JP2022107518A - Information processing system, information processing method, and information processing apparatus - Google Patents

Abstract

To obtain proper solutions at a high speed.SOLUTION: An information processing system includes a storage circuit, and one or more processing circuits for executing parallel operation. The processing circuit calculates energy in multiple neighborhood states with respect to the current state by first parallel operation, calculates an index with which each of the states is selected on the basis of the energy in the multiple neighborhood states, calculates selection probability with respect to the neighborhoods on the basis of the index so that at least one of the neighborhood states is selected, and selects the next state from the neighborhood states on the basis of the selection probability.SELECTED DRAWING: Figure 1

Description

There is an application for application of Article 30, Paragraph 2 of the Patent Law. Website publication date October 21, 2nd year Reiwa 2. Website address https://quantum. fixstars. com / product https: // www. fixstars. com / ja / news / 2143 3. Publisher Fixstars Corporation

The present disclosure relates to information processing systems, information processing methods and information processing devices.

Simulated Annealing Algorithm is one of the leading combinatorial optimization methods. This simulated annealing method (1) defines a transitionable neighborhood from a certain state, (2) initializes an appropriate state, and (3) fixes the temperature and Markov Chain Monte Carlo method (MCMC). Optimize by creating a distribution by, (4) lowering the temperature, repeating the process of (3), and (5) terminating according to the termination conditions. Simulated annealing is a very versatile method in that it can operate if the cost function and its neighborhood in (1) can be defined.

However, simulated annealing has three major problems. The first point is that when the temperature is sufficiently low, the rate of rejecting the results calculated by MCMC increases, making efficient search difficult. The second point is that this rejection is determined by the energy based on the temperature and largely depends on the initial value and the change method of the temperature, but the ideal initial value and the change method differ greatly depending on the optimization target. The ideal temperature conditions for this optimization are also non-trivial. Therefore, there is a problem that the convergence accuracy and the speed are influenced by setting the optimum non-trivial temperature condition for each object or setting the highly versatile temperature. Thirdly, today, it is widely practiced to improve the calculation efficiency by parallel computing using multi-core and many-core processors, but it is necessary to parallelize the above steps for these processors. It is difficult to do so, and the performance improvement by parallelization is limited.

E. Sonuc, et. Al., “A cooperative GPU-based Parallel Multistart Simulated Annealing algorithm for Quadratic Assignment Problem,” October 2018, Engineering Science and Technology, an International Journal, volume 21, issue 5, pp. 843-849 D. J. Earl, et. Al., “Parallel tempering: Theory, applications, and new perspectives,” September 5, 2005, Phys. Chem. Chem. Phys., 2005, 7, pp. 3910-3916

The present disclosure provides an information processing apparatus capable of obtaining a good solution at high speed.

According to one embodiment, the information processing system comprises a storage circuit and one or more processing circuits capable of performing parallel operations. The processing circuit calculates energies in a plurality of neighboring states with respect to the current state by the first parallel calculation, and calculates an index for adopting each of the said states based on the energies in the plurality of neighboring states. , The adoption probability for the plurality of neighborhoods is calculated based on the index so that any one of the plurality of neighborhood states is adopted, and the next state is set to the state of the plurality of neighborhoods based on the adoption probability. Select from.

Further, according to one embodiment, the information processing method calculates energy by the first parallel processing in a plurality of neighboring states with respect to the current state by a processing circuit, and is based on the energy in the plurality of neighboring states. The first probability that each of the above states is adopted is calculated, the second probability that normalizes the first probability so that any one of the states in the plurality of neighborhoods is adopted is calculated, and the second probability is calculated. The next state is selected from the plurality of neighboring states based on.

Further, according to one embodiment, the program calculates the energies in a plurality of neighboring states with respect to the current state by the first parallel processing in the processing circuit, and based on the energies in the plurality of neighboring states, respectively. An index indicating whether or not the said state is adopted is calculated, and the adoption probability for the plurality of neighboring states is calculated based on the index so that any one of the plurality of neighboring states is adopted. Then, an information processing method is executed in which the next state is selected from the plurality of neighboring states based on the adoption probability.

Further, according to one embodiment, the information processing apparatus includes a storage circuit and one or more processing circuits. The processing circuit transitions the temperature by preset scheduling to execute simulated annealing, and in the iterative calculation of the optimization, the energy in the vicinity of the current state calculated by the optimization is the current energy. The number of the neighborhoods that is larger than the energy of the state is counted, the ratio of the counted number of the neighborhoods to the total number of the neighborhoods searched by the optimization is calculated, and the ratio and the neighborhoods are calculated. Based on the ratio adopted based on the temperature when the energy of the current state becomes larger than the energy of the current state, the reverse temperature, which is an index indicating the adoption probability of the neighborhood, is controlled.

The figure which shows typically the information processing system which concerns on one Embodiment. A flowchart showing the processing of simulated annealing. A pseudo code indicating an example of processing for adopting a solution according to an embodiment. A pseudo code showing an example of temperature schedule processing according to an embodiment. A pseudo code showing an example of obtaining the temperature change rate according to one embodiment. The figure which shows an example of the temperature schedule using FIG. The flowchart which shows an example of the parallel processing of the simulated annealing method which concerns on one Embodiment. Pseudo code showing an example of parallel processing of simulated annealing according to an embodiment. The figure which shows a part example of the process which concerns on one Embodiment. The figure which shows the example which changed the order of the steps which concerns on one Embodiment. The figure which shows the description example of the process which concerns on one Embodiment. The figure which shows an example of changing the processing order of work which concerns on one Embodiment. The figure which shows an example of changing the processing order of work which concerns on one Embodiment. The figure which shows an example of changing the processing order of work which concerns on one Embodiment. The figure which shows the example of the selection of the process which concerns on one Embodiment.

Hereinafter, the contents of some embodiments will be described with reference to the drawings. The embodiments shown below are shown as non-limiting examples, and the configuration and the like are not limited to these. In the present disclosure, terms such as "greater than or equal to" and "less than or equal to" may be used, but they are not strictly limited to these terms and may be appropriately read as "greater than or equal to" and "less than or equal to", and vice versa. Is the same.

(Hardware implementation example)
FIG. 1 is a diagram schematically showing an outline of an information processing system 1 according to an embodiment. The information processing system 1 includes, for example, an information processing device 100, external devices 90 and 94, and a network 92. The information processing system 1 is a system that implements a parallel annealing method.

The information processing device 10 includes a processing circuit 100, a storage circuit 102, and an interface 104. These configurations are appropriately connected by a bus 106 that sends and receives data between the configurations.

The processing circuit 100 is a circuit that executes processing such as calculations in the information processing apparatus 10. The processing circuit 100 is configured to include, for example, a general-purpose processor such as a CPU (Central Processing Unit). Further, the processing circuit 100 may include a processor driven as a general-purpose accelerator such as a GPU (Graphics Processing Unit). Further, the processing circuit 100 may be a circuit that executes dedicated processing such as an ASIC (Application Specified Integrated Circuit), or may be a programmable circuit such as an FPGA (Field Programmable Gate Array). These circuits may be composed of digital or analog circuits. The processing circuit 100 may be a circuit including at least two of the above, as long as the information processing can be appropriately executed.

The storage circuit 102 is a circuit for storing data and the like necessary for operations and the like in the information processing apparatus 10. When information processing by software is specifically realized by using hardware resources in the information processing apparatus 10 using the processing circuit 100, the storage circuit 102 is a program, an execution file, etc. required for executing this software. May be stored. The storage circuit 102 may include, for example, a main storage device and an auxiliary storage device. As described above, the storage circuit 102 in FIG. 1 is at least one of a storage and the like for storing non-temporary data and a cache memory and the like such as SRAM (Static Random Access Memory) for storing temporary data. May be provided.

The interface 104 realizes input / output of data to / from the outside of the information processing device 10. For example, the interface 104 may be a device interface connected to the external device 90 or a network interface connected to the network 92. The information received from the interface 104 may be stored in the storage circuit 102 non-temporarily or temporarily.

