Information processing device, information processing method, program

Abstract

The problem of the time required to solve a constrained combinatorial optimization problem becoming excessively long. [Solution] The information processing device of the present disclosure comprises a search unit that searches for solutions to variables included in an optimization problem, a state recording unit that records changes in the state of variables during the solution search process, and a constantization unit that converts the variables included in the optimization problem into constants based on the changes in state, wherein the search unit performs a solution search for the optimization problem in the state in which the variables have been converted into constants.

Description

[Technical Field]

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

[0002] As a method for solving real-world problems, the energy in combinatorial optimization problems is being converted into the form of an Ising model and then solved. For example, the energy of an optimization problem is being formulated in the form of QUBO (Quadratic Unconstrained Binary Optimization), and then solved using simulated annealing.

[0003] However, in combinatorial optimization problems, as the problem scale increases, the number of solution states becomes enormous, and solving the problem can take a long time. On the other hand, in some cases, it is possible to fix some of the variables in the problem. For example, Patent Document 1 describes solving the problem by fixing binary variables in various patterns. [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] Japanese Patent Publication No. 2021-131723 [Overview of the project] [Problems that the invention aims to solve]

[0005] However, as described in Patent Document 1, even when some variables are fixed in a combinatorial optimization problem, there are still many fixed patterns, and the problem persists that the solution time is prolonged.

[0006] Therefore, one of the purposes of this disclosure is to solve the aforementioned problem of prolonged solution times in constrained combinatorial optimization problems.

Means for Solving the Problem

[0007] An information processing apparatus according to one embodiment of the present disclosure includes a search unit that searches for solutions to variables included in an optimization problem, a state recording unit that records state changes of variables during the solution search, a constant conversion unit that converts variables included in the optimization problem into constants based on the state changes, and the search unit performs solution search for the optimization problem in a state where variables are converted into constants. It has such a configuration. Also, an information processing method according to one embodiment of the present disclosure searches for solutions to variables included in an optimization problem, records state changes of variables during the solution search, converts variables included in the optimization problem into constants based on the state changes, and performs solution search for the optimization problem in a state where variables are converted into constants. It has such a configuration. Also, a program according to one embodiment of the present disclosure causes an information processing apparatus to search for solutions to variables included in an optimization problem, record state changes of variables during the solution search, convert variables included in the optimization problem into constants based on the state changes, and perform solution search for the optimization problem in a state where variables are converted into constants. It causes the above processing to be executed. It has such a configuration.

Advantages of the Invention

[0008] With the present disclosure configured as described above, it is possible to suppress the lengthening of the solution time in the combinatorial optimization problem.

Brief Description of the Drawings

[0009] [Figure 1] It is a block diagram showing an example of the configuration of an information processing apparatus according to the present disclosure. [Figure 2] This flowchart shows an example of the processing operation of the information processing device related to this disclosure. [Figure 3] This figure shows an example of the processing process of the information processing device related to this disclosure. [Figure 4] This block diagram shows an example of the hardware configuration of the information processing device related to this disclosure. [Figure 5] This is a block diagram showing an example of the configuration of the information processing device related to this disclosure. [Modes for carrying out the invention]

[0010] <First Embodiment> A first embodiment of this disclosure will be described with reference to the drawings. The drawings may be relevant to any embodiment.

[0011] [composition] The information processing device 10 of this disclosure is used, as an example, to solve a pre-set combinatorial optimization problem with constraints using pseudo-quantum annealing (simulated annealing). Here, an example of a method for solving a combinatorial optimization problem with constraints using pseudo-quantum annealing will be described.

[0012] A constrained combinatorial optimization problem is one in which an objective function and constraints are set, and the goal is to find a solution that minimizes the objective function while satisfying the constraints. Furthermore, as shown in equations 1 and 2, a constrained combinatorial optimization problem can be transformed into a formalized model, such as the Ising model or the QUBO (Quadratic Unconstrained Binary Optimization) model. In this case, as shown in equation 1, the energy value E of the optimization problem can be expressed using objective function terms (terms 1 and 2) and constraint terms (terms 3 and 4), and as shown in equation 2, these can be combined into a single model.

