JP2021189497A - Information processing system, information processing method and program - Google Patents

Abstract

To provide an information processing method which enables a cost function including a non-linear transformation to be usable in a solution search using an annealing machine.SOLUTION: The method includes: means for inputting each object candidate and a cost function into an annealing machine, in which the object candidate performs, for a plurality of objects, processing of inserting a part or the whole of a certain object in a different order, processing of replacing a part or the whole of the certain object with another object, and processing selected from at least one of the replacement of the object with another object and/or order rearrangement; means for obtaining information from the annealing machine on whether or not to execute the processing for each candidate object that the annealing machine determines based on the cost function; and means for determining the cost function based on information indicating whether or not to execute the processing for each object candidate and determining whether or not to execute the processing for each object candidate according to a value of the cost function. The method repeats these pieces of processing.SELECTED DRAWING: Figure 8

Description

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

Quantum annealing is known as a computational technique expected to execute combinatorial optimization processing at high speed and with high accuracy (see, for example, Patent Document 1).

Japanese Unexamined Patent Publication No. 2020-046806

However, quantum annealing machines have the limitation that they can only handle problems up to quadratic functions. Proper use of constraints could allow the use of complex cost functions such as general functions, including non-linear transformations, but the above limitations question the feasibility of that possibility. Was left.

The present invention has been made in view of the above problems, and an object of the present invention is to provide an information processing system, an information processing method, and a program that enable a complicated cost function to be used in a solution search using a quantum annealing machine. ..

The information processing system according to the first aspect of the present invention is a process of inserting a part or all of a certain object in a different order with respect to a plurality of objects, and a part or all of a certain object is another object. For each candidate object and an annealing machine that performs a process selected from at least one of the processes of replacing part or all of, replacing an object with another object, and / or rearranging the order. Information on whether or not to execute processing for each candidate of the object determined by the annealing machine based on the means for inputting the cost function of the object into the annealing machine and the cost function for the annealing machine is obtained from the annealing machine. The target cost function is determined based on the means to be acquired and the information indicating whether or not to execute the process for each of the target object candidates, and each target object candidate is determined according to the value of the target cost function. A means for determining whether or not to execute the process is provided, and the process of the input means, the acquisition means, and the determination means is repeated.

According to this configuration, by separating the target cost function and the cost function for the annealing machine, the cost function for the annealing machine can be used up to the quadratic function, and the target cost function can be complicated such as a function of cubic or higher. Cost function can be used. Further, by causing the information processing system to process the time slot satisfying the constraint condition, the annealing machine can execute the process without worrying about the constraint condition.
can.

The information processing system according to the second aspect of the present invention is the information processing system according to the first aspect, and the means for inputting to the annealing machine is a case where a plurality of types of products are produced on a plurality of production lines. , The process of cutting the time slot of one production line and inserting it into another production line, the process of inserting a part or all of the time slot of a product in one production line into the time slot of another production line, one The process of replacing part or all of the time slots of a product on one production line with part or all of the time slots of a product on another production line, the time slot of each product on one production line and each product on another production line. Each of the candidate objects to perform the process selected from at least one process of the time slot and the rearrangement and / or the rearrangement of the order, and the cost for the annealing machine are input to the annealing machine.

According to this configuration, it is possible to determine a time schedule for producing a plurality of types of products on a plurality of production lines in a shorter time.

The information processing system according to the third aspect of the present invention is the information processing system according to the second aspect, and when the selected process is executed, the process in the previous step is completed. It is executed for the time slot that satisfies the constraint.

This configuration guarantees a contextual constraint that the next step is carried out after the previous step is completed for one product.

The information processing system according to the fourth aspect of the present invention is the information processing system according to the second or third aspect, and the cost function of the object is evaluated as the difference in the end time for each production line is smaller. Contains terms that increase.

According to this configuration, the difference in the end time for each production line can be reduced.

The information processing system according to the fifth aspect of the present invention is the information processing system according to the first aspect, and the means for inputting to the annealing machine is a process of inserting cities in different orders for a plurality of cities. , Each candidate for a city to perform a process selected from at least one of the processes of swapping cities with another city, swapping cities with another city and / or reordering, and the cost for the annealing machine. Enter the function into the annealing machine.

With this configuration, the traveling salesman problem can be solved in a shorter time.

The information processing system according to the sixth aspect of the present invention is the information processing system according to the first aspect, and the means for inputting to the annealing machine is the accommodation facility group for a plurality of accommodation facility groups having different properties. Processing to insert part or all in a different order, processing to replace part or all of accommodations of one nature with part or all of accommodations of another nature, processing to replace accommodations of one nature with another Each of the accommodation candidates that performs the process selected from at least one process of swapping and / or reordering with the property group and the cost function for the annealing machine is input to the annealing machine. ..

According to this configuration, when determining the display order of the plurality of accommodation facility groups so that the plurality of accommodation facility groups are mixed, it can be determined in a shorter time.