The external device 90 may be, for example, an input user interface such as a mouse or keyboard, or an output user interface such as a display. Further, the external device 90 may be a storage device such as a storage connected to the information processing device 10. Further, the external device 90 may be a server, a computer, or the like including a processor that executes a part of the processing of the information processing device 10. In this case, the external device 90 may be provided with a processing circuit such as a CPU or GPU different from the information processing device 10 and an appropriate storage circuit, and may be provided independently or in cooperation with the information processing device 10. It may be an implementation that can realize the processing.

The network 92 is a network including at least one of wired and wireless. The information processing device 10 may be connected to the external device 94 via the network 92.

The external device 94 basically has the same configuration as the external device 90.

In the information processing system 1, the processing is executed by the information processing device 10, but as described above, even if the processing is executed in cooperation with the external devices 90 and 94 in addition to the information processing device 10. good. For example, the processing may be realized by a cluster or the like via the network 92. The embodiments shown below may be realized by the information processing apparatus 10 alone, or may be realized by the information processing system 1 including the configuration of a cluster or the like. That is, it should be noted that in each of the following explanations, the part described as the information processing device 10 can be read as the information processing system 1.

(Implementation of Simulated Annealing)
FIG. 2 is a flowchart showing the processing of simulated annealing. This flowchart shows the processing of a general simulated annealing method, but in the present disclosure, a processing different from the general processing is executed in the processing in a predetermined step of this flowchart. First, the processing of a general simulated annealing method will be described with reference to FIG. Moreover, although it is described using the simulated annealing method, it is not limited to the simulated annealing method and can be applied to other similar optimization algorithms.

First, the processing circuit 100 performs initialization of parameters and states such as temperature required for optimization (S10). If necessary, the processing circuit 100 may store the initialized data in the storage circuit 102.

Next, the processing circuit 100 searches the vicinity of the current state (S20). Here, the state (hereinafter, also referred to as a solution in some cases) is a quantity (scalar, vector, or arbitrary tensor) indicating a point in the search space. By transitioning this state, the information processing apparatus 10 acquires the optimum solution.

Next, the processing circuit 100 calculates the energy (calculated using the cost function and the evaluation function) of the neighboring state searched in S20 (S30). The calculation of this energy is realized by a predetermined function. The processing circuit 100 may use an evaluation function generally used for each target physical phenomenon or event as a function for calculating the energy of the state.

Next, the processing circuit 100 updates the state based on the energy calculated in S30 (S40). The state update is performed, for example, by comparing the energy of the current state with the energy of the searched neighboring state and adopting the comparison result with a probability based on the temperature. For example, when the energy of the searched neighborhood state is smaller than the energy of the current state, the processing circuit 100 updates this neighborhood state as the state of the next step. On the other hand, when the energy of the searched neighborhood state is equal to or higher than the energy of the current state, the current state or the neighborhood state is selected as the state of the next step based on the probability based on the temperature. In a broad sense, the wording of the neighborhood state may be a concept including the current state. That is, in a broad sense, the processing of S40 may mean selecting an appropriate state from the neighboring states as the state of the next step.

Next, the processing circuit 100 determines whether or not the optimization end condition is satisfied (S50). The processing circuit 100 determines the end of processing based on conditions such as reaching a predetermined temperature, repeating updating a predetermined number of times, and energy falling below a predetermined value. This termination condition may be any condition as long as optimization is appropriately realized.

When the termination condition is satisfied (S50: YES), the processing circuit 100 outputs the updated state in S40 and terminates the processing (S60). In addition, necessary information may be output as appropriate. Further, the output timing does not have to be this timing, and for example, the energy value in S30, the updated state information in S40, and the like may be output at an appropriate timing.

If the end condition is not satisfied (S50: NO), the processing circuit 100 updates the temperature (S70) and repeats the optimization process (S20 to S40) until the end condition is satisfied.

The above is the processing flow of the general simulated annealing method. In the present embodiment, in the processing of each step, processing for improving the accuracy and speeding up of the processing is executed.

ここで、E_sは、現在状態のエネルギーであり、E_s+1は、探索された近傍状態のエネルギーである。式(1)のような確率に基づいて、近傍状態のエネルギーの方が大きい、すなわち、ΔE > 0の場合においても解が採択される。γは、正数であり、エネルギー差に対して必要であれば掛け合わせるゲインである。γは、エネルギーの定義によっては1であっても構わない。 (Embodiment for adoption)
Generally, in the simulated annealing process, a major problem is that the state is not updated when the temperature becomes sufficiently low. In S40, when the energy of the next state searched is larger than the energy of the current state, the probability of accepting the solution is expressed as follows as an example. This is shown as an example, and is not limited to this transition probability.

Here, E _s is the energy of the current state, and E _{s + 1} is the energy of the searched neighborhood state. Based on the probability as in Eq. (1), the solution is adopted even when the energy of the neighborhood state is larger, that is, when ΔE> 0. γ is a positive number and is a gain that is multiplied by the energy difference if necessary. γ may be 1 depending on the definition of energy.

FIG. 3 is a pseudo code showing an example (Algorithm 1) of the algorithm for adopting the solution in S40 according to the present embodiment. The adoption of the solution according to an example of the present embodiment will be described with reference to FIG. In this pseudo code, the processing of the update part of the solution (state) will be described. That is, the input is the current solution x and the output is the next solution x'.

1. In the processing circuit 100, let N _x be the number in the vicinity of the current solution x. The number of neighborhoods may be the number of neighborhoods that can be obtained in a predetermined range with respect to the current solution x. However, in general, the number of neighborhoods that can be acquired within a predetermined range is innumerable. Therefore, this number N _x may be predetermined as a predetermined number, or a form in which neighborhoods within this number may be acquired may be acquired. For example, N _x may be a number that can be operated in parallel. It is desirable that the processing circuit 100 searches for a plurality of neighborhoods so that they do not overlap.

2. In this adopted algorithm, the search of N _x neighborhoods set above is executed. Therefore, the processing circuit 100 prepares an array for storing N _x acceptance probabilities p _accepted and a storage area for storing this array. This arrangement may be reserved in advance in the storage circuit 102, and the processing circuit 100 may use this reserved space.

3. After making the above settings, execute parallel computing. The for statement described in 3. means the execution of parallel operations. That is, the processes in this loop are not executed sequentially, but are executed in parallel. For example, different neighborhood solutions are assigned to each GPU calculation core, and N _x operations are executed at the same timing. Hereinafter, it will be described as executing operations in the vicinity of each of the arithmetic cores in the GPU, but the parallelization method is not limited to the one allocated to the arithmetic core of the GPU, as long as the configuration can appropriately realize parallel arithmetic. do not have.

4. For example, calculate ΔE _i in each arithmetic core of GPU. Here, ΔE _i is the difference between the energy calculated in the i-th neighborhood and the energy in the current solution. As an example, this ΔE _i corresponds to the one calculated by using E _{s + 1} in Eq. (2) as the energy in the neighboring state and E _s as the energy in the current state.

5. In each arithmetic core, for example, the arithmetic based on the above equation (1) is executed, and the index for acquiring the adoption probability of the neighboring solution calculated in each arithmetic core is calculated. As can be seen from the fact that this index may be calculated from Eq. (1), it may be calculated using the adoption probability in a general simulated annealing method. When ΔE _i ≤ 0, for example, the adoption probability is 1. The index calculated in the arithmetic core that computes the i-th neighborhood is stored in p _accepted [i].

6. The processing circuit 100 ends the loop processing (parallel processing). For example, the subsequent processing may be executed by atomic calculation, or may be executed on the host side. The above-mentioned p _accepted [i] may be written as a shared memory shared between arithmetic cores as long as it is an array that is appropriately stored, or each arithmetic core may be written at the end of loop processing. It may be in the form of storing the output from.

