processing method

Abstract

The objective is to provide an information processing device, information processing system, program, and information processing method that can assist in creating an Ising model for solving the problem of finding the optimal solution for composite materials with formulation constraints using an annealing-type optimization machine. [Solution] An information processing device that receives bit information representing the optimal solution calculated by an annealing type optimization machine, converts the bit information into composition information of a composite material and displays it on a display device, and assumes that the bit information is configured to include, for each substance mixed in the composite material, an auxiliary bit indicating whether or not the substance is included in the composite material, and a sequence of quantity bits indicating the amount of the substance, and comprises a conversion unit that determines whether or not each substance is included based on the auxiliary bits, calculates the amount of each substance based on the sequence of quantity bits, and generates composition information including identification information and quantity of each substance, and a display unit that displays the composition information on a display device.

Description

[Technical Field]

[0001] This disclosure relates to an information processing device, an information processing system, a program, and an information processing method. [Background technology]

[0002] Conventionally, techniques have been known to rapidly calculate stable combinations of A-sites, B-sites, and anion sites in perovskite crystal structures, even when the number of combinations is enormous, by performing a ground state search using the Ising model or QUBO (Quadratic Unconstrained Binary Optimization) (see, for example, Patent Document 1). [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2021-033768 [Overview of the Initiative] [Problems that the invention aims to solve]

[0004] For example, there are optimal solution search problems that involve selecting the best combination from various formulations, such as searching for the composition of a composite material with optimal properties. Annealing-type optimization machines can solve optimal solution search problems formulated using the Ising model.

[0005] Furthermore, when selecting the optimal combination from various formulations, such as when searching for the composition of a composite material with optimal properties, constraints on the formulation are often imposed. For example, if there are incompatible combinations of substances, conditions related to the combination of substances are imposed as constraints on the formulation. The Ising model allows for the imposition of such constraints on the formulation.

[0006] In the Ising model, constraints (penalty functions) play a role in preventing combinations of ingredients that do not satisfy the constraints from being selected as the optimal combination. However, while constraints must be expressed using Ising-type mathematical formulas (constraint terms), expressing the constraints of ingredient combinations using constraint terms has not been easy.

[0007] This disclosure aims to provide an information processing device, an information processing system, a program, and an information processing method that can assist in creating an Ising model for enabling an annealing-type optimization machine to solve the problem of finding the optimal solution for composite materials subject to formulation constraints. [Means for solving the problem]

[0008] This disclosure comprises the following configuration.

[0009] [1] An information processing device that assists in creating an Ising model for having an annealing-type optimization machine solve an optimal solution search problem for composite materials with constraints on their composition, An input receiving unit configured to accept input of an objective function that formulates the properties of the composite material according to the aforementioned formulation, and the constraints of the formulation, A data creation unit is configured to create an Ising model for causing the annealing-type optimization machine to solve for the optimal solution of the formulation that satisfies the constraint equations that formalize the constraints on the formulation and whose characteristics are optimal. It has, The substance to be mixed into the composite material is the amount of substance i r i The bit representation indicates whether or not the substance i is included in the composite material, The aforementioned constraint equation includes the conditions that satisfy the following equations (1) and (2):

[0010]

number

[0011] [2] The constraint condition equation further includes conditions that satisfy the following equations (3) and (4),

[0012]

Number

[0013] [3] The substance to be mixed with the composite material is the amount of substance i r when the conditions regarding the amount of substance to be mixed with the composite material are set in a continuous number. i However, it is expressed in bit notation by the following formula (5), and whether or not the substance i is included in the composite material is also expressed in bit notation.

[0014]

number

[0015] [4] When the conditions regarding the amount of substance to be mixed into the composite material are set as discrete numbers, the amount of substance i r i The bit representation indicates whether or not the substance i is included in the composite material. An information processing device as described in any one of items [1] through [3].

[0016] [5] Equations (1) and (2) above are the conditions of the aforementioned formulation constraint, which is that substance B is not used when substance A is used. An information processing device as described in any one of items [1] through [4].

[0017] [6] Equations (3) and (4) above are the conditions of the formulation constraint, which is that substance A is not used when substance B is used. [2] The information processing device described above.

[0018] [7] An information processing system comprising an annealing-type optimization machine and an information processing device that assists in creating an Ising model for causing the annealing-type optimization machine to solve a problem of finding the optimal solution for a composite material subject to formulation constraints, An input receiving unit configured to accept input of an objective function that formulates the properties of the composite material according to the aforementioned formulation, and the constraints of the formulation, A data creation unit is configured to create an Ising model for causing the annealing-type optimization machine to solve for the optimal solution of the formulation that satisfies the constraint equations that formalize the constraints on the formulation and whose characteristics are optimal. It has, The substance to be mixed into the composite material is the amount of substance i r i The bit representation indicates whether or not the substance i is included in the composite material, The aforementioned constraint equation includes the conditions that satisfy the following equations (1) and (2):

[0019]

number

[0020] [8] An information processing device that assists in creating an Ising model for an annealing-type optimization machine to solve the problem of finding the optimal solution for composite materials with constraints on their composition, A procedure for receiving input of an objective function that formalizes the properties of the composite material according to the aforementioned formulation, and constraints on the formulation. A procedure for creating an Ising model to have the annealing-type optimization machine solve for the optimal solution of the formulation that satisfies the constraint equations that formalize the constraints on the formulation and whose characteristics are optimal. Make it run, The substance to be mixed into the composite material is the amount of substance i r i The bit representation indicates whether or not the substance i is included in the composite material, The aforementioned constraint equation includes the conditions that satisfy the following equations (1) and (2):

