JP2020181576A - Optimization support device, optimization support method, program, and optimization system - Google Patents

Abstract

To quickly solve an optimization problem.SOLUTION: An optimization support device 10 comprises: an input information acquisition unit 11 that acquires input information on an optimization problem; a decision variable setting unit 12 that sets a decision variable of the optimization problem; an objective function setting unit 13 that sets an objective function of a slave problem in which a partial constraint of the optimization problem is relaxed; an input unit 14 that decomposes the decision variable and inputs, to a quantum computer 20, a coefficient of the objective function as the value of a weight of association between nodes; a result acquisition unit 15 that acquires an optimal solution to the slave problem from the quantum computer 20 and determines an optimal value of the objective function of the slave problem; and an optimal solution determination unit 16 that, based on a relaxed solution obtained by binding the optimal solutions and a relaxed optimal value obtained by adding optimal values together, when provided with the partial constraint, takes the relaxed solution as the optimal solution to the original optimization problem, and when not provided with the partial constraint, takes an executable solution obtained by correcting a violation included in the relaxed solution as the optimal solution to the original optimization problem.SELECTED DRAWING: Figure 1

Description

The present invention relates to an optimization support device, an optimization support method, a program, and an optimization system.

As an optimization problem, there is a distribution / production planning decision problem. In the large-scale distribution / production plan determination problem, the range of the determination variables is limited by a plurality of equations / inequalities described using a plurality of determination variables including binary (for example, 0-1) variables. It contains a combination element that seeks a determinant that minimizes or maximizes the desired function. In such a problem, it is originally desired to obtain an optimum solution in consideration of all the conditions, but if the scale is too large, it becomes difficult to calculate with the current general-purpose computer due to the limitation of the calculation time and the computer memory. Therefore, the solution of the problem divided by the elements such as the period and the process is substituted. As a result, it is unavoidable to operate with a production plan based on a solution that is deteriorated by about 10 to 30% compared to the solution that was originally obtained in a batch.

In the production distribution process including the multi-stage process, for example, for the purpose of simplifying and improving the efficiency of operating conditions (manufacturing work, sorting work, etc.), products are identified by operating conditions and managed by lot number. A lot means a production unit that is a collection of products that can be processed under the same operating conditions. For example, if there are 10 coils manufactured under the same heating and rolling conditions in the hot rolling process, the same lot number is assigned to them and they are collectively managed in units of lots. In each process, it is desirable from the viewpoint of efficiency that a plurality of products with the same lot number are continuously produced. Hereinafter, the process of continuously producing a plurality of products grouped into lots is referred to as "lot grouping".

In each process, it is usually necessary to change the setup every time the lot changes. Setup change refers to changing the settings of processing equipment, replacing parts, maintenance, etc. in each process. It usually takes a lot of time to change the setup. Therefore, it is preferable that the work schedule of each process is created so that the setup change work can be reduced as much as possible. However, in recent years, the product specifications ordered by customers have been subdivided, and there are few product groups that can be put together in large lots. Even if there is a product group that can be put together in a large lot, the delivery time usually varies. If products that can be put together in such a large lot are manufactured in succession with priority, the products that have time to deliver will be manufactured first, and as a result, the products that should be manufactured first will be manufactured first. It may be postponed. Therefore, there is a risk that the production of the postponed product may not be in time for the delivery date.

In addition, the conditions for lot summarization differ for each process. Therefore, depending on the type of product to be manufactured, there may be a combination of products that are grouped into the same lot in one process but not in the same lot in another process. For this reason, it is conceivable to create a schedule individually for each process, but there is a risk that the production efficiency will decrease if the entire process is viewed. In this way, when formulating a production plan that spans a plurality of processes, it is necessary to adjust the trade-off between the delivery date and the production efficiency over the entire process and make an appropriate lot. However, when trying to create a schedule over the entire process, there are the following problems.

That is, there are many combinations of conditions that determine production efficiency, the schedule problem to be solved becomes large-scale, and the solution requires a huge amount of calculation and a large amount of time. Moreover, due to external factors such as process delays and work outages, frequent and rapid schedule revisions (reschedules) are required. For this reason, conventionally, it has been common to create an individual schedule for each process, and it has been difficult to create a schedule that optimizes the processing order of any product in any process over all processes.

Patent Document 1 (Japanese Unexamined Patent Publication No. 2010-97506) relates to a system for creating a work schedule of a production distribution process including a plurality of processes in which a lot in which one or more products are grouped is used as a processing unit. The invention is disclosed.

Japanese Unexamined Patent Publication No. 2010-97506

The invention of Patent Document 1 proposes a system configuration for passing data required between processes, but mentions a specific method for determining a processing order that eliminates a trade-off between delivery time and production efficiency over all processes. Not done.

In order to solve the above problems, the present inventors have recently focused on a quantum computing technique that realizes parallelism on a scale that cannot be realized by a conventional computing device by using superposition of quantum mechanical states. .. Quantum computing technology, for example, has recently become a hot topic: 1) Quantum computers with quantum singing models such as laser networks and quantum annealing machines that specialize in performing optimization calculations using superconducting quantum bits. Technology, 2) Quantum gate-type quantum computer technology that enables general-purpose quantum calculations by combining quantum gates, 3) Technology that specializes in solving the Ising model using digital circuits, inspired by quantum phenomena. Since these are included, these technologies are called quantum computing technologies.

However, as described above, when trying to solve an optimization problem (for example, a mathematical programming problem) by using quantum computing technology in order to optimize the processing order of an arbitrary product in an arbitrary process, the optimization problem is solved in advance. It is necessary to convert the constraint expression of. This is because the current method using quantum computing technology cannot set the constraint formula of the optimization problem, but only the objective function. Therefore, in order to solve the optimization problem using quantum computing technology, for example, for equation constraints, all the target terms on both sides are moved to either the left side or the right side, and a penalty is given for the sum of squares of that side. By imposing, it can be made into an objective function relatively easily. However, for inequality constraints other than equality constraints, a unified objective functioning method is not yet known. Furthermore, the number of available nodes is limited in the devices using quantum computing technology that are currently in practical use, and it is not always sufficient to solve large-scale problems.

The present invention has been made in view of the above circumstances, and it is relatively easy to solve an optimization problem on a scale that is difficult to solve by a general-purpose computer by using a quantum computing technique in which the number of available nodes is limited. The purpose is to provide an optimization support device that can be used.

The gist of the present invention is the following optimization support device and the like.

[1] In a network model including a plurality of nodes and a characteristic function configured with the value of the weight of the connection between the nodes as an input parameter, the base state of the network model in which the value of the characteristic function is the minimum value. It is an optimization support device that solves an optimization problem with a device that uses quantum computing technology to find
An input information acquisition unit that acquires input information related to the optimization problem,
The coefficient of determination variable setting unit that sets the coefficient of determination of the optimization problem,
An objective function setting unit that decomposes the optimization problem into a plurality of child problems in which some constraints are relaxed and sets an objective function for each of the child problems.
The determinant is decomposed into determinants for each of the child problems to obtain variables corresponding to the nodes, and the coefficient of the objective function is input to the device using the quantum computing technique as the value of the weight of the coupling between the nodes. Input section and
In the device using the quantum computing technique, the value of the node when the network model is in the ground state is acquired as the optimum solution of the child problem, and the optimum value of the objective function of the child problem is obtained based on the optimum solution. The result acquisition department and
When it is determined whether or not some of the constraints are satisfied based on the relaxation solution that bundles the optimum solutions and the relaxation optimum value that is the sum of the optimum values, and the part of the constraints is satisfied. The relaxation solution is used as the optimum solution of the original optimization problem, and if some of the constraints are not satisfied, the feasible solution obtained by correcting the violation included in the relaxation solution is used as the original optimization problem. An optimization support device provided with an optimum solution determination unit, which is the optimum solution for the above.