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[0013] Here, in the above equation, s i ,s j is, spin s i ,s j This is a variable representing the state, and is expressed as "-1" or "1", or "0" or "1". In this embodiment, the optimization problem is converted to a QUBO model, and the states of spins i and j are described as being represented as "0" or "1". i and j are the identification numbers of spin s. Also, W in the above equation 2. ij is, spin s i ,s j These are weight parameters set for each combination, and will be referred to as the QUBO matrix below.

[0014] Furthermore, when searching for the spin with the minimum energy E in the aforementioned constrained combinatorial optimization problem using pseudo-quantum annealing, the state of spin s flips from 0 to 1, or from 1 to 0, to transition the solution during the search. In this case, pseudo-quantum annealing always transitions when the evaluation value of the neighboring solutions is good (small), but it can also probabilistically transition even when the evaluation value of the neighboring solutions is poor (large). The probability in this case is determined by the inverse temperature, which is the reciprocal of the value of the temperature parameter, so the information processing device 10 searches for the solution while raising or lowering the inverse temperature.

[0015] Next, an example of the configuration and operation of the information processing device 10 in this embodiment will be described in detail. Figure 1 shows an example of the configuration of the information processing device 10, and Figure 2 shows an example of the operation of the information processing device 10. The information processing device 10 is composed of one or more information processing devices equipped with an arithmetic unit and a storage device. As shown in Figure 1, the information processing device 10 includes a search processing unit 11 and a fixed processing unit 12. The functions of the search processing unit 11 and the fixed processing unit 12 can be realized by the arithmetic unit executing a program for realizing each function stored in the storage device. The information processing device 10 also includes a problem storage unit 15 realized in the storage device.

[0016] The problem memory unit 15 stores information representing a constrained combinatorial optimization problem that is to be solved. One example of a constrained combinatorial optimization problem is the traveling salesman problem. The traveling salesman problem is an optimization problem in which, given the distances between cities, a salesman must visit each city exactly once, and find the route with the minimum travel distance.

[0017] In this embodiment, a constrained combinatorial optimization problem (hereinafter also referred to as the optimization problem), consisting of an objective function and constraints as shown in the following three equations, is set up and stored in the problem storage unit 15.

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[0018] Furthermore, the problem memory unit 15 is equipped with a state memory area, which is a memory area for storing the changes in the state of variables during the process of searching for a solution to the optimization problem, as will be described later. The state memory area is configured to store the state of each variable at each time step, i.e., the state of the solution, and a counter representing the number of times each variable has been changed, as will be described later.

[0019] The search processing unit 11 (search unit, state recording unit) initializes the state memory area (step S1 in FIG. 2) and searches for solutions to the variables included in the optimization problem (step S2 in FIG. 2). For example, the search processing unit 11 performs solution search by the simulated annealing described above. And in the process of solution search, the search processing unit 11 stores in the state memory area the state of each variable at each time, that is, the state of the solution, and a counter representing the number of changes of each variable. Here, an example of the data recorded in the state memory area is shown in FIG. 3. In the example of FIG. 3, at time "0", the state of each variable (x i ) (x1, x2, ···, x n ) that is, the state of the solution is "01101···00101", and at time "1", the state of each variable (x i ) that is, the state of the solution is "11001···00101". And when the time elapses from time "0" to time "1", the first variable x1 changes from "0" to "1", and the third variable x3 changes from "1" to "0". Therefore, the number of changes of the first variable and the third variable is incremented by 1, and the "counter" in the state memory area is stored as "1,0,1,0,0,···,0,0,0,0,0,".

[0020] The search processing unit 11 performs the above-described solution search until a preset total search time elapses, and stores the state of the solution and the counter at each time in the state memory area. In the example of FIG. 3, it is assumed that the total search time is set to 3t. And when the total search time 3t elapses (Yes in step S3 in FIG. 2), the search processing unit 11 outputs the state of the solution at that time as the solution result (step S6 in FIG. 2).

[0021] Here, in the process where the solution search is being performed by the search processing unit 11 as described above, at a predetermined timing, the fixed processing unit 12 performs a process of fixing the variables of the optimization problem to fixed values (step S4 in FIG. 2). And when the variables are fixed at a predetermined timing, the search processing unit 11 updates the optimization problem in accordance with the fixing of the variables (step S5 in FIG. 2), performs solution search for the updated optimization problem, and records the state of the solution and the counter (returns to step S2 in FIG. 2).