The information processing system according to the seventh aspect of the present invention is the information processing system according to any one of the first to the fourth aspects, and the means for determining the above is intended to reduce the target cost function. Case: If the cost function is reduced, the output of the annealing machine is adopted, and if the cost function is not reduced, the output of the annealing machine is not adopted, while the target cost function is intended to be large. If the cost function increases, the output of the annealing machine is adopted, and if the cost function does not increase, the output of the annealing machine is not adopted.

According to this configuration, it is possible to decide whether to adopt or not to adopt the output of the annealing machine.

The information processing method according to the eighth aspect of the present invention is a process of inserting a part or all of a certain object in a different order with respect to a plurality of objects, and a part or all of a certain object is another object. For each candidate object and an annealing machine that performs a process selected from at least one of the processes of replacing part or all of, replacing an object with another object, and / or rearranging the order. Information on whether or not to execute the process for each of the candidate objects determined by the annealing machine based on the process of inputting the cost function of the object to the annealing machine and the cost function for the annealing machine is obtained from the annealing machine. The target cost function is determined based on the process to be acquired and the information indicating whether or not to execute the process for each of the target object candidates, and each target object candidate is determined according to the value of the target cost function. It is an information processing method having a step of determining whether or not to execute a process, and repeating the process of the input step, the acquisition step, and the determination step.

According to this configuration, by separating the target cost function and the cost function for the annealing machine, the cost function for the annealing machine can be used up to the quadratic function, and the target cost function can be complicated such as a function of cubic or higher. Costs can be used. Further, by processing the time slot satisfying the constraint condition, the annealing machine can execute the process without worrying about the constraint condition.

In the program according to the ninth aspect of the present invention, a computer is used to insert a part or all of an object in a different order with respect to a plurality of objects, and a part or all of an object is another object. Each candidate object to perform a process selected from at least one process of replacing part or all of an object, replacing an object with another object, and / or rearranging the order, and an annealing machine. The means for inputting the cost function for the annealing machine to the annealing machine, and the information on whether or not the annealing machine executes processing for each candidate of the object determined based on the cost function for the annealing machine. The target cost function is determined based on the means obtained from the above and the information indicating whether or not to execute the process for each of the target object candidates, and the target object candidate is determined according to the value of the target cost function. It is a program for functioning as a means for deciding whether or not to execute a process for each of them, and is a program for repeating the processes of the input means, the acquisition means, and the determination means.

According to this configuration, by separating the target cost function and the cost function for the annealing machine, the cost function for the annealing machine can be used up to the quadratic function, and the target cost function can be complicated such as a function of cubic or higher. Cost function can be used. Further, by processing the time slot satisfying the constraint condition, the annealing machine can execute the process without worrying about the constraint condition.

According to one aspect of the present invention, by separating the target cost function and the cost function for the annealing machine, the target cost function can be used up to a quadratic function, and the target cost function can be made to be cubic or higher. Complex cost functions such as functions can be used. Further, by processing the time slot satisfying the constraint condition, the annealing machine can execute the process without worrying about the constraint condition.

It is a schematic block diagram of the information processing system which concerns on 1st Embodiment. It is a schematic block diagram of the terminal which concerns on 1st Embodiment. It is a schematic diagram for demonstrating one process which concerns on 1st Embodiment. It is a figure for demonstrating the process of cutting the last time slot of one production line and inserting it into another production line. It is a figure for demonstrating the process of inserting a part or all of the time slot of a product of one production line into the time slot of another production line. It is a figure for demonstrating the process of exchanging a part or all of the time slot of the product of one production line with part or all of the time slot of the product of another production line. It is a figure for demonstrating the time slot of each product of one production line, the time slot of each product of another production line, and / or rearranging the order. It is a flowchart which shows an example of the flow to the process which concerns on 1st Embodiment. In the first embodiment, it is an example of the processing result when two steps are executed. It is a graph which shows the time passage of the target cost function when two steps are executed. In the first embodiment, it is an example of the processing result when four steps are executed. It is a graph which shows the time passage of the target cost function when four steps are executed. In the first embodiment, it is an example of the processing result when six steps are executed. It is a graph which shows the time passage of the target cost function when 6 steps are executed. It is a graph which shows the relationship between the number of processes and the calculation time in 1st Embodiment. It is a schematic diagram which shows the circuit of the initial state in 2nd Embodiment. It is a schematic diagram which shows the circuit after the calculation process in 2nd Embodiment. It is a flowchart which shows an example of the flow to the process which concerns on 2nd Embodiment.

Hereinafter, each embodiment will be described with reference to the drawings. However, more detailed explanation than necessary may be omitted. For example, detailed explanations of already well-known matters and duplicate explanations for substantially the same configuration may be omitted. This is to avoid unnecessary redundancy of the following description and to facilitate the understanding of those skilled in the art.

<First Embodiment>
In addition to the above problems, the first embodiment solves the problem that the quantum annealing machine could not always properly solve the combinatorial optimization problem having constraints.

