JP2022031949A - Information processing apparatus, information processing method, and information processing program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an information processing apparatus, an information processing method, and an information processing program which can efficiently calculate solution of an optimization problem having parameters changing in response to a situation.

SOLUTION: An information processing apparatus 10 according to the present invention has: a prediction unit 12 for predicting parameters for an optimization problem by using a prediction model 12a generated by machine learning; a setting unit 13 for substituting parameters into at least one of an objective function and a function representing limiting conditions to set, to an annealing machine, Hamiltonian including the objective function and the function representing the limiting conditions; an acquiring unit 14 for acquiring, from the annealing machine, a ground state of the Hamiltonian calculated by the annealing machine; and a calculating unit 15 for calculating a candidate for solution of the optimization problem based on the ground state.

SELECTED DRAWING: Figure 1

COPYRIGHT: (C)2022,JPO&INPIT

Description

The present invention relates to an information processing apparatus, an information processing method and an information processing program.

In recent years, machine learning has been applied to various fields. For example, machine learning may be used to predict costs such as the time and amount of money (fuel cost) required to move a certain route, and determine the route so that the route can be moved at a low cost.

For example, in Patent Document 1 below, the predicted cost between two nodes selected from a plurality of nodes corresponding to points on a map is calculated based on graph information, and the two selected nodes are supported. The actual measurement cost between two points on the map is acquired, the predicted cost and the actual measurement cost are stored as learning data, and a learning model that learns the relationship between the predicted cost and the actual measurement cost is generated based on the learning data. , A server device that provides a cost between any two points on a map based on the generated learning model is described.

Patent No. 6562431

However, even if the cost of each route can be predicted, if the number of combinations of routes that can be selected increases, a large amount of calculation is required to optimize the combination. The increase in the amount of computation due to such a combinatorial explosion occurs not only in the case of route optimization but also in general optimization problems.

Therefore, even if the parameters of the optimization problem can be predicted by machine learning, it may be difficult to obtain a solution to the problem.

Therefore, the present invention provides an information processing apparatus, an information processing method, and an information processing program capable of efficiently obtaining a solution of an optimization problem including parameters that change depending on a situation.

The information processing apparatus according to one aspect of the present invention is based on a prediction model generated by machine learning.
A predictor that predicts the parameters of the optimization problem and a Hamiltonian containing the objective function and the function that represents the constraint are set in the annealing machine by substituting the parameter into at least one of the objective function and the function that represents the constraint. It includes a setting unit, an acquisition unit that acquires the Hamiltonian base state calculated by the annealing machine from the annealing machine, and a calculation unit that calculates solution candidates for optimization problems based on the base state.

According to this aspect, the parameters of the optimization problem that change depending on the situation can be predicted by the prediction model, and the solution of the optimization problem including the parameters can be efficiently obtained by the annealing machine.

In the above aspect, the setting unit may set the Hamiltonian including the objective function corresponding to the optimization problem specified by the user among the plurality of optimization problems in the annealing machine.

According to this aspect, one of the objective functions prepared in advance for a plurality of optimization problems is set in the annealing machine by the user selecting one optimization problem from a plurality of optimization problems. It is possible to reduce the burden on the user to set up the annealing machine.

In the above aspect, the setting unit may set the Hamiltonian including the function representing the constraint condition specified by the user among the plurality of constraint conditions in the annealing machine.

According to this aspect, by adopting a format in which the user selects a desired constraint condition from a plurality of constraint conditions, a function representing a plurality of constraint conditions prepared in advance can be set in the annealing machine, and the user can perform annealing. The burden of setting up the machine can be reduced.

In the above aspect, the optimization problem may be a combinatorial optimization problem for a plurality of routes.

In the above aspect, the optimization problem is a route optimization problem that goes around a plurality of bases, and the parameters are the time required to move between the plurality of bases, the distance between the plurality of bases, and the distance between the plurality of bases. Including at least one of the amount of money required to travel, the objective function is to travel the total time required to travel to multiple locations, the total distance traveled to travel to multiple locations, and to travel to multiple locations. It may represent any of the required total amount.

According to this aspect, changes in traffic conditions are made by predicting any of the travel time between bases, the distance between bases, and the amount of money required to move between bases, and by minimizing the objective function using the predicted value as a parameter. It is possible to calculate the optimum patrol route according to the above.

In the above aspect, the parameter may include data for extracting a plurality of bases from a plurality of candidate bases.

According to this aspect, it is possible to optimize the order of visits after narrowing down the bases to be visited.

In the above aspect, the constraint condition may include a condition regarding the time of arrival at a plurality of bases.

According to this aspect, the route can be optimized so that each base can be visited at the scheduled arrival target time.

In the above aspect, the optimization problem may be a combinatorial optimization problem relating to scheduling of human resources or physical resources.

In the above aspect, the optimization problem is a shift optimization problem of the staff assigned to the store, the parameter includes the number of visitors to the store, and the objective function is the number of staff and staff determined based on the number of visitors. May represent at least one of the labor costs of.

According to this aspect, by predicting the number of store visitors and minimizing the objective function using the predicted value as a parameter, it is possible to calculate the optimum staff shift according to the change in the store visit situation.

In the above embodiment, the constraint may include at least one of the conditions relating to the staff's desired leave and the conditions relating to the staff's working group.

According to this aspect, not only the staffing is optimized for the number of customers visiting the store, but also the staffing is optimized.
Shifts can be optimized to fulfill the staff's work wishes.

In the above aspect, the constraint may include a condition regarding the work interval of the staff.

According to this aspect, not only the staffing is optimized for the number of customers visiting the store, but also the staffing is optimized.
Shifts can be optimized to fulfill the staff's work wishes.

In the above embodiment, the optimization problem may be a combinatorial optimization problem relating to the packing of a tangible or intangible object having a capacity.

In the above aspect, the optimization problem is a packing optimization problem in which a plurality of packages are loaded in a plurality of containers, a parameter includes a plurality of packages, and an objective function is a plurality of packages in any of the plurality of containers. It may represent at least one of the load allocation and the distance between multiple packages.

According to this aspect, by predicting the amount of luggage and minimizing the objective function using the predicted value as a parameter, it is possible to calculate the optimum packing according to the change in the amount of luggage to be carried.