[0022] Specifically, when the fixed processing unit 12 (constantization unit) reaches a predetermined constantization timing during the solution search process, it sets each variable x, which is the value of the counter in the state memory area. i Check the number of changes to the variable x, and if it is below a predetermined threshold, i Identify the variable x whose counter value is 4 or less each time t time has elapsed. Here, the constant timing is set to a time interval of "t" and the threshold is set to "4". In the example in Figure 3, each time t time has elapsed, the variable x whose counter value is 4 or less is identified. i To identify this, first, at time t, the variable x whose counter value is 4 or less. i Identify the variables x3, x4, n-4 The value of the counter is 4 or less, and the variables x3, x4, x n-4 The variables are identified and made constants. At this time, the fixed processing unit 12 identifies the variables x3, x4, x n-4 The state at time t, i.e., the value of the solution, is given by the variables x3, x4, x n-4 It is made a constant by being a fixed value. In the example in Figure 3, as shown enclosed by the dotted line, the variables x3, x4, x n-4 The value (1 or 0) representing the state of the solution at time t is given by each variable x3, x4, x n-4 It is treated as a constant value. In the example in Figure 3, the variable treated as a constant is shown as "X", and it is treated as a constant value of either 1 or 0.

[0023] In the example above, the fixing processing unit 12 illustrates a case where the value of the variable at time t, which is the constantization timing, is used as the fixed value of the variable. However, the fixed value of the variable may also be determined according to the variable's value up to that point, i.e., the state of the solution up to that point. For example, the fixing processing unit 12 may use the mode of the solution state, which is the variable's value up to time t, as the fixed value. Alternatively, the fixing processing unit 12 may use the percentage of the solution state, which is the variable's value up to time t, as the fixed value. For example, since the solution state is either 1 or 0, the percentage of the variable's value up to time t that was either 1 or 0 can be calculated, and the variable may be used as the value of the higher percentage. In this case, the variable may also be used as the value of the higher percentage of time when the variable was 1 or 0. Thus, the fixing processing unit 12 may use the number of times the variable has changed as the constant, or the mode of the variable or the percentage of times the variable is a specific value as the constant, or other predetermined statistical values ​​of the variable's state changes.

[0024] Then, from time t onward, the search processing unit 11 updates the optimization problem with the variables treated as constants. For example, the search processing unit 11 updates the objective function and constraints of the optimization problem as shown in equation 4 below.

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[0025] Then, as shown in Figure 3, the search processing unit 11 processes each variable x other than the constant variable. i The counter is initialized to "0", and the solution search for the updated optimization problem is performed in the same way as described above, continuing to record the solution state and the counter. At this time, the constant variable x i From this point onward, no solution search is performed, so the state of the solution remains a constant fixed value, which will be represented as "X" in Figure 3. i In this case, the counter value is not updated, and this will be represented as "Y" in Figure 3.

[0026] Subsequently, at time 2t, when the next constantization timing occurs, the fixed processing unit 12, as described above, controls each variable x, which is the value of the counter in the state storage area. i Check the number of changes and check if the variable x is less than or equal to the threshold of 4. i Identify and make constants the variables x1, x n-2 ,x n-3 The variables are identified and formulated. Then, the search processing unit 11 updates the optimization problem with the variables set to constants, as shown in equation 5 below, and then selects each of the other variables x excluding the constant variables. i The counter is initialized to "0", and the solution search for the updated optimization problem is performed in the same way as described above, continuing to record the solution state and the counter. In the example in Figure 3, the variables x1, x n-3 Since it is reduced to a constant of "0", it will not appear in some of the optimization problems shown in equation 5.

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[0027] Furthermore, after 3t time has elapsed and the set total search time has passed, the search processing unit 11 outputs the state of the searched solution as the final solution. At this time, the search processing unit 11 outputs the final solution including constant variables, for example, "X=00110···10111".

[0028] As described above, in this embodiment, the time required to solve a constrained combinatorial optimization problem can be reduced by fixing the variables in the problem.