The first embodiment aims at optimizing a production schedule when a plurality of types of products are produced on a plurality of production lines. In the first embodiment, it is assumed that one or more of a plurality of types of products are produced in a plurality of production lines of a factory. Further, as an example, the production of the present embodiment has a plurality of processes, and there is a restriction that the process cannot proceed to the next process unless the previous process is completed.

FIG. 1 is a schematic configuration diagram of an information processing system according to the first embodiment. As shown in FIG. 1, the information processing system S includes a terminal 1 which is an example of a digital computer as an example. The terminal 1 is connected to the annealing machine 2 via the communication network CN, and can communicate with the annealing machine 2. Here, as an example, the information processing system S is configured by one terminal 1, but the information processing system S is not limited to this, and may be configured by a plurality of information processing devices.

The terminal 1 is a terminal device used by a user, and is, for example, a mobile phone such as a multifunctional mobile phone (so-called smartphone), a tablet, a notebook computer, a desktop personal computer, or the like. For example, an application including a program according to the present embodiment is installed in the terminal 1, and this application is launched, and the terminal 1 executes a process according to a user's operation. Hereinafter, in the present embodiment, the terminal 1 will be described as an example of a desktop personal computer.

The annealing machine 2 is hardware that performs quantum annealing. The annealing machine 2 is, for example, D-Wave, but is not limited to this.

FIG. 2 is a schematic configuration diagram of a terminal according to the first embodiment. As shown in FIG. 2, the terminal 1 includes, for example, an input interface 11, a communication circuit 12, a storage 13, a memory 14, a display 15, and a processor 16.
The input interface 11 receives an input from the user and outputs an input signal corresponding to the received input to the processor 16.
The communication circuit 12 is connected to the communication network CN and communicates with the annealing machine 2 connected to the communication network CN. This communication may be wired or wireless.

The storage 13 stores an application program and various data for the processor 16 to read and execute. This application may be downloaded and installed via a server or the cloud.
The memory 14 temporarily holds data and programs. The memory 14 is a volatile memory, for example, a RAM (Random Access Memory).

The processor 16 loads the program of the application according to the present embodiment from the storage 13 into the memory 14, and executes a series of instructions included in the program.

The display 17 displays information on the display 17 according to the instructions of the processor 16. The display 17 may be built into the terminal 1 instead of being externally attached.

FIG. 3 is a schematic diagram for explaining one step according to the first embodiment. As shown in FIG. 3, there are three production lines in one process, and FIG. 3 shows a process schedule for each production line. _{The work end time t p, i} of the index i of the production line of the process p is (the number of processes of each product × the sum of the processes) + (the sum of the switching times between the products). _{For example, the process time t p = 1, i = 1} of the index i = 1 of the production line of the process p (= 1) in FIG. 3 is, for example, (number of processes of product A 16 × number of processes 100 + number of processes of product E 32). × Processing time 1000 + Number of processing of product C 24 × Processing time 600) + (Switching time from product A to product E 180 + Switching time from product E to product C 220) = 48400 (sec).

In the present embodiment, the target cost function H is as follows as an example.

Here, t _max = max (tp _{, i} ), that is, t _max is the maximum value of _{the work end time t p, i} of the index i of the production line of the process p. j is an index of the production line, and α and β are coefficients to be adjusted as necessary. Here, the purpose is to make the cost function H smaller, and the second term is that the smaller the difference in the end time for each production line, the smaller the cost function H. Here, as an example, there is an empirical rule that the more the end times of each production line are aligned, the shorter the end time of the entire process is. Therefore, the smaller the difference in the end times of each production line, the smaller the cost function H. The second term is set so as to be. That is, as an example, the target cost function H includes a term as the second term, in which the smaller the difference in the end time of each production line, the higher the evaluation.

Subsequently, the process repeatedly performed in the present embodiment will be described with reference to FIGS. 4 to 7. FIG. 4 is a diagram for explaining a process of cutting the last time slot of one production line and inserting it into another production line. As shown in FIG. 4, of the last time slot of the production line of index i, the portion extended from the last time slot of the production line of index j (time of 2C _{p, i, j} ) is cut in half. Then add it to the last time slot of the production line of another index j. As a result, the work end time of the production line of the index i is shortened to t'p _{, i} = _{t'p, i −c p, i, j} q _{p, i, j,} and the work of the production line of another index j is completed. The time is extended to _{t'p, j} = t'p _{, j} + c _{p, j, i} q _{p, i, j.} This has the effect of shortening the overall work completion time.

