JP2019087273A - Optimization apparatus and optimization apparatus control method - Google Patents

Abstract

To reduce computation time without deteriorating convergence properties.SOLUTION: When a transition controller 20 probabilistically determines whether to accept any one of a plurality of state transitions with reference to a relative relationship between energy change value {-ΔE} and thermal excitation energy, based on temperature value T, energy change value {-ΔE}, and random number value, the transition controller 20 adds an offset value y to the energy change value {-ΔE} and controls the offset value y in the local solution in which the energy is minimized so as to be larger than the case where the energy is not the minimum.SELECTED DRAWING: Figure 1

Description

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

  In the present society, information processing is performed in every field. The information processing is performed using an arithmetic device such as a computer, and prediction, determination, control and the like are performed by computing and processing various data and obtaining meaningful results. Optimization processing is an important field as one of the fields of information processing. For example, there are problems such as minimizing resources and costs necessary for performing a certain process, and finding a solution that maximizes the effect. It will be clear that these issues are of great importance.

  The linear programming problem is a representative of optimization problems. This is to find the value of a variable that maximizes or minimizes an evaluation function represented by a linear sum of a plurality of continuous variables under a constraint represented by a linear sum. It is used in the field. This linear programming problem is known to have excellent solution methods such as simplex method and interior point method, and can efficiently solve problems with hundreds of thousands of variables.

  On the other hand, many optimization problems are known in which variables take discrete values instead of continuous values. For example, there may be a traveling salesman problem for finding the shortest route when going back through multiple cities in order, and a knapsack problem for finding a combination that maximizes the sum of the values when packing different items into knapsack etc. . Such problems are called discrete optimization problems, combinatorial optimization problems, etc., and it is known that it is very difficult to obtain an optimal solution.

  The biggest cause of difficulty in solving discrete optimization problems is that each variable can only take discrete values, so you can use the method of changing the variables continuously in the direction in which the evaluation function is improved to reach the optimal solution There is no such thing. And there are very many values (minimum (large) solutions, local solutions) which locally give extrema of the evaluation function in addition to the values of the variables which give the original optimum value (optimum solution, global solution) . For this reason, it is necessary to take a method like shredding to obtain an optimal solution surely, and the calculation time becomes very long. For discrete optimization problems, which is called NP (Non-deterministic Polynomial) hard problem in computational complexity theory, it is expected that the calculation time for finding the optimal solution will increase exponentially with the size of the problem (ie the number of variables) There are many problems. The traveling salesman problem and the knapsack problem are also NP difficult problems.

  As described above, it is very difficult to reliably obtain the optimal solution of the discrete optimization problem. Therefore, for discrete optimization problems that are important for practical use, solutions using properties inherent to the problems have been devised. As mentioned above, many discrete optimization problems are expected to take exponentially increasing computation time to obtain an exact solution, so many practical solutions are approximate solutions and not optimal solutions. It is possible to obtain a solution in which the value of the evaluation function of something is close to the optimum value.

  With respect to approximate solutions specific to these problems, approximate solutions that can handle a wide range of problems are also known in order to solve without using the nature of the problems. These are called metaheuristic solutions, and include simulated annealing (simulated annealing, SA), genetic algorithms, neural networks, and the like. Although these methods may be less efficient than solutions that take advantage of the nature of the problem, they can be expected to obtain solutions faster than solutions that obtain exact solutions.

Among the above, the present invention relates to a pseudo annealing method.
The pseudo-annealing method is a kind of Monte Carlo method, and is a method of stochastically obtaining a solution using random number values. In the following, the problem of minimizing the value of the evaluation function to be optimized will be described 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.

  Starting from the initial state in which one of the discrete values is substituted for each variable, select a state close to that (for example, a state in which only one variable is changed) from the current state (combination of variable values) and consider the state transition . The energy change for the state transition is calculated, and the state transition is adopted according to the value to stochastically decide whether to change the state or to keep the original state without adopting it. If the adoption probability when energy falls is selected to be larger than when energy rises, a state change occurs in the direction of energy decrease on average, and it can be expected that a state transition to a more appropriate state will occur with the passage of time. Finally, it may be possible to obtain an optimal solution or an approximate solution giving an energy close to the optimal value. If this is adopted when energy drops deterministically, if it is rejected, energy change will be monotonically decreasing in a broad sense with respect to time, but no more changes will occur once the local solution is reached It will As described above, because there are a large number of local solutions in the discrete optimization problem, the state is almost certainly caught by local solutions that are not close to the optimal value. Therefore, it is important to determine probabilistically whether to adopt.