[2] In a network model including a plurality of nodes arranged in a grid pattern and a characteristic function configured by using the value of the weight of the connection between the nodes as an input parameter, the value of the characteristic function is the minimum value. This is an optimization support method that allows a device that uses quantum computing technology to find the base state of a network model to solve an optimization problem.
(1) Acquiring input information regarding the optimization problem, step
(2) Setting the coefficient of determination of the optimization problem, step
(3) A step of decomposing a part of the optimization problem into a plurality of child problems in which some constraints are relaxed and setting an objective function for each of the child problems.
(4) The quantum calculation technique was used by decomposing the determinant into determinants for each of the child problems to obtain variables corresponding to the nodes, and using the coefficient of the objective function as the value of the weight of the connection between the nodes. Input to the device, step,
(5) In the device using the quantum computing technique, the value of the node when the network model is in the ground state is acquired as the optimum solution of the child problem, and the objective function of the child problem is based on the optimum solution. Finding the optimum value, steps, and
(6) Based on the relaxation solution in which the optimum solutions are bundled and the relaxation optimum value obtained by adding the optimum values, it is determined whether or not some of the constraint conditions are satisfied, and the part of the constraint conditions are satisfied. If it is satisfied, the relaxation solution is used as the optimum solution of the original optimization problem, and if some of the constraints are not satisfied, the feasible solution obtained by correcting the violation included in the relaxation solution is used as the original solution. An optimization support method with steps that makes it the optimal solution for an optimization problem.

[3] In a network model including a plurality of nodes arranged in a grid pattern and a characteristic function configured by using the value of the weight of the connection between the nodes as an input parameter, the value of the characteristic function is the minimum value. When making a device using quantum computing technology to find the base state of a network model solve an optimization problem
On the computer
(1) Acquiring input information regarding the optimization problem, step
(2) Setting the coefficient of determination of the optimization problem, step
(3) A step of decomposing a part of the optimization problem into a plurality of child problems in which some constraints are relaxed and setting an objective function for each of the child problems.
(4) The quantum computing technique was used by decomposing the determinant into determinants for each of the child problems to obtain variables corresponding to the nodes, and using the coefficient of the objective function as the value of the weight of the connection between the nodes. Input to the device, step,
(5) In the device using the quantum computing technique, the value of the node when the network model is in the ground state is acquired as the optimum solution of the child problem, and the objective function of the child problem is based on the optimum solution. Finding the optimum value, steps, and
(6) Based on the relaxation solution in which the optimum solutions are bundled and the relaxation optimum value obtained by adding the optimum values, it is determined whether or not some of the constraint conditions are satisfied, and the part of the constraint conditions is satisfied. If it is satisfied, the relaxation solution is used as the optimum solution of the original optimization problem, and if some of the constraints are not satisfied, the executable solution obtained by correcting the violation included in the relaxation solution is used as the original solution. A program that executes steps as the optimal solution for an optimization problem.

[4] A system that optimizes optimization problems.
In a network model including a plurality of nodes arranged in a grid pattern and a characteristic function configured by using the value of the weight of the connection between the nodes as an input parameter, the value of the characteristic function is the minimum value of the network model. A device that uses quantum technology to find the ground state,
An input information acquisition unit that acquires input information related to the optimization problem,
The coefficient of determination variable setting unit that sets the coefficient of determination of the optimization problem,
An objective function setting unit that decomposes the optimization problem into a plurality of child problems in which some constraints are relaxed and sets an objective function for each of the child problems.
The determinant is decomposed into determinants for each of the child problems to obtain variables corresponding to the nodes, and the coefficient of the objective function is input to the device using the quantum computing technique as the value of the weight of the coupling between the nodes. Input section and
In the device using the quantum computing technique, the value of the node when the network model is in the ground state is acquired as the optimum solution of the child problem, and the optimum value of the objective function of the child problem is obtained based on the optimum solution. The result acquisition department and
When it is determined whether or not some of the constraints are satisfied based on the relaxation solution that bundles the optimum solutions and the relaxation optimum value that is the sum of the optimum values, and the part of the constraints is satisfied. The relaxation solution is used as the optimum solution of the original optimization problem, and if some of the constraints are not satisfied, the feasible solution obtained by correcting the violation included in the relaxation solution is used as the original optimization problem. An optimization system equipped with an optimum solution determination unit, which is the optimum solution for.

According to the present invention, an optimization problem on a scale that is difficult to solve by a general-purpose computer can be solved relatively easily by using a quantum computing technique in which the number of available nodes is limited.

It is a block diagram which shows the schematic structure of the optimization system which concerns on this embodiment. It is a figure which shows the hardware configuration of the quantum computer which concerns on this embodiment. It is a figure for demonstrating the principle of a quantum computer. It is a flow chart which shows the operation of the optimization support apparatus which concerns on this embodiment. It is a block diagram which shows an example of the computer which realizes the optimization support apparatus which concerns on this embodiment.

[Device configuration]
First, the schematic configuration of the optimization system according to the present embodiment will be described with reference to FIG. FIG. 1 is a block diagram showing a schematic configuration of an optimization system according to the present embodiment.

As shown in FIG. 1, the optimization system 30 according to the present embodiment includes a general-purpose computer (optimization support device) 10 and a quantum computer (optimization device) 20. The quantum computer 20 is an apparatus using quantum computing technology. The general-purpose computer 10 inputs an optimization problem to be solved (for example, a mathematical programming problem) into the quantum computer 20 in a format that can be processed by the quantum computer 20. Further, the general-purpose computer 10 acquires the solution result of the optimization problem obtained by the quantum computer 20. The quantum computer 20 solves the optimization problem input from the general-purpose computer 10 and outputs the solution result to the general-purpose computer 10.
Hereinafter, a case where a quantum annealing machine using a superconducting qubit is used as the quantum computer 20 will be mainly described as an example. In the following description, "qubit node" is used as an example of "node" corresponding to a variable, "Hamiltonian" is used as an example of "characteristic function", and "Ising model" is used as an example of "network model". "Ising variables" are used as examples of "variables".

(General-purpose computer 10)
First, the general-purpose computer 10 will be described. The general-purpose computer 10 functions as an optimization support device, and as shown in FIG. 1, at least an input information acquisition unit 11, a decision variable setting unit 12, an objective function setting unit 13, an input unit 14, and a result acquisition. A unit 15 and an optimum solution determination unit 16 are provided.

(Input information acquisition unit 11)
The input information acquisition unit 11 acquires the input information necessary for constructing the optimization problem. Examples of input information include the number of processes, the number of products, the lot number, and the delivery date when solving an optimization problem for optimizing the processing order of arbitrary products in arbitrary processes. The input information acquisition unit 11 acquires input information by operating the general-purpose computer 10 by an operator, receiving information transmitted from an external device via a network or the like, or reading information stored in a portable storage medium. To do.

(Coefficient of determination setting unit 12)
The coefficient of determination variable setting unit 12 sets the coefficient of determination of the optimization problem to be solved. For example, when the determination variable setting unit 12 solves an optimization problem for optimizing the processing order of an arbitrary product in an arbitrary process, the determination variable setting unit 12 sets the processing order as a determination variable. A plurality of decision variables may be set. Here, the setting of the decision variable refers to a process of determining what should be the decision variable based on the input information for the general-purpose computer 10. The coefficient of determination includes lot information, delivery date information, and the like.

(Objective function setting unit 13)
The objective function setting unit 13 decomposes the optimization problem to be solved into child problems and sets the objective function for each child problem. Here, the child problem is a problem in which some constraints of the optimization problem to be solved are relaxed. For example, when the objective function setting unit 13 solves an optimization problem for optimizing the processing order in an arbitrary process of an arbitrary product, the process j is relaxed by relaxing the constraint conditions between the processes in the original problem. Decompose each (∈ P) to generate a child problem Pj. Also, for example, when processing multiple jobs with multiple machines, there is an allocation constraint that jobs cannot be allocated more than the load capacity of each machine. By relaxing this constraint, child problems for each job can be solved. It may be divided into. On the other hand, the constraint condition for allocating machines to each job may be relaxed and divided into child problems for each machine.