FIG. 5 is a diagram for explaining a process of inserting a part or all of a time slot of a product on one production line into a time slot of another production line. As shown in FIG. 5, the time slot at the head of the production line of index i is inserted at the break of the production process of another production line of index j. As a result, the work end time of the production line of the index i is shortened to t'p _{, i} = _{t'p, i −c p, i, j} q _{p, i, j,} and the work of the production line of another index j is completed. The time is extended to _{t'p, j} = t'p _{, j} + c _{p, j, i} q _{p, i, j.}

FIG. 6 is a diagram for explaining a process of replacing a part or all of a product time slot of one production line with a part or all of a time slot of a product of another production line. As shown in FIG. 6, the head time slot of the production line of the index i and the last time slot of the production line of another index j are exchanged. As a result, for example, the work end time of the production line of the index i is changed to t'p _{, i} = _{t'p, i −c p, i, j} q _{p, i, j,} and the work of the production line of another index j is changed. The end time is changed to _{t'p, j} = t'p _{, j} + c _{p, j, i} q _{p, i, j.} Here, let the time of the head of the production line of the index i before replacement be _{ap, i, j} , and the time of the head of the production line of the index i after replacement be b _{p, i, j.} , C _{p, i, j} = a _{p, i, j} − b _{p, i, j} . Similarly, let the time of the last time slot of the production line of the index j before replacement be _{ap, i, j} , and the time of the last time slot of the production line of the index j after replacement be b _{p, i, j.} , C _{p, j, j} = a _{p, i, j} − b _{p, i, j} .

FIG. 7 is a diagram for explaining the time slot of each product on one production line and the time slot of each product on another production line, and / or rearranging the order. As shown in FIG. 7, the last time slot of the production line of index i and the last time slot of another production line of index j are exchanged, and then the beginning and last time slots of the production line of index i are exchanged. , Swap the first and last time slots of the production line of another index j. As a result, for example, the work end time of the production line of the index i is changed to t'p _{, i} = _{t'p, i −c p, i, j} q _{p, i, j,} and the work of the production line of another index j is changed. The end time is changed to _{t'p, j} = t'p _{, j} + c _{p, j, i} q _{p, i, j.} Here, if the work end time of the index i production line before replacement is _{ap, i, j} and the work end time of the index i production line after replacement is b _{p, i, j} , c _{p, i, j} = a _{p, i, j} − b _{p, i, j} . Similarly, if the work end time of the production line of the index j before the replacement is _{ap, i, j} and the work end time of the production line of the index j after the replacement is b _{p, i, j} , c _{p, j, j} = a _{p, i, j} − b _{p, i, j} .

Subsequently, an example of the flow in the process according to the first embodiment will be described. FIG. 8 is a flowchart showing an example of the flow in the process according to the first embodiment.

(Step S10) The processor 16 of the terminal 1 functions as a means for inputting to the annealing machine. The means of inputting to the annealing machine is the process of cutting the last time slot of one production line and inserting it into another production line when producing multiple types of products on multiple production lines, one production line. The process of inserting part or all of the time slot of one product into the time slot of another production line, part or all of the time slot of a product of one production line is one of the time slots of the product of another production line. Executes the process of replacing with a part or all, the process of replacing the time slot of each product on one production line with the time slot of each product of another production line, and / or the process selected from at least one of the sort of order. Determine one or more candidates for the target.

The selection of this process may be selected automatically according to the order in which the order of each process is determined in advance, or may be random.

(Step S20) The processor 16 of the terminal 1 is a cost function for the annealing machine.
The target candidate for executing the selected process is transmitted to the annealing machine 2.

In this way, the processor 16 of the terminal 1 functions as a means for inputting to the annealing machine. The means of inputting to the annealing machine is the process of cutting the last time slot of one production line and inserting it into another production line when producing multiple types of products on multiple production lines, one production line. The process of inserting part or all of the time slot of one product into the time slot of another production line, part or all of the time slot of a product of one production line is one of the time slots of the product of another production line. Target to execute the process of replacing with a part or all, the time slot of each product of one production line and the time slot of each product of another production line, and / or the process selected from at least one of order rearrangement. The candidate of the object and the cost function for the annealing machine are input to the annealing machine 2.

In this embodiment, there is a constraint that the next step cannot be carried out unless the previous step is completed for one product. Therefore, when the selected process is executed, it is executed for the time slot that satisfies the constraint that the process in the previous step is completed. This guarantees the contextual constraint that the next process is carried out after the previous process is completed for one product. This constraint condition is considered on the processor 16 side of the terminal 1, and does not need to be considered on the annealing machine 2.

A cost function for annealing is set in the annealing machine separately from the target cost function. The cost function for annealing may be the same when the target cost function is represented by a quadratic function or less. On the other hand, as the cost function for annealing, another cost function may be set when the target cost function is represented by a non-linear function such as a third order or higher. In the present embodiment, the cost function for annealing is also described as being the sum of the second term and the third term of the target cost function.

(Step S30) The annealing machine 2 uses the cost function for the annealing machine to output whether or not to execute the process for each of the target candidates for executing the selected process.

(Step S30) The annealing machine 2 transmits information indicating whether or not to execute the process for each of the target candidates to the terminal 1.

Then, the processor 16 of the terminal 1 obtains information from the annealing machine 2 indicating whether or not to execute the process for each of the target candidates, which is determined by the annealing machine 2 based on the cost function for the annealing machine. Functions as.

(Step S50) When the processor 16 of the terminal 1 receives information indicating whether or not to execute the process for each of the target candidates, it is based on the information indicating whether or not to execute the process for each of the target candidates. Therefore, it functions as a means for determining a target cost function and determining whether or not to execute processing for each target candidate according to the value of the target cost function.