In the above embodiment, the constraint condition may include at least one of a condition relating to the capacity of each of the plurality of containers and a condition relating to the cost of each of the plurality of containers.

According to this aspect, it is possible to optimize the packing of cargo by preventing overloading and reducing the cost of the container.

In the above aspect, the constraint may include a condition regarding the distance between a plurality of packages.

According to this aspect, a plurality of packages placed close to each other are optimized to be loaded in one container, and the transportation cost for transporting the packages to the container is reduced.

In the information processing method according to another aspect of the present invention, the parameters of the optimization problem are predicted by the processor provided in the information processing device and the prediction model generated by machine learning, and the parameters are set to the objective function and the constraint. Assign to at least one of the functions representing the condition to set the Hamiltonian containing the objective function and the function representing the constraint condition in the annealing machine, and obtain the base state of the Hamiltonian calculated by the annealing machine from the annealing machine. And to calculate the solution candidates of the optimization problem based on the base state.

According to this aspect, the parameters of the optimization problem that change depending on the situation can be predicted by the prediction model, and the solution of the optimization problem including the parameters can be efficiently obtained by the annealing machine.

In the information processing program according to another aspect of the present invention, the processor provided in the information processing apparatus is subjected to a prediction unit for predicting the parameters of the optimization problem by a prediction model generated by machine learning, parameters, objective functions and constraints. The setting part that sets the Hamiltonian including the objective function and the function representing the constraint condition to at least one of the functions representing the condition in the annealing machine, and the base state of the Hamiltonian calculated by the annealing machine is obtained from the annealing machine. It functions as an acquisition unit and a calculation unit that calculates solution candidates for optimization problems based on the base state.

According to this aspect, the parameters of the optimization problem that change depending on the situation can be predicted by the prediction model, and the solution of the optimization problem including the parameters can be efficiently obtained by the annealing machine.

INDUSTRIAL APPLICABILITY According to the present invention, it is possible to provide an information processing apparatus, an information processing method, and an information processing program capable of efficiently obtaining a solution of an optimization problem including parameters that change depending on a situation.

It is a figure which shows the functional block of the information processing apparatus which concerns on 1st Embodiment of this invention. It is a figure which shows the physical structure of the information processing apparatus which concerns on 1st Embodiment. It is a figure which shows the correspondence relation of the quantum bit set in the annealing machine by the information processing apparatus which concerns on 1st Embodiment. It is a figure which shows the travel time between bases predicted by the information processing apparatus which concerns on 1st Embodiment. It is a figure which shows the constraint condition about the visit time set by the information processing apparatus which concerns on 1st Embodiment. It is a flowchart of the route optimization processing which is performed by the information processing apparatus which concerns on 1st Embodiment. It is a figure which shows the correspondence relation of the quantum bit set in the annealing machine by the information processing apparatus which concerns on 2nd Embodiment of this invention. It is a figure which shows the constraint condition about the desired leave of the staff set by the information processing apparatus which concerns on 2nd Embodiment. It is a figure which shows the correspondence relation of the quantum bit set in the annealing machine by the information processing apparatus which concerns on 2nd Embodiment. It is a flowchart of shift optimization processing which is effective by the information processing apparatus which concerns on 2nd Embodiment. It is a figure which shows the correspondence relation of the quantum bit set in the annealing machine by the information processing apparatus which concerns on 3rd Embodiment of this invention. It is a figure which shows the correspondence relation of the quantum bit set in the annealing machine by the information processing apparatus which concerns on 3rd Embodiment. It is a figure which shows the correspondence relation of the quantum bit set in the annealing machine by the information processing apparatus which concerns on 3rd Embodiment. It is a figure which shows the distance between the baggage set by the information processing apparatus which concerns on 3rd Embodiment. It is a flowchart of the packing optimization processing which is effective by the information processing apparatus which concerns on 3rd Embodiment.

An embodiment of the present invention will be described with reference to the accompanying drawings. In each figure, those with the same reference numerals have the same or similar configurations.

[First Embodiment]
FIG. 1 is a diagram showing a functional block of the information processing apparatus 10 according to the first embodiment of the present invention. The information processing apparatus 10 includes a designated acquisition unit 11, a prediction unit 12, a setting unit 13, an acquisition unit 14, and a calculation unit 15. The information processing device 10 is composed of a general-purpose computer. The information processing device 10 is connected to the user terminal 20 and the annealing machine 30 via a communication network such as the Internet. The user terminal 20 is composed of a general-purpose computer, and may be a personal computer or a smartphone. The annealing machine 30 is a computer that calculates the ground state of the Hamiltonian of the set Ising model, and may be, for example, a quantum annealing machine that calculates the ground state of the Hamiltonian by quantum annealing. Further, the annealing machine 30 may be replaced with a quantum computer that calculates the ground state of the Hamiltonian by acting the quantum gate on the qubit. However, the annealing machine 30 does not have to be a quantum annealing machine, and may be configured by any type of computer including a classical computer. Further, the information processing apparatus 10 is connected to a hybrid computer composed of an annealing machine 30 such as a quantum annealing machine and a general-purpose classical computer, and even if the hybrid computer is set to the Hamiltonian of the Ising model and its ground state is calculated. good.

The designation acquisition unit 11 acquires the designation of the type of the optimization problem to be solved by the information processing apparatus 10 from the user terminal 20. The designation acquisition unit 11 is a user terminal 20 from among a plurality of optimization problems.
You may get the specification of the type of optimization problem selected by. Further, the designation acquisition unit 11 acquires the designation of the constraint condition to be satisfied when solving the optimization problem. The designation acquisition unit 11 may acquire the designation of the constraint condition selected by the user terminal 20 from the plurality of constraint conditions.

The prediction unit 12 predicts the parameters of the optimization problem by the prediction model 12a generated by machine learning. The prediction model 12a includes, for example, a regression model and a classification model generated by supervised learning, and a regression model and a classification model generated by a deep learning method. The data input to the prediction model 12a may be numerical data, image data, audio data or text data, and the data output by the prediction model 12a is numerical data that is a parameter of the optimization problem.

