WO2022003784A1 - 不整合判定装置、方法、および、コンピュータ読取可能な記録媒体 - Google Patents
不整合判定装置、方法、および、コンピュータ読取可能な記録媒体 Download PDFInfo
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- 238000009472 formulation Methods 0.000 description 4
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- G—PHYSICS
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Definitions
- the present invention is a computer-readable recording medium recording an inconsistency determination device, an inconsistency determination method, and an inconsistency determination program for determining whether or not an inconsistency has occurred in an expression representing energy in a combinatorial optimization problem. Regarding.
- Patent Document 1 describes solving a combinatorial optimization problem by simulated annealing.
- combinatorial optimization problems include the traveling salesman problem, the knapsack problem, and the graph partitioning problem.
- combinatorial optimization problems are not limited to these problems.
- the energy function of the Zing model or the energy function of QUADO is input to the computer that solves the combinatorial optimization problem by simulated annealing or quantum annealing.
- the Ising model is a statistical mechanics model that expresses the behavior of a magnetic material by individual spins, but it can also be applied to the solution of combinatorial optimization problems.
- the state of each spin is represented by "1" or "-1".
- QUABO is also known as a model in which the state of each spin is represented by "1" or "0".
- the energy function of the Ising model and the energy function of QUABO can be converted to each other.
- j represents a time and v and u represent a city.
- W uv is the distance between the city u and the city v, and is predetermined as a constant for each group of cities. ⁇ and ⁇ are predetermined as constants.
- Equation (1) expresses the constraint that the salesman does not pass through the same city more than once.
- Equation (1) represents the constraint that the salesman exists in only one city at one time.
- the third term on the right side of equation (1) represents the distance between cities that the salesman passes through.
- the third term on the right side is not a term representing a constraint.
- the third term on the right side is a term representing a matter for which the value is to be minimized for the user who wants to obtain the solution of the traveling salesman problem.
- an objective function a term that does not represent a constraint and that represents a matter for which a user who wants to obtain a solution of a combinatorial optimization problem wants to minimize the value. That is, the third term on the right side in the equation (1) is an objective function.
- equation (1) If an equation representing the energy in the combinatorial optimization problem as illustrated in equation (1) is created, the equation is converted into the energy function of the Ising model or the energy function of QUA. This conversion method is known.
- s i and s j are variables representing the spin state. The subscript in this variable identifies the spin. J ij is a constant corresponding to i and j, and h i is a constant corresponding to i.
- x i and x j are variables representing the spin state. The subscript in this variable identifies the spin.
- Q ij is a constant corresponding to i and j.
- Equations (2) and (3) are quadratic equations of variables representing spin states. Further, the equation (1) is also a quadratic equation of a variable representing the spin state. Therefore, the equation (1) can be converted into the equation (2) or the equation (3).
- the variable representing the spin state can be used.
- the order can be lowered to 2.
- the variables used for the above replacement are called auxiliary variables. Therefore, even if the order of the variable representing the spin state is 3rd or higher in the formula obtained by the formulation, the energy function of the Ising model (formula (2)) or QUABO can be obtained by using the auxiliary variable. Energy function (Equation (3)) can be obtained.
- the Ising model or QUA's energy function is obtained, apply that energy function to simulated annealing to identify the state of each spin when energy is minimized. Then, the optimum solution can be obtained by interpreting the state of each spin according to the combinatorial optimization problem (in this example, the traveling salesman problem).
- Non-Patent Document 1 describes how various constraints are expressed in a formulated formula (formula expressing energy in a combinatorial optimization problem) that is converted into an energy function of QUA. ing.
- the formula can be converted into the energy function of the Ising model or the energy function of QUA. .. Then, by performing annealing on the energy function, a solution to the combinatorial optimization problem can be obtained.
- the solution of the combinatorial optimization problem may not be appropriate. Even if the user can determine that the solution of the combinatorial optimization problem is not appropriate, it is difficult for the user to identify the cause. Annealing is a probabilistic process, so even if the input energy function is appropriate, it is possible to derive an inappropriate solution. In addition, as described above, an inappropriate solution may be derived due to an inconsistency in the formula formulated by the user.
- the inconsistency determination device has an inconsistency in an expression representing energy in a combinatorial optimization problem, in which the state of each spin is converted into an energy function of a model represented by a first value or a second value. It is characterized by comprising an inconsistency determination means for determining whether or not it has occurred.
- the inconsistency determination method is in an equation expressing energy in a combinatorial optimization problem in which a computer transforms the state of each spin into an energy function of a model represented by a first value or a second value. It is characterized in that it is determined whether or not an inconsistency has occurred.
- the computer-readable recording medium is an expression representing energy in a combination optimization problem, in which the state of each spin is converted into an energy function of a model represented by a first value or a second value by a computer. It is a computer-readable recording medium on which an inconsistency determination program for executing an inconsistency determination process for determining whether or not an inconsistency has occurred is recorded.
- a formulated formula (a formula representing energy in a combinatorial optimization problem) is converted into an energy function of QUABO will be described as an example.
- the variable representing the spin state takes a value of 1 or 0.
- the present invention may also be applied when the formulated equation is converted into an energy function of the Ising model.