7. Calculate the sum of the p _accepted values calculated by each arithmetic core, p _sum . This process may be executed on the host side after the above parallel process is completed, or may be further accelerated by a parallel operation using a reduction operation or the like during the execution of the processes 3 to 6. good.

8. Next, find p _accepted [i] / p _sum for i and standardize p _accepted . Due to this standardized probability (probability of adopting a solution), one neighborhood is always adopted as the next solution from N _x neighborhoods. It should be noted that standardization is given as an example of calculation for the distribution of probabilities, and standardization is not essential. In addition, standardization is not limited to the sum of indicators divided by individual indicators. If standardization is not performed, the process in 8. can be omitted, and even in this case, it is possible to select to transition the state with an appropriate probability based on the acquired p _accepted . Just do it.

9. The processing circuit 100 _extracts one is from N _x based on this standardized probability. As described above, by standardizing, one of all the neighborhoods is selected, and the solution is not rejected. Obtain one solution using a general method in which one solution is selected based on the individually set probability in both cases where the index is standardized as the adoption probability and when it is not standardized. You may use the method of

10. Processing circuit 100 updates the state x'near the selected _isth neighborhood as the next solution.

11. Then, the processing circuit 100 outputs the next solution x'and ends the processing of S30 to S40 in FIG.

As described above, in updating the solution, the processing speed can be improved by selecting the solution without rejecting the solution due to the temperature. In particular, it is possible to improve the search efficiency of the vicinity in the latter half of the optimization in which the temperature is lowered. As shown above, the search for the neighborhood can be parallelized, so for example, by using a GPU that can use tens of thousands of cores as parallel processing, the search for a solution can be realized efficiently. be able to.

It does not have to be a GPU, and a CPU, vector machine, or other architecture that is effective for parallel processing can be used.

In the above, the selection probability is calculated based on ΔE, but the probability of selection may be further changed depending on the value of ΔE. For example, in the process of calculating p _accepted , the probability may be set so that the transition such that ΔE <0 is prioritized. Similarly, the transition such that ΔE = 0 may be controlled to have a higher priority than the case where ΔE> 0, or conversely, it may be controlled to lower the priority. As an example, the processing circuit 100 calculates p _accepted [j] = p based on Eq. (1) regardless of whether ΔE is positive or negative, and by standardizing this p _accepted , one of the neighborhoods is selected. You may. Further, in the transition of this solution, the processing circuit 100 may set the value of p _accepted so as to lower the priority of the neighborhood once searched based on the tabu search.

Further, even when the cases are divided by ΔE, the priority may be set in ΔE in each arithmetic core, and the neighboring states may be stored in the array of the determined priority. For example, when ΔE is negative, the arithmetic core that calculates the state of each neighborhood is stored in the array of the first priority, and when ΔE is positive, it is stored in the array of the second priority. , ΔE = 0, it may be stored in a third priority array. Then, as one final solution, the first priority array may be selected in order.

For example, when the neighborhood is stored in the array of the first priority, one state may be extracted from this array and used as the next solution. If the neighborhood is not stored in the first priority array, the neighborhood is extracted from the second priority array by referring to the second priority array. Similarly, if the neighborhood is not stored in the second priority array, the next solution is obtained by referring to the third priority array. In this way, it is possible to expand the search space for the solution while suppressing the case where the solution is stagnant.

(Embodiment for temperature update)
The temperature update will be described below. Unless otherwise specified, the reciprocal of temperature T (or a value proportional to the reciprocal of temperature T) is defined as β, and this β is referred to as inverse temperature. In this embodiment, the reverse temperature β is used to define the solution selection. For example, the selection probability shown in Eq. (1) can be rewritten as follows.

FIG. 4 is a pseudo code showing an example of an algorithm (Algorithm 2-1) for the temperature update process. First, as parameters, the update frequency f _β of the reverse temperature, the initial value β _init of the reverse temperature, and the maximum number of steps step _max are set. This maximum number of steps, step _max , defines the number of temperature transitions in the optimization. This process is, for example, a process that conceives of the process of S70 in FIG.

1. ～ 3. First, initialize each variable. S _e and s _n are used to measure the average acceptance rate (hereinafter referred to as the retrograde acceptance probability) in the deteriorated neighborhood. s _e is information that represents the total acceptance rate of the deteriorated neighborhood. Deterioration means that ΔE> 0 during parallel processing of the above-mentioned solution adoption algorithm. s _n is the number of observed neighborhoods that deteriorate. The number of observed neighborhoods is the number of neighborhoods to be searched for in the solution adoption algorithm, and may be a fixed value when N _x is a fixed value. The reverse temperature β is initialized to the initial value β _init .

4. Based on the above parameters, perform the reverse temperature control in the above adopted algorithm. In general simulated annealing, for example, the temperature is lowered linearly or exponentially to cause a monotonous decrease in a broad sense. In the present embodiment, the inverse temperature is not monotonically reduced depending on the situation of ΔE, and the temperature is controlled without being bound by a function such as a linear function or an exponential function. This temperature update process is repeated _max times as described above.

5. The processes described in 6 to 12 below are the processes executed during the above Algorithm 1.

6., 7. These processes are explained in Algorithm 1 above, so the details are omitted.

8. ～ 11. After ΔE _i is calculated, each core measures the average acceptance rate when ΔE _i > 0, that is, when the solution is aggravated in the update of the solution. Since this processing is executed during parallel processing, it may be realized by, for example, an atomic operation. The processing circuit 100 counts the sum of the acceptance rates in the vicinity where the solution has been _aggravated as se by this processing. Also, as s _n , set the number of deteriorated neighborhoods in the processing in the loop. In addition, in updating the reverse temperature, another appropriate process may be used without using the number of neighbors that deteriorate. In the case of such a modification, the processing in this paragraph may be omitted if it is not necessary.

12. ~ 13. For example, other parallel processing of Algorithm 1 is executed.

14. Determine whether to update the reverse temperature in the current loop. Although the judgment is made at this point, this judgment may be made before Algorithm 1. In this case, in the execution of Algorithm 1, the algorithm in which the processes of 8 to 10 are omitted may be executed. As another example, by setting a flag, it may be possible to omit it at the timing when the processes of 8. to 10. are not updated. By doing so, the number of atomic operations can be reduced. Since such processing does not always improve in speed depending on the processing target, it may be appropriately set for each target, each program, and each optimization. When the condition of 14. is satisfied, that is, when the reverse temperature is updated, the following processes 15. to 19. are executed to update the reverse temperature.

15. First, by calculating the current step step / maximum number of steps step _max , the progress p of the current stage with respect to the entire process is obtained.

16. Next, the rate of change Δβ of β is calculated by the processing of Algorithm 2-2 described later. This Δβ is calculated by s _e obtained in 9., s _n obtained in 13., and p obtained in 15.

17. Based on Δβ obtained in 16., update the inverse temperature β with β = β (1-Δβ).

18., 19. Reinitialize s _e and s _n .

By this series of processing, the reciprocal of the temperature β, which is the reciprocal of the temperature, is updated every predetermined step f _β . This reverse temperature increases or decreases according to the rate of change calculated in 16. This increase / decrease will be described.

FIG. 5 is a pseudo code showing an example (Algorithm 2-2) of the above-mentioned processing for obtaining Δβ. As shown in 16. in Fig. 4, in this algorithm, the input is the degree of progress of processing p, the number of neighborhoods that deteriorate s _e , and the number of observed neighborhoods s _n . Then, the output is a ratio Δβ that is multiplied by the update of the reverse temperature. What is required as a parameter is the maximum amount of change Δβ _max of the reverse temperature.

1. First, calculate the ratio r _real of the deteriorated neighborhood in the searched neighborhood. This ratio is obtained by the ratio s _e / s _n of the input variables.

2. The processing circuit 100 acquires r _target as a target value of the deterioration rate of the neighborhood depending on p. This r _target may be calculated in advance or may be calculated by a parameter determined by the target. As described above, this target value is represented by, for example, a linear function, an exponential function, or the like. If it is calculated in advance, it may be stored in the storage circuit 102.