Here, the objective function for each child problem includes a term obtained by multiplying the amount of violation of the relaxed constraint by a multiplier (Lagrange multiplier λ, which will be described later). In addition, the objective function of the child problem pays a penalty for violation of the constraints and the elements of the evaluation index (J _j2 , J _p4 , J _p5 , J _j6 described later) that express the matters to be evaluated originally. Including the elements of the constraint expression (J _j1 and J _j3 described later) expressed by the formula that imposes (Note that J _j2 is a formula that imposes a penalty for the violation of the constraint condition in the original problem. Although it is an element of the constraint expression, it is positioned as an element of the evaluation index by relaxing the constraint in this child problem). The evaluation index element and the constraint expression element include weight elements (q ₁ , q ₂ , q ₃ , q _Big , which will be described later) that represent the weights of the respective elements. The elements of the evaluation index include, for example, lot summarization and evaluation of on-time delivery. In addition, the elements of the constraint expression include the constraint that any product must be assigned in any processing order, the constraint that the processing of the next process does not start until the processing of the previous process is completed in the arbitrary product, and the post-process. Including restrictions such as performing post-process processing at predetermined intervals so that processing is not interrupted.

When the optimization problem to be solved includes an inequality constraint, the objective function setting unit 13 is an element of the constraint expression in which the occurrence or non-occurrence of each side of the inequality constraint is converted into the form of the product of the determinants (described later). J _j1 , J _j2 , J _j3 ) and a weighting element (q _Big , which will be described later) that is set to be large when the inequality constraint is not satisfied are set.

The objective function setting unit 13 creates an objective function for each of the above child problems at least for each constraint condition, integrates the created objective functions, and sets them as the final objective function. At this time, the final objective function is represented by a quadratic polynomial of the decision variable. Here, the weight elements included in each objective function created for each constraint condition are reflected in the coefficients of each term of the polynomial added up for each term in the final objective function. The coefficients of each of these terms are hereinafter referred to as "coefficients of the objective function".

(Input unit 14)
The input unit 14 decomposes the determinant variable of the original problem set by the determinant variable setting unit 12 into the determinant variable of each child problem, and arranges the nodes in a grid pattern in the quantum computer 20 (that is, the singing variable described later). ), And the coefficient of the objective function for each child problem set by the objective function setting unit 13 is input to the quantum computer 20 as a coefficient (coupling weight) indicating the relationship between each node (ising variable). To do. Depending on the quantum computer used, since the number of nodes to be combined from one node is limited, it may not be possible to express the weighting coefficients of all the connections as it is. In such a case, for example, measures may be taken to effectively increase the number of nodes to be combined by assigning a plurality of nodes to one Ising variable. Further, in the description of the embodiment of the present invention, the arrangement of the nodes will be described as a grid pattern, but the arrangement of the nodes is not limited to the grid pattern and can have any shape.

(Result acquisition unit 15)
The result acquisition unit 15 acquires the calculation result of the quantum computer 20 calculated based on the coefficient of the objective function input by the input unit 14 (the optimum solution which is a combination of the optimum (convergence) values of the singing variables of the child problem). To do. Specifically, the measured values in the ground state of the nodes (Ising variables) are acquired as the values (optimal solutions) of the decision variables corresponding to those nodes (Ising variables). Further, the result acquisition unit 15 obtains the optimum value of the objective function (Hamiltonian) of the child problem based on the acquired optimum solution. Specifically, the objective function value calculated by substituting the acquired optimal solution into the objective function of the child problem is set as the optimal value.

(Optimal solution determination unit 16)
The optimum solution determination unit 16 bundles the optimum solutions of each child problem acquired by the result acquisition unit 15 to obtain a relaxed solution of the original optimization problem. Further, the optimum solution determination unit 16 adds the optimum values of the objective functions of each child problem acquired by the result acquisition unit 15 to obtain the relaxation optimum value of the original optimization problem. Here, the optimal solution determination unit 16 determines whether or not the relaxed solution that bundles the optimal solutions of each child problem acquired by the result acquisition unit 15 satisfies some of the relaxed constraints, and if so, relaxes. Let the solution be the optimal solution to the original problem. On the other hand, if some of the relaxed constraints are not satisfied, the optimal solution determination unit 16 sets the executable solution obtained by correcting the violation included in the relaxed solution as the optimal solution of the original optimization problem. If some of the relaxed constraints are not satisfied, the optimal solution determination unit 16 updates the objective function based on the relaxed solution and the relaxed optimal value. Specifically, the optimum solution determination unit 16 obtains a sub-gradient vector, which is the violation amount, for each relaxed constraint, and corrects the violation part of the relaxation solution to make it a feasible solution (provisional optimum solution). Then, the optimum solution determination unit 16 substitutes the executable solution into the objective function of the original problem and obtains a provisional optimum value.

Here, when the optimization problem is a minimization problem, the provisional optimum value is compared with the upper bound value obtained so far, and if the provisional optimum value is smaller, the upper bound is obtained by the provisional optimum value. Update the value. Further, the optimum solution determination unit 16 compares the relaxation optimum value obtained from the optimum value of the objective function of each child problem acquired by the result acquisition unit 15 with the lower bound value immediately before the update in the original optimization problem. , If the relaxation optimum value is larger, the lower bound value is updated by the relaxation optimum value.

On the other hand, when the optimization problem is a maximization problem, the provisional optimum value is compared with the lower bound value obtained so far, and if the provisional optimum value is larger, the lower bound value is updated by the provisional optimum value. To do. Further, the optimum solution determination unit 16 compares the relaxation optimum value obtained from the optimum value of the objective function of each child problem acquired by the result acquisition unit 15 with the upper bound value immediately before the update in the original optimization problem. If the optimum relaxation value is smaller, the upper bound value is updated by the optimum relaxation value.

Then, the optimum solution determination unit 16 updates the objective function of each child problem based on the sub-gradient vector which is the violation amount for each relaxed constraint, and the updated upper bound value and lower bound value. The objective function of each child problem is updated by updating the multiplier (Lagrange multiplier λ, which will be described later) that is multiplied by the violation amount for the constraint condition relaxed in the child problem.

When the relaxation solution that bundles the optimum solutions of each child problem acquired by the result acquisition unit 15 does not satisfy the relaxed constraint, the objective function setting unit 13 sets the objective function updated by the optimum solution determination unit 16 to the child. Reset as the objective function for each problem. Then, the reset objective function is input to the quantum computer 20 by the input unit 14, and the calculation result (optimal solution of each child problem) for the updated objective function is acquired by the result acquisition unit 15. In addition, the result acquisition unit 15 obtains the optimum value of the objective function (Hamiltonian) of each child problem based on the calculation result of the updated objective function. The optimum solution determination unit 16 further updates the objective function of each child problem based on the optimum solution and the optimum value of each of these child problems. This series of operations converges to a predetermined state (the relaxation solution satisfies some of the relaxed constraint conditions, or a predetermined end condition (the difference between the upper bound value and the lower bound value is less than the threshold value). ) Continues. Then, when some of the previously relaxed constraints are satisfied, the relaxation solution that bundles the latest optimal solutions acquired by the result acquisition unit at that time is set as the optimum solution of the original optimization problem. If the predetermined termination condition is satisfied first, the best feasible solution obtained at that time is set as the optimum solution of the original optimization problem. The solution of the optimization problem is displayed by a display unit (not shown).

(Quantum computer 20)
Next, the quantum computer 20 will be described. FIG. 2 is a diagram showing a hardware configuration of the quantum computer 20 according to the present embodiment. Further, FIG. 3 is a diagram for explaining the principle of the quantum computer. Here, an example will be described in which a quantum computer generates a Hamiltonian by associating a node of the Ising model with a determinant and a coefficient indicating a relationship between lattices with a coefficient of an objective function. However, these are not limited to the above, and may be a lattice model of any dimension such as the Heisenberg model.