In the pseudo-annealing method, it has been proved that the state reaches the optimum solution at the limit of time (the number of iterations) infinity if the adoption (permissive) probability of the state transition is determined as follows.
(1) For the energy change (energy decrease) value (−ΔE) accompanying the state transition, the allowable probability p of the state transition is determined by any one of the following functions f ().

Here, T is a parameter called a temperature value and is changed as follows.
(2) The temperature value T is logarithmically reduced to the number of iterations t as expressed by the following equation.

Here, T ₀ is an initial temperature value, and it is desirable to take it sufficiently large according to the problem.
If the steady state is reached after sufficient iterations using the permissible probability expressed by the equation (1), the occupancy probability of each state follows the Boltzmann distribution for the thermal equilibrium state in thermodynamics. And since the occupancy probability of the low energy state increases when the temperature is gradually lowered from the high temperature, the low energy state should be obtained when the temperature is sufficiently lowered. This method is called pseudo-annealing because it is similar to the state change when the material is annealed. At this time, the stochastic occurrence of a state transition in which energy rises corresponds to thermal excitation in physics.

  As described above, in the pseudo-annealing method, an optimum solution can be obtained if the number of iterations is taken infinitely, but in reality it is necessary to obtain a solution with a limited number of iterations, so the optimum solution can not be determined reliably. In the above equation, the temperature drops very slowly, so the temperature does not drop sufficiently in a finite time. Therefore, the actual pseudo-annealing method often lowers the temperature faster rather than logarithmic temperature change.

  FIG. 13 shows a conceptual configuration of the optimization apparatus by the pseudo annealing method. However, in the following description, although the case where a plurality of state transition candidates are generated is described, the basic basic pseudo-annealing method generates one transition candidate one by one.

The optimizing device 10 includes a state holding unit 11 which holds the current state S (values of a plurality of state variables). In addition, the energy calculating unit 12 calculates the energy change value {−ΔE _i } of each state transition when the state transition from the current state S occurs due to any of the values of the plurality of state variables changing. is there. The optimization apparatus 10 includes a temperature control unit 13 that controls the temperature value T, and a transition control unit 14 that controls a state change.

The transition control unit 14 selects one of a plurality of state transitions according to the relative relationship between the energy change value {−ΔE _i } and the thermal excitation energy based on the temperature value T, the energy change value {−ΔE _i }, and the random value. It decides probabilistically whether to accept or not.

When the transition control unit 14 is further subdivided, the transition control unit 14 generates state transition candidates from the energy change value {−ΔE _i } and the temperature value T with respect to each candidate. And the possibility determination unit 14b for determining whether to permit or not. Furthermore, it has a transition determination unit 14c that determines a candidate to be adopted from the accepted candidates, and a random number generation unit 14d for generating a random variable.

The operation in one iteration is as follows. First, the candidate generating unit 14a generates one or more candidates (candidate numbers {Ni}) of state transition from the current state S held in the state holding unit 11 to the next state. The energy calculating unit 12 calculates an energy change value {−ΔE _i } for each state transition listed as a candidate using the current state S and the state transition candidate. The availability determination unit 14b uses the temperature value T generated by the temperature control unit 13 and the random variable (random number value) generated by the random number generation unit 14d, according to the energy change value {−ΔE _i } of each state transition. The state transition is permitted by the allowable probability of the equation (1). Then, the availability determination unit 14b outputs availability {fi} of each state transition. When there are a plurality of permitted state transitions, the transition determination unit 14 c randomly selects one of them using a random number value. Then, the transition determination unit 14 c outputs the transition number N of the selected state transition and the transition availability f. If there is an allowed state transition, the value of the state variable stored in the state holding unit 11 is updated according to the adopted state transition.

  Starting from the initial state, the above-mentioned repetition is repeated while lowering the temperature value by the temperature control unit 13, and the operation is ended when an end determination condition such as reaching a certain number of repetitions or energy falls below a certain value is satisfied. . The answer that the optimization device 10 outputs is the state at the end. However, in reality, the temperature value does not become 0 with a limited number of iterations, and the occupancy rate of the state has a distribution represented by Boltzmann distribution etc. even at the end, and it must be an optimal value or a good solution. There is no limit. Therefore, it is a realistic solution to hold the lowest energy obtained so far during the iteration and finally output it.