3. The processing circuit 100 calculates and outputs Δβ based on the difference between the target value and the calculated value, that is, the difference between r _target and r _real . For example, the processing circuit 100 calculates and outputs Δβ = Δβ _max (r _target --r _real ).

FIG. 6 is a diagram showing the transition of an example of the temperature schedule. The dashed line indicates the ideal retrograde adoption probability (corresponding to r _target ) in optimization, and the solid line indicates the measured retrograde adoption probability (corresponding to r _real ). The horizontal axis shows the number of times the temperature (reverse temperature) is updated, and the vertical axis shows the retrograde adoption probability. The processing circuit 100 does not directly regulate the temperature, but controls the reverse temperature until the next reverse temperature update based on the temperature and the ratio of the current deteriorated neighborhood. By performing the processing in this way, the retrograde adoption probability can be brought close to the ideal value based on the measured value of the retrograde adoption probability without directly controlling the temperature.

The processing circuit 100 controls the reverse temperature as shown in FIGS. 4 to 6. With reference to FIG. 6, when the probability of retrograde adoption in the current step is higher than the ideal retrograde adoption probability based on the temperature schedule, the reverse temperature is controlled so as to reduce the retrograde adoption probability. This is based on Equation 3 of Algorithm 2-2.

If the retrograde adoption probability in the current step is higher than the ideal retrograde adoption probability, the output of Algorithm 2-2 is large in the negative direction, and the inverse temperature is higher than 17. of Algorithm 2-1. This result affects the value of 5. of Algorithm 1 and reduces the probability of being adopted if the searched neighborhood deteriorates.

On the contrary, when the retrograde adoption probability in the current step is lower than the ideal retrograde adoption probability, the output of Algorithm 2-2 is increased in the positive direction and the inverse temperature is controlled to be low. As a result, the calculation in 5. of Algorithm 1 increases the probability of being adopted when the searched neighborhood deteriorates.

In this way, instead of directly controlling the temperature, the processing circuit 100 in this embodiment controls the adoption probability with respect to the ideal adoption probability schedule. As described above, the processing circuit 100 lowers the retrograde adoption probability when the rate of retrograde adoption in the actual neighborhood is higher than the ideal retrograde adoption probability, and increases the retrograde adoption probability in the opposite case.

As described above, by controlling the retrograde adoption probability, if the rate of deterioration in the observed and searched neighborhood is larger than ideal, the probability of deterioration is controlled to be higher than the current step, and the deterioration is performed. If the ratio is smaller than ideal, the probability of deterioration is controlled to be lower than the current step. By controlling in this way, it is possible to control the probability that the solution will be adopted in the case of adaptively reversing.

The original role of temperature is to adjust the rate of deterioration of the neighborhood being searched for, and changing this temperature is highly problem-dependent and difficult to adjust for various problems. .. On the other hand, as in the present embodiment, by controlling the acceptance probability based on the statistical information, it is possible to reduce the dependence on the problem.

The pseudo codes in FIGS. 4 and 5 are shown as an example, and the calculations in the algorithm may not be the same. For example, the methods of calculating the retrograde adoption probability, such as 1 and 2 in FIG. 5, are not limited to these, and may be any one that can appropriately control the retrograde adoption probability as described above. In addition, the ideal retrograde adoption probability, which is the broken line shown in FIG. 6, is drawn as a linear function as an example, but this is not limited to this, and the adoption probability is appropriately set with respect to the temperature as in the exponential function. Any function may be set. For example, a function equivalent to the reciprocal, or a function represented by the reciprocal of a logistic function such as a sigmoid function or a hyperbolic cosine function can be mentioned, but the function is not limited thereto.

As another example of the above, instead of controlling by the number of deterioration neighborhoods, some value, for example, a predetermined value or the adoption probability based on the temperature schedule is added to the adoption probability of the deterioration neighborhood, or , The adoption probability in the case of deterioration may be controlled by multiplying. For example, the adoption probability may be controlled by adding the adoption probabilities of the neighborhoods instead of the number of the neighborhoods that deteriorate.

Furthermore, the update itself of 17. of FIG. 4 may be changed instead of 1 and 2 of FIG. For example, it is not limited to multiplying by a certain ratio, and this ratio may be changed by using inertia, moving average, or the like.

In recent years, quantum annealing machines have been attracting attention as hardware that executes optimization problems at high speed, and many efforts have been made to realize operations similar to quantum annealing machines using simulated annealing on classical computers. In these efforts, after describing the problem with the Ising model, the model is expressed in the QUBO (Quadratic Unconstrained Binary Optimization) format corresponding to this Ising model and optimization is executed. This formulation is done using binary variables 0 and 1. You can also describe optimization problems directly in QUBO format.

When optimizing for variables with few variables or low-dimensional relevance, it is possible to realize operations using these 0 and 1 binaries. On the other hand, when there are many variables or the relationships between variables are complicated, the problem is expressed in binary format, and optimization using binary variables increases the calculation cost.

In particular, when the state transition in the search for the neighboring state is repeated by the simulated annealing method, the restrictions in the transition process become very large and the calculation load becomes high.

Therefore, the calculation cost can be reduced by expanding to an integer variable instead of a binary variable. After expanding to an integer variable, it becomes easy to repeat the search for the neighborhood using the above algorithm. In this way, variables and constraints representing states such as the current state and states in the vicinity thereof may be realized by using integers.

(Implementation for parallel processing)
In each of the above algorithms, parallelization is realized for the search of the neighborhood, but it is possible to further improve the particle size of parallelization. The information processing apparatus 10 may, for example, execute a plurality of simulated annealing methods in parallel. In the simulated annealing method executed in parallel, the above-mentioned neighborhood search algorithm is realized in parallel.

FIG. 7 is a flowchart showing processing when the simulated annealing method is executed in parallel. The information processing device 10 executes two-step parallelization. The outer parallel processing is parallel processing in which simulated annealing is executed based on each state (replica). The inner parallel processing is a parallel processing in which the annealing method itself is executed by searching for a neighborhood with respect to the state based on the above-described embodiment or a method similar thereto. In the following, the search for the neighborhood based on Algorithm 1 etc. will be referred to as the first parallel processing, and the parallel optimization based on FIG. 7 etc. will be referred to as the second parallel processing.

First, the processing circuit 100 that executes the processing (second parallel processing) for each replica selects the initial state (initial value) (S100). At the beginning of optimization, this initial state may be set to a predetermined initial state set in advance, or a randomly given state may be acquired. Further, the process may be a process of setting the reverse temperature together with the state.

Simulated annealing is then performed on each replica (S110). In this simulated annealing method, the parallel processing described in FIGS. 3 to 6 is executed in the neighborhood search. This simulated annealing method may be executed by the first parallel processing.

Next, in each replica, it is determined whether or not to update the optimum solution acquired at the present stage acquired by annealing, and if updating, the optimum solution is updated (S120). To determine whether to update, for example, the energy value of the result of annealing in the previous stage stored in the replica is compared with the energy value of the result of annealing in the current stage, and the energy in the current stage becomes smaller. You may update it if you have one. This update may also be adopted even when the energy value increases at a rate based on the parameter by using a parameter based on the temperature.

Next, the processing circuit 100 determines whether or not the termination condition is satisfied based on the optimum solution output by each replica in the second parallel processing (S50). This determination may be made under the same conditions as the process of S50 in FIG. 2, such as performing the repeated calculation a predetermined number of times, the energy falling below the predetermined value, and the like. When referring to the energy value, the energy value for the solution obtained in a plurality of replicas may be compared and the minimum one may be selected, or the energy value may be determined by another method.

If the end condition is satisfied, the status is output (S60) and the process ends.

On the other hand, if the end condition is not satisfied, the process from S100 is repeated. Here, in the second and subsequent processing of S100, among the solutions obtained from a plurality of replicas, the optimum solution, for example, the solution having the minimum energy value, and the reverse temperature may be set as the initial state.