In the Ising model, the quantum computer 20 includes a plurality of nodes (Ising variables) arranged in a grid pattern and a Hamiltonian configured with a value of the weight of the connection between the nodes (the coefficient of the objective function described above) as an input parameter. , Quantum annealing to find the base state of the Ising model, which minimizes the Hamiltonian value using quantum fluctuation (quantum annealing), and solving the Ising model using a digital circuit inspired by quantum phenomena. It is a computer that performs calculations using. Quantum annealing machines use a qubit as a basic unit, which can superimpose two different states at the same time.

In this embodiment, as shown in FIG. 2, an example in which a quantum annealing machine is used as the quantum computer 20 is shown. The quantum computer 20 combines a plurality of qubit nodes 21 arranged in a grid pattern (corresponding to the above-mentioned nodes), a qubit control unit 22 that controls each qubit node 21, and each qubit node 21. The device 23, the coupler control unit 24 that controls the coupler 23, and each qubit node 21 (bit nodes 1, 2, ..., N) when the rising model is in the ground state (minimum value). A reading unit 25 that measures and outputs a value (value of a qubit variable) is provided.

As shown in FIG. 3, the qubit node 21 can be realized by a superconducting ring or the like. For example, a superconducting ring can be configured by making a ring (closed circuit) out of a metal such as niobium, making it extremely low temperature, and allowing a current in one direction and a current in the opposite direction to exist at the same time. At this time, if the respective currents correspond to the upward (+1) and downward (-1) of the Ising spin, a state of ± 1 exists in the circuit at the same time.

The qubit control unit 22 has a mechanism in which another superconducting circuit is sandwiched between the superconducting rings and the superconducting current can be inverted. For example, qubit control unit 22 controls the magnetic flux applied to the superconducting ring qubit node 21 in order to realize the coefficients (h _i) or transverse magnetic field of the primary term of customizing variables in equation 2 described below. By reversing the superconducting current flowing through the superconducting ring, the upward (+1) and downward (-1) Ising spins can be appropriately exchanged (spin directions are reversed). Then, the magnetic field applied to this superconducting ring is adjusted to search for the optimum state.

The coupler 23 is composed of a superconducting ring prepared separately from the qubit nodes 21 so as to promote magnetic interaction between the superconducting rings corresponding to the different qubit nodes 21.

The coupler control unit 24 sets the weight of the coupling between the qubit nodes (superconducting ring) 21 based on the value of the coefficient of the objective function (H) input from the general-purpose computer 10. For example, the coupler control unit 24 controls the magnetic flux applied to the superconducting ring of the coupler 23 in order to realize the coefficient (J _ij ) of the quadratic term of the Ising variable in Equation 2 described later.

Here, the Hamiltonian configured by using the value of the weight of the coupling between each qubit node 21 as an input parameter is expressed by the following mathematical formula 1. In Equation 1, the first term indicates the state of the Ising model, the second term indicates the alternating magnetic field called the transverse magnetic field, and the alternating magnetic field causes a transition between ± 1 states to search for the optimum solution. Take the lead.

In the quantum annealing machine, in order to obtain the ground state of the Ising model, first, the state of each spin is quantum mechanically uncertain (the probability of each qubit being upward (+1) and downward (-1) is 1/2, respectively. To the most chaotic state). Then, in the initial state (t = 0), A (0) = 0 and B (0) = 1. The initial state is a state in which all spin combinations are superposed by a transverse magnetic field, and when the transverse magnetic field is dominant, this state is the state with the minimum energy. Then, with the passage of time (t> 0), A (t) gradually approaches 1 and B (t) approaches 0. Then, when the predetermined finite time (t = τ) is reached, the transverse magnetic field is stopped so that A (τ) = 1 and B (τ) = 0 (the second term is zero). ..

In other words, in the initial state, only the transverse magnetic field is applied, and the state where all the spin sequences are overlapped creates the state with the lowest energy, and while gradually weakening the value of the transverse magnetic field, the contribution of the original Ising model Hamiltonian. To increase. At this time, a phenomenon of quantum adiabatic time evolution (a phenomenon that starts from the minimum energy state and slowly evolves in time, always stays in the minimum energy state) occurs. Then, in the end, the Hamiltonian takes the minimum value, which is the ground state (minimum energy state) of the Ising model, and the solution of the optimization problem is reached.

After the weight of the coupling between the qubit nodes (superconducting rings) 21 is set by the combiner control unit 24 based on the input from the general-purpose computer 10 (that is, the input of the coefficient of the objective function (H)), the reading unit 25 When the zing model becomes the ground state (minimum energy state) due to the above action by the qubit control unit 22, the value of each zing variable σ _q of the qubit node 21 at this time is read out. The reading unit 25 outputs the value of each Ising variable read here to the general-purpose computer 10 as a solution to the optimization problem.

The process by which the quantum computer 20 measures the value (value of the Ising variable) of each node when the Ising model is in the ground state (minimum value) is not limited to the quantum annealing machine. For example, a computer specialized in performing calculations using characteristics such as solving an Ising model using a digital circuit inspired by a quantum phenomenon may be used. Further, an adiabatic model such as a lattice model and a circuit model using an arbitrary quantum circuit are equivalent in quantum calculation. For this reason, quantum computation using quantum annealing is equivalent to a quantum circuit that continuously operates a quantum gate, and the Hamiltonian's singing model is realized by arbitrary hardware that reproduces a quantum circuit that combines quantum gates. It does not matter if it is a quantum computer.

According to the optimization system as described above, even if it is a large-scale optimization problem that is difficult to solve by a general-purpose computer using the quantum computer 20 in which the number of qubits that can be used is limited, it is relatively relatively. It can be easily solved. For example, even if it is a problem of optimizing a multi-stage process processing schedule that has a large number of products and processes and includes complicated constraints (inequality constraints, etc.), it can be solved by the quantum computer 20 and only a conventional general-purpose computer can be used. It is possible to shorten the time required for the calculation as compared with the case of solving by using. In the above embodiment, a plurality of child problems are solved by one quantum computer 20 (each child problem is continuously processed), but the present invention is not limited to this, and each child problem is not limited to this. May be solved by different quantum computers 20 (each child problem is processed in parallel), or only some of the child problems may be solved by different quantum computers 20.

[Specific example of device]
Hereinafter, a specific setting method in the determination variable setting unit 12 and the objective function setting unit 13 of the general-purpose computer 10 and a specific update method in the optimum solution determination unit 16 will be described using the following optimization model as an example.

(Optimized model)
As a determination variable of the optimization problem to be solved, for example, an assigned variable x _j [i] [representing the processing order k in each process j of each product i in a plurality of processes (hereinafter, also referred to as "multi-stage process"). There is k] (i ∈ N, k ∈ K (j), j ∈ J). This set of assigned variables x _j [i] [k] is decomposed into determinants of each child problem and mapped to each node of the Ising model. The time range K (j) to be considered in step j is K (j) = {1, 2, ..., J (n-1) + 1}.

On the other hand, for example, the Hamiltonian of the Ising model in which the value of the interaction between the nodes is set is set according to the lot information such as the irregularity of lots and the delivery date information such as the deviation from the delivery date. For example, in a certain step j, it is assumed that the lots l (i ₁ ) and l (i ₂ ) are different from the products i ₁ and i ₂ (l (i ₁ ) ≠ l (i ₂ )). At this time, when i ₁ and i ₂ are processed in the adjacent processing orders k and (k + 1), lots cannot be combined. When the condition is satisfied, the assigned variables x _j [i ₁ ] [k] and x _j [i ₂ ] [k + 1] are both true. At this time, the objective function input as the Hamiltonian shall include a weight element set sufficiently larger than the assumed objective function value. Here, the weight element is a coefficient indicating the interaction between the nodes (Ising variables) corresponding to the assigned variables x _j [i ₁ ] [k] and x _j [i ₂ ] [k + 1], that is, x _j [. It is the value of the weight that connects the nodes of i ₁ ] [k] and x _j [i ₂ ] [k + 1], and is for the product x _j [i ₁ ] [k] · x _j [i ₂ ] [k + 1]. Corresponds to the weight.