[0029] Note that in the above, the variable x occurs at the time of constantization. i The example given shows that the threshold for the number of changes required to make the variable constant is 4, but this number can be any number and may change depending on the time taken to find the solution. For example, a large threshold may be set in the early stages of the solution search, when rapid changes in variables are expected due to simulated annealing, and a smaller threshold may be set as the solution search time progresses. In the later stages of the solution search, when variable changes are expected to stabilize, an even lower threshold may be set.

[0030] Furthermore, while the above example illustrates a case where the constantization timing occurs every t-hour intervals, it is not limited to fixed intervals; it may also occur at varying intervals. For example, in the early stages of the solution search, when rapid changes in variables are expected, as mentioned above, longer time intervals may be used. As the solution search progresses, shorter time intervals may be used, and in the later stages of the solution search, when changes in the state of variables are expected to stabilize, even shorter time intervals may be used.

[0031] Furthermore, while the fixed processing unit 12 is configured to set variables to fixed values ​​based on changes in their state, other variables may also be set to fixed values ​​depending on the content of the optimization problem in which predetermined variables have been set to fixed values. For example, if the constraint is a one-hot constraint where only one of the five variables is "1", and one predetermined variable is set to a fixed value of "1" based on changes in its state, then the remaining four variables can all be set to a fixed value of "0" according to the constraint. Also, for example, if the constraint is that the sum of the five variables is 3 or more, and two predetermined variables are set to a fixed value of "0" based on changes in their state, then the remaining three variables can all be set to a fixed value of "1" according to the constraint. In this way, the fixed processing unit 12 may also set other variables, which are determined by the content of the optimization problem, such as constraints in which predetermined variables have been set to fixed values.

[0032] Furthermore, the search processing unit 11 may change the constant variables back to non-constant variables as described above. In this case, the search processing unit 11 may change the constant variables back to non-constant variables depending on the change in the state of the variables during the solution search process. For example, the search processing unit 11 may change the constant variables back to non-constant variables if the state of the solution does not change or the solution does not improve even after continuing the solution search for a certain period of time. Then, the search processing unit 11 further searches for solutions for the variables in the optimization problem in the state where the constant variables have been changed back to non-constant variables.

[0033] <Second Embodiment> Next, a second embodiment of the present disclosure will be described with reference to the drawings. This embodiment shows an outline of the information processing device, etc., described in the above-described embodiment. Note that the drawings may be relevant to any embodiment.

[0034] First, the hardware configuration of the information processing device 100 in this disclosure will be described. The information processing device 100 is composed of a general information processing device, and as an example, it is equipped with the following hardware configuration as shown in Figure 4. ·CPU(Central Processing Unit)101(Arithmetic unit) ROM (Read Only Memory) 102 (Storage Device) • RAM (Random Access Memory) 103 (Storage Device) • Program group 104 loaded into RAM 103 • Storage device 105 for storing the program group 104 • Drive device 106 for reading and writing to external storage medium 110 of the information processing device. • Communication interface 107 connecting to a communication network 111 outside the information processing device. • Input / output interface 108 for data input and output. • Bus 109 connecting each component

[0035] Figure 4 shows an example of the hardware configuration of the information processing device 100, and the hardware configuration of the information processing device is not limited to the case described above. For example, the information processing device may consist of only a part of the configuration described above, such as not having a drive device 106. In addition, the information processing device may use a GPU (Graphic Processing Unit), DSP (Digital Signal Processor), MPU (Micro Processing Unit), FPU (Floating point number Processing Unit), PPU (Physics Processing Unit), TPU (Tensor Processing Unit), quantum processor, microcontroller, or a combination thereof instead of the CPU described above.

[0036] The information processing device 100 can be equipped with the search unit 121, state recording unit 122, and constant unit 123 shown in Figure 5 by having the CPU 101 acquire the program group 104 and execute it. The program group 104 is, for example, stored in advance in a storage device 105 or ROM 102, and the CPU 101 loads it into RAM 103 and executes it as needed. The program group 104 may also be supplied to the CPU 101 via a communication network 111, or it may be stored in advance in a storage medium 110, and the drive device 106 reads the program and supplies it to the CPU 101. However, the search unit 121, state recording unit 122, and constant unit 123 described above may be constructed with dedicated electronic circuits to realize these means.