The setting unit 13 assigns the predicted parameter to at least one of the objective function and the function representing the constraint condition, and sets the Hamiltonian including the objective function and the function representing the constraint condition in the annealing machine 30. Here, the objective function is a function to be minimized (or maximized) in the optimization problem, and the function representing the constraint condition becomes 0 or a negative value when the constraint condition is satisfied, and the constraint condition is not satisfied. Can be a function that has a positive value. The setting unit 13
A Hamiltonian representing an optimization problem as an Ising model is set in the annealing machine 30.

The acquisition unit 14 acquires the ground state of the Hamiltonian calculated by the annealing machine 30 from the annealing machine 30. The Hamiltonian ground state of the Ising model is the combination of the values of multiple spins that has the minimum energy. The acquisition unit 14 acquires not only the Hamiltonian ground state calculated by the annealing machine 30, but also a plurality of states including relatively low-energy states such as the first excited state and the second excited state from the annealing machine 30. You may.

The calculation unit 15 calculates solution candidates for the optimization problem based on the Hamiltonian ground state calculated by the annealing machine 30. The calculation unit 15 converts the Hamiltonian ground state represented by the spin value into a solution candidate of the optimization problem.

According to the information processing apparatus 10 according to the present embodiment, the parameters of the optimization problem that change depending on the situation are predicted by the prediction model 12a, and the solution of the optimization problem including the parameters is efficiently obtained by the annealing machine 30. Can be done.

The setting unit 13 sets the Hamiltonian including the objective function corresponding to the optimization problem specified by the user among the plurality of optimization problems in the annealing machine 30. The setting unit 13
A Hamiltonian containing an objective function corresponding to an optimization problem specified by the user using the user terminal 20 is set in the annealing machine 30. By adopting a format in which the user selects one optimization problem from a plurality of optimization problems, one of the objective functions prepared in advance for the plurality of optimization problems can be set in the annealing machine 30, and the user can set the annealing machine 30. The burden of setting the annealing machine 30 can be reduced.

The setting unit 13 sets the Hamiltonian including the function representing the constraint condition specified by the user among the plurality of constraint conditions in the annealing machine 30. The setting unit 13 presents to the user one or a plurality of constraints prepared in advance for the specified optimization problem, and the user terminal 2
A Hamiltonian containing a function representing a constraint condition specified by the user using 0 is set in the annealing machine 30. By adopting a format in which the user selects a desired constraint condition from a plurality of constraint conditions, a function representing a plurality of constraint conditions prepared in advance can be set in the annealing machine 30, and the user sets the annealing machine 30. The burden can be reduced.

FIG. 2 is a diagram showing a physical configuration of the information processing apparatus 10 according to the present embodiment. The information processing device 10 includes a CPU (Central Processing Unit) 10a corresponding to a calculation unit, a RAM (Random Access Memory) 10b corresponding to a storage unit, and a ROM (Read only) corresponding to the storage unit.
Memory) 10c, a communication unit 10d, an input unit 10e, and a display unit 10f. Each of these configurations is connected to each other via a bus so that data can be transmitted and received. In this example, the case where the information processing apparatus 10 is composed of one computer will be described, but the information processing apparatus 10 may be realized by combining a plurality of computers. Further, the configuration shown in FIG. 2 is an example, and the information processing apparatus 10 may have configurations other than these, or may not have a part of these configurations.

The CPU 10a is a control unit that controls execution of a program stored in the RAM 10b or ROM 10c, calculates data, and processes data. The CPU 10a is a calculation unit that executes a program (information processing program) for solving an optimization problem using a prediction by machine learning and an annealing machine. The CPU 10a receives various data from the input unit 10e and the communication unit 10d, displays the calculation result of the data on the display unit 10f, and stores the data in the RAM 10b.

The RAM 10b is a storage unit capable of rewriting data, and may be composed of, for example, a semiconductor storage element. The RAM 10b may store data such as a program executed by the CPU 10a and parameters of a predicted optimization problem. It should be noted that these are examples, and data other than these may be stored in the RAM 10b, or a part of these may not be stored.

The ROM 10c is a storage unit capable of reading data, and may be composed of, for example, a semiconductor storage element. The ROM 10c may store, for example, an information processing program or data that is not rewritten.

The communication unit 10d is an interface for connecting the information processing device 10 to another device. The communication unit 10d may be connected to a communication network such as the Internet.

The input unit 10e receives data input from the user, and may include, for example, a keyboard and a touch panel.

The display unit 10f visually displays the calculation result by the CPU 10a, and may be configured by, for example, an LCD (Liquid Crystal Display). The display unit 10f may display solution candidates for the optimization problem.

The information processing program may be stored and provided in a storage medium readable by a computer such as RAM 10b or ROM 10c, or may be provided via a communication network connected by the communication unit 10d. In the information processing apparatus 10, the CPU 10a executes an information processing program to realize various operations described with reference to FIG. It should be noted that these physical configurations are examples and do not necessarily have to be independent configurations. For example, the information processing device 10 is an LS in which a CPU 10a and a RAM 10b or a ROM 10c are integrated.
I (Large-Scale Integration) may be provided. Further, the information processing device 10 is a CP.
GPU (Graphical Processing Unit) in place of U10a or in addition to CPU10a
), ASIC (Application Specific Integrated Circuit), F
It may be equipped with a PGA (Field-Programmable Gate Array).

FIG. 3 is a diagram showing a correspondence relationship T1 of qubits set in the annealing machine 30 by the information processing apparatus 10 according to the first embodiment. The information processing apparatus 10 according to the first embodiment calculates solution candidates for a route optimization problem that patrols a plurality of bases. In this example, the plurality of bases are three bases represented by l = 1 to 3, but in general, the number of bases may be 4 or more.

In this embodiment, an example of calculating a solution candidate of a route optimization problem that patrols a plurality of bases will be described, but in general, the optimization problem may be a combinatorial optimization problem related to a plurality of routes. Such optimization problems include the transportation route optimization problem and the traveling salesman problem. Specifically, the number of passengers at multiple bus stops is predicted, and the route through multiple bus stops is used. It includes the problem of finding the optimum, predicting the amount of work related to multiple jobs, and finding the order in which it is best to perform the multiple tasks. In the following, the case of a route optimization problem that goes around a plurality of bases will be described, but by appropriately reading the qubit allocation, the objective function, and the function representing the constraint condition, the information processing apparatus 10 can be used in another combinatorial optimization problem. Can be applied to.