FIG. 14 is a circuit level block diagram of a configuration example of an operation portion required for a transition control unit, particularly an availability determination unit in a normal pseudo annealing method in which candidates are generated one by one.
The transition control unit 14 includes a random number generation circuit 14 b 1, a selector 14 b 2, a noise table 14 b 3, a multiplier 14 b 4, and a comparator 14 b 5.

The selector 14b2 selects and outputs the energy change value {−ΔE _i } calculated for each state transition candidate that corresponds to the transition number N which is a random number value generated by the random number generation circuit 14b1. .

  The function of the noise table 14b3 will be described later. As the noise table 14b3, for example, a memory such as a random access memory (RAM) or a flash memory can be used.

The multiplier 14b4 outputs a product (corresponding to the above-mentioned thermal excitation energy) obtained by multiplying the temperature value T by the value output from the noise table 14b3.
The comparator 14b5 outputs a comparison result obtained by comparing the multiplication result output from the multiplier 14b4 with -ΔE, which is the energy change value selected by the selector 14b2, as the transition possibility f.

  The transition control unit 14 shown in FIG. 14 basically implements the above-described function as it is, but the mechanism for permitting state transition with the allowance probability represented by the equation (1) has been described so far. I will supplement this as it is not explained.

  A comparator that outputs 1 with tolerance probability p and 0 with (1-p) has two inputs A and B, outputs 1 when A> B, and outputs 0 when A <B The tolerance probability p can be realized by inputting into the input A and the uniform random number taking the value of the interval [0, 1) into the input B. Therefore, the above function can be realized by inputting into the input A of this comparator the value of the allowance probability p calculated using the equation (1) from the energy change value and the temperature value T.

  That is, a circuit that outputs 1 when f (ΔE / T) is larger than u, where f is a function used in the equation of (1) and u is a uniform random number taking values in the interval [0, 1), Can realize the function of

This may be left as it is, but the same function can be realized even if the following modification is made. Even if the same monotonically increasing function is applied to two numbers, the magnitude relationship does not change. Therefore, the output does not change even if the same monotonically increasing function is applied to the two inputs of the comparator. When the inverse function f ⁻¹ of f is adopted as the monotonically increasing function, it is understood that a circuit that outputs 1 is acceptable when −ΔE / T is larger than f ⁻¹ (u). Furthermore, since the temperature value T is positive, it may be a circuit that outputs 1 when -ΔE is larger than Tf ^-1 (u). The noise table 14b3 in FIG. 14 is a conversion table for realizing the inverse function f ⁻¹ (u), and is a table for outputting the value of the following function to the input obtained by discretizing the interval [0, 1) It is.

The transition control unit 14 includes a latch for holding the determination result and the like, a state machine for generating the timing thereof, and the like, but these are omitted in FIG. 14 for the sake of simplicity.
FIG. 15 is an operation flow of the transition control unit 14 in the conventional example. The operation flow is a step of selecting one state transition as a candidate (S1), a step of determining availability of state transition by comparing an energy change value with respect to the state transition, a product of a temperature value and a random number value (S2). If yes, the state transition is adopted, and if not, there is a step (S3) of disapproving.

  From the above explanation, it can be imagined to some extent that the pseudo annealing method is general purpose and very attractive, but there is 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 properly adjust how to lower the temperature according to the problem. This can be described as follows using FIG.

  There are many local solutions with poor degree of approximation in the path of the state transition from the initial value to the optimal solution and the approximate solution. In order to escape from these local solutions quickly enough, a high temperature is needed to allow sufficient thermal excitation. However, since the spread of energy in the Boltzmann distribution is large at high temperatures, an optimal solution or a low-approximate good approximate solution (hereinafter referred to as a good solution) and a local solution with a relatively high approximation of energy (hereinafter referred to as a bad solution) The difference in occupancy probability of) is small. For this reason, even if the local solution can be escaped quickly, the destinations to go are dispersed to many bad solutions, and the probability of reaching a good solution is very small. In order to increase the occupancy probability of a good solution, it is necessary to have a low temperature such that the energy of thermal excitation is sufficiently smaller than the energy difference with a bad solution. However, in this case, since the energy of the thermal excitation is small, the probability of being able to cross the energy mountain in the middle of the path becomes very low, and almost no state change occurs. Therefore, it is necessary to gradually increase the occupancy probability of a good solution by slowly progressing an intermediate temperature which can go over a mountain to some extent and which is slightly different from the occupancy probability. If the method of lowering the temperature is too slow, the temperature does not decrease so much in finite time, so the probability of occupancy of a good solution eventually does not increase. On the other hand, if it is dropped too fast, the temperature drops before it escapes the local solution, and it remains trapped by the bad solution. Therefore, as the temperature decreases, the rate of change must be sufficiently reduced, and sufficient waiting must be made to approach the Boltzmann distribution at that temperature.