[0037] The search unit 121 performs a solution search for the variables included in the optimization problem. The state recording unit 122 records the state changes of the variables during the solution search process. The constantization unit 123 constantizes the variables included in the optimization problem based on the state changes. Then, the search unit 121 performs a solution search for the optimization problem with the variables constantized.

[0038] By being configured as described above, this disclosure can suppress the prolonged time required to solve a constrained combinatorial optimization problem.

[0039] Furthermore, at least one of the functions of the search unit 121, state recording unit 122, and constant unit 123 described above may be executed on an information processing device installed and connected to any location on the network, that is, it may be executed using so-called cloud computing.

[0040] Furthermore, the aforementioned programs can be stored and supplied to a computer using various types of non-transitory computer-readable media. Non-transitory computer-readable media include various types of tangible storage media. Examples of non-transitory computer-readable media include magnetic recording media (e.g., flexible disks, magnetic tapes, hard disk drives), magneto-optical recording media (e.g., magneto-optical disks), CD-ROMs (Read Only Memory), CD-Rs, CD-R / Ws, and semiconductor memory (e.g., mask ROMs, PROMs (Programmable ROMs), EPROMs (Erasable PROMs), flash ROMs, and RAMs (Random Access Memory)). Programs may also be supplied to a computer using various types of transient computer-readable media. Examples of transient computer-readable media include electrical signals, optical signals, and electromagnetic waves. Transitory computer-readable media can be supplied to a computer via wired communication channels such as electric wires and optical fibers, or via wireless communication channels.

[0041] Although the present disclosure has been described above with reference to embodiments, the present disclosure is not limited to the embodiments described above. Various modifications to the structure and details of the present disclosure are possible, as can be understood by those skilled in the art within the scope of the present disclosure. Furthermore, each of the embodiments described above can be combined with other embodiments as appropriate.

[0042] <Note> Some or all of the above embodiments may also be described as follows. The general configuration of the information processing apparatus, information processing method, and program in this disclosure is described below. However, this disclosure is not limited to the configuration described in the following notes. Furthermore, some or all of the configurations and functions described in Appendices 2 to 8, which are dependent on Appendice 1 below, may also be dependent on Appendices 9 and 10 in the same way as Appendices 2 to 8. Moreover, not limited to Appendices 1, 9, and 10, some or all of the configurations and functions described as appendices may also be dependent on similar hardware, software, various recording means for recording software, or systems, without departing from the embodiments described above. (Note 1) A search unit that searches for solutions to the variables included in the optimization problem, A state recording unit that records the state changes of variables during the solution search process, A constantization unit that converts the variables included in the optimization problem into constants based on the state change, Equipped with, The search unit performs a solution search for an optimization problem with the variables set to constants. Information processing device. (Note 2) The information processing device described in Appendix 1, The constant-setting unit constants a predetermined variable based on the statistical values ​​of the state change in the predetermined variable. Information processing device. (Note 3) The information processing device described in Appendix 2, The constant-setting unit constants a predetermined variable based on the number of times the value of the predetermined variable has been changed. Information processing device. (Note 3.1) The information processing device described in Appendix 3, The constant-setting unit, when the number of times the value of a predetermined variable changes at a predetermined timing is less than or equal to a preset number, sets the predetermined variable to a constant according to the value of the variable up to that point. Information processing device. (Appendix 3.2) The information processing device described in Appendix 3, The constant-setting unit, when the number of changes in the value of a predetermined variable at a predetermined timing is less than or equal to a preset number, sets the predetermined variable to its value at that time, or to the mode of the variable's values ​​up to that point. Information processing device. (Appendix 3.3) The information processing device described in Appendix 3, The constant-setting unit constants the predetermined variable if the number of times the value of the predetermined variable changes at a predetermined timing is less than or equal to the number of times it changes according to the solution search time. Information processing device. (Note 4) The information processing device described in Appendix 2, The constant-setting unit constants a predetermined variable based on the proportion of times that the value of the predetermined variable was a specific value. Information processing device. (Note 4.1) The information processing device described in Appendix 4, The constant-setting unit constants a predetermined variable to a specific value according to the ratio of the value of the predetermined variable. Information processing device. (Note 5) The information processing device described in Appendix 1, The constant-setting unit changes the timing of constant-setting a predetermined variable according to the elapsed time of the solution search. Information processing device. (Note 5.1) The information processing device described in Appendix 5, The constant-setting unit is configured such that the interval between setting predetermined variables to constants becomes longer as the elapsed time of solution search decreases. Information processing device. (Note 6) The information processing device described in Appendix 1, The constant-setting unit constants predetermined variables included in the optimization problem based on the state change, and also constants other variables according to the content of the optimization problem in the state in which the predetermined variables have been constanted. Information processing device. (Note 6.1) The information processing device described in Appendix 6, The constant-setting unit constants other variables according to the content of the constraints of the optimization problem in the state in which predetermined variables have been constant-set. Information processing device. (Note 7) The information processing device described in Appendix 1, The search unit performs the solution search by treating the constant variables as non-constant variables. Information processing device. (Note 8) The information processing device described in Appendix 1, The search unit performs the solution search by treating variables that have been made constant as variables that have not been made constant, in accordance with the state changes of the variables during the solution search process. Information processing device. (Note 9) We perform a solution search for the variables included in the optimization problem. Record the changes in the state of variables during the solution search process. Based on the aforementioned state changes, the variables included in the optimization problem are made constants. We perform a solution search for an optimization problem with the variables set to constants. Information processing methods. (Note 10) In an information processing device, We perform a solution search for the variables included in the optimization problem. Record the changes in the state of variables during the solution search process. Based on the aforementioned state changes, the variables included in the optimization problem are made constants. We perform a solution search for an optimization problem with the variables set to constants. A program that executes a process. [Explanation of Symbols]