- FIG. 1 is a block diagram showing a configuration example of the inconsistency determination device according to the first embodiment of the present invention.
- the inconsistency determination device 1 of the first embodiment includes an input unit 2, a division unit 3, an inconsistency determination unit 4, and a presentation unit 5.
- a formalized formula (a formula representing energy in a combinatorial optimization problem) is input to the input unit 2.
- the input unit 2 may be realized by a data reading device that reads data recorded on a data recording medium such as an optical disk (in this embodiment, an expression representing energy in a combinatorial optimization problem).
- a data reading device that reads data recorded on a data recording medium such as an optical disk (in this embodiment, an expression representing energy in a combinatorial optimization problem).
- the input unit 2 is not limited to such a data reading device, and may be an input device such as a keyboard for the user to input an expression.
- the division unit 3 takes in an expression (an expression representing energy in a combinatorial optimization problem) via an input unit 2. Then, the division unit 3 divides the equation into a plurality of terms.
- ⁇ , ⁇ , and ⁇ are constants.
- x i , x 1 , and x 2 are variables representing the spin states, and the spin is identified by the subscript in this variable.
- the variable representing the spin state takes a value of 1 or 0.
- the spins are identified by an integer from 1 to N.
- c i is a constant corresponding to i.
- the division unit 3 divides the right side of the equation (4) into terms. As a result, , ⁇ (1-x 1 ) 2 , ⁇ (1-x 2 ) 2 , and Each term of is obtained.
- ⁇ (1-x 1 ) 2 and ⁇ (1-x 2 ) 2 correspond to the constraint terms.
- the objective function is a term that does not represent a constraint and represents a term that a user who wants to obtain a solution of a combinatorial optimization problem wants to minimize the value.
- the formula A and the formula B may be the variables themselves representing the spin states.
- the formulas A and B may be formulas using variables representing the spin states.
- the formula A and the formula B may be, for example, a constant (for example, “1” or the like).
- the first constraint term represents the constraint of the following equation (5).
- the inconsistency determination unit 4 determines that the inconsistency regarding the constraint has occurred in the input expression (the expression representing the energy in the combinatorial optimization problem) when there is an inconsistency between the specified constraints. do. Further, the inconsistency determination unit 4 determines that there is no inconsistency regarding the constraint in the input expression when there is no inconsistency between the specified constraints.
- the inconsistency determination unit 4 substitutes the "expression representing the constraint” into another "expression representing the constraint", and determines whether or not the inconsistency has occurred as a result.
- the inconsistency determination unit 4 may substitute a plurality of "expressions representing constraints” into one "expression representing constraints”. If the "expression representing the constraint” is substituted into another "expression representing the constraint” and a mismatch occurs as a result, the inconsistency determination unit 4 determines the constraint corresponding to the "assigned expression" and the constraint. Judge that there is an inconsistency with the constraint corresponding to the "assigned expression”.
- the inconsistency determination unit 4 determines that the constraints corresponding to the expressions other than the "assigned expression" and the "assigned expression” are not related to the above-mentioned inconsistency. If no inconsistency has occurred as a result of the assignment, the inconsistency determination unit 4 has an inconsistency between the constraint corresponding to the "assigned expression” and the constraint corresponding to the "assigned expression". It is determined that there is no such thing.
- the presentation unit 5 displays the determination result by the inconsistency determination unit 4 on, for example, a display device (not shown in FIG. 1) included in the inconsistency determination device 1.
- a display device not shown in FIG. 1
- the fact that there is an inconsistency regarding the constraint in the equation is displayed on the display device.
- the presentation unit 5 displays the determination result on the display.
- the division unit 3, the inconsistency determination unit 4, and the presentation unit 5 are realized by, for example, a CPU (Central Processing Unit) of a computer that operates according to an inconsistency determination program.
- the CPU may read the inconsistency determination program from a program recording medium such as a program storage device of a computer, and operate as the division unit 3, the inconsistency determination unit 4, and the presentation unit 5 according to the inconsistency determination program. This point is the same in the second embodiment described later.
- FIG. 2 is a flowchart showing an example of the processing progress of the first embodiment. The matters already explained will be omitted as appropriate.
- the division unit 3 divides the expression into a plurality of terms (step S1).
- the inconsistency determination unit 4 extracts all two or more constraint terms from each term obtained in step S1 and specifies the constraint for each constraint term (step S2).
- the inconsistency determination unit 4 determines whether or not there is an inconsistency between the specified constraints (step S3).
- the inconsistency determination unit 4 may substitute the "expression representing the constraint" into another "expression representing the constraint” and determine whether or not the inconsistency occurs as a result. If an inconsistency occurs as a result of the substitution, the inconsistency determination unit 4 may determine that there is an inconsistency between the constraint corresponding to the substituted expression and the constraint corresponding to the substituted expression. If no inconsistency occurs as a result of the substitution, the inconsistency determination unit 4 determines that there is no inconsistency between the constraint corresponding to the substituted expression and the constraint corresponding to the substituted expression. good.
- the inconsistency determination unit 4 determines that the input expression has an inconsistency regarding the constraint (step S4).
