JP7004906B2 - Optimization device and control method of optimization device - Google Patents

Description

The present invention relates to an optimization device and a control method for the optimization device.

Information processing is performed in all fields in today's society. These information processing is performed by an arithmetic unit such as a computer, and prediction, determination, control, etc. are performed by calculating and processing various data and obtaining meaningful results. One of these information processes is optimization, which is an important field. Obviously, these are very important, for example, the problem of finding a solution that minimizes the resources and costs required to do something, or maximizes its effectiveness.

It is known that many of the optimization problems called discrete optimization problems, combinatorial optimization problems, etc. are very difficult to solve because variables take discrete values instead of continuous values. .. The biggest reason why it is difficult to solve a discrete optimization problem is that there are a large number of states called local solutions that are not optimal solutions but have the smallest values in the local neighborhood.

Since there is no efficient general solution for solving discrete optimization problems, it is necessary to use an approximate solution that utilizes the properties unique to the problem or a method called metaheuristic that does not rely much on the properties of the problem.

The contents described below relate to the solution method using the Markov chain Monte Carlo method among the latter, and in particular, to the exchange Monte Carlo method or the pseudo-annealing method in a broad sense called the replica exchange method.

Simulated annealing is a method of finding the optimum solution by probabilistically changing the state (value of a variable vector) using a random number. In the following, the problem of minimizing the value of the evaluation function to be optimized will be explained as an example, and the value of the evaluation function will be called energy. In the case of maximization, the sign of the evaluation function may be changed.

In simulated annealing, if the acceptance (allowable) probability of a state transition is determined as follows using the energy change and temperature associated with that transition, the state reaches the optimum solution at the limit of infinite time (number of iterations). It has been proven to do.

Here, T is a parameter representing the temperature, and it is desirable that the initial value thereof be sufficiently large according to the problem and gradually lowered sufficiently.
In the pseudo-annealing method as described above, the optimum solution can be obtained by taking an infinite number of iterations, but in reality, it is necessary to obtain the solution with a finite number of iterations, so that the optimum solution cannot be reliably obtained. Moreover, since the temperature drops very slowly as described above, the temperature does not drop sufficiently in a finite time. Therefore, in actual simulated annealing, the temperature is often lowered faster than the temperature change that is guaranteed to converge theoretically.

In the actual simulated annealing method, the above iterations are repeated while lowering the temperature, starting from the initial state, and when the end judgment conditions such as reaching a certain number of iterations or the energy falling below a certain value are satisfied, the operation is performed. finish. The answer to be output is the state at the end. However, in reality, the temperature does not become 0 with a finite number of iterations, so even at the end, the occupancy probability of the state has a distribution expressed by the Boltzmann distribution, etc., and it is not always the optimum value or a good solution. do not have. Therefore, the realistic solution is to keep the energy obtained so far in the middle of the iteration at the lowest state and output it at the end.

As you can imagine from the above explanation, simulated annealing is versatile and very attractive, but it has a problem that the calculation time becomes relatively long because the temperature needs to be lowered slowly. Furthermore, there is also a problem that it is difficult to appropriately adjust how to lower the temperature according to the problem. If the temperature is lowered too slowly, the temperature does not drop so much in a finite time, and the energy range of the final heat distribution becomes wide, so that the probability of occupying a good solution does not increase. On the other hand, if it is lowered too fast, the temperature will drop before the local solution escapes, and the bad solution will remain trapped, reducing the probability of obtaining a good solution.

In the replica exchange method, Monte Carlo search using multiple temperatures (hereinafter referred to as stochastic search) is performed at the same time, the energies of each state are compared for each number of iterations, and the states for two temperatures are exchanged with an appropriate probability. It is a method of performing an operation.

FIG. 9 is a diagram showing a configuration example of an optimization device using a normal replica exchange method. The optimization device 50 has a plurality of replicas (annealed portions 51a0, 51a1, ..., 51ai, ..., 51an in FIG. 9) and an exchange control unit 52, unlike an optimization device using a normal pseudo-annealing method. .. The exchange control unit 52 gives temperature information (hereinafter, the reciprocal of β _i (reciprocal of T) (0 ≦ i ≦ n)) to the annealing units 51a0 to 51an.

FIG. 9 shows an example of the annealed portion 51ai. Other annealed parts have the same structure. The annealing unit 51ai has a state holding unit 60, an evaluation function calculation unit 61, and a transition control unit 62.
The state holding unit 60 holds the values of a plurality of state variables included in the evaluation function. Further, the state holding unit 60 is a value of a plurality of state variables (value of the above variable vector) based on the flag f indicating whether or not the state transition is possible and the number (index) N of the state variable indicated by the flag f. Update the state s _i .