[0021]

number

[0022] [9] An Ising model creation support method for an information processing device that assists in creating an Ising model for an annealing-type optimization machine to solve an optimal solution search problem for composite materials with constraints on the composition, The system accepts input of an objective function that formalizes the properties of the composite material according to the aforementioned formulation, and constraints on the formulation. The process involves creating an Ising model for the annealing-type optimization machine to solve for the optimal solution of the formulation that satisfies the constraint equations that formalize the constraints on the formulation and also optimizes the characteristics. The substance to be mixed into the composite material is the amount of substance i r i The bit representation indicates whether or not the substance i is included in the composite material, The aforementioned constraint equation includes the conditions that satisfy the following equations (1) and (2):

[0023]

number

[0024]

[10] An information processing device that assists in creating an Ising model for having an annealing-type optimization machine solve an optimal solution search problem for composite materials with constraints on their composition, An input receiving unit configured to accept input of an objective function that formulates the properties of the composite material according to the aforementioned formulation, and the constraints of the formulation, A data creation unit is configured to create an Ising model for causing the annealing-type optimization machine to solve for the optimal solution of the formulation that satisfies the constraint equations that formalize the constraints on the formulation and whose characteristics are optimal. It has, The substance to be mixed into the composite material is the amount of substance i r i The bit representation indicates whether or not the substance i is included in the composite material, The aforementioned constraint equations include conditions that satisfy the following equations (6), (7), and (8):

[0025]

number

[0026] According to this disclosure, we can provide an information processing device, an information processing system, a program, and an information processing method that can assist in creating an Ising model for having an annealing-type optimization machine solve an optimal solution search problem for composite materials with formulation constraints. [Brief explanation of the drawing]

[0027] [Figure 1] This is a diagram illustrating an example of an information processing system according to this embodiment. [Figure 2] This is a hardware configuration diagram of an example of a computer according to this embodiment. [Figure 3] This is an explanatory diagram illustrating an example of the constraints on the formulation. [Figure 4] This is an explanatory diagram illustrating an example of the constraints on the formulation. [Figure 5] This is a diagram illustrating an example of an information processing system according to this embodiment. [Figure 6] This diagram illustrates an example of bit representation for matter. [Figure 7A] This diagram illustrates a specific example of the bit representation of "Substance 1". [Figure 7B] This diagram illustrates a specific example of the bit representation of "Substance 1". [Figure 7C] This diagram illustrates a specific example of the bit representation of "Substance 1". [Figure 8] This diagram illustrates an example of bit representation for matter. [Figure 9] This diagram illustrates an example of bit notation for the composition of composite materials. [Figure 10A] This is an explanatory diagram illustrating an example of the constraint conditions shown in equations (12) and (13). [Figure 10B] This is an explanatory diagram illustrating an example of the constraint conditions shown in equations (12) and (13). [Figure 11A] This is an explanatory diagram illustrating an example of the constraint conditions shown in equations (14) and (15). [Figure 11B] This is an explanatory diagram illustrating an example of the constraint conditions shown in equations (14) and (15). [Figure 12A] This figure illustrates an example of how to use the constraints shown in equations (14) and (15). [Figure 12B] This figure illustrates an example of how to use the constraints shown in equations (14) and (15). [Figure 12C] This figure illustrates an example of how to use the constraints shown in equations (14) and (15). [Figure 12D] This figure illustrates an example of how to use the constraints shown in equations (14) and (15). [Figure 13A] This figure illustrates examples of how to use the constraints shown in equations (14) and (15), and equations (16) and (17). [Figure 13B] This figure illustrates examples of how to use the constraints shown in equations (14) and (15), and equations (16) and (17). [Figure 14] This is a flowchart showing an example of the processing procedure of the information processing system according to this embodiment. [Figure 15] This figure illustrates an example of how to use the constraints shown in equation (18). [Figure 16] This figure illustrates an example of how to use the constraints shown in equation (18). [Modes for carrying out the invention]

[0028] Next, embodiments of the present invention will be described in detail. However, the present invention is not limited to the following embodiments.

[0029] <System Configuration> Figure 1 is a configuration diagram of an example of an information processing system according to this embodiment. The information processing system 1 shown in Figure 1 has a configuration comprising an annealing-type optimization machine 10 and an information processing device 12. The annealing-type optimization machine 10 and the information processing device 12 are connected via a communication network 18 such as a local area network (LAN) or the Internet, enabling data communication.

[0030] The annealing-type optimization machine 10 is an example of a device that solves optimal solution search problems (optimization problems) using the Ising model. An optimization problem is a problem in which the objective function is minimized or maximized among solutions that satisfy the constraints. In an optimization problem, the desired solution is expressed using decision variables. The objective function is a function in which the value to be minimized or maximized is expressed using the decision variables. The constraints are relational expressions in which the requirements that must be satisfied are expressed using the decision variables.

[0031] Furthermore, combinatorial optimization problems are optimization problems that have a combinatorial structure. A combinatorial optimization problem is the problem of finding a combination of decision variables that minimizes or maximizes an objective function among combinations of decision variables that satisfy the constraints.