- the presentation unit 5 presents the constraint in which the inconsistency has occurred, and also presents that the input expression has an inconsistency regarding the constraint (step S5).
- the inconsistency determination unit 4 determines that there is no inconsistency regarding the constraint in the input expression (step S6). In this case, the presentation unit 5 presents that the input expression has no constraint inconsistency (step S7).
- the presentation unit 5 may present the information to the user by displaying the information on the display device (not shown in FIG. 1) included in the inconsistency determination device 1. However, the presentation unit 5 may present the information to the user in another aspect. This point is the same in other embodiments.
- the following shows various constraints and the constraints represented by those constraints.
- the equations A, B, and C shown below may be variables themselves representing spin states. Further, the formulas A, B, and C shown below may be formulas using variables representing the spin states. Further, the formula A, the formula B, and the formula C shown below may be constants (for example, “1” or the like).
- Consistency determination unit 4 extracts the constraint term represented by "constant x (formula A x formula B)"
- the constraint corresponding to this constraint term is "formula A + formula B ⁇ 1".
- constraint term there may be a constraint term expressed as "constant x (1-formula A-formula B + formula A x formula B)".
- This constraint term represents the constraint of "formula A + formula B ⁇ 1". That is, when the inconsistency determination unit 4 extracts a constraint term represented by "constant x (1-formula A-formula B + formula A x formula B)", "formula A +” is used as a constraint corresponding to this constraint term.
- the constraint of equation B ⁇ 1 is specified.
- Constant x (formula A-formula A x formula B)
- This constraint term represents the constraint "Equation A ⁇ Equation B”. That is, when the inconsistency determination unit 4 extracts a constraint term represented by "constant x (formula A-formula A x formula B)", "formula A ⁇ formula B” is used as a constraint corresponding to this constraint term. Specify the constraint.
- Constant x (formula A x formula B + formula A x formula C + formula B x formula C)
- This constraint term represents the constraint of "formula A + formula B + formula C ⁇ 1". That is, when the inconsistency determination unit 4 extracts a constraint term represented by "constant x (formula A x formula B + formula A x formula C + formula B x formula C)", as a constraint corresponding to this constraint term, The constraint "Equation A + Expression B + Expression C ⁇ 1" is specified.
- Constant x (formula A + formula B-2 x formula A x formula B)
- the inconsistency determination unit 4 determines whether or not there is an inconsistency between the specified constraints. As described above, the inconsistency determination unit 4 may substitute the "expression representing the constraint" into another "expression representing the constraint” and determine whether or not the inconsistency occurs as a result. If an inconsistency occurs as a result of the substitution, the inconsistency determination unit 4 may determine that there is an inconsistency between the constraint corresponding to the substituted expression and the constraint corresponding to the substituted expression. If no inconsistency occurs as a result of the substitution, the inconsistency determination unit 4 determines that there is no inconsistency between the constraint corresponding to the substituted expression and the constraint corresponding to the substituted expression. good.
- the inconsistency determination unit 4 specifies a constraint for each constraint term among the terms obtained by dividing the formulated formula. Then, the inconsistency determination unit 4 determines whether or not there is an inconsistency between the specified constraints, and if there is an inconsistency, it is determined that an inconsistency regarding the constraint has occurred in the formulated expression. do. If there is no inconsistency, it is determined that there is no constraint-related inconsistency in the formulated expression. Therefore, according to the present embodiment, it is possible to determine whether or not an inconsistency has occurred in the formulated formula.
- Embodiment 2 Since the inconsistency determination device of the second embodiment of the present invention can be represented by the block diagram shown in FIG. 1, like the inconsistency determination device of the first embodiment, the second embodiment is used. An embodiment will be described. The same matters as in the first embodiment will be omitted as appropriate.
- the input unit 2 and the division unit 3 in the second embodiment are the same as the input unit 2 and the division unit 3 in the first embodiment.
- the inconsistency determination device 1 of the second embodiment determines whether or not an inconsistency regarding auxiliary variables has occurred in the equation representing the energy in the combinatorial optimization problem.
- the auxiliary variable represents the spin state in order to reduce the order of the variable representing the spin state to 2 when the order of the variable representing the spin state is 3 or more in the formula obtained by the formulation.
- the inconsistency determination unit 4 stores the formula using the auxiliary variable in advance.
- this pre-stored expression will be referred to as a pattern expression.
- the variables other than the auxiliary variables are variables representing the spin state in QUA.
- the order of the variable representing the spin state is 2.
- x 1 , x 2 , and x 3 are variables representing the spin states, and the spin is identified by the subscript in this variable. Further, y is an auxiliary variable.
- y is an auxiliary variable.
- the auxiliary variable is generally not used other than the equation (7) in the equation including the equation (7).
- the inconsistency determination unit 4 stores the pattern expression exemplified in the expression (7) in advance.
- the inconsistency determination unit 4 may store other pattern expressions in advance.
- the inconsistency determination unit 4 may store a plurality of pattern expressions.
- the division unit 3 takes in the formula representing the energy in the combinatorial optimization problem via the input unit 2. Then, the division unit 3 divides the equation into a plurality of terms.