The evaluation function calculation unit 61 calculates the energy change accompanying the change (state transition) of the state variable. For example, when the evaluation function is represented by an Ising model represented by a combination between two state variables, and only one state variable transition is allowed at a time, the evaluation function calculation unit 61 determines the value of each state variable. Based on the coupling coefficient indicating the strength of the coupling between the state variables, the number N, and the flag f, the energy change accompanying each change (state transition) of the plurality of state variables is calculated. Energy change ΔE _{i, j} indicates the energy change accompanying the change of the jth state variable. The value of the coupling coefficient corresponding to the optimization problem to be calculated is stored in a memory or a register in advance. If the merit function is not an singing model, or if multiple state variable transitions are allowed at once, the state transition number and the changing state variable number do not always match, but the energy change with respect to the state transition number is appropriate. I just need to be able to calculate. The evaluation function calculation unit 61 can be realized by using a logic circuit such as a product-sum calculation circuit.

The transition control unit 62 uses the energy changes ΔE _{i and j} and the inverse temperature β _i assigned by the exchange control unit 52 to determine the acceptance probability of the state transition of the jth state variable, as in the normal simulated annealing method. A probabilistic search is performed by determining by the following (Equation 2).

In (Equation 2), the function f is the same as (Equation 1-1), and for example, the Metropolis method of (Equation 1-2) is used. The transition control unit 62 outputs a flag f indicating whether or not the state transition is possible and a number of the state transition indicated by the flag f, based on the above-mentioned acceptance probability of the state transition. Further, the transition control unit 62 updates and outputs the energy E _i based on the energy changes ΔE _{i and j} .

The exchange control unit 52 observes the energy E in each annealed portion at a fixed number of repetitions, uses the energy E in two of the annealed portions 51a0 to 51an, and the reverse temperature β, and is represented by the following (Equation 3). The value of each state variable in the two annealed parts is exchanged based on the exchange probability to be made. Instead of the value of the state variable, the reverse temperature supplied to each of the two annealed parts may be exchanged.

In (Equation 3), β _i is the reverse temperature given to the annealing section 51ai, β _j is the reverse temperature given to the j-th annealing section (not shown), E _i is the energy in the annealing section 51ai, and E _j is used. It is the energy in the j-th annealing part. Further, in (Equation 3), the function f is the same as that in (Equation 1-1), and for example, the Metropolis method of (Equation 1-2) is used.

Even with such exchange, the probability distribution of each temperature state converges to the Boltzmann distribution for that temperature. And the relaxation time required to converge to this distribution can be significantly shorter than when no exchange is performed.

As the two annealed portions to be exchanged, those having similar supplied temperatures (for example, those supplied with adjacent temperatures) are selected so that the exchange probability does not become too small.
In the optimization device 50, when the annealing sections 51a0 to 51an that perform iterative processing many times are realized by a dedicated circuit and the functions of the exchange control section 52 are realized by software, two annealing sections with similar temperatures are obtained by passing a pointer. The values (or temperature information) of each state variable of may be exchanged. In this case, it is not necessary to perform a sort process for arranging the information for identifying the annealed portions 51a0 to 51an in ascending or descending order of temperature for each replacement.

Japanese Unexamined Patent Publication No. 6-309408 Japanese Unexamined Patent Publication No. 9-179897

By the way, in order to speed up the movement of data between a plurality of annealing units and the exchange control unit, it is better to realize the exchange control unit with a dedicated circuit than to realize it with software. When the exchange control unit is realized by a dedicated circuit, the actual data itself is exchanged without using a pointer. Therefore, it is better to exchange temperature information whose amount of data is smaller than the value of each state variable.

However, when the replica exchange method is realized in a dedicated circuit using a correspondence table in which the temperature is associated with the identification information of each annealed part, the above sort process is performed in order to select the annealed part having a similar temperature. And the circuit for that purpose increases the circuit scale of the optimizer.

In one aspect, it is an object of the present invention to suppress an increase in the circuit scale of an optimization device that performs pseudo-annealing operation by the replica exchange method.

In one embodiment, when a state transition occurs in which the value of any of the plurality of state variables included in the evaluation function representing energy changes, the change in the energy accompanying the change in the value of each of the plurality of state variables. A plurality of annealed portions for probabilistically determining which value change of the plurality of state variables is accepted based on the temperature, a first identification information for identifying each of the plurality of annealed portions, and the plurality of ablation portions. The correspondence relationship with the temperature assigned to each of the bleached portions is shown, and the first correspondence information in which the first identification information is arranged in the order of the lowest or the highest temperature, and the first identification information and the temperature. It is a candidate for exchanging the temperature from the plurality of ablated portions based on the first correspondence information, which shows the correspondence relationship and holds the second correspondence information in which the temperature is arranged in the order of the first identification information. The first and second annealed parts are selected and the temperature is exchanged according to the exchange probability based on the energy and the temperature of each of the first and second annealed parts. When it is determined whether or not to perform the above and the exchange is performed, the first correspondence information and the second correspondence information are updated, and the temperature information representing the temperature is obtained based on the updated second correspondence information. An optimization device having an exchange control unit for supplying each of the corresponding plurality of annealed parts is provided.