Here, as in the present embodiment, when the target cost function is to be reduced, the determination means adopts the output of the annealing machine if the cost function is reduced, and the cost function is reduced. Otherwise, the output of the annealing machine will not be adopted.

When the purpose is to increase the target cost function, the means for determining the cost function adopts the output of the annealing machine if the cost function increases, and if the cost function does not increase, the determining means of the annealing machine. The output may not be adopted.

(Step S60) The processor 16 of the terminal 1 determines whether or not it has been repeated a predetermined number of times, and if it has not been repeated a predetermined number of times, returns to step S10 and repeats the process. On the other hand, when it is repeated a predetermined number of times, the processor 16 of the terminal 1 ends the processing of this flowchart.

FIG. 9 is an example of the processing result when the two steps are executed in the first embodiment. As shown in FIG. 9, each time slot is filled with almost no gap in the manufacturing process, and the end time is 41860 [sec]. FIG. 10 is a graph showing the passage of time of a target cost function when two steps are executed. The execution time is 45.9 seconds for 10000 MCS, and the minimum solution is almost reached at 5000 MCS.

FIG. 11 is an example of the processing result when the four steps are executed in the first embodiment. As shown in FIG. 11, each time slot is assigned in the manufacturing process, and the end time is 51880 [sec]. FIG. 12 is a graph showing the passage of time of the target cost function when the four steps are executed. The execution time is 101.86 seconds for 10000 MCS.

FIG. 13 is an example of the processing result when the six steps are executed in the first embodiment. As shown in FIG. 13, each time slot is assigned in the manufacturing process, and the end time is 65380 [sec]. FIG. 14 is a graph showing the passage of time of the target cost function when the six steps are executed. The execution time is 148.92 seconds for 10000 MCS.

FIG. 15 is a graph showing the relationship between the number of processes and the calculation time in the first embodiment. As shown in FIG. 15, the calculation time increases linearly as the number of processes increases.

As described above, the information processing system S according to the first embodiment cuts the time slot of one production line (for example, the time slot of the latter half of a certain product) when a plurality of types of products are produced on a plurality of production lines. The process of inserting into another production line, the process of inserting part or all of the time slot of a product in one production line into the time slot of another production line, the process of inserting a part of the time slot of a product in one production line. Or the process of replacing all of them with some or all of the time slots of products on another production line, replacing the time slots of each product on one production line with the time slots of each product on another production line, and / or ordering. Each of the target candidates for executing the process selected from at least one of the alternative processes and the cost function for the annealing machine are input to the annealing machine. Further, the information processing system S includes means for acquiring information from the annealing machine indicating whether or not to execute processing for each of the target candidates, which is determined by the annealing machine based on the cost function for the annealing machine. Further, the information processing system S determines a target cost function based on the information indicating whether or not to execute the process for each of the target candidates, and the target candidate is determined according to the value of the target cost function. A means for deciding whether or not to execute the process for each is provided. The information processing system S repeats the processing of the input means, the acquisition means, and the determination means.

With this configuration, it is possible to determine a time schedule for producing a plurality of types of products on a plurality of production lines in a shorter time. In addition, by separating the target cost function and the cost function for the annealing machine, the cost function for the annealing machine can be used up to a quadratic function, and the target cost function can be used as a general function including a non-linear transformation such as a third-order or higher function. Functions can be used. Further, by causing the information processing system S to perform processing on a time slot satisfying the constraint condition, the annealing machine can execute the processing without worrying about the constraint condition.

Although the case where the manufacturing is a plurality of steps has been described in the first embodiment, the same can be applied even if the manufacturing is a single step.

<Second embodiment>
Subsequently, the second embodiment will be described. The first embodiment aims at optimizing the production schedule when a plurality of types of products are produced on a plurality of production lines. The second embodiment aims to solve the traveling salesman problem. The traveling salesman problem is that given the set of cities and the cost of traveling between each of the two cities (here, for example, the distance), the total travel cost of the traveling circuit that goes around all the cities exactly once and returns to the starting point. It is a combinatorial optimization problem that finds the smallest one (finds the shortest route when a salesman makes a round trip to a plurality of predetermined cities only once).

In this embodiment, it is assumed that there are cities from 0 to 23 as an example. In this case, the target cost function and the cost function for annealing are the same, which is the total distance traveled. The second embodiment has different constraints from the first embodiment, and the second embodiment also has the constraint that a specific city must be visited at a specific timing. May be good. This constraint condition is considered on the processor 16 side of the terminal 1, and does not need to be considered on the annealing machine 2.

As a processing step, for example, the processor 16 of the terminal 1 prepares 0 and 1 whether or not to switch the city to be visited in the Xth place and the city to be visited in the Yth place with respect to the visit order in the initial state. , The annealing machine decides whether to adopt the replacement of the Xth visited city and the Yth visited city, and the processor 16 of the terminal 1 adopts it if the total travel distance is shortened as a result of adoption. , Do not adopt if the total travel distance is long.