[0032] The annealing-type optimization machine 10 may be implemented as a quantum computer using the quantum annealing method, or as an Ising machine (annealing machine) in which the quantum annealing method is implemented using digital circuits such as FPGA (Field Programmable Gate Array) or GPU (Graphics Processing Unit). The annealing-type optimization machine 10 may also be implemented as a digital annealer (registered trademark), which is an example of an Ising machine.

[0033] The annealing-type optimization machine 10 solves an optimization problem reduced to an Ising model by the convergence behavior of that Ising model. The Ising model can also be represented using QUBO. The energy function of the Ising model and the cost function of QUBO are equivalent through a variable transformation.

[0034] The Ising model is a statistical mechanics model that describes the behavior of magnetic materials. The Ising model has the property that the spin state is updated in such a way that the energy (Hamiltonian) is minimized due to the interaction between the spins of a magnetic material, ultimately resulting in the minimum energy. The annealing-type optimization machine 10 reduces the optimization problem to the Ising model and solves the optimization problem by finding the state that minimizes the energy, thereby finding that state as the optimal solution.

[0035] The information processing device 12 is a device operated by a user, such as a PC, tablet, or smartphone. The information processing device 12 assists a user who wants to have an annealing-type optimization machine 10 solve an optimization problem in creating an Ising model for the annealing-type optimization machine 10 to solve that optimization problem, as described below.

[0036] Furthermore, the information processing device 12 creates input information for the annealing-type optimization machine 10, which is input to the annealing-type optimization machine 10 in order to solve the optimization problem, based on the user's operations. The input information to be input to the annealing-type optimization machine 10 includes the objective function and constraints written in the Ising type, which are created as described later.

[0037] By inputting input information for the annealing-type optimization machine 10 into the annealing-type optimization machine 10, the user can have the annealing-type optimization machine 10 solve an optimization problem that has been reduced to an Ising model.

[0038] In this way, the information processing device 12 assists the user in creating an Ising model for the annealing-type optimization machine 10 to solve the optimization problem. The information processing device 12 also receives the optimal solution to the optimization problem solved by the annealing-type optimization machine 10 and outputs it so that the user can verify it, such as by displaying it on a display device.

[0039] Note that the information processing system 1 in Figure 1 is just one example; it may also be a system where a user accesses and uses the information processing device 12 from a user terminal (not shown) connected to the information processing device 12 via a communication network 18.

[0040] Furthermore, the annealing-type optimization machine 10 may be implemented as a cloud computing service. For example, the annealing-type optimization machine 10 may be available by calling an API (Application Programming Interface) via a communication network 18.

[0041] Furthermore, the annealing-type optimization machine 10 is not limited to being implemented as a cloud computing service; it may also be implemented on-premises or operated by another company. The annealing-type optimization machine 10 may also be implemented using multiple computers.

[0042] Furthermore, in the form in which users access and use the information processing device 12, the information processing device 12 may be implemented as a cloud computing service, on-premise, operated by another company, or implemented using multiple computers. Needless to say, the information processing system 1 in Figure 1 can have various system configurations depending on the application and purpose.

[0043] <Hardware Configuration> The information processing device 12 in Figure 1 is implemented, for example, by a computer 500 with the hardware configuration shown in Figure 2.

[0044] Figure 2 is a hardware configuration diagram of an example of a computer according to this embodiment. The computer 500 in Figure 2 is equipped with an input device 501, a display device 502, an external interface 503, RAM 504, ROM 505, a CPU 506, a communication interface 507, and an HDD 508, and each is interconnected via bus B. Note that the input device 501 and the display device 502 may be used in a connected configuration.

[0045] The input device 501 includes a touch panel, operation keys and buttons, a keyboard and mouse, etc., used by the user to input various signals. The display device 502 consists of a display such as a liquid crystal or organic EL that displays the screen, and a speaker that outputs sound data such as voice and sound. The communication interface 507 is an interface for the computer 500 to perform data communication.

[0046] Furthermore, HDD508 is an example of a non-volatile storage device that stores programs and data. The programs and data stored include the OS, which is the basic software that controls the entire computer 500, and applications that provide various functions on the OS. Note that computer 500 may use a drive device that uses flash memory as a storage medium (for example, a solid-state drive: SSD) instead of HDD508.

[0047] External I / F 503 is an interface to external devices. External devices include recording media 503a, etc. This allows computer 500 to read and / or write to recording media 503a via external I / F 503. Recording media 503a include flexible disks, CDs, DVDs, SD memory cards, USB memory, etc.

[0048] ROM505 is an example of non-volatile semiconductor memory (storage device) that can retain programs and data even when the power is turned off. ROM505 stores programs and data such as the BIOS, OS settings, and network settings that are executed when the computer 500 starts up. RAM504 is an example of volatile semiconductor memory (storage device) that temporarily holds programs and data.

[0049] The CPU 506 is an arithmetic unit that controls and implements the functions of the entire computer 500 by reading programs and data from storage devices such as the ROM 505 and HDD 508 onto the RAM 504 and executing processing. The information processing device 12 according to this embodiment can implement various functions as described later. The hardware configuration of the annealing-type optimization machine 10 will not be described.

[0050] <Example of a problem to be solved as an optimization problem> The following describes an example of solving a composite material composition problem as an optimization problem, where the composition of a composite material with optimal properties is found within the constraints of its composition.