The information processing apparatus 10 sets a qubit in the annealing machine 30 so that all combinations of the base l and the visit order n can be represented. In this example, since the number of bases is three, nine qubits are set and the order of visits is represented by the value of the qubits. For example, l = 0
If you visit the base of l = 1 second, the base of l = 1 first, and the base of l = 2 third, x _{q = 3} = 1, x _{q = 1} = 1, x _{q = 8} = 1 and the other qubits are represented by the value 0.

When finding a solution that visits each base only once, Q is the set of qubits for a certain base l.
The function f ₁ (l), which is expressed as _l and expresses the constraint condition expressed by the following mathematical formula (1), is added to the Hamiltonian.

Further, when the set of qubits related to a certain visit order m is expressed as Q _m , the function f representing the constraint condition expressed by the following mathematical formula (2) in order to exclude the solution that visits two or more bases at once. ₂ (
n) is added to the Hamiltonian.

Then, when the set of qubits for a certain visit order m is expressed as Q _m , the objective function f ₃ (m).
Is expressed by the following mathematical formula (3). Here, cost_time represents the time required to move between the two bases.

The information processing apparatus 10 sets the Hamiltonian including the function representing the constraint conditions of the mathematical formulas (1) and (2) and the objective function of the mathematical formula (3) in the annealing machine 30. Specifically, the Hamiltonian set in the annealing machine 30 by the information processing apparatus 10 according to the present embodiment is represented by the following mathematical formula (4).

The objective function corresponding to the route optimization problem is either the total time required to visit multiple bases, the total travel distance required to visit multiple bases, or the total amount required to visit multiple bases. Represents. In the case of this example, the objective function represents the total time required to visit a plurality of bases.

FIG. 4 shows the travel time T2 between bases predicted by the information processing apparatus 10 according to the first embodiment.
It is a figure which shows. The travel time between bases is an example of cost_time in the formula (3) and is a parameter of the objective function. If the optimization problem is a route optimization problem, the parameter is
Includes either the time required to move between multiple bases, the distance between multiple bases, or the amount of money required to move between multiple bases. Although FIG. 4 shows the travel time between bases, the same applies when the amount of money required for moving between a plurality of bases and the amount of money required for moving between a plurality of bases are parameters.

In the case of this example, the travel time between the bases l = 0 and l = 1 is 2, the travel time between the bases l = 0 and l = 2 is 3, and the travel time between the bases l = 1 and l = 2. The travel time between is 4. These values are
It is a predicted value predicted by the prediction model 12a. The information processing apparatus 10 predicts the travel time between bases and minimizes the objective function using the predicted value as a parameter, so that the optimum patrol route can be calculated according to the change in traffic conditions.

If the objective function is not the total time required to patrol a plurality of bases but the total travel distance required to patrol a plurality of bases, the objective function f ₃ (m) is calculated by the following formula (5). Represent. Here, distance represents the distance between two bases. In this case as well, the Hamiltonian is expressed by the mathematical formula (4).

If the objective function is not the total time required to visit a plurality of bases but the total amount required to visit a plurality of bases, the objective function f ₃ (m) is calculated by the following formula (6). It is represented by. Here, cost represents the amount of money required to visit the two bases. The amount of money required to visit the two bases may be approximated by a value obtained by multiplying the time required to visit the two bases by a predetermined number of times. In this case as well, the Hamiltonian is expressed by the mathematical formula (4).

As described above, according to the information processing apparatus 10 according to the present embodiment, any of the travel time between bases, the distance between bases, and the amount of money required for movement between bases is predicted, and the objective function using the predicted value as a parameter is used. By minimizing, it is possible to calculate the optimum patrol route according to changes in traffic conditions.

The information processing apparatus 10 may predict the base to be visited. In that case, the parameter includes data for extracting a plurality of sites to be visited from a plurality of candidate sites. In this example, the case of visiting three bases is described, but for example, the visiting bases may be narrowed down to three out of the five bases, and the order of visits may be optimized for the three bases. ..
In this way, it is possible to optimize the order of visits after narrowing down the bases to be visited.

FIG. 5 is a diagram showing a constraint condition T3 regarding a visit time set by the information processing apparatus 10 according to the first embodiment. The constraint condition may include a condition regarding the time of arrival at a plurality of bases. In the figure, the arrival target time is shown for the base l = 0 to 2.

Further, when the set of qubits related to a certain visit order k is expressed as Q _k , if it is necessary to satisfy the condition regarding the time of arrival at a plurality of bases, the function f representing the constraint condition expressed by the following mathematical formula (7). Using ₆ (m), add Σ _{m = 0} ² f ₆ (m) to the Hamiltonian. Here, lim
it_time is the arrival target time shown in FIG.

In this way, the route can be optimized so that each base can be visited at the scheduled arrival target time.

FIG. 6 is a flowchart of the route optimization process performed by the information processing apparatus 10 according to the first embodiment. First, the information processing apparatus 10 accepts the designation of the route optimization problem from the user who uses the user terminal 20 (S10).

Further, the information processing apparatus 10 accepts the designation of the constraint condition from the user (S11). Since the constraint conditions include essential conditions and arbitrary conditions, the information processing apparatus 10 may accept the user to select whether or not to specify any of the arbitrary conditions. In the case of the present embodiment, the constraint conditions represented by the mathematical formulas (1) and (2) are indispensable, but the constraint conditions represented by the mathematical formula (7) are arbitrary. You may accept the choice of whether or not to specify the constraint condition represented by 7).

Next, the information processing apparatus 10 predicts the base to be visited and the time required for movement between the bases by the prediction model 12a (S12). The information processing apparatus 10 may predict the distance between bases or the amount of money required for movement between bases by using the prediction model 12a.

After that, the information processing apparatus 10 substitutes the predicted value into the objective function, and sets the Hamiltonian including the objective function and the function representing the constraint condition in the annealing machine 30 (S13). Then, the information processing apparatus 10 sends an instruction to the annealing machine 30 to calculate the ground state of the Hamiltonian, and acquires the ground state of the Hamiltonian from the annealing machine 30 (S).
14).

Finally, the information processing apparatus 10 calculates solution candidates for the optimization problem based on the ground state (
S15). In this way, solution candidates for the route optimization problem can be obtained.