[0043] 10 Information Processing Devices 11 Search Processing Unit 12 Fixing Processing Unit 15 Problem storage 100 Information Processing Devices 101 CPU 102 ROM 103 RAM 104 Program Groups 105 Storage device 106 Drive unit 107 Communication Interface 108 Input / Output Interfaces 109 Bus 110 Storage medium 111 Communication Network 121 Search Department 122 Status Recording Unit 123 Constantization part

Claims

1. A search unit that searches for solutions to the variables included in the optimization problem, A state recording unit that records the state changes of variables during the solution search process, A constantization unit that converts the variables included in the optimization problem into constants based on the state change, Equipped with, The search unit performs a solution search for an optimization problem with the variables set to constants. Information processing device.

2. An information processing apparatus according to claim 1, The constant-setting unit constants a predetermined variable based on the statistical values ​​of the state change in the predetermined variable. Information processing device.

3. An information processing apparatus according to claim 2, The constant-setting unit constants a predetermined variable based on the number of times the value of the predetermined variable has been changed. Information processing device.

4. An information processing apparatus according to claim 2, The constant-setting unit constants a predetermined variable based on the proportion of times that the value of the predetermined variable was a specific value. Information processing device.

5. An information processing apparatus according to claim 1, The constant-setting unit changes the timing of constant-setting a predetermined variable according to the elapsed time of the solution search. Information processing device.

6. An information processing apparatus according to claim 1, The constant-setting unit constants predetermined variables included in the optimization problem based on the state change, and also constants other variables according to the content of the optimization problem in the state in which the predetermined variables have been constanted. Information processing device.

7. An information processing apparatus according to claim 1, The search unit performs the solution search by treating the constant variables as non-constant variables. Information processing device.

8. An information processing apparatus according to claim 1, The search unit performs the solution search by treating variables that have been made constant as variables that have not been made constant, in accordance with the state changes of the variables during the solution search process. Information processing device.

9. We perform a solution search for the variables included in the optimization problem. Record the changes in the state of variables during the solution search process. Based on the aforementioned state changes, the variables included in the optimization problem are made constants. We perform a solution search for an optimization problem with the variables set to constants. Information processing methods.

10. In an information processing device, We perform a solution search for the variables included in the optimization problem. Record the changes in the state of variables during the solution search process. Based on the aforementioned state changes, the variables included in the optimization problem are made constants. We perform a solution search for an optimization problem with the variables set to constants. A program that executes a process.

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