[0051] For example, in this embodiment, we utilize the formulation constraints shown in Figure 3. Figure 3 is an explanatory diagram of an example of formulation constraints. A composite material is composed of multiple groups of materials. Figure 3 shows an example in which a composite material is composed of "Material Group 1" and "Material Group 2". Figure 3 shows an example in which formulation constraints exist for each group of materials that make up the composite material.

[0052] The constraints on the composition shown in Figure 3 include the following items: number of mixtures, continuous / discrete, and quantity. The number of mixtures is a condition relating to the number of substances included in the substance group that are mixed into the composite material, with a minimum and maximum number of mixtures set. Continuous / discrete is a condition relating to the quantity of substances mixed into the composite material, with a setting indicating whether the quantity of substances mixed into the composite material is continuous or discrete.

[0053] The quantity is a condition relating to the amount of substance to be mixed into the composite material, and the amount of substance to be mixed into the composite material is set. If the amount of substance to be mixed into the composite material is a continuous number, the quantity has a minimum and a maximum quantity set. If the amount of substance to be mixed into the composite material is a discrete number, the quantity is set to the amount of that substance.

[0054] For example, the formulation constraints in Figure 3 indicate that "Material Group 1" contains five types of "Material 1" to "Material 5," and that between one and three types of materials from these five "Material 1" to "Material 5" are mixed into the composite material. Furthermore, the formulation constraints in Figure 3 indicate that "Material Group 2" contains three types of "Material 6" to "Material 8," and that between zero and two types of materials from these three "Material 6" to "Material 8" are mixed into the composite material.

[0055] Furthermore, in this embodiment, we utilize the formulation constraints shown in Figure 4. Figure 4 is an explanatory diagram of an example of formulation constraints. Figure 4 is an example of conditions relating to the combination of substances included in the group of substances shown in Figure 3, where a combination of substances to be avoided is set when there is an incompatible combination of substances. As shown in Figure 4, the setting of the combination of substances to be avoided may be set within the same group of substances, such as the combination of "substance 1" and "substance 4" in Figure 3, or it may be set within different groups of substances, such as "substance 1" and "substance 6" in Figure 3.

[0056] In this embodiment, the objective is to find the optimal material composition that satisfies the constraints of the composition shown in Figures 3 and 4 and results in optimal properties for the composite material.

[0057] <Functional Configuration> The configuration of the information processing system 1 according to this embodiment will now be described. Figure 5 is a configuration diagram of an example of the information processing system according to this embodiment. Note that parts of the configuration diagram in Figure 5 that are not necessary for the explanation of this embodiment have been omitted as appropriate.

[0058] The annealing-type optimization machine 10 shown in Figure 5 has a call reception unit 20 and an optimal solution calculation unit 22. The information processing device 12 has an input reception unit 30, a conversion unit 32, a data creation unit 34, a display unit 36, a material information storage unit 50, and a constraint condition information storage unit 52.

[0059] The input receiving unit 30 is an input interface that accepts user operations. The input receiving unit 30 receives information from the user that is necessary to have the annealing-type optimization machine 10 solve a combinatorial optimization problem. For example, the input receiving unit 30 accepts input of an objective function that formalizes the properties of a composite material according to the composition of the materials.

[0060] The objective function is a function that formalizes the properties of the composite material according to the composition of the materials, and is designed so that the smaller the value, the closer the material is to the properties desired by the user. For example, the properties desired by the user may be high performance or low cost. In addition, the input receiving unit 30 accepts input of composition constraints, such as those shown in Figures 3 and 4.

[0061] The conversion unit 32 converts the constraint conditions of the blending into a constraint expression. The constraint expression is an Ising-type mathematical formula that formalizes the constraint conditions of the blending. The constraint expression is formulated to be "0" when the constraint conditions of the blending are satisfied, and to be a large value when the constraint conditions of the blending are not satisfied.

[0062] For example, the constraint equation is formulated so that it takes a large value if at least one of the following conditions is not met for each group of materials that make up the composite material: the condition regarding the number of materials included in the group that are mixed into the composite material, and the condition regarding the amount of material mixed into the composite material.

[0063] The equation-type constraint shown in equation (6) and the inequality-type constraint shown in equation (7) can be expressed using an Ising-type mathematical formula.

[0064]

number

[0065] Furthermore, since E1 and E2 are Ising-type formulas, they can be expressed in QUBO type as shown in equation (9) below.

[0066]

number

[0067] The material information storage unit 50 stores the properties (performance, cost, etc.) of the materials included in the material group. For example, the properties of a composite material can be represented by the sum of the values ​​obtained by multiplying the properties of the materials mixed into the composite material by the mixing ratio.

[0068] The call reception unit 20 of the annealing-type optimization machine 10 receives a call from the information processing device 12 and receives input information for the annealing-type optimization machine 10 created from the above equation (8) from the information processing device 12.

[0069] The optimal solution calculation unit 22 minimizes the Ising model E based on the input information received by the call reception unit 20 {x i We obtain}. Minimize the Ising model E {x i Obtaining} is equivalent to obtaining a composite material composition that satisfies the constraints of the formulation expressed in E2 and minimizes the objective function expressed in E1.

[0070] The optimal solution calculation unit 22 can calculate the optimal solution for a material composition that satisfies the constraint equations that formalize the constraints on the composition and also optimizes the properties of the composite material. The call reception unit 20 transmits the optimal solution calculated by the optimal solution calculation unit 22 to the information processing device 12.