Also, in one embodiment, a method of controlling an optimizing device is provided.

On one aspect, it is possible to suppress an increase in the circuit scale of an optimization device that performs pseudo-annealing operation by the replica exchange method.

It is a figure which shows an example of the optimization apparatus of 1st Embodiment. It is a figure which shows an example of the optimization apparatus of the 2nd Embodiment. It is a figure which shows an example of each correspondence information. It is a flowchart which shows the flow | flow of the operation of the example of the optimization apparatus of 2nd Embodiment. It is a figure which shows the update example of the 1st correspondence information and the 2nd correspondence information. It is a flowchart which shows the process flow of an example when the function of the exchange control part shown in FIG. 9 is realized by software. It is a figure which shows the optimization apparatus of the comparative example which realized the function of the exchange control part shown in FIG. 9 by a dedicated circuit. It is a flowchart which shows the operation flow of the example of the optimization apparatus of the comparative example shown in FIG. It is a figure which shows the configuration example of the optimization apparatus which used the ordinary replica exchange method.

Hereinafter, embodiments for carrying out the invention will be described with reference to the drawings.
(First Embodiment)
FIG. 1 is a diagram showing an example of an optimization device according to the first embodiment.

The optimization device 10 of the first embodiment has an annealing unit 11a0, 11a1, ..., 11ai, ..., 11an, and an exchange control unit 12.
The annealed portions 11a0 to 11an are the same as the annealed portions 51a0 to 51an shown in FIG. That is, each of the annealing portions 11a0 to 11an calculates the change in energy E accompanying the change in the value of each of the plurality of state variables when the state transition in which the value of any of the plurality of state variables changes occurs. Then, each of the annealing portions 11a0 to 11an performs a stochastic search by probabilistically determining which value of the plurality of state variables is to be accepted based on the change in energy E and the temperature. In addition, different temperatures are assigned to each of the annealed portions 11a0 to 11an.

The exchange control unit 12 includes a first correspondence information holding unit 12a, a second correspondence information holding unit 12b, an exchange calculation circuit 12c, and an output control circuit 12d.
The first correspondence information holding unit 12a holds the first correspondence information 15. The first correspondence information 15 shows the correspondence relationship between the identification information (hereinafter referred to as a replica number) for identifying each of the annealed portions 11a0 to 11an and the temperature assigned to each of the annealed portions 11a0 to 11an, and the replica number is used. They are arranged in ascending or descending order of temperature.

The second correspondence information holding unit 12b holds the second correspondence information 16. The second correspondence information 16 shows the above correspondence and arranges the temperatures in the order of the replica numbers.
In the example of FIG. 1, the temperatures T0 to Tn increase in the order of temperatures T0, T1, T2, T3, ..., Tn. Therefore, in the example of FIG. 1, the first correspondence information 15 is an array of replica numbers in ascending order of temperature.

The temperature may be represented not by the temperature itself but by information that identifies the temperature. An example using the information for identifying the temperature will be described in the second embodiment.
The first correspondence information holding unit 12a and the second correspondence information holding unit 12b are, for example, storage circuits such as registers. Further, the first correspondence information holding unit 12a and the second correspondence information holding unit 12b are volatile memories such as RAM (Random Access Memory), and non-volatile memories such as flash memory and EEPROM (Electrically Erasable Programmable Read Only Memory). You may.

The exchange calculation circuit 12c is a candidate for exchanging temperatures from the annealed portions 11a0 to 11an based on the first correspondence information 15 held in the first correspondence information holding unit 12a. Select the annealed part. Then, the exchange calculation circuit 12c determines whether or not to exchange the temperature according to the exchange probability based on the energy E and the temperature of each of the first annealed portion and the second annealed portion, and performs the exchange. The first correspondence information 15 and the second correspondence information 16 are updated.

For example, the exchange operation circuit 12c selects two replica numbers arranged in ascending order of temperature from the first correspondence information 15 from the top, and between the two annealed parts identified by the two replica numbers. Determine if the temperature can be exchanged.

Since the replica numbers of the first correspondence information 15 are arranged in ascending order of temperature (may be in descending order of temperature), the exchange operation circuit 12c selects, for example, two replica numbers from the top, so that the adjacent temperatures are adjacent to each other. You can select two annealed parts to which are assigned. The exchange calculation circuit 12c can select two annealed portions having similar temperatures even if two replica numbers are selected, such as every other one from the top.