Further, in the second embodiment, the means for inputting to the annealing machine is a process of inserting a certain object (here, a city) in a different order for a plurality of objects (here, a city), and a certain object (here, here). At least one process of replacing an object (here a city) with another object (here a city), replacing an object (here a city) with another object (here a city) and / or rearranging the order. Input each candidate of the object to execute the process selected from and the cost function for the annealing machine into the annealing machine.

FIG. 16 is a schematic diagram showing a circuit in an initial state in the second embodiment. As shown in FIG. 16, each city is shown with a number and the route is shown by a solid line. The circuit in the initial state is randomly determined.

FIG. 17 is a schematic diagram showing a circuit after calculation processing in the second embodiment. As shown in FIG. 17, each city is connected by a solid line so that the total travel distance is the shortest.

<Processing contents of digital computer including cut &flip>
The processing contents of the digital computer including cut and flip will be described below with three usage examples.

(1) Simple usage example In the traveling salesman problem, when the number of the visited city is assigned as 1, 2, 3, 4, 5, the answer is given by the order combination of the numbers. For example, "5, 2, 3, 1, 4" is the answer. In this case, going around the city in the order of 5, 2, 3, 1, 4 means that the total travel distance becomes the shortest. Here, one city such as "1" or "2" may be cut and the cut cities may be exchanged (flip), or a plurality of consecutive cities such as "5, 2" and "1, 4" may be used. You may cut and swap (flip) multiple cut cities. Prepare an even number of this cut. That is, prepare multiple city candidates to be replaced. Flip is the swapping of these cut cities.

In the case of "5, 2, 3, 1, 4", the cut candidates (that is, the city candidates to be replaced) are "2" and "1" (however, the city candidates to be replaced are not adjacent to each other and are separated from each other. Condition), if the output value of the annealing machine is 0, it means that "2" and "1" remain (the result is "5, 2, 3, 1, 4"), and the output value of the annealing machine is 1. In the case of, it means to change to "1" and "2" (the result is "5, 1, 3, 2, 4").
The terminal 1, which is an example of a digital computer, executes a process of proposing a candidate to be cut (that is, a candidate for a city to be replaced). Then, the terminal 1 compares the increase / decrease of the target cost function when the candidates to be cut (that is, the candidates of the cities to be replaced) are replaced.

Prepare a cost function for the annealing machine based on the candidate of the city to be replaced and the increase / decrease proposed in the above procedure. Specifically, a cost function of ΔEi × Σi is prepared for the numerical value ΔEi indicating whether the cost increases or decreases when the i-th pair of city candidates to be exchanged is exchanged (flip). This Σi is a binary variable that takes 0 and 1. Add this term by the number of pairs and solve the problem of minimizing the sum with an annealing machine. In the case of the traveling salesman problem, since it is a term that is independently determined for each pair i, if ΔEi is negative for each pair i, Σi is set to 1 to minimize the cost function.

(2) Slightly advanced usage example In the above usage example, processing can also be performed by considering candidates to be cut independently (that is, candidate cities to be replaced) and determining whether or not to adopt them.
However, in this method, there is an option to design a cost function for the city candidates to be replaced more flexibly, and the interaction between the city candidates to be replaced, for example, the cut is adjacent, stepping from the above example avoiding continuous cuts. In order to match, the cost function is not determined independently in the replacement, it cannot be written as ΔEi, and it has a quadratic term called ΔEijΣiΣj (one is adopted (Σi = +1), but the other is not adopted (Σj). = 0), it is also possible to prepare a cost function in consideration of the case where both are adopted (Σi = Σj = + 1), etc.).

(3) Advanced usage example Similarly, when there is a route such as "8,2,5,3,6,4,7,1", as a city candidate to be replaced, "5,3,6,4" etc. You may extract four consecutive cities. The replacement of cities inside this cut is 4! It's a street, but this 4! You can also swap (flip) the city lines to the best one on the street. In that case, 4! It can be a cost function to get the best out of the street (this is the conventional traveling salesman problem, a cost function excluding the condition of traveling).
At that time, the following cost function E (x) is used by removing the traveling condition from the conventional traveling salesman problem.

Here sigma _i is the binary variable 0 or 1, between points (i, j) the distance d _ij between, paragraph, and for imposing a constraint paragraph to always visit once at different timings It is a term. N is the total number of cities that can be visited. t is an index representing the time, and T is equal to the number N of points to be considered. Further, σ _{i and t} are information of 0 and 1 indicating whether or not the i point is visited at time t, and λ is the strength of the coercive force satisfying the constraint condition. Thus, the cost function for annealing and / or the cost function of interest includes a parameter representing the distance between cities.

Hereinafter, an example of the flow in the process according to the second embodiment will be described with reference to FIG. FIG. 18 is a flowchart showing an example of the flow in the process according to the second embodiment. Here, as an example, the above simple usage example will be described as a premise.