Then, the general-purpose computer 10 causes the quantum computer 20 to calculate a solution in which the Hamiltonian takes the minimum value, that is, the ground state (minimum energy state) of the Ising model. Then, based on the values of the assigned variables x _j [i] [k] in each node in the ground state, the optimum conditions regarding the processing order of any process of any product can be found. Hereinafter, a more detailed description will be given based on the specific problem setting.

(Problem setting)
Consider the problem of finding the optimum processing order in each process in a processing process in which the product manufacturing process spans multiple processes. In this problem, the processing order in each process evaluates that the same lot is grouped into as large a lot as possible in the continuous processing order, that is, the setup change due to the lot change is minimized. Further, as a restriction between processes, it is a condition for starting the processing of the product in the next process that the processing of the previous process is completed for any product. The objective function shall evaluate the number of lot changes and late delivery and early production with different penalties.

The definitions of the symbols used in the assumptions and formulation are as follows.
-The target product set is N (= 1, 2, ... i, ..., N).
- the (in the final step) delivery of each product i and d _i, the affiliation lot in step j and l _ij. This value is given.
-The process set is J (= 1, 2, ... j, ..., p).
-The processing time of any product i in any step j shall be uniformly the same, and the processing time shall be the unit time.
-Products that have not been processed in the upstream process cannot be processed in the downstream process. That is, it is assumed that a product processed in the processing order (processing time) k in the jth step can be processed in the j + 1 process if it is after the processing order (processing time) k. The time range K (j) to be considered in step j is K (j) = {1, 2, ..., J (n-1) + 1}.
Thing - each product i is the final step (J = p) and delivery time d _i is given in, if the processing time of the final step is larger than this is the delivery delay, which was too much to make early if smaller than this And each shall impose a different penalty.

(Quantum annealing formulation)
The method of converting the formulated multi-step processing order model into the Ising model used for quantum annealing calculation will be described in detail below.

Setting of Ising variable (node of Ising model) Assign variable x _j [i] [k] (i ∈ N, k ∈ K (j), j ∈ J) representing the processing order k in each process j of each product i Let it be an Ising variable. Here, according to the above assumption, the processing timing (time) of the same product is after the manufacturing order in the previous process in the second and subsequent steps (j ≧ 2). For example, in the second step, the possible processing time range is (1 ≦ k ≦ 2n-1). Since this range is expanded as the process progresses, it is set as "k ∈ K (j)". Corresponding to this, for the target product set, i ∈ N∪E (j). E (j) represents a dummy product that is virtually processed at a time when processing is not performed.

Conversion method to Hamiltonian In a quantum computer, the Hamiltonian of the Ising model is represented by H (σ) in Equation 2 below. Hamiltonian H (σ) is, Ising variable σ _i take two values of ± 1 (i = 1, ... , Q) and σ _i · _{h i} multiplied by the weight parameter _{h i} in, and two of the Ising variable σ _i It is a value obtained by multiplying the product of σ _{j by} the weight parameter J _ij, and is the sum of J _ij and σ _i σ _j representing the interaction energy between the two ing variables, and means the total energy. The Ising variable is σ _i ∈ {-1,1}, but in a mathematical model in a normal mathematical programming problem, the variable s _i is modeled as s _i ∈ {0,1}. In that case, variable transformation of σ _i = s _i -1 or s _i = (σ _i +1) / 2 is performed.

Here, it is necessary to convert all the models formulated by the conventional computing device into Hamiltonians. In particular, the conversion method of the constraint formula, which has been modeled by an inequality in the conventional computing device, becomes an issue, but the conversion is performed as follows.

For example, assume that the optimization model includes an inequality constraint of "characteristic value x ≤ characteristic value y". At this time, if the event A that "characteristic value x is k or more" and the event B that "characteristic value y is less than k" are satisfied for any k at the same time, the inequality constraint is violated. Event A and event occurrence whether the customizing variables each sigma _A of _B, sigma as long association with _B, to sigma _A, is the interaction between σ _B σ _A · σ _B indicating that both events to occur simultaneously By imposing a penalty, the same effect as the inequality constraint can be achieved. The specific conversion method is as follows.

The Ising variable x _j [i] [k] (i ∈ N, k ∈ K (j), j ∈ J) indicates that any product i is in any processing order k in any step j. Must be assigned. Further, in any step j, any product i including a dummy material must be assigned to an arbitrary processing order (time) k. The product allocation constraint and the processing order allocation constraint can be described as the following formulas 3 and 4.

In a quantum computer, these restrictions can be expressed by the following mathematical formula 5. In the following formula, the first term corresponds to the processing order allocation constraint, and the second term corresponds to the product allocation constraint. The following equation imposes a penalty in the order of processing that violates each allocation constraint, and is "Σ i ∈ _{N ∪ E (j)} x _j [i] [k]" and "Σ _{k ∈ K (j)} x _j". A term for increasing the eigenvalue q _Big is added to the processing order in which "[i] [k]" takes a value other than 1. If q _Big is increased "sufficiently", "Σ i ∈ _{N ∪ E (j)} x _j [i] [k]" and "Σ _{k ∈ K (j)} x _j [i] [k]" are other than 1. When the value of is taken, the Hamiltonian becomes large, and the energy related to the condition becomes large, and as a result, the above allocation constraint is satisfied.

In the multi-step process processing schedule, if the process is not completed in the pre-process j of the product i, the process of the product i cannot be started in the post-process (j + 1). This constraint can be described as Equation 6 below. To define the decomposer problem for each process, it is necessary to relax this constraint and incorporate the violation amount into the objective function as a Lagrange mitigation term.

The amount of violation of the constraint condition shown in the above formula 6 is the following formula 7.

When incorporating into the objective function of the decomposition problem for each step j as a Lagrange relaxation term, the term obtained by multiplying Equation 7 by the Lagrange multiplier λ _{j, i, lj} is decomposed for each j and reflected as Equation 8 excluding the constant term. To.

Therefore, the Lagrange relaxation term J _j2 in the objective function of the child problem of step j is given by Equation 9. Equation 9 relaxes the inter-process constraint that is a constraint in the original problem (processing in the next process cannot be performed until the processing in the previous process is completed), and decomposes the amount of violation of the constraint into child problems. Now that it is no longer a constraint and it is allowed to violate it, the weight (q _Big ) term is no longer needed.

In the processing after the second step (j ≧ 2), the first processing start is not always k = 1 due to the inter-process constraint. For example, in the second step, the time when the first processing is performed is 1 ≦ k ≦ 2n. There is a possibility of -1. Further, if the first process is performed at k = 3, the final process must be performed at k = n-2 (= 3 + n-1). That is, it is necessary to prevent a gap in processing in the middle. Not _creating a gap in the processing order means that "Σ i _{∈ N} xj [i] [k]" does not become "1, 0, 1" in the continuous processing order k-1, k, k + 1. Since they are equivalent, this constraint is expressed by Equation 10 below.

However, since the above equation is an inequality constraint, it cannot be directly used as the Hamiltonian of the Ising model. Here, the present inventors examined the events in the continuous processing, and in the continuous processing, "the dummy processing is switched to the actual processing only once in the processing order k, k + 1" (event 1). I found. The present inventors have also found that "such switching never occurs (event 2) only when the process can be started from k = 1". Then, event 1 and event 2 are mutual exclusivity events when continuous processing is realized, and either of them always occurs. This constraint is expressed by Equation 11. The first term of the equation 11 corresponds to the number of times the dummy process is switched to the actual process, and the second term corresponds to the occurrence or non-occurrence of the event 2. In the continuous process, the total number is required to be 1, and in any case. Since this sum is never less than 1, it can be modeled by defining the interaction of two Ising variables without making it a square term. Then, if the q _Big of the following equation 9 is increased "sufficiently", the Hamiltonian becomes large and the energy related to the condition becomes large, and as a result, it is possible to avoid the formation of a gap in the middle of the processing.