- the inconsistency determination unit 4 determines whether or not there is a combination of terms corresponding to the pattern expression stored in advance, which is a combination of terms obtained by division by the division unit 3. Then, the inconsistency determination unit 4 specifies an auxiliary variable when the combination exists.
- the inconsistency determination unit 4 stores in advance the pattern expression exemplified in the equation (7). Therefore, the inconsistency determination unit 4 is a combination of terms obtained by division, and as a combination of terms corresponding to the pattern expression stored in advance, "x 1 x 2 ", "-2 x 1 y", It is determined whether or not there is a combination of five terms applicable to "-2 x 2 y", "x 3 y", and "3 y". Then, when the combination exists, the inconsistency determination unit 4 specifies the variable corresponding to “y” as an auxiliary variable.
- the inconsistency determination unit 4 when the specified auxiliary variable is used in the term not included in the above combination, the inconsistency regarding the auxiliary variable is found in the formula representing the energy in the combinatorial optimization problem. Judge that it has occurred. As described above, since the auxiliary variable is generally not used other than the equation (7) in the equation including the equation (7), it may be determined in this way.
- the inconsistency determination unit 4 is an expression representing the energy in the combination optimization problem. It is determined that there is no inconsistency regarding auxiliary variables in.
- the presentation unit 5 displays on the display device the determination result as to whether or not there is an inconsistency regarding the auxiliary variable in the formulated expression. Further, when the auxiliary variable specified by the inconsistency determination unit 4 is used in a term not included in the above combination, that term may also be displayed.
- FIG. 3 is a flowchart showing an example of the processing progress of the second embodiment. The matters already explained will be omitted as appropriate.
- Step S11 is the same as step S1 (see FIG. 2) in the first embodiment.
- the inconsistency determination unit 4 determines whether or not there is a combination of terms obtained by division by the division unit 3 and corresponding to the pattern expression stored in advance (step S12). ).
- step S12 When there is such a combination (Yes in step S12), the inconsistency determination unit 4 specifies an auxiliary variable (step S13).
- the inconsistency determination unit 4 determines whether or not the auxiliary variable is used in the term not included in the combination (step S14).
- the inconsistency determination unit 4 determines that the input expression has an inconsistency regarding the auxiliary variable (step S15). Then, the presentation unit 5 presents that the input expression has an inconsistency regarding the auxiliary variable (step S16). At this time, the presentation unit 5 may also present a term that is not included in the combination and in which an auxiliary variable is used.
- the inconsistency determination unit 4 determines that the input expression has no inconsistency regarding the auxiliary variable (step S17). Then, the presentation unit 5 presents that the input expression has no inconsistency regarding the auxiliary variable (step S18).
- step S17 executes S18.
- Auxiliary variables are generally not used in expressions that include pattern expressions other than pattern expressions. Then, in the present embodiment, the inconsistency determination unit 4 specifies an auxiliary variable when it is determined that there is a combination of terms obtained by division and which corresponds to the pattern expression stored in advance. do. Then, the inconsistency determination unit 4 determines that an inconsistency regarding the auxiliary variable has occurred in the formulated expression when the auxiliary variable is used in the term not included in the combination. Further, the inconsistency determination unit 4 determines that there is no inconsistency regarding the auxiliary variable in the formulated expression when the auxiliary variable is not used in the term not included in the combination. Therefore, according to the present embodiment, it is possible to determine whether or not an inconsistency has occurred in the formulated formula.
- FIG. 4 is a block diagram showing a configuration example of the inconsistency determination device according to the third embodiment of the present invention. Elements similar to the elements of the first embodiment and the second embodiment are designated by the same reference numerals as those shown in FIG.
- the inconsistency determination device 1 of the third embodiment includes an input unit 2, an inconsistency determination unit 4, and a presentation unit 5.
- a formalized formula (a formula representing energy in the combinatorial optimization problem) and a character string defining each variable representing the spin state are input to the input unit 2.
- the input unit 2 is, for example, a character that defines data recorded on a data recording medium such as an optical disk (in the present embodiment, an expression representing energy in a combinatorial optimization problem and each variable representing a spin state). It may be realized by a data reading device that reads a column). However, the input unit 2 is not limited to such a data reading device, and may be an input device such as a keyboard for the user to input an expression and a character string.
- FIG. 5 shows an example of a character string in which each variable representing the spin state is defined according to PyQUABO.
- the character string illustrated in FIG. 5 is a character string in which N variables from x 1 to x N are defined as variables representing the spin state.
- the description mode of the character string in which each variable representing the spin state is defined is not limited to the description mode according to PyQUABO.
- the inconsistency determination unit 4 takes in a formulated expression (an expression representing energy in the combinatorial optimization problem) and a character string defining each variable representing the spin state via the input unit 2. Then, the inconsistency determination unit 4 identifies each variable (each variable representing the spin state) defined by the character string.
- the inconsistency determination unit 4 determines whether or not there is a variable that is not used in the formulated expression among the variables defined in the character string. If there is a variable that is not used in the formulated expression among the variables defined by the character string, the inconsistency determination unit 4 is used in the formulated expression even though it is defined. It is determined that an inconsistency that there is a variable that does not exist occurs in the formulated expression. Also, if there are no variables that are not used in the formulated expression among the variables defined in the character string (in other words, all the variables defined in the character string are used in the formulated expression. If this is the case), the inconsistency determination unit 4 determines that no inconsistency has occurred in the formulated expression.