The exchange operation circuit 12c is realized by, for example, a circuit as shown below.
The exchange calculation circuit 12c corresponds to two replica numbers selected from the circuit that selects two replica numbers from the top from the first correspondence information 15 and the energy E supplied from the annealing portions 11a0 to 11an. It has a circuit to select one. Further, the exchange calculation circuit 12c obtains the exchange probability _pij represented by (Equation 3) based on the temperature associated with the two replica numbers selected from the first correspondence information 15 and the two selected energies E. It has a circuit for calculation (including a calculation circuit for an exp function). Further, the exchange calculation circuit 12c is a circuit that generates a random number, a circuit that determines whether or not exchange is possible based on the comparison result between the random number and the exchange probability _pij , and a first correspondence information 15 and a second correspondence when exchanging. This can be realized by using a circuit or the like that updates the information 16.

The output control circuit 12d supplies temperature information representing the temperature (reverse temperature β in the example of FIG. 1) to each of the corresponding annealing portions 11a0 to 11an based on the updated second correspondence information 16a. The output control circuit 12d supplies, for example, the temperature information indicating the temperature of the updated second correspondence information 16a to the corresponding annealing portion in order from the top or at the same time. Since the temperatures of the second correspondence information 16 are arranged in the order of the replica numbers, the output control circuit 12d can easily select the temperature information to be supplied to the annealing portions 11a0 to 11an.

In the example of FIG. 1, the output control circuit 12d has a circuit that converts the temperature into the reverse temperature β in order to supply the reverse temperature β to the annealing portions 11a0 to 11an as the temperature information. However, the output control circuit 12d may supply the temperature itself to the annealing portions 11a1 to 11an. In that case, the annealed portions 11a1 to 11an may be used by converting the temperature to the reverse temperature β by using a conversion table or the like.

Hereinafter, an example of the operation of the optimization device 10 according to the first embodiment will be described with reference to FIG.
When the exchange calculation circuit 12c receives the respective energies E of the annealing portions 11a0 to 11an, the exchange calculation circuit 12c selects two replica numbers from the top from the first correspondence information 15. For example, in the first correspondence information 15 as shown in FIG. 1, replica numbers = i, 0 are first selected.

Then, the exchange calculation circuit 12c selects the energy E corresponding to the two selected replica numbers from the respective energies E of the annealing portions 11a0 to 11an. Further, the exchange calculation circuit 12c has a temperature associated with the two replica numbers selected from the first correspondence information 15 (temperatures T0 and T1 when replica numbers = i and 0 are selected) and two selected replica numbers. Based on the energy, the exchange probability _{pij represented} by (Equation 3) is calculated. When the annealed portions 11ai and 11a0 having replica numbers = i and 0 are candidates for replacement, in (Equation 3), β _i = 1 / T0, β _j = 1 / T1 and E _i are the annealed portions 11ai. The energy, Ej, is the energy of the annealed portion _11a0 .

Further, the exchange calculation circuit 12c generates a random number, determines whether or not the exchange is possible based on the comparison result between the random number and the exchange probability _pij , and when the exchange is performed, the first correspondence information 15 and the second correspondence information 16 To update. When temperature information is exchanged in the annealed portions 11ai and 11a0 having replica numbers = i and 0, the first correspondence information 15 and the second correspondence information 16 are updated and the first correspondence information 15a is updated as shown in FIG. And the second correspondence information 16a are obtained.

For example, in the first correspondence information 15 as shown in FIG. 1, the replica number associated with the temperature T1 and the replica number associated with the temperature T2 are subsequently selected, and the same processing is repeated. After that, the replica numbers are similarly selected two by two, and the same process is repeated. Then, when the replica number associated with the last temperature Tn of the first correspondence information 15 is selected, the output control circuit 12d outputs the temperature information based on the updated second correspondence information. It is supplied to each of the corresponding annealed portions 11a0 to 11an.

Each of the annealed portions 11a0 to 11an performs a stochastic search again using the supplied temperature information, and after a predetermined number of iterations, the processing of the exchange control unit 12 as described above is performed. After the process of the exchange control unit 12 as described above is repeated, for example, a predetermined number of times, the operation of the optimization device 10 ends. It should be noted that each of the annealing portions 11a0 to 11an holds the minimum value of energy calculated each time the stochastic search of a predetermined number of iterations is performed and the value of each state variable at the minimum value. When the processing of the exchange control unit 12 as described above is repeated a predetermined number of times, each of the annealing units 11a0 to 11an sets the minimum value of energy at that time and the value of each state variable at the minimum value. , For example, output to a display device or a computer (not shown). For example, among the lowest values of energy output by each of the annealing portions 11a0 to 11an, the value of each state variable at the time of the smallest value is the solution of the optimization problem.