As mentioned above, there are two items to be evaluated in the multi-step process processing order model: "small deviation in the final process processing order with respect to the delivery date" (delivery date information) and "lot cohesion with respect to the processing order" (lot information). Is. The former can be modeled by the following formulas 12 and 13. Formula 12 represents a penalty for late delivery, and Formula 13 represents a penalty for time that is too early for delivery. By multiplying the Ising variables x _p [i] [k] representing the processing time in the final step p of each product i by a value proportional to the deviation with respect to the delivery date, the model is such that the larger the deviation, the larger the Hamiltonian, that is, the energy. Has been made. Further, q ₁ and q ₂ are weight (proportional) coefficients for distinguishing a penalty for late delivery and early delivery (usually, the weight q _{1 for} late delivery is larger than the weight q _{2 for} early delivery. Set to).

The latter "group of lots for processing order" can be modeled by the following mathematical formula 14. Here, LC _j represents a set of product pairs (i ₁ , i ₂ ) having different lots (l (i ₁ ) ≠ l (i ₂ )) in step j. Equation 12 shows two Zing variables x _j [i ₁ ] [k] and x _j [corresponding to the processing of product pairs (i ₁ , i ₂ ) belonging to LC _j in a continuous processing order k, k + 1. It represents the energy of interaction between two inging variables, which is the product of i ₂ ] [k + 1] multiplied by the weighting factor q ₃ which represents the penalty for uncoordinated lots. Therefore, this model is modeled so that the Hamiltonian, that is, the energy, is large when the lots are different in the continuous processing order, that is, when the lots are not grouped. Therefore, the larger q ₃ is, the more the lots are in the ground state. It can be expected that they will converge in a cohesive processing order.

The Hamiltonian J _j can be expressed by the following equation 15 and equation 16 relates sum considering all of the above objective function.

Here, a guideline for setting the weighting coefficients q _Big , q ₁ , q ₂ , and q ₃ of J _j1 , J _j2 , J _j3 , J _p4 , J _p5 , and J _j6 is shown. J _j1 , J _j2 , and J _j3 are constraint expressions _converted into objective functions, which should be expressed as constraint expressions in conventional computers. Therefore, when a violation occurs, the original objective function Setting q _Big so that the value is sufficiently larger (for example, about 10 times) than the sum of J _p4 , J _p5 , and J _j6 corresponding to the above is the meaning of "sufficiently large". In the formulas 15 and 16, the coefficients of the quadratic terms of x such as x _j [i ₁ ] [k] and x _j [i ₂ ] [k + 1] correspond to J _ij of the formula 2, and the formulas 15 and 16 _{x j [i 1] [k} ] first order term of x, such as contained in corresponds to _{h i} in equation 2.

As described above, the coefficient-determined variables set by the coefficient-determined variable setting unit 12 are associated with the qubit nodes arranged in a grid pattern in the quantum computer 20. Further, the coefficient of the objective function for the child problem set by the objective function setting unit 13 is input to the quantum computer 20 as a coefficient (coupling weight) indicating the relationship between each qubit node (ising variable).

Here, the specific function is described using an Ising variable having a value of ± 1, but it may of course be given in the QUAO format using a variable having a binary value of 0 and 1.

[Device operation]
Next, the operation of the optimization support device 10 in the present embodiment will be described with reference to FIG. FIG. 4 is a flow chart showing the operation of the optimization support device according to the present embodiment. In the following description, FIG. 1 will be referred to as appropriate. Further, in the present embodiment, the optimization support method is implemented by operating the optimization support device 10. Therefore, the description of the optimization support method in the present embodiment is replaced with the following description of the operation of the optimization support device 10.

The optimization support device 10 in the present embodiment is an Ising model including a plurality of qubit nodes arranged in a grid pattern and a Hamiltonian configured with a weight value of coupling between the qubit nodes as an input parameter. The quantum computer 20 for finding the ground state of the Ising model, in which the value of the Hamiltonian becomes the minimum value using fluctuations, is made to solve the optimization problem.

Here, as shown in FIG. 4, the input information acquisition unit 11 acquires the input information necessary for constructing the optimization problem (S1). Examples of input information include the number of processes, the number of products, the lot number, and the delivery date when solving an optimization problem for optimizing the processing order of arbitrary products in arbitrary processes. More specifically, it is a process set J, product information (product set i, lot attribute for each process, delivery date, etc.), and evaluation weight parameters (q _Big , q ₁ , q ₂ , q _3, etc.).

The coefficient of determination variable setting unit 12 sets the coefficient of determination of the optimization problem to be solved (S2). For example, when the determination variable setting unit 12 solves an optimization problem for optimizing the processing order of an arbitrary product in an arbitrary process, the determination variable setting unit 12 sets the processing order k as a determination variable.

The objective function setting unit 13 decomposes into a plurality of child problems in which some constraints of the optimization problem to be solved are relaxed, and sets an objective function for each child problem (S3). When a constraint condition is included in the optimization problem to be solved, the objective function setting unit 13 determines that the objective function for each child problem is the amount of violation of the relaxed constraint condition multiplied by a multiplier (Lagrange multiplier λ, which will be described later). Includes terms. In addition, an objective function including an element that imposes a penalty for the violation of the constraint condition is set. Specifically, the objective function setting unit 13 also violates the elements of the evaluation index (for example, J _j2 , J _p4 , J _p5 , J _j6 ) expressing the matters to be evaluated originally by mathematical expressions, and the constraint conditions. An objective function including the elements of the constraint expression (for example, J _j1 and J _j3 ) expressed by a mathematical formula that imposes a penalty is set. Further, the evaluation index element and the constraint expression element include a weight element (for example, q ₁ , q ₂ , q ₃ , q _Big ) representing the weight of each element. Here, when the optimization problem includes an inequality constraint, the objective function setting unit 13 expresses the constraint expression represented by a mathematical formula including at least the term of the product of the determinants set by the determinant variable setting unit 12. An objective function that includes elements (eg J _j1 , J _j3 ) and weight elements (eg q _Big ) that are set sufficiently larger than the expected reference value (objective function value) when the constraint is violated. Set.

The objective function setting unit 13 creates the above objective functions at least for each constraint condition (for example, J _j1 , J _j2 , J _j3 , J _p4 , J _p5 , J _j6 ), and integrates the created objective functions. And set it as the final objective function (for example, J _j , J _p ). As the Lagrange multiplier λ of J _j2 , the latest value updated by the equation 20 is used by the optimum solution determination unit 16.

In the above embodiment, the objective function setting unit 13 is described as generating the objective function based on the input information acquired by the input information acquisition unit 11, but the present invention is not limited to this, and the user. The objective function generated by the above may be input (including manual input) to the general-purpose computer 10.

The input unit 14 decomposes the determinants set by the determinant setting unit 12 into determinants for each child problem, and the decomposed determinants are arranged in a grid pattern in the quantum computer 20 (that is, the qubit nodes (that is, that is). The quantum computer 20 uses the coefficient of the objective function for the child problem set by the objective function setting unit 13 corresponding to the qubit variable) as a coefficient (coupling weight) indicating the relationship between each qubit node (ising variable). (S4).

The result acquisition unit 15 acquires the calculation result (optimal solution of each child problem) of the quantum computer 20 calculated based on the coefficient of the objective function of each child problem input by the input unit 14 (S5). Specifically, the measured values of the qubit nodes (Ising variables) in the ground state are acquired as the values of the determinants of each child problem corresponding to those qubit nodes (Ising variables), and each child problem is also obtained. Find the optimal value of the objective function (Hamiltonian) of each child problem based on the optimal solution of.

The optimum solution determination unit 16 bundles the optimum solutions acquired by the result acquisition unit 15 to obtain an alleviated solution. Further, the optimum solution determination unit 16 adds the optimum values acquired by the result acquisition unit 15 to obtain the relaxation optimum value. The optimum solution determination unit 16 updates the objective function based on the relaxation solution and the relaxation optimum value (S6).