[Second Embodiment]

FIG. 7 shows the annealing machine 30 by the information processing apparatus 10 according to the second embodiment of the present invention.
It is a figure which shows the correspondence relation T4 of the qubit set in. The information processing apparatus 10 according to the second embodiment calculates solution candidates for the shift optimization problem of the staff assigned to the store.

In this embodiment, an example of calculating a solution candidate of a shift optimization problem of staff assigned to a store will be described, but in general, the optimization problem is a combinatorial optimization problem related to scheduling of human resources or physical resources. It's okay. Such optimization problems include job shop scheduling problems, specifically, problems of predicting the number of incoming calls to a call center and optimizing the shift of call center staff, and machines such as manufacturing machines and copy machines. Includes the problem of predicting the busyness of jobs to be executed by and optimizing job scheduling. In the following, the case of the shift optimization problem of the staff assigned to the store will be described, but by appropriately reading the qubit allocation, the objective function, and the function representing the constraint condition, the information processing apparatus 10 can be used in another combinatorial optimization problem. Can be applied to.

In this example, a plurality of staffs (workers) assigned to the group (set) s = 0 are represented by w = 0,1 and a plurality of staffs assigned to the group s = 1 are w = 1. ， ，
There are two people represented by 2. Here, the group is a group by role such as a kitchen group of a restaurant, a cash register group, and a waiter group. Also, in this example, the date (day)
) Is set for 3 days of d = 0 to 2.

The information processing apparatus 10 sets a qubit in the annealing machine 30 so that all combinations of a plurality of staff and working days can be represented. In this example, since a maximum of two staff members are assigned to two groups for three days, 12 qubits are set, and the value of the qubits indicates the group to which each staff member belongs and the working days. For example, day =
At 0, a staff member with w = 1 is assigned to set = 0, a staff member with w = 2 is assigned to set = 1, and d.
At ay = 1, staff with w = 0 at set = 0, staff with w = 1 at set = 1, staff with w = 0 at set = 0 at day = 2, and staff with w = 2 at set = 1. When arranging x _{q = 3} = 1, x _{q = 9} = 1, x _{q = 1} = 1, x _{q = 7} = 1, x _{q = 2} = 1, x _{q = 11}
= 1, the other qubits are represented by the value 0.

When setting the number of people to be assigned to a certain group on a certain day, the set of qubits related to the group s and the date d is expressed as Q _{s, d} , and the objective function f ₁ (s, d) expressed by the following mathematical formula (8).
) To Hamiltonian. Here, max_assign_num is the maximum number of people assigned to the group s and the date d.

The information processing apparatus 10 according to the present embodiment predicts the number of visitors to the store by the prediction model 12a. That is, in the present embodiment, the parameter includes the number of visitors to the store, and the objective function represents at least one of the number of staff and the labor cost of the staff determined based on the number of visitors. For example, the information processing device 10 has max_ based on the prediction of the number of visitors to the store.
Set the loss_num and set the objective function as in the formula (1).

Further, when setting a constraint condition for excluding a solution in which one staff member is placed in a plurality of groups, the set of qubits related to the staff w and the date d is expressed as Q _{w, d} , and the following formula (9) is used. A function f ₂ (w, d) representing the constraint condition represented by is added to the Hamiltonian.

FIG. 8 is a diagram showing a constraint condition T5 regarding a staff's desired vacation set by the information processing apparatus 10 according to the second embodiment. In the figure, the day on which the worker wants to take a vacation is indicated by 1, and the other days are indicated by blanks.

When the information processing apparatus 10 sets a constraint condition for a staff's desired vacation, the information processing apparatus 10 expresses a set of qubits related to the staff and the date for which the desired vacation is set as Q _N , and the constraint expressed by the following mathematical formula (10). Add the conditional function f ₃ to the Hamiltonian.

The information processing apparatus 10 sets the Hamiltonian including the function representing the constraint conditions of the mathematical formulas (9) and (10) and the objective function of the mathematical formula (8) in the annealing machine 30. Specifically, the Hamiltonian set in the annealing machine 30 by the information processing apparatus 10 according to the present embodiment is represented by the following mathematical formula (11).

According to the information processing apparatus 10 according to the present embodiment, the number of visitors to the store is predicted, and by minimizing the objective function using the predicted value as a parameter, the optimum staff shift according to the change in the store visit situation can be performed. Can be calculated.

When the information processing apparatus 10 sets a constraint condition regarding the standard vacation days of the staff, the information processing apparatus 10 expresses the set of qubits related to the staff w as Q _w , and the function f ₄ (representing the constraint condition expressed by the following mathematical formula (12)). Using w), add Σ _{w = 0} ² f ₄ (w) to the Hamiltonian. Here, s
tendard_workday represents the standard number of working days for a staff member.

When the information processing apparatus 10 sets the labor cost of the staff as the objective function, the set of qubits related to the staff w is expressed as Q _w , and the objective function f ₅ (w) expressed by the following mathematical formula (13).
Add Σ _{w = 0} ² f ₅ (w) to the Hamiltonian using. Here, cost represents the labor cost of the staff, and group_num represents the number of groups in which the staff can be assigned.
For example, staff w = 1 can be placed at set = 0,1 so that group_num (
w = 1) = 2.

When the information processing apparatus 10 sets the labor cost of the staff as the objective function, the set of qubits related to the staff w is expressed as Q _w , and the objective function f ₆ (w) expressed by the following mathematical formula (14).
May be added to the Hamiltonian using Σ _{w = 0} ² f ₅ (w). Here, group_
cost represents the labor cost for each group. For example, the labor cost of group s = 0 is set to 2, and the labor cost of group s = 1 is set to 1.

The information processing apparatus 10 expresses a set of qubits related to the staff w, the date d, and the group s as Q _{w, d, s} , and the function f ₇ (w, d) representing the constraint condition expressed by the following mathematical formula (15). , S)
May be used to add Σ _{w = 0} ² Σ _{d = 0} ² Σ _{s = 0} ¹ f ₇ (w, d, s) to the Hamiltonian. The function f ₇ (w, d, s) has a positive value when the same staff is assigned to different groups over two consecutive days. Therefore, by adding Σ _{w = 0} ² Σ _{d = 0} ² Σ _{s = 0} ¹ f ₇ (w, d, s) to the Hamiltonian, if the same staff works for two consecutive days, they will be placed in the same group. The shift is optimized so that.