- the presentation unit 5 displays the determination result by the inconsistency determination unit 4 on, for example, a display device (not shown in FIG. 4) included in the inconsistency determination device 1. For example, when it is determined that an inconsistency that there is a variable that is defined but not used in the formulated formula exists in the formulated formula, the presentation unit 5 Displays information to that effect on the display device. At this time, the presentation unit 5 may also display variables that are defined but not used in the formulated formula. Further, when it is determined that no inconsistency has occurred in the formulated formula, the presentation unit 5 displays information to that effect on the display device.
- the inconsistency determination unit 4 and the presentation unit 5 are realized by, for example, the CPU of a computer that operates according to the inconsistency determination program.
- the CPU may read the inconsistency determination program from a program recording medium such as a program storage device of a computer and operate as the inconsistency determination unit 4 and the presentation unit 5 according to the inconsistency determination program.
- FIG. 6 is a flowchart showing an example of the processing progress of the third embodiment. The matters already explained will be omitted as appropriate.
- the inconsistency determination unit 4 captures an expression representing energy in the combinatorial optimization problem and a character string defining each variable representing the spin state via the input unit 2 (step S31).
- the case where the inconsistency determination unit 4 captures the character string shown in FIG. 5 will be described as an example.
- step S32 the inconsistency determination unit 4 identifies each variable defined by the captured character string (step S32).
- the mismatch determination unit 4 x 1, x 2, x 3 defined by the character string shown in FIG. 5, ..., to identify the N variables of x N.
- the inconsistency determination unit 4 is used in the captured expression among the variables defined by the captured character string (x 1 , x 2 , x 3 , ..., X N in this example). It is determined whether or not there is a variable that has not been set (step S33).
- the inconsistency determination unit 4 is formulated even though it is defined. It is determined that an inconsistency that there is a variable that is not used in the equation occurs in the formulated equation (step S34). Then, the presentation unit 5 presents that an inconsistency has occurred in the formulated formula (step S35). At this time, the presentation unit 5 may also present variables that are defined but not used in the formulated formula.
- the inconsistency determination unit 4 has an inconsistency in the formulated expression. It is determined that it has not occurred (step S36). Then, the presentation unit 5 presents that no inconsistency has occurred in the formulated expression (step S37).
- the defined variable (variable representing the spin state) is generally used in a formulated formula. Then, in the present embodiment, if there is a variable that is not used in the formulated formula among the defined variables, it is determined that an inconsistency has occurred in the formulated formula, and the defined variable is determined. If all of the above are used in the formulated formula, it is determined that there is no inconsistency in the formulated formula. Therefore, according to the present embodiment, it is possible to determine whether or not an inconsistency has occurred in the formulated formula.
- a formulated formula (a formula representing energy in a combinatorial optimization problem) is converted into an energy function of QUABO.
- the variable representing the spin state takes a value of 1 or 0.
- the present invention may also be applied when the formulated equation is transformed into an energy function of the Ising model. In this case, the variable representing the spin takes a value of 1 or -1.
- the energy function of QUAB and the energy function of Ising model can be converted to each other. Therefore, the formulated formula determined that no inconsistency has occurred may be converted into the energy function of the QUA, and the energy function may be further converted into the energy function of the Ising model.
- FIG. 7 is a schematic block diagram showing a configuration example of a computer according to the inconsistency determination device 1 according to each embodiment of the present invention.
- the computer 1000 includes a CPU 1001, a main storage device 1002, an auxiliary storage device 1003, an interface 1004, a data reading device 1005, and a display device 1006.
- the inconsistency determination device 1 of each embodiment of the present invention is realized by the computer 1000.
- the operation of the inconsistency determination device 1 is stored in the auxiliary storage device 1003 in the form of an inconsistency determination program.
- the CPU 1001 reads the inconsistency determination program from the auxiliary storage device 1003, deploys it to the main storage device 1002, and executes the process described in each of the above embodiments according to the inconsistency determination program.
- Auxiliary storage 1003 is an example of a non-temporary tangible medium.
- Other examples of non-temporary tangible media include magnetic disks, optical magnetic disks, CD-ROMs (Compact Disk Read Only Memory), DVD-ROMs (Digital Versatile Disk Read Only Memory), which are connected via interface 1004. Examples include semiconductor memory. Further, when the program is distributed to the computer 1000 by the communication line, even if the distributed computer 1000 expands the program to the main storage device 1002 and executes the process described in each of the above embodiments according to the program. good.
- each component may be realized by a general-purpose or dedicated circuit (circuitry), a processor, or a combination thereof. These may be composed of a single chip or may be composed of a plurality of chips connected via a bus. A part or all of each component may be realized by the combination of the circuit or the like and the program described above.
- the plurality of information processing devices and circuits may be centrally arranged or distributed.
- the information processing device, the circuit, and the like may be realized as a form in which each is connected via a communication network, such as a client-and-server system and a cloud computing system.