Specifically, the optimum solution determination unit 16 compares the lower bound value immediately before the update in the optimization problem with the relaxation optimum value, updates the lower bound value, and corrects the violation included in the relaxation solution. Update the upper bound value based on the possible solution. The optimal solution determination unit 16 calculates the subgradient vector G based on the relaxed solution with the amount of violation of the relaxed constraint as an element. Then, the optimum solution determination unit 16 updates the multiplier (Lagrange multiplier λ, which will be described later) to the amount of violation of the relaxed constraint condition by the subgradient vector, the updated lower bound value, and the updated upper bound value. This updates the objective function.

(Update of lower bound value)
Relaxation solution x _{j_opt} [i] [k] obtained from the quantum computer 20 for the child problem Pj generated by decomposing each process j (∈ P) by relaxing the constraints between the processes in the original problem. and solution relaxation solution _{x relx} a bundle of, when the optimum value of each child problems Pj and _{V J_opt,} relaxation optimum value _{V relx} taken a sum over them in the entire process is determined from equation 17. Compare V _relx with the preset lower bound value Z _LB, and if Z _LB <V _relx holds (assuming a minimization problem), update the lower bound value Z _LB with V _relx . However, when adding the optimum values of the child problems, if the original constant term is omitted in J _j2 , it is necessary to consider it. This is indicated by "-(p-1)" in the second term of Equation 17. In the case of the maximization problem, V _relx is compared with the preset upper bound value Z _UB, and if Z _UB > V _relx is satisfied, the upper bound value Z _UB is updated with V _relx . To do.

(Update of upper bound value)
By using the mitigation solution x _relex and shifting the processing time of the subsequent process until the violation disappears, the part that violates the inter-process constraint is corrected, and the executable solution x _fes is derived. Hereinafter, the correction method will be described in detail according to the examples shown in Table 1.

In the example shown in Table 1, the inter-process constraint between the process j and the process (j + 1) (that is, if the process is not completed in the pre-process j of the product i, the process of the product i cannot be started in the post-process (j + 1). The products that violate the above restrictions are product 5 and product 1. In step j, the product 5 is processed with k = 2, but in step j + 1, it is processed with k = 1, so that the time is reversed by one time. In product 1, k = 5 is processed in step j, but in step j + 1, k = 2 is processed, so that the time is reversed by 3 times. Therefore, in order to avoid the reversal phenomenon, the processing order in step j + 1 may be shifted back by 3 hours, which is the maximum reversal time. The smooth results are shown in the "j + 1 correction" column of Table 1. When a feasible solution _{x fes} after correction, the _{V fes} obtained by calculating the objective function on the basis of the feasible solutions _{x fes,} compared with the upper bound value _{Z UB} previously _{set, V fes} <Z _{When UB} is established (assuming the minimization problem), the upper bound value Z _UB is updated with V _fes . In the case of the maximization problem, V _fes is compared with the preset lower bound value Z _LB, and when V _fes> Z _LB is satisfied, the lower bound value Z _LB is updated with V _fes .

The method of modifying the mitigation solution is not limited to the examples shown in Table 1. For example, a method of resolving the original problem including inter-process constraints by using only the product of the violating part as a variable can be considered. In this way, referring to the mitigation solution that integrates the solutions of the child problems, by making the above adjustments to it, the process of obtaining an executable solution and the original problem that is the objective function value at that time The process of finding the boundary value is called adjustment.

(Calculation of subgradient vector G)
A column gradient vector G, which is a vector having a constraint violation amount for the inter-process constraint (Equation 9) relaxed based on the relaxation solution xrelx described above, is calculated. Since the mathematical formula 9 is defined for i ∈ N, l = 1, ..., K (j) -1, j ∈ P \ 1, the dimension of G is n × (K (j) -1) × ( It becomes p-1), and each element becomes the corresponding constraint violation amount, and can be calculated by the formula 18 by a general-purpose computer.

(Calculation of Lagrange multiplier λ)
Based on the lower bound value Z _LB , the upper bound value Z _UB, and the subgradient vector G obtained as described above, the Lagrange multiplier update step size ξ is calculated by Equation 18. Using the obtained ξ, the Lagrange multiplier λ ^(r) is updated to λ ^{(r + 1)} by Equation 19.

The optimum solution determination unit 16 updates the equation 9 by using the updated Lagrange multiplier λ ^{(r + 1)} to update the objective function input to the quantum computer 20. The updated objective function is input to the quantum computer 20 by the input unit 14, and the calculation result (optimal solution of each child problem) for the updated objective function is acquired by the result acquisition unit 15 for each child problem. The optimum value of the objective function (Hamiltonian) of each child problem is obtained based on the optimum solution. The optimum solution determination unit 16 updates the objective function based on the calculation result (optimum solution) and the optimum value. This series of operations converges to a predetermined state (the relaxation solution satisfies some of the relaxed constraint conditions, or a predetermined end condition (the difference between the upper bound value and the lower bound value is less than the threshold value). ) Continues. In FIG. 4, these conditions are collectively referred to as “predetermined conditions”. Then, when some of the previously relaxed constraints are satisfied, the relaxation solution that bundles the latest optimal solutions acquired by the result acquisition unit at that time is set as the optimum solution of the original optimization problem. If the predetermined termination condition is satisfied first, the best feasible solution obtained at that time is set as the optimum solution of the original optimization problem. The solution of the optimization problem is displayed by a display unit (not shown).

(program)
The program in this embodiment may be any program that causes a computer to execute steps S1 to S6 shown in FIG. By installing this program on a computer and executing it, the optimization support device and the optimization support device according to the present embodiment can be realized. In this case, the CPU (Central Processing Unit) of the computer serving as the information processing device includes the input information acquisition unit 11, the determination variable setting unit 12, the objective function setting unit 13, the input unit 14, the result acquisition unit 15, and the optimum solution determination unit 16. It functions as and performs processing.

Moreover, the program in this embodiment may be executed by a computer system constructed by a plurality of computers. In this case, for example, each computer functions as one of the input information acquisition unit 11, the decision variable setting unit 12, the objective function setting unit 13, the input unit 14, the result acquisition unit 15, and the optimum solution determination unit 16, respectively. You may.

[Physical configuration]
Here, a computer that realizes the optimization support device by executing the program in the present embodiment will be described with reference to the drawings. FIG. 5 is a block diagram showing an example of a computer that realizes the optimization support device according to the present embodiment.

As shown in FIG. 5, the computer 110 includes a CPU 111, a main memory 112, a storage device 113, an input interface 114, a display controller 115, a data reader / writer 116, and a communication interface 117. Each of these parts is connected to each other via a bus 121 so as to be capable of data communication.

The CPU 111 expands the programs (codes) of the present embodiment stored in the storage device 113 into the main memory 112 and executes them in a predetermined order to perform various operations. The main memory 112 is typically a volatile storage device such as a DRAM (Dynamic Random Access Memory). Further, the program in the present embodiment is provided in a state of being stored in a computer-readable recording medium 120. The program in this embodiment may be distributed on the Internet connected via the communication interface 117.

Further, specific examples of the storage device 113 include a semiconductor storage device such as a flash memory in addition to a hard disk drive. The input interface 114 mediates data transmission between the CPU 111 and input devices 118 such as a keyboard and mouse. The display controller 115 is connected to the display device 119 and controls the display on the display device 119.

The data reader / writer 116 mediates the data transmission between the CPU 111 and the recording medium 120, reads the program from the recording medium 120, and writes the processing result in the computer 110 to the recording medium 120. The communication interface 117 mediates data transmission between the CPU 111 and another computer.

Specific examples of the recording medium 120 include a general-purpose semiconductor storage device such as CF (Compact Flash (registered trademark)) and SD (Secure Digital), a magnetic storage medium such as a flexible disk, or a CD-. Examples include optical storage media such as ROM (Compact Disk Read Only Memory).

The optimization support device in the present embodiment can also be realized by using the hardware corresponding to each part instead of the computer in which the program is installed. Further, the optimization support device may be partially realized by a program and the rest may be realized by hardware.

According to the present invention, it is possible to quickly optimize the processing order of any process of any product.