The above-mentioned neighborhood search process may be appropriately executed using a multi-core processor or a many-core processor. For example, when a GPU is used as an arithmetic unit, it may be executed by arithmetic block parallel, thread parallel, or parallel arithmetic using a plurality of boards. Here, thread parallel means processing a plurality of threads in parallel. Further, in the present disclosure, the operation block parallel means a parallelization concept in which threads are grouped and one step higher than the thread parallel. As a non-limiting example, a shared memory that can be accessed at high speed from each thread in the same arithmetic block may be provided.

For example, parallel operation may be executed for each replica, or parallel operation may be executed for each neighborhood in the replica. By performing the operations in parallel in this way, it is possible to realize the neighborhood search at high speed in a metaheuristic method such as Simulated Annealing as shown in FIG. As shown in FIG. 2, the metaheuristic method is to calculate the energy of a plurality of neighboring states for each initial state (initial value) (S30) and update the state (S40. To obtain the adoption probability). Includes at least index calculation, adoption probability calculation, and selection of next state).

As another example, in the known best solutions output by a plurality of replicas (optimal solutions output by each replica in the above), a predetermined number of states are acquired from the one with the smallest energy value, and a predetermined value is set as the initial value of the next process. The known best solution may be distributed according to the ratio of. For example, the first best solution, which is the minimum energy at the present stage, and the second best solution, which is the second smallest energy, may be assigned as the initial states of a plurality of replicas.

Specifically, assuming that there are 50 replicas, the first best solution may be set as the initial state for 30 replicas, and the second best solution may be set as the initial state for 20 replicas. The known best solution to be selected may be 3 or more, and the distribution ratio is not limited to the above. The number of known best solutions to be selected may be a predetermined value, or as another example, known best solutions having an energy value equal to or less than the minimum energy value multiplied by a predetermined value may be distributed.

As another example, a plurality of states within a predetermined range may be extracted from the first best solution and the like and sorted. In this case, the energy, the reverse temperature, etc. may be recalculated according to the statistical value or the like, or the energy, the reverse temperature, etc. for the state of the first best solution or the like may be used.

When obtaining a plurality of best solutions as described above, the optimization parameters of the first predetermined number pattern are given to the first best solution at the stage of searching for the solution in the next iteration, and the second best solution is obtained. The neighborhood search may be executed by giving the optimization parameters of the second predetermined number pattern equal to or less than the first predetermined number. Of course, the solution is not limited to the first best solution and the second best solution, and three or more best solutions may be obtained.

Here, the optimization parameters are parameters related to the retrograde adoption probability and temperature scheduling. As a more specific example, the optimization parameter may be at least one of, but is not limited to, the target value of the retrograde adoption probability, the scheduling parameter of the target value, or the update frequency of the reverse temperature. do not have.

As yet another example, the predetermined order state of the known best solutions output by a plurality of replicas (for example, the known best solution of the median energy value and the known best solution of the maximum energy value) may be set as the initial state of at least one replica. .. As another example, a state based on a statistic such as an average value of the state may be used as the initial value of at least one replica. By adding a replica that sets a state other than the state in which the energy has the minimum value or a value close to the minimum value as the initial value in this way, a wide range of states can be searched.

In addition, a form in which a state or the like is randomly selected may be used, or a form in which an initial state is adopted at a ratio based on an energy value stored (shared between replicas) in each replica, for example, energy. The form may be selected so that the smaller the value, the higher the probability of being adopted. In this way, various methods can be implemented for selecting the initial state.

In the optimization stage, a neighborhood search for each initial value (initial state) may be assigned to a parallel computing block such as a GPU. The arithmetic cores of the same arithmetic block can, for example, execute neighborhood searches based on the same initial values in parallel. By using a plurality of operation blocks, operations from a plurality of initial values can be executed in parallel. Higher-speed optimization can be executed by performing parallel operations on neighboring states and evaluations based on each initial value.

From the states searched from a plurality of initial values, a plurality of states may be selected based on a preset rule and these may be set as new initial values. By reassigning this new initial value to the calculation block, parallel calculation can be appropriately executed for the new initial value as well.

When allocating arithmetic blocks for each initial value as described above, the number of arithmetic blocks in optimization may be set as a divisor of the number of arithmetic blocks suitable for GPU or the like. By setting it as a divisor, it is possible to execute parallel operations of neighborhood search in which initial values are appropriately set for each unit in an arithmetic core such as GPU. Further, one GPU or the like may be the same arithmetic block. That is, when a plurality of GPUs or the like are used, it is possible that each GPU or the like executes a neighborhood search from the same initial value.

Further, when a plurality of arithmetic blocks are assigned to one replica, different optimization parameters (for example, temperature parameters) may be assigned to each arithmetic block. By using different optimization parameters for the same initial value, optimization can be performed using the states in different search paths.

FIG. 8 shows an example (Algorithm 3) of the algorithm for the second parallel processing of FIG. 7 as pseudo code. The output is the solution obtained by optimization. As parameters, the number of replicas to be executed at the same time n _r and the number of optimization iterations n _iter are defined. The number of replicas executed at the same time is the number of replicas that execute the above-mentioned second parallel processing at the same time.

1. First, prepare the array result [n _r ] that stores the optimal solution in the replica. result is an array of structures that store, for example, state, reverse temperature, and energy for each element. For example, it has a structure of result [i] = (x ⁱ , β ⁱ , E ⁱ ). x ⁱ is the state in the i-th replica, β ⁱ is the inverse temperature in the i-th replica, and E ⁱ is the energy in the i-th replica.

2. This loop represents how many times the annealing performed in parallel is repeated. That is, it means that optimization using annealing in parallel in n _r replicas is repeated n _iter times.

3. On the other hand, this loop is a loop that represents the second parallel processing of annealing. It means that the processes from 4 to 17 are optimized by annealing in parallel in n _r ways using n _r replicas. That is, the processes in this loop are not executed sequentially, but are executed in parallel.

4. ～ 8. Set the initial value for the replica. At the beginning of the loop, the initial value of the replica state is set by the process of 5. For example, it may be in a state given in advance or in a state of being acquired by a random number. The initial energy may be a sufficiently large value (for example, the maximum value in the variable type). The initial value of the reverse temperature sets the initial value of the temperature set for all replicas.

From the second loop, the replica state is selected from result [] and set by the process of 7. As the selection method, as described in the flowchart above, for example, the state in which the energy is minimized is selected, or some states are distributed according to a predetermined ratio.

9. This loop sets how much annealing optimization to perform for each replica. For example, this loop defines how many times the processing corresponding to the processing of Algorithm 2-1 is executed, and in this case, the number of repetitions may be determined based on the number of temperature updates. MaxStep indicates the number of repetitions.

10. Here, the processing of Algorithm 1, 2-1, 2-2 (first parallel processing) is executed. It should be noted that the processing is not limited to exactly the same as the above-mentioned algorithm. For example, an algorithm such as Algorithm 1 that does not perform parallel search of the neighborhood may be used (processing that does not use the first parallel processing), but of course, it is better to execute the search of the neighborhood by the first parallel processing. .. Similarly, optimization using only Algorithm 1 may be performed without controlling the reverse temperature, such as Algorithm 2-1 and the like. In addition, the update rate of the reverse temperature may be defined according to Algorithm 2-2. As described above, the processing in this line may be any one that can appropriately realize the processing by annealing, but from the viewpoint of accuracy and calculation speed, the above Algorithm 1, 2-1, including the first parallel processing It is desirable that the process conforms to 2-2.

11. ～ 15. Based on the state obtained by the above algorithm, the best energy, inverse temperature, and solution are updated by the energy value. The details are as described in the above flowchart. For example, in the i-th replica, the best energy value obtained in the process of 10., the inverse temperature giving this best energy, and the state with respect to the best energy are set as E ⁱ _best , β ⁱ _best , and x ⁱ _best , respectively. The final output of the process of 10. may be updated, or the state of the minimum energy in the process of 10. may be updated.