As such, the constraints may include at least one of the conditions relating to the staff's desired leave and the conditions relating to the staff's working group. With such constraints, it is possible not only to optimize the staffing for the number of customers visiting the store, but also to optimize the shift so as to fulfill the staff's work wishes.

In addition, the constraint condition may include a condition regarding the work interval of the staff. Even with such constraints, it is possible not only to optimize the staffing for the number of customers visiting the store, but also to optimize the shift so as to fulfill the staff's work wishes.

FIG. 9 is a diagram showing a correspondence relationship T6 of qubits set in the annealing machine by the information processing apparatus 10 according to the second embodiment. Correspondence relationship T6 is a specific day (day in this example)
= 1) and for a specific group (set = 0 in this example), time t = 0 ~
Qubits are set in the annealing machine 30 so that all combinations of staff w = 0 to 1 can be represented for 2.

In this example, the time is t = 0, 1, 2 and the staff is w = 0, 1, so 5
One qubit is set, and the value of the qubit represents the working hours of each staff member. For example, staff with w = 1 at time = 0, staff with w = 1 at time = 1, time.
When staffing w = 0 and w = 1 is assigned to = 2, x _{q = 3} = 1, x _{q = 4} = 1, x _{q = 2} =
1, x _{q = 5} = 1, and other qubits are represented by the value 0.

When setting the number of people to be assigned for a certain time, the set of qubits for the time t is expressed as Q _t , and the objective function f ₁ (t) represented by the following mathematical formula (16) is added to the Hamiltonian. Here, assign_num is the number of people assigned with respect to time t.

The information processing apparatus 10 according to the present embodiment predicts the number of visitors to the store by the prediction model 12a. That is, in the present embodiment, the parameter includes the number of visitors to the store, and the objective function represents at least one of the number of staff and the labor cost of the staff determined based on the number of visitors. For example, the information processing apparatus 10 sets the assigned number of people assign_num with respect to the time t based on the prediction of the number of visitors to the store, and sets the objective function as in the mathematical formula (16).

As a constraint condition, the information processing apparatus 10 may set a condition for preventing the working hours of the staff from jumping. The information processing apparatus 10 expresses a set of qubits related to staff w as Q _w , a set of qubits related to staff w and time t as Q _{w, t} , and a constraint condition expressed by the following mathematical formula (17). The representing function f ₂ (w) may be added to the Hamiltonian.

The information processing apparatus 10 sets the Hamiltonian including the function representing the constraint condition of the mathematical formula (17) and the objective function of the mathematical formula (16) in the annealing machine 30. Specifically, the Hamiltonian set in the annealing machine 30 by the information processing apparatus 10 according to the present embodiment is
It is expressed by the following mathematical formula (18).

According to the information processing apparatus 10 according to the present embodiment, the number of store visitors for each time zone is predicted, and the objective function using the predicted value as a parameter is minimized, so that the optimum function is adjusted according to the change in the store visit situation. Staff shifts can be calculated.

When the information processing apparatus 10 sets the labor cost of the staff as the objective function, the set of qubits related to the staff w is expressed as Q _w , and the objective function f ₃ expressed by the following equation (19) or equation (20). Using (w), add Σ _{w = 0} ¹ f ₃ (w) to the Hamiltonian. Here, co
st represents the labor cost of the staff. Further, group_cost represents the labor cost for each group. For example, the labor cost of group s = 0 is set to 2, and the labor cost of group s = 1 is set to 1.

FIG. 10 is a flowchart of the shift optimization process performed by the information processing apparatus 10 according to the second embodiment. First, the information processing apparatus 10 accepts the designation of the shift optimization problem from the user who uses the user terminal 20 (S20).

Further, the information processing apparatus 10 accepts the designation of the constraint condition from the user (S21). Since the constraint conditions include essential conditions and arbitrary conditions, the information processing apparatus 10 may accept the user to select whether or not to specify any of the arbitrary conditions. In the case of this embodiment, the constraint condition represented by the mathematical formula (9) is indispensable, but the mathematical formulas (10), (12), (15) and (
Since the constraint condition represented by 17) is arbitrary, the information processing apparatus 10 uses mathematical formulas (10) and (1).
2), (15) and (17) may be accepted to select whether or not to specify the constraint conditions, respectively.

Next, the information processing apparatus 10 predicts the number of visitors to the store by the prediction model 12a (
S22). The information processing apparatus 10 may predict the distance between bases or the amount of money required for movement between bases by using the prediction model 12a.

After that, the information processing apparatus 10 substitutes the predicted value into the objective function, and sets the Hamiltonian including the objective function and the function representing the constraint condition in the annealing machine 30 (S23). Then, the information processing apparatus 10 sends an instruction to the annealing machine 30 to calculate the ground state of the Hamiltonian, and acquires the ground state of the Hamiltonian from the annealing machine 30 (S).
24).

Finally, the information processing apparatus 10 calculates solution candidates for the optimization problem based on the ground state (
S25). In this way, solution candidates for the route optimization problem can be obtained.

[Third Embodiment]
FIG. 11 is a diagram showing a correspondence relationship T7 of qubits set in the annealing machine by the information processing apparatus 10 according to the third embodiment of the present invention. The information processing apparatus 10 according to the third embodiment calculates solution candidates for a packing optimization problem of packing a load in a container.

In this embodiment, an example of calculating a solution candidate of a packing optimization problem of packing a load in a container will be described, but in general, the optimization problem is a combinatorial optimization problem relating to the packing of a tangible or intangible object having a capacity. It may be there. Such optimization problems include bin-packing problems and knapsack problems, specifically, predicting the workload of multiple jobs and the skills of those who perform the tasks, and assigning multiple jobs to whom. The question of finding the best, predicting the demand for multiple products and the visibility of the shelves, the question of finding the best shelf to display multiple products, and the time zone when multiple advertisements are aired. It involves the question of finding out if it is best to do.
In the following, the case of the packing optimization problem of packing luggage in a container will be described, but by appropriately reading the functions representing the qubit allocation, the objective function, and the constraint condition, the information processing apparatus 10 can be used as another combinatorial optimization problem. Can be applied.

In this example, there are three types in which the container number (container_no) is represented by t = 0 to 2, and the item number (item_no) is represented by i = 0 to 2.