[0071] Note that the configuration diagram in Figure 5 is just one example. Various configurations are possible for the information processing system 1 according to this embodiment. In addition, although this embodiment describes an example in which the input receiving unit 30 receives input of constraint conditions for the composition, it may also receive input of a formalized constraint expression.

[0072] <Bit representation of matter> The following bit representations, used to express the quantities of each substance, are necessary to represent the constraints on the composition using the Ising model. For example, the bit representation of a substance is as shown in Figure 6.

[0073] Figure 6 illustrates an example of bit representation of a substance. The substance is represented by the amount of substance i r in equation (10). i This is represented in bit notation, along with the auxiliary variable q of substance i. i0 This bitwise indicates whether or not substance i is included in the composite material.

[0074]

number

[0075] Auxiliary variable q i0 is the amount of substance i r i If the quantity of substance i is not 0 (substance i is included in the composite material), then it becomes "0", and the quantity of substance i r i It becomes "1" when it is 0 (substance i is not included in the composite material).

[0076] For example, the bit representation of "Substance 1" with one significant digit after the decimal point and a quantity between "2 and 10" is as shown in Figures 7A to 7C. Figures 7A to 7C illustrate specific examples of the bit representation of "Substance 1".

[0077] Maximum amount M of "Substance 1" i,MAX The answer is "10". Therefore, C m <M i,MAX The largest natural number that satisfies this condition is m i The result is "7". The number of bits that need to be reserved for "Substance 1" is the auxiliary variable n. i0 Adding the auxiliary bits that represent this, the total becomes 8 bits.

[0078] For example, if the amount of "substance 1" is "4.2", the value of the auxiliary bit will be "0" because "substance 1" is included in the composite material. The values ​​of the bits "j=1~7" to represent the amount of "substance 1" "4.2" will be "1" for 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".

[0079] Furthermore, for example, the bit representation of a substance may be as shown in Figure 8. Figure 8 is a diagram illustrating an example of bit representation of a substance. The quantity r of substance i i This is expressed in bit notation by equation (11), and the auxiliary variable n of substance i. i0 This bitwise indicates whether or not substance i is included in the composite material.

[0080]

number

[0081] By using the bit notation described above to represent the amount of each substance, the composition of a composite material can be represented by bit notation as shown in Figure 9. Figure 9 illustrates an example of bit notation for the composition of a composite material.

[0082] Figure 9 shows an example where "Material Group 1," which constitutes a composite material, contains five types of "Material 1" to "Material 5." "Material 1," "Material 2," and "Material 5" are examples of materials whose quantities are set as continuous numbers. "Material 3" and "Material 4" are examples of materials whose quantities are set as discrete numbers.

[0083] The number of bits that need to be reserved for "Substance 1" to "Substance 5" depends, as mentioned above, on whether the amounts of substances to be mixed into the composite material are set as continuous or discrete numbers, and on the amount of each substance. 1j ~q 5j This is a bit representation of the quantities of "Substance 1" to "Substance 5". For example, if the smallest unit of quantity is 0.1 and the maximum quantity of "Substance 1" is "30", then the quantity of "Substance 1" is q. 11 ~q 19 It can be represented in bit notation by q. Also, the quantity of "substance 3", which has three discrete values ​​of "3", "5", and "10", is q 31 ~q 33 This can be represented in bitwise terms.

[0084] When used in the annealing-type optimization machine 10, the bit representation is the one-dimensional vector representation {x} shown in equation (9). i} can be used. By concatenating the bit representations of the substances included in all the material groups that make up the composite material, the composition of the composite material can be expressed in the one-dimensional vector representation {x} shown in equation (9). i It can be represented as}.

[0085] <Constraints> In this embodiment, when solving the combination optimization problem of the blending of substances that optimizes the properties of the composite material among the compositions of the composite material composed of a plurality of substance groups, the following constraints are imposed.

[0086] 《Constraint 1》 In this embodiment, the constraints shown in Formula (12) and Formula (13) are imposed for each substance i.

[0087]

Number

[0088] The inequality-type constraint of Formula (12) determines that when the auxiliary variable q i0 on the left side is "1", the second term on the left side is "0", and when the auxiliary variable q i0 on the left side is "0", the second term on the left side is "1 to m i ". It is a constraint condition for this determination.

[0089] p The inequality-type constraint of Formula (13) is a constraint condition for determining that when the auxiliary variable q i0 on the left side is "0", the second term on the left side is not "0". The inequality constraints of Formula (12) and Formula (13) are such that the auxiliary variable q i0 of substance i is q i =0 when r i0 >0 and q i =0 when r i0This is a constraint condition to ensure that the value = 1 is maintained.

[0090] Figures 10A and 10B are explanatory diagrams illustrating examples of the constraints shown in equations (12) and (13). Figures 10A and 10B show calculation examples of equations (12) and (13) for "Substance 1". For "Substance 1" in quantities of "2 to 10", m i The result is "7".

[0091] When using "Substance 1," the constraint is satisfied if the bit array representing the amount of "Substance 1" contains a bit of "1," as shown in the table in Figure 10A. Conversely, when using "Substance 1," the constraint is violated if the bit array representing the amount of "Substance 1" does not contain a bit of "1."

[0092] When "Substance 1" is not used, the constraint is satisfied if the bit array representing the amount of "Substance 1" does not contain a bit of "1", as shown in the table in Figure 10B. Conversely, when "Substance 1" is not used, the constraint is violated if the bit array representing the amount of "Substance 1" contains a bit of "1".