(Step S110) The processor 16 of the terminal 1 receives information regarding the traveling salesman problem. Information about the traveling salesman problem here includes places to visit (eg, cities), location coordinates, distance information between places, and the like.

(Step S120) The processor 16 of the terminal 1 sets the initial value of the answer. Here, the initial value of the answer is represented by order data such as "1, 2, 3, 4, 5, 6, 7, 8". The initial value of the answer may be predetermined or may be set by a random number.

(Step S130) The processor 16 of the terminal 1 determines a candidate for a city pair to be replaced.

(Step S140) The processor 16 of the terminal 1 transmits a cost function for the annealing machine and a candidate for a city pair to be replaced. Here, the cost function for the annealing machine is set in the terminal 1 according to the above-mentioned simple usage example, a slightly advanced usage example, and an advanced usage example. The cost function for this annealing machine is, for example, a coefficient value applied to a matrix of a quadratic form (QUAdratic Unconstrained Binary Optimization) form necessary for the use of quantum annealing.

(Step S150) The annealing machine 2 performs optimization of the cost function for the annealing machine.

(Step S160) The annealing machine 2 transmits to the terminal 1 information on whether or not to replace the candidate city pair obtained by executing step S150. Here, the information on whether or not to replace the city pair is 0 or 1 information. This is also the case with a slightly advanced use case.

In the case of an advanced usage example, the information transmitted from the annealing machine 2 to the terminal 1 in this step 160 is, for example, only data of 0 and 1, but it is for "5, 3, 6, 4". For example, it is 0 or 1 information indicating in what order the replacement is performed. For example, in the case of [[0,0,0,1], [0,0,1,0], [1,0,0,0], [0,1,0,0]], the fourth and third It means that the second, first, and second numbers are rearranged in this order. For example, the order of the original numbers is "5, 3, 6, 4" (the first is 5, the second is 3, and the third is. In the case of 4), the sixth and fourth are matrix data consisting of 0 and 1 meaning to sort from "5, 3, 6, 4" to "4, 6, 5, 3".

(Step S170) The processor 16 of the terminal 1 is adopted when the target cost function (or energy) is lowered when the cities are replaced based on the information on whether to replace the city candidates. Even if the processor 16 of the terminal 1 raises the target cost function (or energy), it is determined to be adopted or not adopted by a probabilistic standard (for example, Markov chain Monte Carlo method).

(Step S180) The processor 16 of the terminal 1 determines whether or not the termination condition is satisfied. If the end condition is not satisfied, the process returns to step S130 and the process is repeated. When the termination condition is satisfied, the processor 16 of the terminal 1 ends the processing of this flowchart.

<Third embodiment>
Subsequently, the third embodiment will be described. In the second embodiment, the purpose is to solve the traveling salesman problem, but in the third embodiment, the listing of the business hotel group and the listing of the resort hotel group are mixed on the WEB page. With the goal.

The target cost function and the cost function for the annealing machine are set to the following cost function E (x) by using _{the similarity degree dij of the i-th and j-th hotels.} The third and fourth terms are necessary for each hotel to be displayed only once in each order.

Where N is the total number of hotels. h _i is the favorability of the i-th hotel, σ _{i, t} is the value of 0 or 1 indicating whether hotel i is selected for the list order (posting order) t on the WEB page, the third term and the fourth term. The term is a constraint term for answering one hotel in which one is always selected and in what order, and λ is the strength of the coercive force that satisfies the constraint condition. T is the total number of hotels listed. In addition, h _i may indicate the ranking of the i-th hotel. When the cost function E (x) becomes smaller, the annealing machine and the information processing system adopt the execution of the selected process. Thus, the cost function for annealing and / or the cost function of interest includes at least one of a parameter representing hotel similarity and a parameter representing hotel favorability and / or ranking.

In this case, in the third embodiment, the means for inputting to the annealing machine is a part or all of a certain object (for example, a business hotel group) for a plurality of objects (here, a business hotel group and a resort hotel group). Processing to insert in different order, processing to replace part or all of one object (for example, business hotel group) with part or all of another object (for example, resort hotel group), object (for example, business hotel group) Swap with another object (eg, resort hotel group) and / or perform a process selected from at least one process of the order, and a cost function for the annealing machine. Input to the annealing machine 2. Here, the business hotel group and the resort hotel group have been described as an example of a plurality of accommodation facilities having different properties (or types), but the present invention is not limited to this, and is applied to, for example, an inn group and a hotel group. It may be applicable to a plurality of accommodation facilities having different properties (or types).

The information processing system S described in the above-described embodiment has described an example of one terminal, but the present invention is not limited to this, and the information processing system S may be made to function by a plurality of information processing devices. In this case, at least a part of the information processing system S may be configured by hardware or software. When configured by software, a program that realizes at least a part of the functions of the information processing system S may be stored in a recording medium such as a flexible disk or a CD-ROM, read by a computer, and executed. The recording medium is not limited to a removable one such as a magnetic disk or an optical disk, and may be a fixed recording medium such as a hard disk device or a memory.