As described above, in the optimization device 10 of the first embodiment, the exchange control unit 12 holds the first correspondence information 15 and the second correspondence information 16, and when the temperature is exchanged, the first correspondence information 15 is used. The second correspondence information 16 is updated. This eliminates the need for a circuit that sorts the replica numbers in ascending or descending order of temperature for each temperature exchange, and suppresses an increase in the circuit scale of the optimizing device 10. Further, since the optimization device 10 does not perform the sorting process, the time required for the exchange process can be shortened.

The exchange calculation circuit 12c may select two annealing parts to which the adjacent temperature is not assigned from the first correspondence information 15, but by selecting two annealing parts to which the adjacent temperature is assigned. , The exchange probability _pij increases and the calculation efficiency increases.

(Second embodiment)
FIG. 2 is a diagram showing an example of an optimization device according to a second embodiment. In FIG. 2, the same elements as those of the optimization device 10 shown in FIG. 1 are designated by the same reference numerals.

In the optimization device 20 of the second embodiment, the exchange control unit 21 is different from the optimization device 10 of the first embodiment.
The exchange control unit 21 includes a first correspondence information holding unit 21a, a second correspondence information holding unit 21b, a third correspondence information holding unit 21c, an exchange calculation circuit 21d, and an output control circuit 21e.

The first correspondence information holding unit 21a and the second correspondence information holding unit 21b are not the temperature itself, but the temperature identification information for identifying the temperature, the first correspondence information showing the correspondence relationship with the replica number, and the second correspondence information. Hold. The first correspondence information is the replica numbers arranged in ascending order or the highest temperature order, and the second correspondence information is the temperature identification information arranged in the order of replica numbers.

The third correspondence information holding unit 21c holds the third correspondence information which shows the correspondence relationship between the temperature and the temperature identification information which identifies the temperature.
The exchange calculation circuit 21d has a first annealing section and a second annealing section that are candidates for exchanging temperatures from the annealing sections 11a0 to 11an based on the first correspondence information held in the first correspondence information holding section 21a. Select a department. Then, the exchange calculation circuit 21d determines whether or not to exchange the temperature according to the exchange probability based on the energy E and the temperature of each of the first annealed portion and the second annealed portion, and performs the exchange. In that case, the first correspondence information and the second correspondence information are updated. Since the exchange calculation circuit 21d uses the temperature instead of the temperature identification information when determining the exchange probability, the replica number that identifies each of the first annealed portion and the second annealed portion based on the third correspondence information. Converts the temperature identification information associated with to temperature. When updating the first correspondence information, the exchange calculation circuit 21d may replace the temperature identification information associated with the above two replica numbers.

The exchange operation circuit 21d is realized by, for example, a circuit as shown below.
The exchange calculation circuit 21d is a circuit that selects two replica numbers from the top from the first correspondence information, and one of the energies E supplied from the annealing portions 11a0 to 11an corresponding to the two selected replica numbers. Have a circuit to choose from. Further, the exchange calculation circuit 21d has a circuit that converts the temperature identification information associated with the two replica numbers selected from the first correspondence information into the temperature based on the third correspondence information. Further, the exchange calculation circuit 21d has a circuit (including a subtraction circuit, an exp function calculation circuit, etc.) for calculating the exchange probability _pij represented by (Equation 3) based on the temperature and the two selected energies. .. Further, the exchange calculation circuit 21d is a circuit that generates a random number, a circuit that determines whether or not exchange is possible based on the comparison result between the random number and the exchange probability _pij , and a first correspondence information and a second correspondence information when exchanging. It can be realized by using a circuit that updates and.

Unlike the output control circuit 12d of the optimization device 10 of the first embodiment, the output control circuit 21e converts the temperature identification information of the updated second correspondence information into the corresponding temperature based on the third correspondence information. do. Then, the output control circuit 21e converts the temperature into the reverse temperature β, and supplies the reverse temperature β to each of the corresponding annealing portions 11a0 to 11an.

FIG. 3 is a diagram showing an example of each correspondence information. In the example of FIG. 3, the temperature number is used as an example of the temperature identification information. Further, FIG. 3 shows an example in which the number of annealed portions 11a0 to 11an, that is, the number of replicas is 16.

In the first correspondence information 25, the replica numbers from 0 to 15 are arranged in the order of the temperature numbers. In the second correspondence information 26, the temperature numbers from 0 to 15 are arranged in the order of the replica numbers. In the third correspondence information 27, the temperatures T0 to T15 are arranged in the order of the temperature numbers. The temperatures T0 to T15 increase in the order of temperatures T0, T1, T2, T3, ..., T15. Therefore, in the example of FIG. 3, in the first correspondence information 25, the second correspondence information 26, and the third correspondence information 27, the smaller the value of the temperature number, the lower the temperature. Therefore, the first correspondence information 25 is an array of replica numbers in ascending order of temperature.