[0093] Furthermore, since each substance i is subject to the constraints shown in equations (12) and (13), if there are 20 substances i, then 20 × 2 = 40 constraints are imposed. Constraint 1 is the auxiliary variable q i0 This becomes a constraint.

[0094] 《Constraint condition 2》 In this embodiment, when there are incompatible combinations of substances, the constraints shown in equations (14) and (15) are imposed for each combination of substances to be avoided. Here, we will explain an example where substance A and substance B are incompatible. Equations (14) and (15) represent the constraint that substance B should not be used when substance A is used.

[0095]

number

[0096] The constraint of the inequality in equation (14) is the auxiliary variable q on the left side. A0 If is "1", then the second term on the left side is "0~m B Determine that this is the case, and the auxiliary variable q on the left side A0 This is a constraint condition for determining whether the second term on the left side is "0" when the first term is "0".

[0097] The constraint of the inequality in equation (15) is the auxiliary variable q on the left side. A0 This is a constraint condition for determining whether the second term on the left side is "0" when q is "1". Note that the constraints on the inequalities in equations (14) and (15) are the auxiliary variable q of substance i. i0 However, r i When >0, q i0 =0 and r i When = 0, q i0 It is necessary to impose the constraint that the value must be 1.

[0098] Figures 11A and 11B are explanatory diagrams illustrating examples of the constraints shown in equations (14) and (15). Figure 11A shows an example of calculating equations (14) and (15), which are constraints on substance B when substance A is used. For substance B in quantities of "2 to 10", m b The result is "7".

[0099] The constraint "When substance A is used, substance B is not used" is satisfied if the bit array representing the amount of substance B does not contain a "1" bit, as shown in the table in Figure 11A. Conversely, the constraint "When substance A is used, substance B is not used" is violated if the bit array representing the amount of substance B contains a "1" bit.

[0100] The constraint "Use substance B when substance A is not used" is satisfied if the bit array representing the amount of substance B contains a "1" bit, as shown in the table in Figure 11B. The constraint "Use substance B when substance A is not used" is violated if the bit array representing the amount of substance B does not contain a "1" bit.

[0101] Furthermore, for each incompatible combination of substances, the constraints shown in equations (14) and (15) are imposed. Conversely, to ensure the same applies, the constraints shown in equations (16) and (17) are also imposed on substance A. Equations (16) and (17) represent the constraint that substance A cannot be used when substance B is used.

[0102]

number

[0103] The constraint of the inequality in equation (16) is the auxiliary variable q on the left side. B0 If is "1", then the second term on the left side is "0~m ADetermine that this is the case, and the auxiliary variable q on the left side B0 This is a constraint condition for determining whether the second term on the left side is "0" when the first term is "0".

[0104] The constraint of the inequality in equation (17) is the auxiliary variable q on the left side. B0 If is "1", then the second term on the left side is "0~m B This is a constraint condition for determining whether the condition is acceptable. Note that the constraints of the inequalities in equations (16) and (17) are the auxiliary variable q of substance i. i0 However, r i When >0, q i0 =0 and r i When = 0, q i0 It is necessary to impose the constraint that the value must be 1.

[0105] Further details of this embodiment will be explained. Figures 12A to 12D illustrate examples of the use of the constraints shown in equations (14) and (15). Note that in Figures 12A to 12D, m B Here is an example of substance B where the value is "7".

[0106] The constraint in Figure 12A, "When substance A is used, substance B is not used," is related to the auxiliary variable q. A0 The auxiliary variable q is "0", B0 The condition is satisfied because the bit array representing the amount of substance B contains a bit of "1", and therefore the condition is met.

[0107] The constraint condition in Figure 12B, "Use substance B when substance A is not used," is related to the auxiliary variable q. A0 The auxiliary variable q is "1", and B0 The condition is satisfied because the bit value is "0" and the bit array representing the amount of substance B contains a bit of "1".

[0108] The constraint in Figure 12C, "If substance A is not used, then substance B is also not used," is related to the auxiliary variable q. A0 The auxiliary variable q is "1", and B0 The condition is satisfied because the bit array representing the amount of substance B contains a bit of "1", and therefore the condition is met.

[0109] The constraint in Figure 12D, "When substance A is used, substance B is also used," is related to the auxiliary variable q. A0 The auxiliary variable q is "0", B0 Since the bit array representing the amount of substance B contains a bit of "1", the condition is not met, resulting in a constraint violation.

[0110] Figures 12A to 12D show an example where constraints are imposed on substance B. To demonstrate the reverse, we will now explain an example where similar constraints are imposed on substance A.

[0111] Figures 13A to 13B illustrate examples of how to use the constraints shown in equations (14) and (15), and equations (16) and (17). Note that in Figures 13A to 13B, m A and m B Here is an example where the value is "7".

[0112] The constraint condition in Figure 13A, "Use substance B when substance A is not used," is related to the auxiliary variable q. A0 The auxiliary variable q is "0", B0 The condition is satisfied because the bit array representing the amount of substance B contains a bit of "1", and therefore the condition is met.

[0113] The constraint in Figure 13B, "When substance B is used, substance A is not used," is related to the auxiliary variable q. A0 The auxiliary variable q is "1", and B0 The condition is satisfied because the bit array representing the amount of substance A is "0" and does not contain a bit of "1".

[0114] Thus, the constraints shown in equations (16) and (17), which are the inverse of the constraints shown in equations (14) and (15), also hold true.