Further, a program that realizes at least a part of the functions of the information processing system S may be distributed via a communication line (including wireless communication) such as the Internet. Further, the program may be encrypted, modulated, compressed, and distributed via a wired line or a wireless line such as the Internet, or stored in a recording medium.

As described above, the present invention is not limited to the above embodiment as it is, and at the implementation stage, the components can be modified and embodied within a range that does not deviate from the gist thereof. In addition, various inventions can be formed by an appropriate combination of the plurality of components disclosed in the above-described embodiment. For example, some components may be removed from all the components shown in the embodiments. Further, components over different embodiments may be combined as appropriate.

1 Terminal 11 Input interface 12 Communication circuit 13 Storage 14 Memory 15 Display 16 Processor 17 Camera 2 Annie ring machine S Information processing system

Claims (9)

For multiple objects, the process of inserting part or all of one object in a different order, the process of replacing part or all of one object with part or all of another object, and the process of replacing an object with another. A means of inputting into the annealing machine a cost function for the annealing machine, each candidate for the object to perform the process selected from at least one process of swapping with the object and / or rearranging the order.
A means for obtaining information from the annealing machine as to whether or not to execute processing for each candidate of the object, which is determined by the annealing machine based on the cost function for the annealing machine.
The target cost function is determined based on the information indicating whether or not to execute the process for each of the candidate objects, and the process is executed for each of the candidate objects according to the value of the target cost function. As a means of deciding whether or not
Equipped with
An information processing system that repeats the processing of the input means, the acquisition means, and the determination means. The means for inputting to the annealing machine is a process of cutting a time slot of one production line and inserting it into another production line when producing a plurality of types of products on a plurality of production lines, and there is one production line. The process of inserting part or all of a product time slot into a time slot of another production line, part or all of a product time slot of one production line, or part or all of a product time slot of another production line. Performs a process selected from at least one process of replacing all, replacing the time slot of each product on one production line with the time slot of each product on another production line, and / or rearranging the order. The information processing system according to claim 1, wherein each candidate of an object and a cost function for the annealing machine are input to the annealing machine. The information processing system according to claim 2, wherein when the selected process is executed, the information processing system is executed for a time slot that satisfies the constraint that the process in the previous step is completed. The information processing system according to claim 2 or 3, wherein the cost function of the object includes a term in which the evaluation becomes higher as the difference in the end time for each production line becomes smaller. The means of inputting to the annealing machine is one of the processes of inserting cities in different orders, swapping cities with different cities, swapping cities with different cities, and / or rearranging the order of multiple cities. The information processing system according to claim 1, wherein each candidate of a city that executes a process selected from at least one process and a cost function for the annealing machine are input to the annealing machine. The means for inputting to the annealing machine is a process of inserting a part or all of the accommodation group in a different order for a plurality of accommodation groups having different properties, and a process of inserting a part or all of the accommodation group of a certain property into another. A process selected from at least one process of replacing part or all of a group of accommodations of a nature, replacing an accommodation group of one property with an accommodation group of another property, and / or rearranging the order. The information processing system according to claim 1, wherein each candidate of an accommodation facility to be executed and a cost function for the annealing machine are input to the annealing machine. When the purpose of the determination means is to reduce the target cost function, the output of the annealing machine is adopted if the cost function is reduced, and the output of the annealing machine is adopted if the cost function is not reduced. On the other hand, when the purpose is to increase the target cost function, the output of the annealing machine is adopted if the cost function increases, and the output of the annealing machine is not adopted unless the cost function increases. The information processing system according to any one of claims 1 to 4. For multiple objects, the process of inserting part or all of one object in a different order, the process of replacing part or all of one object with part or all of another object, and the process of replacing an object with another. A process of inputting into the annealing machine a cost function for the annealing machine and each candidate of the object to execute the process selected from at least one process of swapping with the object and / or rearranging the order.
A process of acquiring information from the annealing machine as to whether or not to execute processing for each candidate of the object, which is determined by the annealing machine based on the cost function for the annealing machine.
The target cost function is determined based on the information indicating whether or not to execute the process for each of the candidate objects, and the process is executed for each of the candidate objects according to the value of the target cost function. The process of deciding whether or not
Have,
An information processing method that repeats the processes of the input step, the acquisition step, and the determination step. Computer,
For multiple objects, the process of inserting part or all of one object in a different order, the process of replacing part or all of one object with part or all of another object, and the process of replacing an object with another. A means of inputting into the annealing machine a cost function for the annealing machine, each candidate for the object to perform the process selected from at least one process of swapping with the object and / or rearranging the order.
A means for obtaining information from the annealing machine as to whether or not to execute processing for each candidate of the object, which is determined by the annealing machine based on the cost function for the annealing machine.
The target cost function is determined based on the information indicating whether or not to execute the process for each of the candidate objects, and the process is executed for each of the candidate objects according to the value of the target cost function. As a means of deciding whether or not
It is a program to function as
A program that repeats the processing of the input means, the acquisition means, and the determination means.

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