- FIG. 8 is a block diagram showing an outline of the inconsistency determination device of the present invention.
- the inconsistency determination device 1 of the present invention includes an inconsistency determination means 9.
- the inconsistency determination means 9 represents the energy in the combinatorial optimization problem in which the state of each spin is converted into the energy function of the model represented by the first value or the second value. Determine if there is an inconsistency in the expression.
- Appendix 2 A dividing means for dividing the formula representing the energy into a plurality of terms is provided.
- the inconsistency determination means is From the plurality of terms, two or more constraint terms that represent constraints are extracted.
- the inconsistency determination device according to Appendix 1, which determines that an inconsistency has occurred in the formula representing the energy when there is an inconsistency between the constraints represented by the two or more extracted constraint terms.
- the constraint expressed by the constraint term is expressed by an expression
- the inconsistency determination means is If an inconsistency occurs when an expression representing a constraint is assigned to an expression representing another constraint, it is determined that there is an inconsistency between the constraint corresponding to the assigned expression and the constraint corresponding to the assigned expression.
- the inconsistency determination device according to Appendix 2.
- a dividing means for dividing the formula representing the energy into a plurality of terms is provided.
- the inconsistency determination means is A formula using an auxiliary variable for lowering the order of the variable representing the spin state to 2 is stored in advance. It is determined whether or not there is a combination of terms obtained by division and corresponding to the above-mentioned formula stored in advance. If there is the combination, identify the auxiliary variable and The inconsistency determination device according to Appendix 1, which determines that an inconsistency has occurred in the equation representing the energy when the auxiliary variable is used in a term not included in the combination.
- the inconsistency determination means is Incorporate the character string that defines each variable that expresses the spin state together with the formula that expresses the energy.
- the description in Appendix 1 which determines that an inconsistency has occurred in the formula representing the energy when there is a variable not used in the formula expressing the energy among the variables defined by the character string. Inconsistency determination device.
- Appendix 7 The computer The formula expressing the energy is divided into a plurality of terms, and the formula is divided into a plurality of terms. From the plurality of terms, two or more constraint terms that represent constraints are extracted. The inconsistency determination method according to Appendix 6, wherein it is determined that an inconsistency has occurred in the formula representing the energy when there is an inconsistency between the constraints represented by the two or more extracted constraint terms.
- Appendix 8 The computer The formula expressing the energy is divided into a plurality of terms, and the formula is divided into a plurality of terms.
- a formula using an auxiliary variable for lowering the order of the variable representing the spin state to 2 is stored in advance. It is determined whether or not there is a combination of terms obtained by division and corresponding to the above-mentioned formula stored in advance. If there is the combination, identify the auxiliary variable and The inconsistency determination method according to Appendix 6, wherein it is determined that an inconsistency has occurred in the formula representing the energy when the auxiliary variable is used in a term not included in the combination.
- Appendix 9 The computer Incorporate the character string that defines each variable that expresses the spin state together with the formula that expresses the energy.
- the description in Appendix 6 which determines that an inconsistency has occurred in the formula representing the energy when there is a variable not used in the formula expressing the energy among the variables defined by the character string. Inconsistency judgment method.
- Appendix 11 To the computer A division process for dividing the expression representing the energy into a plurality of terms is executed. In the inconsistency determination process, Two or more constraint terms, which are terms representing constraints, are extracted from the plurality of terms. The computer according to Appendix 10, which records an inconsistency determination program for determining that an inconsistency has occurred in the formula representing energy when there is an inconsistency between the constraints represented by two or more extracted constraint terms. A readable recording medium.
- the computer pre-stores an expression using an auxiliary variable for lowering the order of the variable representing the spin state to 2.
- a division process for dividing the expression representing the energy into a plurality of terms is executed.
- the inconsistency determination process It is a combination of terms obtained by division, and the presence or absence of a combination of terms corresponding to the above formula stored in the computer in advance is determined.
- the auxiliary variable is specified, and the auxiliary variable is specified.
- the computer reading according to Appendix 10 which records an inconsistency determination program for determining that an inconsistency has occurred in the formula representing the energy when the auxiliary variable is used in a term not included in the combination. Possible recording medium.
- the present invention is suitably applied to an inconsistency determination device that determines whether or not an inconsistency has occurred in an equation representing energy in a combinatorial optimization problem.