[0115] According to this embodiment, if there are incompatible combinations of substances, constraints can be imposed on each combination of substances to be avoided so that the incompatible combination is not selected as the optimal combination. For example, if there are combinations of substances that do not mix due to poor compatibility, and these combinations are known in advance, then unnecessary searches can be avoided by imposing constraints as described above.

[0116] 《Constraint condition 3》 In this embodiment, if there is a combination of incompatible substances, in addition to imposing the constraints shown in equations (12) and (13) above on each substance i, the constraint shown in equation (18) is imposed on the substance i to which the constraint is to be applied.

[0117]

number

[0118] This section describes an example where substance A and substance B are incompatible and cannot be used together. Figure 15 illustrates an example of using the constraint condition shown in equation (18). Note that in Figure 15, the number of substances i to which the constraint condition is imposed is "2".

[0119] The constraint condition in Figure 15(A), "When substance A is used, substance B is not used," is related to the auxiliary variable q. A0 The auxiliary variable q is "0", B0 Since the left side is "1" and the left side is "1", the condition is satisfied.

[0120] The constraint condition in Figure 15(B), "Use substance B when substance A is not used," is related to the auxiliary variable q. A0 The auxiliary variable q is "1", and B0Since the left side is "0" and the left side is "1", the condition is satisfied.

[0121] The constraint in Figure 15(C), "If substance A is not used, then substance B is also not used," is related to the auxiliary variable q. A0 The auxiliary variable q is "1", and B0 Since the left side is "1" and the left side is "2", the condition is satisfied.

[0122] The constraint in Figure 15(D), "When substance A is used, substance B is also used," is related to the auxiliary variable q. A0 The auxiliary variable q is "0", B0 Since is "0", the left side is "0", so equation (18) is not satisfied, resulting in a constraint violation.

[0123] Next, we will explain an example where substances A, B, and C are incompatible and cannot be used simultaneously. Figure 16 illustrates an example of using the constraints shown in equation (18). Note that in Figure 16, the number of substances i to which the constraints are imposed is "3".

[0124] The combinations of using and not using substances A, B, and C result in 8 possibilities, as shown in the table in Figure 16. (Auxiliary variable q) A0 The value of q is "0" when substance A is used and "1" when it is not used. (Auxiliary variable q) B0 The value of q is "0" when substance B is used and "1" when it is not used. (Auxiliary variable q) C0 The value is "0" when substance C is used and "1" when it is not used.

[0125] The constraint condition "None of substances A, B, or C are used" is expressed by the auxiliary variable q A0 The auxiliary variable q is "1", and B0 The auxiliary variable q is "1", and C0 Since the left side is "1" and the left side is "3", the condition is satisfied.

[0126] The constraint condition "use only substance A" is expressed by the auxiliary variable q A0 The auxiliary variable q is "0", B0The auxiliary variable q is "1", and C0 Since the left side is "1" and the left side is "2", the condition is satisfied.

[0127] The constraint condition "use only substance B" is expressed by the auxiliary variable q A0 The auxiliary variable q is "1", and B0 The auxiliary variable q is "0", C0 Since the left side is "1" and the left side is "2", the condition is satisfied.

[0128] The constraint condition "use only substance C" is expressed by the auxiliary variable q A0 The auxiliary variable q is "1", and B0 The auxiliary variable q is "1", and C0 Since the left side is "0" and the left side is "2", the condition is satisfied.

[0129] The constraint condition "use substance B and substance C" is expressed by the auxiliary variable q A0 The auxiliary variable q is "1", and B0 The auxiliary variable q is "0", C0 Since the left side is "0" and the left side is "1", equation (18) is not satisfied, resulting in a constraint violation.

[0130] The constraint condition "use substance A and substance C" is expressed by the auxiliary variable q A0 The auxiliary variable q is "0", B0 The auxiliary variable q is "1", and C0 Since the left side is "0" and the left side is "1", equation (18) is not satisfied, resulting in a constraint violation.

[0131] The constraint condition "use substance A and substance B" is expressed by the auxiliary variable q A0 The auxiliary variable q is "0", B0 The auxiliary variable q is "0", C0 Since the left side is "1", equation (18) is not satisfied, resulting in a constraint violation.

[0132] The constraint condition "use substance A, substance B, and substance C" is expressed by the auxiliary variable q A0 The auxiliary variable q is "0", B0The auxiliary variable q is "0", C0 Since is "0", the left side is "0", so equation (18) is not satisfied, resulting in a constraint violation.

[0133] According to this embodiment, if there are incompatible combinations of substances, constraints can be imposed to prevent incompatible combinations from being selected as the optimal combination. For example, if there are combinations of substances that do not mix due to poor compatibility, and these combinations are known in advance, then imposing constraints as described above can avoid unnecessary searching.

[0134] <Processing> Figure 14 is a flowchart showing an example of the processing procedure of the information processing system according to this embodiment.

[0135] In step S100, the information processing device 12 receives input from the user of information necessary to have the annealing-type optimization machine 10 solve a combinatorial optimization problem. For example, the information processing device 12 receives input of an objective function that formalizes the properties of the composite material according to the composition of the materials. The information processing device 12 also receives input of constraints on the composition.

[0136] In step S102, the information processing device 12 converts the formulation constraint conditions received as input in step S100 into constraint expression formulas. Based on the information of constraint expression formulas defined according to substance i stored in the constraint expression information storage unit 52, the information processing device 12 converts the formulation constraint conditions into constraint expression formulas. Note that the process of converting the formulation constraint conditions into constraint expression formulas may be performed by the user.