Hereinafter, an example of the operation of the optimization device 20 according to the second embodiment will be described.
FIG. 4 is a flowchart showing an operation flow of an example of the optimization device according to the second embodiment. Although not shown, as initialization processing, for example, by controlling a control device (not shown), the first correspondence information 25, the second correspondence information 26, and the third correspondence information 27 are the first correspondence information holding unit. It is written in 21a, the second correspondence information holding unit 21b, and the third correspondence information holding unit 21c. Then, the output control circuit 21e supplies the initial value of the reverse temperature β to each of the annealed portions 11a0 to 11an based on the second correspondence information 26.

Steps S1 to S5 are processes performed in each of the annealed portions 11a0 to 11an. Each of the annealing portions 11a0 to 11an initializes the number of iterations of the stochastic search (step S1), and then performs the above-mentioned stochastic search using the inverse temperature β given by the exchange control unit 21 (step S1). S2). Each of the annealed portions 11a0 to 11an increments the number of iterations each time one stochastic search is completed (step S3). Then, each of the annealing portions 11a0 to 11an determines whether or not the number of iterations has reached a predetermined value (step S4), and if the number of iterations has not reached a predetermined value, the process of step S2 is performed. repeat. Each of the annealing units 11a0 to 11an transmits energy E to the exchange control unit 21 when the number of iterations reaches a predetermined value (step S5).

The processes of steps S6 to S15 are processes performed by the exchange control unit 21.
The exchange calculation circuit 21d of the exchange control unit 21 receives energy E from each of the annealing units 11a0 to 11an (step S6). Since the exchange calculation circuit 21d selects the replica numbers of the two annealing parts to which the adjacent temperatures are assigned in order from the one corresponding to the temperature number = 0, 1 in the first correspondence information 25, the temperature number to be selected is selected. (Hereinafter referred to as the selected temperature number) is initialized to 0 and 1 (step S7).

After the processing of step S7, the exchange calculation circuit 21d selects the two annealing portions to which the adjacent temperatures are assigned by selecting the two replica numbers associated with the selected temperature numbers in the first correspondence information 25. (Step S8). For example, in the first correspondence information 25 as shown in FIG. 3, first, the annealed portion of the replica number = 6 associated with the selected temperature number = 0 and the replica number associated with the selected temperature number = 1 = The annealed portion of 8 is selected. In the second process of step S8, the annealed portion identified by the replica number associated with the selected temperature number = 1 and the annealed portion identified by the replica number associated with the selected temperature number = 2 are selected. Ru. Similarly, from the third time onward, two replica numbers are selected in order from the top of the first correspondence information 25, and the annealed portion identified by the selected replica number is selected as a candidate for exchanging temperature information.

After that, since the exchange calculation circuit 21d uses the temperature instead of the temperature number when obtaining the exchange probability _pij , the current two selected temperature numbers are converted into two temperatures based on the third correspondence information 27. Then, the exchange calculation circuit 21d calculates the exchange probability _pij from the obtained two temperatures and the energies of the two annealed portions identified by the two selected replica numbers (step S9).

Then, the exchange calculation circuit 21d generates a random number, and determines whether or not the exchange is possible based on the comparison result between the random number and the exchange probability _pij (step S10). For example, when the random number is the exchange probability _pij or more, the exchange calculation circuit 21d enables the exchange of temperature information, and when the random number is smaller than the exchange probability _pij , the exchange of the temperature information is rejected.

When the temperature information can be exchanged, the exchange calculation circuit 21d updates the first correspondence information 25 and the second correspondence information 26 (step S11).
FIG. 5 is a diagram showing an example of updating the first correspondence information and the second correspondence information.

In FIG. 5, in FIG. 3, the temperature is between the annealed portion of the replica number = 13 associated with the temperature number = 10 and the annealed portion of the replica number = 11 associated with the temperature number = 11. An update example for exchanging information is shown.

In the updated first correspondence information 25a and second correspondence information 26a, the temperature number = 10 is associated with the replica number = 11, and the temperature number = 11 is associated with the replica number = 13. The exchange calculation circuit 21d may replace the replica number = 11 and the replica number = 13 when updating the first correspondence information 25, and when updating the second correspondence information 26, the temperature number = 10 and the temperature. The number = 11 may be replaced.

After that, the exchange calculation circuit 21d increments the selected temperature number (step S13) when the current selected temperature number is not the last selected temperature number (14 and 15 in the example of FIG. 3) (step S12: No). , The process from step S8 is repeated. On the other hand, when the current selected temperature number is the last selected temperature number (step S12: Yes), the output control circuit 21e corresponds to the temperature information (reverse temperature β) based on the updated second correspondence information. It is transmitted to each of the annealed portions 11a0 to 11an (step S14).