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Abstract
Description
図1は、本発明の第1の実施形態の不整合判定装置の構成例を示すブロック図である。第1の実施形態の不整合判定装置1は、入力部2と、分割部3と、不整合判定部4と、提示部5とを備える。
本発明の第2の実施形態の不整合判定装置は、第1の実施形態の不整合判定装置と同様に、図1に示すブロック図で表すことができるので、図1を用いて第2の実施形態を説明する。第1の実施形態と同様の事項については、適宜、説明を省略する。
図4は、本発明の第3の実施形態の不整合判定装置の構成例を示すブロック図である。第1の実施形態や第2の実施形態の要素と同様の要素には、図1に示す符号と同一の符号を付す。第3の実施形態の不整合判定装置1は、入力部2と、不整合判定部4と、提示部5とを備える。
個々のスピンの状態を第1の値または第2の値で表すモデルのエネルギー関数に変換される、組合せ最適化問題におけるエネルギーを表す式の中に不整合が生じているか否かを判定する不整合判定手段を備える
ことを特徴とする不整合判定装置。
前記エネルギーを表す式を複数の項に分割する分割手段を備え、
前記不整合判定手段は、
前記複数の項の中から、制約を表す項である制約項を2個以上抽出し、
抽出した2個以上の制約項が表す制約間に不整合がある場合に、前記エネルギーを表す式の中に不整合が生じていると判定する
付記1に記載の不整合判定装置。
制約項が表す制約が式で表され、
前記不整合判定手段は、
制約を表す式を、別の制約を表す式に代入したときに不整合が生じるならば、代入した式に対応する制約と、代入された式に対応する制約の間に不整合があると判定する
付記2に記載の不整合判定装置。
前記エネルギーを表す式を複数の項に分割する分割手段を備え、
前記不整合判定手段は、
スピンの状態を表す変数の次数を2に下げるための補助変数を用いた式を予め記憶し、
分割によって得られた項の組合せであって、予め記憶している前記式に該当する項の組合せの有無を判定し、
前記組合せが有る場合に、前記補助変数を特定し、
前記組合せに含まれない項で前記補助変数が用いられている場合に、前記エネルギーを表す式の中に不整合が生じていると判定する
付記1に記載の不整合判定装置。
前記不整合判定手段は、
前記エネルギーを表す式とともに、スピンの状態を表す各変数を定義した文字列を取り込み、
前記文字列で定義された各変数のうち、前記エネルギーを表す式で用いられていない変数がある場合に、前記エネルギーを表す式の中に不整合が生じていると判定する
付記1に記載の不整合判定装置。
コンピュータが、
個々のスピンの状態を第1の値または第2の値で表すモデルのエネルギー関数に変換される、組合せ最適化問題におけるエネルギーを表す式の中に不整合が生じているか否かを判定する
ことを特徴とする不整合判定方法。
前記コンピュータが、
前記エネルギーを表す式を複数の項に分割し、
前記複数の項の中から、制約を表す項である制約項を2個以上抽出し、
抽出した2個以上の制約項が表す制約間に不整合がある場合に、前記エネルギーを表す式の中に不整合が生じていると判定する
付記6に記載の不整合判定方法。
前記コンピュータが、
前記エネルギーを表す式を複数の項に分割し、
スピンの状態を表す変数の次数を2に下げるための補助変数を用いた式を予め記憶し、
分割によって得られた項の組合せであって、予め記憶している前記式に該当する項の組合せの有無を判定し、
前記組合せが有る場合に、前記補助変数を特定し、
前記組合せに含まれない項で前記補助変数が用いられている場合に、前記エネルギーを表す式の中に不整合が生じていると判定する
付記6に記載の不整合判定方法。
前記コンピュータが、
前記エネルギーを表す式とともに、スピンの状態を表す各変数を定義した文字列を取り込み、
前記文字列で定義された各変数のうち、前記エネルギーを表す式で用いられていない変数がある場合に、前記エネルギーを表す式の中に不整合が生じていると判定する
付記6に記載の不整合判定方法。
コンピュータに、
個々のスピンの状態を第1の値または第2の値で表すモデルのエネルギー関数に変換される、組合せ最適化問題におけるエネルギーを表す式の中に不整合が生じているか否かを判定する不整合判定処理を実行させる
不整合判定プログラムを記録したコンピュータ読取可能な記録媒体。
前記コンピュータに、
前記エネルギーを表す式を複数の項に分割する分割処理を実行させ、
前記不整合判定処理で、
前記複数の項の中から、制約を表す項である制約項を2個以上抽出させ、
抽出した2個以上の制約項が表す制約間に不整合がある場合に、前記エネルギーを表す式の中に不整合が生じていると判定させる
不整合判定プログラムを記録した付記10に記載のコンピュータ読取可能な記録媒体。
前記コンピュータは、スピンの状態を表す変数の次数を2に下げるための補助変数を用いた式を予め記憶し、
前記コンピュータに、
前記エネルギーを表す式を複数の項に分割する分割処理を実行させ、
前記不整合判定処理で、
分割によって得られた項の組合せであって、予め前記コンピュータに記憶されている前記式に該当する項の組合せの有無を判定させ、
前記組合せが有る場合に、前記補助変数を特定させ、
前記組合せに含まれない項で前記補助変数が用いられている場合に、前記エネルギーを表す式の中に不整合が生じていると判定させる
不整合判定プログラムを記録した付記10に記載のコンピュータ読取可能な記録媒体。
前記コンピュータに、
前記不整合判定処理で、
前記エネルギーを表す式とともに、スピンの状態を表す各変数を定義した文字列を取り込ませ、