FIG. 12 is a diagram showing a correspondence relationship T8 of qubits set in the annealing machine by the information processing apparatus 10 according to the third embodiment. In this example, the container number (contain)
er_no) There are two types in which the capacity is represented by c = 0,1 for each of t = 0 to 2, and the block is b = 0,1 for each of the item numbers (item_no) i = 0 to 2. There are two types represented.

FIG. 13 is a diagram showing a correspondence relationship T9 of qubits set in the annealing machine by the information processing apparatus 10 according to the third embodiment. In this example, the item number (item_no)
) Numbers num = 0 to 4 are assigned to each of the containers t = 0 to 2 for each of i = 0 to 2.

The information processing apparatus 10 sets a qubit in the annealing machine 30 so that it can represent all combinations in which a plurality of items are loaded in a plurality of containers. In this example, i =
There is one block for the items 1 and 2, and two blocks for the item i = 0. The container with t = 0 and 2 has a capacity of 2 units, and the container with t = 1 has a capacity of 1 unit. For example, a block of b = 0 of an item of i = 0 is packed using the capacity of c = 0 of a container of t = 0, and a block of b = 1 of an item of i = 0 is c = of a container of t = 0. Packed with capacity of 1, b = 0 blocks of i = 1 items packed with c = 0 capacity of t = 1 container, b = 0 blocks of i = 2 items t = When packing using the capacity of c = 0 of 2 containers, z _{p = 7} = 1, z _{p = 13} = 1, z _{p = 19} = 1, z _{p = 22} = 1, and other quantum bits are 0. It is represented by the value. The qubit _{x q} set by the correspondence T7 and the qubit yo set by the correspondence T9 are used as auxiliary _qubits for the qubit zp set by the correspondence T8.

When all items are packed in one of the containers, the set of qubits related to the item i and the block b is expressed as _{Pi, b} , and the objective function f ₁ (i, b) expressed by the following formula (21).
) To Hamiltonian.

The information processing apparatus 10 according to the present embodiment predicts the amount of a plurality of packages by the prediction model 12a. That is, in the present embodiment, the parameter includes a plurality of cargo quantities, and the objective function represents at least one of the allocation of which of the plurality of packages the plurality of packages is to be loaded and the distance between the plurality of packages. .. For example, the information processing apparatus 10 sets the number of blocks for each item (baggage) based on the prediction of the amount of the plurality of baggage, and sets the objective function as in the mathematical formula (21).

Further, when setting a constraint condition for allocating luggage so as not to exceed the capacity limit for each container, the set of qubits related to the item i and the container t is expressed as O _{i, t} and is expressed by the following mathematical formula (22). A function f ₂ (i, t) representing the constraint condition is added to the Hamiltonian.

The qubit _yo is an auxiliary qubit, and since it is directly associated with the qubit _zp that directly represents the allocation of luggage to the container, the function f ₃ (representing the constraint condition expressed by the following equation (23)) (
i, t) and the function f ₄ (i, t) representing the constraint condition expressed by the mathematical formula (24) are added to the Hamiltonian.

Further, when a constraint condition is set so that one load is allocated to the unit capacity of each container, the set of qubits related to the container t and the capacity c is expressed as P _{t, c} , and the following formula (25) is used. A function f ₅ (t, c) representing the represented constraint is added to the Hamiltonian.

The information processing apparatus 10 includes a function representing the constraint conditions of the mathematical expressions (22) to (25) and the mathematical expression (21).
A Hamiltonian containing the objective function of) is set in the annealing machine 30. Specifically, the Hamiltonian set in the annealing machine 30 by the information processing apparatus 10 according to the present embodiment is expressed by the following mathematical formula (26).

According to the information processing apparatus 10 according to the present embodiment, the amount of luggage is predicted, and by minimizing the objective function using the predicted value as a parameter, the optimum packing is calculated according to the change in the amount of luggage to be carried. can do.

When a constraint condition is set using the auxiliary qubit x _q , the set of qubits related to the item i, the container t, and the number n is expressed as O _{i, t, n} , and the constraint condition expressed by the following equation (27). Σ _{i = 0} ² Σ _{t = 0} ² f ₆ (i, t) is added to the Hamiltonian using the function f ₆ (i, t) representing.

When the information processing apparatus 10 sets a constraint condition for reducing the cost of the container, the set of qubits represented by the correspondence relationship T7 is represented by Q, and the constraint condition represented by the following mathematical formula (28) is represented. The function f ₇ may be added to the Hamiltonian. Here, container_c
ost is a predetermined container cost.

As such, the constraint may include at least one of a condition relating to the capacity of each of the plurality of containers and a condition relating to the cost of each of the plurality of containers. This can prevent overloading and optimize the packing of the cargo by reducing the cost of the container.

FIG. 14 shows a distance T10 between luggage set by the information processing apparatus 10 according to the third embodiment.
It is a figure which shows. In the figure, the distance between the luggage with i = 0 and the luggage with i = 1 is 2, and i =
It is shown that the distance between the 0 baggage and the i = 2 baggage is 3 and the distance between the i = 1 baggage and the i = 2 baggage is 4. When loading a plurality of packages in a container, it is desirable that the plurality of packages loaded in one container are placed close to each other because the transportation cost is reduced.

When the information processing apparatus 10 sets a constraint condition for loading a load placed as close as possible to one container, the set of qubits related to the container t is expressed as Q _t and is expressed by the following mathematical formula (29). Σ _{t = 0} ² f ₈ (t) may be added to the Hamiltonian using the function f ₈ (t) representing the constraints. Here, distance is the distance between the luggage shown in FIG.

As such, the constraints may include conditions relating to the distance between the plurality of packages. This is optimized so that a plurality of packages placed close to each other can be loaded in one container, and the transportation cost for transporting the packages to the container is reduced.

When the information processing apparatus 10 sets a constraint condition for loading one type of luggage in the same container as much as possible, the set of qubits related to the item i is expressed as Q _i , and the following formula (3)
Σ _{i = 0} ² f ₉ (i) may be added to the Hamiltonian using the function f ₉ (i) representing the constraint condition represented by 0).

When the information processing apparatus 10 sets a constraint condition for allocating one container for each baggage, the set of qubits related to the item i is expressed as Q _i , and the constraint condition expressed by the following mathematical formula (31) is expressed. Σ _{i = 0} ² f ₁₀ (i) may be added to the Hamiltonian using the represented function f ₁₀ (i).