After that, when the end condition (for example, whether or not the process of the exchange control unit 21 as described above is repeated a predetermined number of times) is not satisfied (step S15: No), the process from step S1 is repeated. When the end condition is satisfied (step S15: Yes), although not shown, for example, the minimum value of each energy of the annealed portions 11a0 to 11an and the value of each state variable at the minimum value are set. , Output to a display device (or computer, etc.) not shown. Then, the processing of the optimization device 20 is completed.

The order of each of the above processes is an example, and may be replaced as appropriate.
As described above, even in the optimization device 20 of the second embodiment, the exchange control unit 21 holds the first correspondence information 25 and the second correspondence information 26, and when the temperature is exchanged, the first correspondence information 25 is used. The second correspondence information 26 is updated. As a result, the same effect as that of the optimization device 10 of the first embodiment can be obtained.

Further, in the optimization device 20 of the second embodiment, the exchange calculation circuit 21d replaces the temperature number having a smaller amount of data than the temperature, instead of the actual temperature (for example, represented by a floating point method). , The amount of data to be moved can be made smaller than when temperature is used. Further, in the optimization device 20, the third correspondence information holding unit 21c is increased as compared with the optimization device 10 of the first embodiment, but in the first correspondence information holding unit 21a and the second correspondence information holding unit 21b, the third correspondence information holding unit 21c is increased. Since the temperature number is held instead of the temperature, the circuit scale can be reduced as a whole as compared with the optimization device 10.

(Comparative example)
FIG. 6 is a flowchart showing a processing flow of an example when the function of the exchange control unit shown in FIG. 9 is realized by software.

The processing of steps S20 to S24 is the same as the processing of steps S1 to S5 shown in FIG. The processing of steps S25 to S34 is realized by software. When the function of the exchange control unit 52 is realized by software, for example, the first correspondence information 25 and the third correspondence information 27 as shown in FIG. 3 are used. Therefore, the processing of steps S25 to S29 is the same as the processing of steps S6 to S10 shown in FIG.

In the process of updating the correspondence information in step S30, unlike the process of step S11 in FIG. 4, the replica number associated with the temperature number is replaced by using the pointer. Therefore, it is not necessary to perform the sort process or the search process for searching for the annealed portion to which the adjacent temperature is assigned.

The processing of steps S31 to S34 is the same as the processing of steps S12 to S15 shown in FIG.
In this way, the function of the exchange control unit 52 can be realized by software, but in order to speed up the movement of data between the plurality of annealing units and the exchange control unit, it is more dedicated than the exchange control unit realized by software. It is better to realize it with a circuit.

FIG. 7 is a diagram showing an optimization device of a comparative example in which the function of the exchange control unit shown in FIG. 9 is realized by a dedicated circuit. In FIG. 7, the same elements as those of the optimization device 20 shown in FIG. 2 are designated by the same reference numerals.

In the optimization device 30 of the comparative example, the exchange control unit 31 is different from the exchange control unit 21 of the optimization device 20 of the second embodiment.
The exchange control unit 31 includes a second correspondence information holding unit 31a, a third correspondence information holding unit 31b, a sort processing circuit 31c, and an exchange processing circuit 31d.

The second correspondence information holding unit 31a holds the second correspondence information 26 as shown in FIG. 3, and the third correspondence information holding unit 31b holds the third correspondence information 27 as shown in FIG.
The sort processing circuit 31c performs a sort process of arranging the replica numbers of the second correspondence information 26 in ascending order (or higher order) of the assigned temperature.

The exchange processing circuit 31d selects a first annealed portion and a second annealed portion, which are candidates for exchanging temperatures, based on the information obtained by sorting the second correspondence information 26. Then, the exchange processing circuit 31d determines whether or not to exchange the temperature according to the exchange probability based on the energy E and the temperature of each of the first annealed portion and the second annealed portion, and exchanges the temperature. In that case, the second correspondence information 26 is updated. Since the exchange processing circuit 31d uses the temperature instead of the temperature number when obtaining the exchange probability, the exchange processing circuit 31d converts the temperature number into the corresponding temperature based on the third correspondence information 27.

Further, the exchange processing circuit 31d converts the temperature number of the updated second correspondence information into the corresponding temperature based on the third correspondence information 27. Then, the exchange processing circuit 31d supplies the reverse temperature β to each of the corresponding annealed portions 11a0 to 11an.

FIG. 8 is a flowchart showing an operation flow of an example of the optimization device of the comparative example shown in FIG. 7.
The processing of steps S40 to S46 is the same as the processing of steps S1 to S7 shown in FIG. After the process of step S46, the sort process as described above is performed (step S47). The processing of steps S48 to S50 is the same as the processing of steps S8 to S10 shown in FIG.