10 General-purpose computer (optimization support device)
11 Input information acquisition unit 12 Coefficient of determination setting unit 13 Objective function setting unit 14 Input unit 15 Result acquisition unit 16 Optimal solution determination unit 20 Quantum computer (optimizer)
21 Quantum bit node 22 Quantum bit control unit 23 Coupler 24 Coupler control unit 25 Read unit 30 Optimization system 110 Computer 111 CPU
112 Main memory 113 Storage device 114 Input interface 115 Display controller 116 Data reader / writer 117 Communication interface 118 Input device 119 Display device 120 Recording medium 121 Bus

Claims (10)

In a network model including a plurality of nodes and a characteristic function configured with the value of the weight of the connection between the nodes as an input parameter, a quantum for obtaining the base state of the network model in which the value of the characteristic function is the minimum value. It is an optimization support device that allows a device using calculation technology to solve an optimization problem.
An input information acquisition unit that acquires input information related to the optimization problem,
The coefficient of determination variable setting unit that sets the coefficient of determination of the optimization problem,
An objective function setting unit that decomposes the optimization problem into a plurality of child problems in which some constraints are relaxed and sets an objective function for each of the child problems.
The determinant is decomposed into determinants for each of the child problems to obtain variables corresponding to the nodes, and the coefficient of the objective function is input to the device using the quantum computing technique as the value of the weight of the coupling between the nodes. Input section and
In the device using the quantum computing technique, the value of the node when the network model is in the ground state is acquired as the optimum solution of the child problem, and the optimum value of the objective function of the child problem is obtained based on the optimum solution. The result acquisition department and
When it is determined whether or not some of the constraints are satisfied based on the relaxation solution that bundles the optimum solutions and the relaxation optimum value that is the sum of the optimum values, and the part of the constraints is satisfied. The relaxation solution is used as the optimum solution of the original optimization problem, and if some of the constraints are not satisfied, the feasible solution obtained by correcting the violation included in the relaxation solution is used as the original optimization problem. An optimization support device provided with an optimum solution determination unit, which is the optimum solution for the above. When the partial constraint condition is not satisfied, the optimum solution determination unit updates the objective function based on the relaxation solution and the relaxation optimum value.
The optimization support device according to claim 1, wherein the objective function setting unit resets the objective function updated by the optimal solution determination unit as an objective function for each of the child problems. When the optimization problem is a minimization problem, the optimum solution determination unit compares the lower bound value immediately before the update with the relaxation optimum value to determine the lower bound value when some of the constraints are not satisfied. If the optimization problem is updated and the optimization problem is a maximization problem, the upper bound value immediately before the update is compared with the relaxation optimum value, the upper bound value is updated, and the upper bound value or the upper bound value is used. Update the objective function,
The optimization support device according to claim 2. The optimum solution determination unit updates the upper bound value based on the feasible solution when the optimization problem is a minimization problem when some of the constraints are not satisfied, and the optimization problem. If is a maximization problem, the lower bound value is updated and the objective function is updated based on the upper bound value or the lower bound value.
The optimization support device according to claim 2 or 3. The optimum solution determination unit repeatedly updates the objective function until the partial constraint condition is satisfied or a predetermined end condition is satisfied, and when the partial constraint condition is satisfied first. At that time, the relaxation solution that bundles the latest optimum solutions acquired by the result acquisition unit is set as the optimum solution of the original optimization problem, and if the predetermined end condition is satisfied first, at that time. The optimization support device according to any one of claims 2 to 4, wherein the best feasible solution obtained is the optimum solution of the original optimization problem. The objective function setting unit sets an objective function including a term obtained by multiplying the violation amount for the relaxed constraint condition by a multiplier.
The optimization support device according to any one of claims 1 to 5. Based on the relaxation solution, the optimum solution determination unit uses the subgradient vector calculated with the violation amount for the relaxed constraint as an element, the updated lower bound value, and the updated upper bound value to obtain the multiplier. Update,
The optimization support device according to claim 6. In a network model including a plurality of nodes arranged in a grid pattern and a characteristic function configured by using the value of the weight of the connection between the nodes as an input parameter, the value of the characteristic function is the minimum value of the network model. It is an optimization support method that allows a device using quantum computing technology to find the base state to solve an optimization problem.
(1) Acquiring input information regarding the optimization problem, step
(2) Setting the coefficient of determination of the optimization problem, step
(3) A step of decomposing a part of the optimization problem into a plurality of child problems in which some constraints are relaxed and setting an objective function for each of the child problems.
(4) The quantum computing technique was used by decomposing the determinant into determinants for each of the child problems to obtain variables corresponding to the nodes, and using the coefficient of the objective function as the value of the weight of the connection between the nodes. Input to the device, step,
(5) In the device using the quantum computing technique, the value of the node when the network model is in the ground state is acquired as the optimum solution of the child problem, and the objective function of the child problem is based on the optimum solution. Finding the optimum value, steps, and
(6) Based on the relaxation solution in which the optimum solutions are bundled and the relaxation optimum value obtained by adding the optimum values, it is determined whether or not some of the constraint conditions are satisfied, and the part of the constraint conditions are satisfied. If it is satisfied, the relaxation solution is used as the optimum solution of the original optimization problem, and if some of the constraints are not satisfied, the feasible solution obtained by correcting the violation included in the relaxation solution is used as the original solution. An optimization support method with steps that makes it the optimal solution for an optimization problem. In a network model including a plurality of nodes arranged in a grid pattern and a characteristic function configured by using the value of the weight of the connection between the nodes as an input parameter, the value of the characteristic function is the minimum value of the network model. When making a device using quantum computing technology to find the base state solve an optimization problem
On the computer
(1) Acquiring input information regarding the optimization problem, step
(2) Setting the coefficient of determination of the optimization problem, step
(3) A step of decomposing a part of the optimization problem into a plurality of child problems in which some constraints are relaxed and setting an objective function for each of the child problems.
(4) The quantum computing technique was used by decomposing the determinant into determinants for each of the child problems to obtain variables corresponding to the nodes, and using the coefficient of the objective function as the value of the weight of the connection between the nodes. Input to the device, step,
(5) In the device using the quantum computing technique, the value of the node when the network model is in the ground state is acquired as the optimum solution of the child problem, and the objective function of the child problem is based on the optimum solution. Finding the optimum value, steps, and
(6) Based on the relaxation solution in which the optimum solutions are bundled and the relaxation optimum value obtained by adding the optimum values, it is determined whether or not some of the constraint conditions are satisfied, and the part of the constraint conditions is satisfied. If it is satisfied, the relaxation solution is used as the optimum solution of the original optimization problem, and if some of the constraints are not satisfied, the executable solution obtained by correcting the violation included in the relaxation solution is used as the original solution. A program that executes steps as the optimal solution for an optimization problem. A system that optimizes optimization problems
In a network model including a plurality of nodes arranged in a grid pattern and a characteristic function configured by using the value of the weight of the connection between the nodes as an input parameter, the value of the characteristic function is the minimum value of the network model. A device that uses quantum technology to find the ground state,
An input information acquisition unit that acquires input information related to the optimization problem,
The coefficient of determination variable setting unit that sets the coefficient of determination of the optimization problem,
An objective function setting unit that decomposes the optimization problem into a plurality of child problems in which some constraints are relaxed and sets an objective function for each of the child problems.
The determinant is decomposed into determinants for each of the child problems to obtain variables corresponding to the nodes, and the coefficient of the objective function is input to the device using the quantum computing technique as the value of the weight of the coupling between the nodes. Input section and
In the device using the quantum computing technique, the value of the node when the network model is in the ground state is acquired as the optimum solution of the child problem, and the optimum value of the objective function of the child problem is obtained based on the optimum solution. The result acquisition department and
When it is determined whether or not some of the constraints are satisfied based on the relaxation solution that bundles the optimum solutions and the relaxation optimum value that is the sum of the optimum values, and the part of the constraints is satisfied. The relaxation solution is used as the optimum solution of the original optimization problem, and if some of the constraints are not satisfied, the feasible solution obtained by correcting the violation included in the relaxation solution is used as the original optimization problem. An optimization system equipped with an optimum solution determination unit, which is the optimum solution for.

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