[0137] In step S104, the information processing device 12 creates an Ising model from the objective function and constraint equations for the annealing-type optimization machine 10 to solve.

[0138] In step S106, the information processing device 12 creates input information in a data format usable by the annealing-type optimization machine 10 from the created Ising model and transmits it to the annealing-type optimization machine 10. The input information in a data format usable by the annealing-type optimization machine 10 includes the contents of the objective function and constraint equations. The input information for the annealing-type optimization machine 10 is, for example, an electronic file to be transmitted to the annealing-type optimization machine 10.

[0139] In step S108, the information processing device 12 transmits input information for the annealing-type optimization machine 10 to the annealing-type optimization machine 10. The annealing-type optimization machine 10 calculates the optimal solution (the composition of materials that results in the optimal properties of the composite material) from among the solutions that satisfy the constraint conditions (conditions for composition constraints) according to the received input information.

[0140] In step S110, the annealing-type optimization machine 10 transmits information representing the calculated optimal solution to the information processing device 12. The information processing device 12 converts the information representing the optimal solution (bit information) received from the annealing-type optimization machine 10 into user-friendly information such as the composition of the composite material and outputs it. For example, the information processing device 12 displays the composition (material name) of the optimal composite material and the amount of that material.

[0141] The composite material composition explored as the optimal solution in this embodiment can be used to control composite material production equipment, such as aluminum alloy manufacturing equipment, which produces composite materials by specifying the substances to be mixed and the amounts of those substances. Furthermore, this embodiment can also be used to explore the compounding composition of semiconductor materials as an example of composite materials. Examples of semiconductor materials include resist materials, adhesives, tackifiers, encapsulants, etc., and are composite materials composed of multiple resins, additives, and / or fillers.

[0142] As described above, the information processing system 1 according to this embodiment can support the creation of an Ising model for having the annealing-type optimization machine 10 solve an optimization problem of a composite material with constraints on its composition.

[0143] Although this embodiment has been described above, it will be understood that various modifications to the form and details are possible without departing from the spirit and scope of the claims. Although the present invention has been described above based on examples, the present invention is not limited to the above examples, and various modifications are possible within the scope described in 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, the contents of which are incorporated herein by reference in their entirety. [Explanation of symbols]

[0144] 1. Information Processing System 10 Annealing-type optimization machine 12 Information Processing Devices 18. Communication Networks 20 Call Reception Department 22 Optimal Solution Calculation Unit 30 Input reception section 32 Conversion section 34 Data Creation Department 36 Display section 50 Material information storage unit 52 Constraint expression information storage unit

Claims

1. An information processing device that receives bit information representing the optimal solution calculated by an annealing type optimization machine, converts the bit information into composition information of a composite material, and displays it on a display device, Assuming that the bit information includes, for each substance mixed into the composite material, an auxiliary bit indicating whether or not that substance is included in the composite material, and a sequence of quantity bits indicating the amount of that substance, A conversion unit that determines the presence or absence of each substance based on the auxiliary bits, calculates the amount of each substance based on the quantity bit sequence, and generates composition information including the identification information and the amount of each substance, A display unit that displays the composition information on the display device, An information processing device having

2. The conversion unit decomposes the bit information, which is represented by a one-dimensional vector notation formed by concatenating bit sequences corresponding to multiple substances, into the auxiliary bits and quantity bit sequences for each substance to generate the composition information. The information processing apparatus according to claim 1.

3. The conversion unit calculates the amount based on a binary coefficient for substances whose quantity is set as a continuous number, and calculates the amount based on bits associated with discrete values ​​for substances whose quantity is set as a discrete number. The information processing apparatus according to claim 1 or 2.

4. It further has a material information storage unit that stores the properties of the substances included in the group of substances, The conversion unit calculates the properties of the composite material based on the properties of the material stored in the material information storage unit and the quantity thereof. The display unit displays the properties of the composite material along with the composition information on the display device. The information processing apparatus according to claim 1 or 2.

5. The system further includes an output unit that outputs control information specifying the type and amount of substances to be mixed, based on the composition information generated by the conversion unit. The aforementioned control information is used to control a composite material production apparatus that produces composite materials. The information processing apparatus according to claim 1 or 2.

6. The annealing type optimization machine is connected to the information processing device via a communication network, and the information processing device receives the bit information via the communication network. The information processing apparatus according to claim 1 or 2.

7. The system comprises an annealing type optimization machine and the information processing device described in claim 1, The information processing device receives the bit information representing the optimal solution calculated by the annealing type optimization machine, and the information processing device displays the composition information on the display device. Information processing system.

8. On the computer, A function to receive bit information representing the optimal solution calculated by an annealing-type optimization machine, A function that determines the presence or absence of each substance based on the auxiliary bits included in the aforementioned bit information, calculates the amount of each substance based on the quantity bit sequence, and generates composition information of the composite material including the identification information of each substance and the aforementioned quantity, A function to display the aforementioned composition information on a display device, A program to execute.

9. The annealing-type optimization machine receives bit information representing the optimal solution it has calculated. Based on the auxiliary bits included in the bit information, the presence or absence of each substance is determined, the amount of each substance is calculated based on the quantity bit sequence, and composition information of the composite material is generated, including the identification information of each substance and the amount. The composition information is displayed on a display device. Information processing methods.

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