After the process of step S50, the second correspondence information 26 is updated according to the result of determining whether or not the exchange is possible (step S51). The processing of steps S52 to S55 is the same as the processing of steps S12 to S15 shown in FIG. 4, but after incrementing the selected temperature number, the sorting processing of step S47 is repeated.

In the optimization device 30 of the comparative example as described above, the sort processing circuit 31c that performs the sort process of the second correspondence information 26 is used. However, for example, in order to sort N elements by the bubble sort algorithm, it takes N (N-1) / 2 cycle calculation time.

On the other hand, in the optimization device 20 of the second embodiment, since the sort process is unnecessary, the sort process circuit 31c is also unnecessary, the increase in the circuit scale can be suppressed, and the calculation time is shortened. can.

Although one viewpoint of the optimization device of the present invention and the control method of the optimization device has been described above based on the embodiment, these are merely examples and are not limited to the above description.

10 Optimization device 11a0-11an Annealing part 12 Exchange control unit 12a First correspondence information holding unit 12b Second correspondence information holding unit 12c Exchange calculation circuit 12d Output control circuit 15, 15a First correspondence information 16, 16a Second correspondence information E Energy β reverse temperature

Claims (5)

When a state transition occurs in which the value of any of a plurality of state variables included in the evaluation function representing energy changes, the change in energy and the temperature associated with the change in the value of each of the plurality of state variables are used. Multiple burn-in parts that probabilistically determine which value change of multiple state variables is to be accepted,
The correspondence relationship between the first identification information for identifying each of the plurality of annealed portions and the temperature assigned to each of the plurality of annealed portions is shown, and the first identification information is given in ascending order or higher temperature. The first correspondence information arranged in order, the correspondence relationship between the first identification information and the temperature are shown, and the second correspondence information in which the temperature is arranged in the order of the first identification information is held, and the first correspondence information is held. A first and second annealed portions, which are candidates for exchanging the temperature, are selected from the plurality of annealed portions, and each of the first annealed portion and the second annealed portion is selected. It is determined whether or not to exchange the temperature according to the exchange probability based on the energy and the temperature of the above, and when the exchange is performed, the first correspondence information and the second correspondence information are updated. , An exchange control unit that supplies temperature information representing the temperature to each of the corresponding plurality of annealing units based on the updated second correspondence information.
Optimizer with. The temperature in the first correspondence information and the second correspondence information is represented by the second identification information for identifying the temperature.
The exchange control unit holds a third correspondence information indicating a correspondence relationship between the temperature and the second identification information, and based on the third correspondence information, the first annealing section and the second annealing section. The optimization device according to claim 1, wherein the second identification information associated with the first identification information that identifies each of the above is converted into the temperature. The exchange control unit
The first correspondence information holding unit which holds the first correspondence information and
A second correspondence information holding unit that holds the second correspondence information, and
Based on the first correspondence information held in the first correspondence information holding section, the first annealing section and the second annealing section are selected, and the temperature is exchanged according to the exchange probability. An exchange calculation circuit that updates the first correspondence information and the second correspondence information when it is determined whether or not the information is exchanged and exchange is performed.
An output control circuit that supplies the temperature information to each of the corresponding plurality of annealed portions based on the updated second correspondence information.
The optimization device according to claim 1 or 2. The optimization device according to any one of claims 1 to 3, wherein the first annealing portion and the second annealing portion are two annealing portions having adjacent temperatures. When a state transition occurs in which the value of any of the plurality of state variables included in the evaluation function representing the energy changes in each of the plurality of burned parts, the energy of the plurality of state variables is changed due to the change of the value of each of the plurality of state variables. Based on the change and the temperature, it is probabilistically determined which value of the plurality of state variables is to be changed.
The exchange control unit shows the correspondence between the first identification information for identifying each of the plurality of annealing portions and the temperature assigned to each of the plurality of annealing portions, and the first identification information is the temperature. The first correspondence information arranged in the order of the lowest or the highest, and the second correspondence information in which the temperature is arranged in the order of the first identification information, showing the correspondence relationship between the first identification information and the temperature, are retained. Based on the first correspondence information, the first annealed portion and the second annealed portion, which are candidates for exchanging the temperature, are selected from the plurality of annealed portions, and the first annealed portion and the second ablated portion are selected. It is determined whether or not to exchange the temperature according to the exchange probability based on the energy and the temperature of each of the annealed portions of the annealed portion, and when the exchange is performed, the first correspondence information and the second correspondence The information is updated, and based on the updated second correspondence information, the temperature information representing the temperature is supplied to each of the corresponding plurality of annealing portions.
How to control the optimizer.

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