In the latter case, the memory area for storing energy, reverse temperature, and state is secured even in the optimization, and the stored energy becomes smaller after the processing of 10. For example, the execution of 5. in Fig. 4. If so, the energy, reverse temperature, and state may be updated. By doing so, even when the case of deterioration due to the reverse temperature is finally output, the state or the like can be updated using the optimum value acquired in the process of optimization.

17. Store the solution for the best energy obtained in the processes of 4. to 16. in result [i].

Then, in the loops 3 to 17. from the second time onward, the state that was optimal as the initial value of each replica up to the previous loop in the process of 7. It is possible to set a state in which various optimizations can be realized.

As described above, parameters such as a good solution and reverse temperature can be shared with other replicas, and the periphery of the good solution can be efficiently searched. By executing the search in this way, it is possible to solve the simulated annealing process in which it is difficult to arrange the solution, set the initial temperature, and the like during the execution of the optimization.

In the process of 7. in Fig. 8, the same state may be set for multiple replicas, but even in this case, Simulated Annealing is a highly random method, so it differs for each replica. It is possible to converge on the state and secure diversity. From the above, even when the arrangement of the initial solution, the initial parameters, etc. are not obvious in order to find a better solution, by using the method according to the present embodiment, the solution can be searched for in a wider range at the initial stage. While gradually narrowing the range, it is possible to search for a solution within a narrow range with high accuracy and high performance.

According to the above-described embodiment, it is possible to improve the convergence speed, control the transition to an appropriately deteriorating state based on the ideal retrograde adoption probability, and use a multi-core or many-core processor. It is possible to execute an algorithm that effectively realizes parallel computing in a device including.

(Implementation example)
Hereinafter, as an example without limitation, a specific example will be described using optimization of the job shop scheduling problem, which is a schedule management problem in the manufacturing process.

The job shop scheduling problem is, for example, an optimization problem that determines how to allocate jobs to efficiently proceed when processing a plurality of jobs (products) using a plurality of machines. This optimization can be performed by various conditions such as, for example, the most time-efficient, the earliest product can be shipped, or the number of products manufactured does not fluctuate on an average time. In this implementation example, how to solve this job shop scheduling problem in the above-described embodiment will be described. In the present application, the processing order of work (product) for a certain machine may be simply referred to as a process. Further, although the job shop scheduling problem will be described below as an example, the method of the present application can be widely applied to a schedule problem for determining the processing order, such as a traveling salesman problem.

For example, as a scheduling optimization, when the order of one job and another is swapped, in the binary format, for example, for the matrix shown in binary, the corresponding pair of two elements is used. Equivalent to swapping. In this order change, it is necessary to determine whether or not the constraint condition is satisfied. For example, constraints on rows, constraints on columns, and other constraints need to be determined before and after swapping, and when the relationships between variables become complicated, enormous computational costs are spent in determining these constraints.

On the other hand, for example, by expressing the work as an integer value, these exchanges can be realized only by exchanging two variables arranged in order in chronological order. Moreover, by expressing it as an integer value, it is possible to reduce the dimension of the variable. Therefore, the optimization can be realized by paying attention to the cost function considering only the work order. Further, since it is possible to realize a neighborhood in which a plurality of jobs are exchanged only by exchanging variables, it is possible to further improve the efficiency of neighborhood search.

Although the job shop scheduling problem is dealt with here as an example without limitation, it can be applied to other scheduling problems as well.

FIG. 9 is a diagram showing an example in a part of the initial state (state before optimization) of the process table according to the embodiment. It shows which work A to F is processed by each machine 1 to 4 at each time 1 to 3. Regarding this schedule, for example, consider acquiring a schedule that can reduce some cost and improve performance by optimization. For example, a case where the work in the machine 3 is exchanged will be given.

FIG. 10 shows an example in which the processes of the machine 3 in the schedule of FIG. 9 are replaced. As shown in FIG. 10, the process of the machine 3 which was B, C, F is replaced with F, C, B or B, F, C as a neighborhood search, and then the evaluation value is acquired. Then, heuristics or metaheuristics are used to optimize the schedule. The information processing system 1 executes schedule optimization so that the evaluation is high or the energy is low, for example.

The evaluation or energy is calculated based on information such as acceleration / delay of processing time that is changed by exchanging each work, for example. The information processing system 1 may calculate an evaluation value using, for example, the number of products manufactured per actual processing time, the delivery delay time, the acceleration / delay of pipeline processing, the estimated yield, and the like.

This evaluation or energy is not limited to the machine 3, but heuristics and metaheuristics are used to carry out this evaluation or energy. Then, the information processing system 1 optimizes based on the evaluation using the plurality of replicas in the above-described embodiment and the reverse temperature.

FIG. 11 shows an expression showing a process formulated by QUBO variables when optimizing a quantum annealing machine or an operation similar to a quantum annealing machine by using simulated annealing on a classical computer, and the present embodiment. It is a figure which shows the implementation of the process which concerns on. As shown in the figure on the left, the process in the form that realizes optimization using quantum computing is to represent the state in a binary representation of 0 and 1 in a matrix with time steps and work IDs. Implemented by. For example, in the figure on the left, the schedule is expressed such that the work of ID 1 at time 1 and the work of ID 3 at time 2.

State transitions, here work changes, etc., require changes that involve variable constraint violations. In the QUBO model, the process is expressed in this way. For example, when exchanging the job with job ID 3 at time 2 and the job with job ID 4 at time 4, "1" in the 3rd row and 2nd column of the matrix and "1" in the 4th row and 4th column are used, respectively. , It is necessary to replace with "0" in the 4th row and 2nd column and "0" in the 3rd row and 4th column.

However, when this binary representation is used, the dimension of the variable becomes higher when the work is processed sequentially in each process, and when the transition in annealing is repeated, there are many restrictions that must be taken into consideration in the transition. , The calculation cost becomes high by the calculation considering such a constraint condition. For example, in the above example, there are restrictions on the replacement of the values in the 3rd row and the replacement of the values in the 4th row, and the replacement of the values in the 2nd column and the replacement of the values in the 4th column, respectively. Each has its own restrictions. Such constraints must be executed each time the optimization neighborhood is searched, and there is a possibility that the calculation cost will be very high in the constraints on variables and other factors.

Therefore, in the present embodiment, for example, the calculation cost can be significantly reduced by expanding the variable described in binary in quantum annealing to an integer variable. The figure on the right is an extension of the expression of the work ID to an integer variable. For example, the process P1 is the process represented by the matrix in the figure on the left, and each process in this process can be arbitrarily replaced. In addition, as shown as P2, P3, and P4 in the right figure of FIG. 11, since integer representation can be performed for a plurality of processes in the same manner, the dimension of the variable is reduced as compared with the case of expressing with the QUBO variable. be able to.

FIG. 12 is a diagram showing an example of switching the processing order (neighborhood search) in the process according to the embodiment. The information processing system 1 replaces jobs 3 and 4, which are processes at times 2 and 4 in process P1, for example, in the annealing process. In FIG. 12, only the processes related to one step P1 are replaced, but the present invention is not limited to this.

FIG. 13 is a diagram showing another example of changing the processing order of the steps according to the embodiment. In the information processing system 1, for example, in the annealing process, the processing order of a plurality of processes may be exchanged.

Although FIG. 12 has been described as, for example, changing the processing order in one product in the process, it may mean the replacement of two products in the process. In this case, FIG. 13 means the replacement of two products in a plurality of steps.

FIG. 14 is a diagram showing still another example of changing the processing order in the process according to the embodiment. The information processing system 1 may replace the same combination of processes in a plurality of steps, for example. In FIG. 14, the processing order of all jobs 2 and 3 is exchanged, but the processing order is not limited to this. The processing circuit 10 may replace the processing order of the work of the same combination in the combination of any plurality of processes, for example, not all the processes.

For the above-mentioned replacement of the processing order in the annealing process, a cost may be set for each combination to be replaced. The information processing system 1 may execute the calculation of the energy value in the annealing process by formulating the cost.