前記文字列で定義された各変数のうち、前記エネルギーを表す式で用いられていない変数がある場合に、前記エネルギーを表す式の中に不整合が生じていると判定させる
不整合判定プログラムを記録した付記10に記載のコンピュータ読取可能な記録媒体。
2 入力部
3 分割部
4 不整合判定部
5 提示部
Claims (13)
- 個々のスピンの状態を第1の値または第2の値で表すモデルのエネルギー関数に変換される、組合せ最適化問題におけるエネルギーを表す式の中に不整合が生じているか否かを判定する不整合判定手段を備える
ことを特徴とする不整合判定装置。 - 前記エネルギーを表す式を複数の項に分割する分割手段を備え、
前記不整合判定手段は、
前記複数の項の中から、制約を表す項である制約項を2個以上抽出し、
抽出した2個以上の制約項が表す制約間に不整合がある場合に、前記エネルギーを表す式の中に不整合が生じていると判定する
請求項1に記載の不整合判定装置。 - 制約項が表す制約が式で表され、
前記不整合判定手段は、
制約を表す式を、別の制約を表す式に代入したときに不整合が生じるならば、代入した式に対応する制約と、代入された式に対応する制約の間に不整合があると判定する
請求項2に記載の不整合判定装置。 - 前記エネルギーを表す式を複数の項に分割する分割手段を備え、
前記不整合判定手段は、
スピンの状態を表す変数の次数を2に下げるための補助変数を用いた式を予め記憶し、
分割によって得られた項の組合せであって、予め記憶している前記式に該当する項の組合せの有無を判定し、
前記組合せが有る場合に、前記補助変数を特定し、
前記組合せに含まれない項で前記補助変数が用いられている場合に、前記エネルギーを表す式の中に不整合が生じていると判定する
請求項1に記載の不整合判定装置。 - 前記不整合判定手段は、
前記エネルギーを表す式とともに、スピンの状態を表す各変数を定義した文字列を取り込み、
前記文字列で定義された各変数のうち、前記エネルギーを表す式で用いられていない変数がある場合に、前記エネルギーを表す式の中に不整合が生じていると判定する
請求項1に記載の不整合判定装置。 - コンピュータが、
個々のスピンの状態を第1の値または第2の値で表すモデルのエネルギー関数に変換される、組合せ最適化問題におけるエネルギーを表す式の中に不整合が生じているか否かを判定する
ことを特徴とする不整合判定方法。 - 前記コンピュータが、
前記エネルギーを表す式を複数の項に分割し、
前記複数の項の中から、制約を表す項である制約項を2個以上抽出し、
抽出した2個以上の制約項が表す制約間に不整合がある場合に、前記エネルギーを表す式の中に不整合が生じていると判定する
請求項6に記載の不整合判定方法。 - 前記コンピュータが、
前記エネルギーを表す式を複数の項に分割し、
スピンの状態を表す変数の次数を2に下げるための補助変数を用いた式を予め記憶し、
分割によって得られた項の組合せであって、予め記憶している前記式に該当する項の組合せの有無を判定し、
前記組合せが有る場合に、前記補助変数を特定し、
前記組合せに含まれない項で前記補助変数が用いられている場合に、前記エネルギーを表す式の中に不整合が生じていると判定する
請求項6に記載の不整合判定方法。 - 前記コンピュータが、
前記エネルギーを表す式とともに、スピンの状態を表す各変数を定義した文字列を取り込み、
前記文字列で定義された各変数のうち、前記エネルギーを表す式で用いられていない変数がある場合に、前記エネルギーを表す式の中に不整合が生じていると判定する
請求項6に記載の不整合判定方法。 - コンピュータに、
個々のスピンの状態を第1の値または第2の値で表すモデルのエネルギー関数に変換される、組合せ最適化問題におけるエネルギーを表す式の中に不整合が生じているか否かを判定する不整合判定処理を実行させる
不整合判定プログラムを記録したコンピュータ読取可能な記録媒体。 - 前記コンピュータに、
前記エネルギーを表す式を複数の項に分割する分割処理を実行させ、
前記不整合判定処理で、
前記複数の項の中から、制約を表す項である制約項を2個以上抽出させ、
抽出した2個以上の制約項が表す制約間に不整合がある場合に、前記エネルギーを表す式の中に不整合が生じていると判定させる
不整合判定プログラムを記録した請求項10に記載のコンピュータ読取可能な記録媒体。 - 前記コンピュータは、スピンの状態を表す変数の次数を2に下げるための補助変数を用いた式を予め記憶し、
前記コンピュータに、
前記エネルギーを表す式を複数の項に分割する分割処理を実行させ、
前記不整合判定処理で、
分割によって得られた項の組合せであって、予め前記コンピュータに記憶されている前記式に該当する項の組合せの有無を判定させ、
前記組合せが有る場合に、前記補助変数を特定させ、
前記組合せに含まれない項で前記補助変数が用いられている場合に、前記エネルギーを表す式の中に不整合が生じていると判定させる
不整合判定プログラムを記録した請求項10に記載のコンピュータ読取可能な記録媒体。 - 前記コンピュータに、
前記不整合判定処理で、
前記エネルギーを表す式とともに、スピンの状態を表す各変数を定義した文字列を取り込ませ、
前記文字列で定義された各変数のうち、前記エネルギーを表す式で用いられていない変数がある場合に、前記エネルギーを表す式の中に不整合が生じていると判定させる
不整合判定プログラムを記録した請求項10に記載のコンピュータ読取可能な記録媒体。
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