FIG. 15 is a flowchart of the packing optimization process performed by the information processing apparatus 10 according to the third embodiment. First, the information processing apparatus 10 accepts the designation of the packing optimization problem from the user who uses the user terminal 20 (S30).

Further, the information processing apparatus 10 accepts the designation of the constraint condition from the user (S31). Since the constraint conditions include essential conditions and arbitrary conditions, the information processing apparatus 10 may accept the user to select whether or not to specify any of the arbitrary conditions. In the case of the present embodiment, the constraint conditions represented by the mathematical formulas (22), (23), (24) and (25) are indispensable, but the mathematical formulas (27), (28), (29) and (30) Since the constraint conditions represented by (31) and (31) are arbitrary, the information processing apparatus 10 uses mathematical expressions (27), (28), (29), (30), and (31).
You may accept the choice of whether or not to specify the constraint condition represented by.

Next, the information processing apparatus 10 predicts the amount of luggage by the prediction model 12a (S32).
).

After that, the information processing apparatus 10 substitutes the predicted value into the objective function, and sets the Hamiltonian including the objective function and the function representing the constraint condition in the annealing machine 30 (S33). Then, the information processing apparatus 10 sends an instruction to the annealing machine 30 to calculate the ground state of the Hamiltonian, and acquires the ground state of the Hamiltonian from the annealing machine 30 (S).
34).

Finally, the information processing apparatus 10 calculates solution candidates for the optimization problem based on the ground state (
S35). In this way, solution candidates for the packing optimization problem are obtained.

The embodiments described above are for facilitating the understanding of the present invention, and are not for limiting the interpretation of the present invention. Each element included in the embodiment and its arrangement, material, condition, shape, size, and the like are not limited to those exemplified, and can be appropriately changed. Further, it is possible to partially replace or combine the configurations shown in different embodiments.

10 ... Information processing device, 10a ... CPU, 10b ... RAM, 10c ... ROM, 10d ... Communication unit, 10e ... Input unit, 10f ... Display unit, 11 ... Designation acquisition unit, 12 ... Prediction unit, 12a ... Prediction model, 13 ... setting unit, 14 ... acquisition unit, 15 ... calculation unit, 20 ... user terminal, 30 ... annealing machine

Claims (17)

A prediction unit that predicts the parameters of the optimization problem using a prediction model generated by machine learning,
A setting unit that assigns the parameter to at least one of the objective function and the function representing the constraint condition and sets the Hamiltonian including the objective function and the function representing the constraint condition in the annealing machine.
An acquisition unit that acquires the ground state of the Hamiltonian calculated by the annealing machine from the annealing machine, and
A calculation unit that calculates solution candidates for the optimization problem based on the ground state,
Information processing device equipped with. The setting unit sets the Hamiltonian including the objective function corresponding to the optimization problem specified by the user among the plurality of optimization problems in the annealing machine.
The information processing apparatus according to claim 1. The setting unit sets the Hamiltonian including a function representing the constraint condition specified by the user among the plurality of constraint conditions in the annealing machine.
The information processing apparatus according to claim 1 or 2. The optimization problem is a combinatorial optimization problem for a plurality of routes.
The information processing apparatus according to any one of claims 1 to 3. The optimization problem is a route optimization problem that goes around a plurality of bases.
The parameter includes at least one of the time required to move between the plurality of bases, the distance between the plurality of bases, and the amount of money required to move between the plurality of bases.
The objective function represents one of the total time required to visit the plurality of bases, the total travel distance required to visit the plurality of bases, and the total amount of money required to visit the plurality of bases. ,
The information processing apparatus according to claim 4. The parameter includes data for extracting the plurality of bases from the plurality of candidate bases.
The information processing apparatus according to claim 5. The constraint includes a condition relating to the time of arrival at the plurality of locations.
The information processing apparatus according to claim 5 or 6. The optimization problem is a combinatorial optimization problem relating to scheduling of human resources or physical resources.
The information processing apparatus according to any one of claims 1 to 3. The optimization problem is a shift optimization problem for staff assigned to stores.
The parameter includes the number of visitors to the store.
The objective function represents at least one of the number of staff and the labor cost of the staff, which is determined based on the number of visitors.
The information processing apparatus according to claim 8. The constraint comprises at least one of the conditions relating to the staff's desired leave and the conditions relating to the staff's working group.
The information processing apparatus according to claim 9. The constraint includes a condition relating to the work interval of the staff.
The information processing apparatus according to claim 9 or 10. The optimization problem is a combinatorial optimization problem relating to the packing of a tangible or intangible object having a capacity.
The information processing apparatus according to any one of claims 1 to 3. The optimization problem is a packing optimization problem in which a plurality of packages are loaded in a plurality of containers.
The parameters include the amount of the plurality of packages.
The objective function represents at least one of the allocation of which of the plurality of packages the plurality of packages is to be loaded and the distance between the plurality of packages.
The information processing apparatus according to claim 12. The constraint includes at least one of a condition relating to the capacity of each of the plurality of containers and a condition relating to the cost of each of the plurality of containers.
The information processing apparatus according to claim 13. The constraint includes a condition relating to the distance between the plurality of packages.
The information processing apparatus according to claim 13 or 14. Depending on the processor installed in the information processing device
Predicting the parameters of the optimization problem by the prediction model generated by machine learning,
Substituting the parameter into at least one of the objective function and the function representing the constraint condition, and setting the Hamiltonian containing the objective function and the function representing the constraint condition in the annealing machine.
Obtaining the ground state of the Hamiltonian calculated by the annealing machine from the annealing machine and
To calculate the solution candidates of the optimization problem based on the ground state,
Information processing method to execute. The processor installed in the information processing device,
A prediction unit that predicts the parameters of an optimization problem using a prediction model generated by machine learning.
A setting unit that assigns the parameter to at least one of the objective function and the function representing the constraint condition, and sets the Hamiltonian including the objective function and the function representing the constraint condition in the annealing machine.
An acquisition unit that acquires the ground state of the Hamiltonian calculated by the annealing machine from the annealing machine, and a calculation unit that calculates solution candidates for the optimization problem based on the ground state.
An information processing program that functions as.

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