For example, different costs are assigned to the case where the processing order of work 3 and 4 is changed as shown in Fig. 12 and the case where the processing order of work 2 and 3 is changed as shown in Fig. 14, and the energy value considering this cost is assigned. It may be calculated. Further, different costs may be assigned to the cost related to the replacement of the processing order in one process as shown in FIG. 12 and the cost related to the replacement of the processing order in a plurality of processes as shown in FIG.

By formulating the cost in this way, optimization can be realized while the administrator constrains the processing order of the process to some extent.

In the present embodiment, the neighborhood search is executed as shown in FIGS. 12 to 14 as some non-limiting examples, but this process can be executed as a parallel process. The information processing system 1 can execute many neighborhood searches at the same timing by performing parallel processing. According to the processing method using the replica shown above, the annealing process can be realized in parallel.

FIG. 15 is a diagram showing a state of replacement of processing in a process in a plurality of replicas and an example of extracting a part of energy values. Here, eight replicas of replicas R1 to R8 are extracted as some replicas. Replicas R1 and R2 have the same initial state. Similarly, replicas R3, R4, replicas R5, R6, replicas R7, R8 have the same initial state.

The hollow right arrow in the figure indicates the annealing process and indicates that the process shown on the left side of the arrow is optimized for each replica to the process shown on the right side of the arrow by annealing. The numbers in rows A and B in the table to the right of the arrow are numbers indicating the work actually processed at each of the times 1 to 7. The numbers shown to the right of the table are the optimized energies for each replica. These processes are executed according to the processes in the replica of FIG. 8 based on FIGS. 4 and 5.

After being optimized for each replica, the information processing system 1 acquires replicas with overlapping energy values as candidates for the initial value of the next annealing cycle by deleting all but one result. The information processing system 1 then orders the candidates from the replicas acquired based on energy. This is done according to the algorithm shown in Figure 8. For example, in the example of FIG. 11, the solutions obtained from replicas R2, R5, and R8 are stored in result [i] in this order, and the best solution is updated. Then, according to the algorithm of FIG. 8, the next initial value is selected from the ordered candidates, and the operation of the next iteration is executed.

In this embodiment, after optimization for each replica, replicas with overlapping energy values are deleted except for one result, but the method for deleting duplicate replicas is not limited to this. do not have. For example, whether or not a plurality of replicas are duplicated may be determined based on whether or not one or a plurality of steps are the same, rather than whether or not the energy values are the same.

Further, as shown in FIG. 15, the same initial value may be given to a plurality of replicas. This corresponds to setting the same initial value between replicas in the replica settings shown in the 3rd to 17th lines in the algorithm shown in FIG. In the example of FIG. 8, it appears that all replica values are initialized with the same default values, but it is not limited to this. For example, as shown in FIG. 15, the same default value may be used for a plurality of replica groups, and different default values may be used among different replica groups.

The information processing system 1 may assign the evaluation of the state of the vicinity to each initial value to a plurality of arithmetic blocks such as GPUs. For example, if there are 100 jobs and each job is replaced only once, the combination is ₁₀₀ C ₂ = 4950, and if one arithmetic block can perform parallel processing in 1024 threads, then 4950/1024 = 4.8. , 5 loop operations are required. On the other hand, by executing this process in 5 arithmetic blocks, the evaluation value in this replacement can be acquired by one loop arithmetic.

The selection of the initial value is not limited to the above. For example, the information processing system 1 selects a plurality of states from the final state of the previous loop derived from the plurality of initial values based on a preset rule, and searches the neighborhood again using these as new initial values. May be executed.

When implemented on a GPU or the like, the information processing system 1 can also set the number of the above-mentioned plurality of arithmetic blocks to be a divisor of the number of arithmetic blocks that can be paralleled.

When processing by a metaheuristic method is executed independently for each initial value from multiple initial values, it is possible to use the GPU efficiently by making this number a divisor of the number of parallel arithmetic blocks. .. In the information processing system 1, for example, when the number of parallel arithmetic blocks is 80, the number of replicas that give initial values is 2, 4, 5, 8, ..., which is a divisor of 80. The number of each replica calculated in parallel can be equalized. As a result, it becomes possible to use the GPU efficiently. Similarly, when the information processing system 1 is provided with a plurality of GPUs, the number of usable GPUs based on the divisor of the number of parallels can be used.

In this way, the information processing system 1 may perform enumeration and evaluation of replacement candidates of the processing sequence in parallel with the arithmetic blocks of the GPU, in parallel with threads, and in parallel with a plurality of boards. In the following cases, such an implementation has the effect of increasing the speed and improving the accuracy.

Further, as described above, it is also possible to search for a solution using different optimization parameters such as temperature for the same initial value by using different arithmetic blocks.

The information processing system 1 may configure a plurality of replicas for the same initial value as described above. When the metaheuristic method is simulated annealing, the information processing system 1 sets different values for various parameters such as temperature parameters, so that the size of the selected neighborhood area is different. Search can be realized. By implementing in this way, the search in a wide range is realized in the replica where the reverse temperature is set small, and in the replica where the reverse temperature is set large, the fine grain size in a narrow range is realized. The search can be realized.

Such an implementation is also effective in a search method such as tabu search, and it is possible to implement the same in other metaheuristic methods.

Further, the process of searching for a solution from the process order given as the initial value may be executed with a plurality of initial values and a plurality of (two or more) optimization parameters. In this case, a plurality of candidates that are highly evaluated during the search may be extracted, one or a plurality of optimization parameters may be given to the extracted processing order, and the solution search may be executed again. That is, when the information processing system 1 executes the process of searching for a solution from the processing order given at the initial stage with a plurality of initial values and a plurality of optimization parameters, the information processing system 1 extracts a plurality of candidates who have obtained a high evaluation during the search. Then, a plurality of optimization parameters may be given to the extracted processing order, and the search shown in FIG. 8 or the like may be executed.

As described above, the optimization parameter may be at least one of the target value of the retrograde adoption probability, the scheduling parameter of the target value, or the update frequency of the reverse temperature, but is not limited to these. do not have.

For example, as described in the example of FIG. 15, the information processing system 1 stores the solutions obtained from a plurality of different replicas R2, R5, and R8 in the result [i] in this order, and updates the best solution. .. Then, the information processing system 1 may realize optimization by using, for example, a plurality of best solutions extracted from the upper level among these best solutions and initializing them as default values of the next replica.

The information processing system 1 may use, for example, the best solution obtained from the replica R2 as the initial value of the next replicas R1 to R4. Then, the best solution obtained from the replica R5 may be the next replica R5, R6, and the best solution obtained from the replica R8 may be the next replica R7, R8. Then, optimization parameters such as temperature (reverse temperature) may be given to each replica. By assigning different numbers of replicas to the ordered candidates in this way, it is possible to efficiently execute a wider-range and high-grain size neighborhood search in the best solution with good evaluation (low energy).

In the above, the processing of work in the process is used, but this is not a concept bound by these words. For example, work may mean another concept such as processing (process), task, subtask, used / generated / processed product (product), and process may mean process, pipeline, etc. It can also be replaced. The same applies to the description of the scope of claims.

The information processing system 1 has been determined to perform optimization using simulated annealing over the plurality of embodiments described above, but the optimization method that can be used is not limited to this. As another example, the information processing system 1 can be applied by incorporating the concept corresponding to the temperature of simulated annealing in other evolutionary algorithms and metaheuristic optimization algorithms.

To summarize the contents of the present disclosure, the information processing system includes a storage circuit and one or more processing circuits capable of executing parallel operations. The processing circuit calculates the energy in a plurality of neighborhood states with respect to the current state by the first parallel processing, and determines whether or not each of the plurality of neighborhood states is adopted based on the energy in the plurality of neighborhood states. Calculate the indicated index, calculate the adoption probability for multiple neighboring states based on the calculated index so that any one of the multiple neighboring states is adopted, and based on this adopted probability, the next state Is selected from the plurality of neighboring states.

In the above processing, the processing circuit may standardize the index and acquire the adoption probability. Further, as shown in the above-described embodiment, the processing circuit may perform the above processing as the processing for optimizing the annealing. In this case, the index may be calculated based on the temperature or the difference between the energy of the current state and the energy of the neighboring state. The processing circuit may acquire this index as the adoption probability that the next nearby state is selected.

As described above, for example, as shown in FIG. 6, the processing circuit has a retrograde adoption probability in which the energy of the state in the vicinity after the transition in the calculation stage up to the current stage is larger than the energy of the state before the transition. And, based on the pre-scheduled ideal retrograde adoption probability, the reverse temperature can be controlled so that the retrograde adoption probability approaches the ideal retrograde adoption probability. Then, the processing circuit may calculate an index for determining the adoption probability based on the reverse temperature.

The processing circuit may use a plurality of replicas showing the current state, and the first parallel processing may be executed in the replica as a part of the second parallel processing. In this case, the processing circuit updates the state based on the energy calculated by each first parallel processing, and can select the state of the next replica from the plurality of states updated as the second parallel processing.

As described in the specific example, the processing circuit may describe the state using an integer value. In a scheduling problem, at least one of the changes in the processing order of one product on a machine, the swapping of two products, or the swapping of the processing order of two products in the same combination on multiple machines, is in multiple neighborhood states. It may be at least one of them.

The processing circuit may include a GPU having one or more arithmetic blocks, and can execute a metaheuristic method for a plurality of initial values in the current state. Multiple neighborhood states for each initial value are, for example, at least one of GPU arithmetic block parallelism, thread parallelism, and parallelization using multiple GPUs for enumerating and evaluating the combination of components in multiple neighborhood states. You may process using one. Further, by using a plurality of arithmetic blocks, it is possible to enumerate and evaluate a combination of correction candidates for at least one plurality of initial values. Further, the number of arithmetic blocks may be a divisor of the number of arithmetic blocks that can be paralleled. Further, for the same initial value, a search for a neighborhood using different optimization parameters may be executed using different arithmetic blocks.

In the process of selecting a plurality of neighboring states, the processing circuit may extract and order a plurality of candidates that have obtained a higher evaluation than the other states among the plurality of states based on energy, and based on this ordering. For example, a neighborhood search using different optimization parameters may be performed using different arithmetic blocks for candidates whose order is earlier. As a result, it is possible to realize a search in a wider range than other candidates for the candidates having a high order.

Methods of performing each of the above using a processing circuit are also included in the present disclosure. Similarly, the present disclosure also includes a program that specifically realizes information processing by software in a processing circuit that is hardware. Of course, the processing circuit may be incorporated as a part of an information processing device or an information processing system.

The aspects of the present disclosure are not limited to the above-described embodiments, but include various possible modifications, and the effects of the present disclosure are not limited to the above-mentioned contents. The components in each embodiment may be applied in an appropriate combination. That is, various additions, changes and partial deletions are possible without departing from the conceptual idea and purpose of the present disclosure derived from the contents defined in the claims and their equivalents.

1: Information processing system,
10: Information processing equipment,
100: Processing circuit,
102: Memory circuit,
104: Interface,
106: Bus,
90, 94: External device,
92: Network

Claims (16)

It includes a storage circuit and one or more processing circuits capable of executing parallel operations.
The processing circuit
By the first parallel processing, energy is calculated in a plurality of neighborhood states with respect to the current state, and it is shown whether or not each of the plurality of neighborhood states is adopted based on the energy in the plurality of neighborhood states. Calculate the index,
The adoption probability for the plurality of neighborhood states is calculated based on the index so that any one of the plurality of neighborhood states is adopted.
Based on the adoption probability, the next state is selected from the plurality of neighboring states.
Information processing system. The processing circuit
The index calculated from the plurality of neighborhood states is standardized, and the adoption probability is acquired.
The information processing system according to claim 1. The processing circuit performs optimization based on simulated annealing based on the selected state.
The index corresponds to the temperature and the probability of selecting a solution in simulated annealing calculated based on the difference between the energy of the current state and the energy of the nearby state.
The information processing system according to claim 1 or 2. The processing circuit
In the stages up to the present stage, the reciprocal adoption probability in which the energy in the neighboring state after the transition is larger than the energy in the state before the transition and the ideal retrograde adoption probability scheduled in advance are used as the basis. The reverse temperature, which is the reciprocal of the temperature, is controlled so that the retrograde adoption probability is close to the ideal retrograde adoption probability.
The information processing system according to claim 3. The processing circuit
Calculate the index based on the reverse temperature.
The information processing system according to claim 4. The processing circuit
The first parallel processing in a plurality of replicas in the current state is executed by the second parallel processing,
In each of the replicas, the state is updated based on the energy calculated by the first parallel processing.
From the state updated by the second parallel processing, the state of the next replica is selected.
The information processing system according to any one of claims 1 to 5. The processing circuit describes the current state and the plurality of neighboring states using integer values.
The information processing system according to any one of claims 1 to 6. In a scheduling problem, the processing circuit changes the processing order of one product on one machine, swaps the processing order of two products, or swaps the processing order of two products of the same combination on multiple machines. The state obtained by the operation of at least one of the above is defined as at least one of the plurality of neighboring states.
The information processing system according to any one of claims 1 to 7. The processing circuit
The information according to any one of claims 1 to 8, which searches for the plurality of neighboring states corresponding to the respective optimization parameters by using a plurality of optimization parameters different from each other with respect to the current state. Processing system. The processing circuit
Based on the energies of the plurality of current states, a plurality of the current states that have obtained a higher evaluation than the others among the plurality of current states are extracted.
From claim 1, the search for the plurality of neighborhoods corresponding to the respective optimization parameters is performed again using the plurality of optimization parameters different from each other for at least one of the plurality of extracted current states. The information processing system according to claim 5, or any of claims 7 to 9. The processing circuit includes one or more GPUs (Graphics Processing Units).
The GPU has one or more arithmetic blocks capable of parallel processing with each other.
A metaheuristic technique that involves calculating the energy, calculating the index, calculating the adoption probability, and selecting the next state for one or more neighboring states relative to the current state. Execution is performed using at least one of the GPU's arithmetic block parallel, thread parallel, or parallel using multiple boards.
The information processing system according to any one of claims 1 to 10. The processing circuit
The information processing system according to claim 11, wherein the execution of the metaheuristic method for at least one of the one or a plurality of current states is executed by using the plurality of the arithmetic blocks. The number of the plurality of arithmetic blocks is a divisor of the number of arithmetic blocks that can be paralleled.
The information processing system according to claim 12. By the processing circuit
The energy is calculated by the first parallel processing in multiple neighboring states with respect to the current state.
Based on the energy in the plurality of neighboring states, the first probability that each of the above states is adopted is calculated.
A second probability normalizing the first probability is calculated so that any one of the states in the plurality of neighborhoods is adopted.
Based on the second probability, the next state is selected from the plurality of neighboring states.
Information processing method. In the processing circuit
By the first parallel processing, the energy in multiple neighboring states with respect to the current state is calculated,
Based on the energy in the plurality of neighboring states, an index indicating whether or not each of the above states is adopted is calculated.
The adoption probability for the plurality of neighborhood states is calculated based on the index so that any one of the plurality of neighborhood states is adopted.
Based on the adoption probability, the next state is selected from the plurality of neighboring states.
A program that executes an information processing method. Equipped with a storage circuit and one or more processing circuits,
The processing circuit
The temperature is transitioned by preset scheduling to perform simulated annealing optimization.
In the iterative calculation of the optimization, the number of the neighborhoods whose energy in the vicinity of the current state calculated by the optimization is larger than the energy of the current state is counted.
The ratio of the counted number of the neighborhoods to the total number of the neighborhoods searched by the optimization was calculated.
Based on the ratio and the ratio adopted based on the temperature when the energy in the vicinity becomes larger than the energy in the current state, the reverse temperature, which is an index indicating the adoption probability in the vicinity, is controlled. do,
Information processing device.

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