  Thus, in the original pseudo-annealing method, it is necessary to slowly lower the temperature since it is intended to escape from the local solution only by thermal excitation by the temperature, and it is necessary to adjust it appropriately according to the problem. There's a problem.

  It is possible to alleviate the problem of being caught by the local solution for this problem by methods other than temperature control. For example, Patent Documents 1 and 2 dynamically change the temperature control method and the evaluation function, and Patent Document 3 dynamically changes the generation method of the neighborhood which is the state transition destination. In the early stage, a wide range of search is performed, and in the final stage, a high-accuracy search is performed in a narrow range to reduce calculation time.

  These require relatively complex operations such as dynamically replacing a plurality of functions and taking statistics to grasp how a search proceeds. If possible, it is desirable to make it possible to reduce the calculation time in a simpler and more general method.

Japanese Patent Application Laid-Open No. 6-19507 Unexamined-Japanese-Patent No. 9-34951 gazette Japanese Patent Application Laid-Open No. 10-293756

H. Zhu et. Al., “A Boltzmann Machine with Non-rejective Move,” IEICE Trans. Fundamentals vol. E85-A, No. 6. pp. 1229-1235, June 2002

  As described above, taking a long time to escape the local solution is a major factor that increases the calculation time of the pseudo annealing method. Therefore, if there is a method to promote the escape of the local solution, it is expected that the calculation time can be significantly shortened. However, simply escaping from the local solution does not always make the computation time faster. As described above, there are a large number of bad solutions, so even if they are thrown out randomly from a certain local solution, they will only get caught by the bad solutions around them. It is desirable not only to let it escape, but to let it transition to a better state.

  A hint for getting out in a better direction is in the convergence theory of pseudo annealing above. This theorem indicates that it proceeds in a direction that can be determined by determining whether or not state transition is possible according to the state transition probability of the Metropolis method or Gibbs method.

  In the local solution, since the probability of state transition is very small, selection of transition candidates is repeated many times, and the branching ratio of the state transition after that is proportional to the transition probability of the Metropolis method or Gibbs method. Therefore, if the absolute value can be increased while maintaining the relative ratio of the permissible probability of each state transition, the branching ratio of each state transition is maintained, and therefore the stay at the local solution does not adversely affect the convergence. The time can be shortened, and the calculation time can be shortened.

  The problem to be solved by the present invention is to obtain means for promoting the escape from the local solution without changing the evaluation function and the state transition generation method, etc. dynamically and without losing the convergence. More specifically, it is to obtain means for increasing the absolute value while maintaining the relative ratio of the permissible probability of each state transition in the local solution.

  Non-Patent Document 1 is one such method. The above-mentioned problems can be solved by appropriately correcting what is described in this document. In this method, the acceptance probability for all state transitions is calculated, and the adoption probability is adopted in proportion to the original allowance probability by adopting the allowance probability that the ratio of the value to the random value having the exponential distribution becomes maximum. You can choose the transition. This method is very effective because it can keep the probability of staying in the original state as well as maintaining the relative ratio of the allowance probability. However, there is a problem that the calculation amount in the calculation of the allowable probability and the generation of the random number is large.

  An object of the present invention is to obtain the same effect in a simpler method, that is, the effect that the calculation time can be shortened without losing the convergence.

  In one embodiment, the optimization device receives a state holding unit that holds values of a plurality of state variables included in an evaluation function representing energy, and changes in any of the values of the plurality of state variables. When a state transition occurs, an energy calculation unit that calculates the change value of the energy for each of a plurality of state transitions, a temperature control unit that controls a temperature value indicating temperature, the temperature value, and the change value An offset value is added to the change value when it is determined probabilistically whether or not to accept any of the plurality of state transitions based on the relative relationship between the change value and the thermal excitation energy based on a random value and And a transition control unit configured to control the offset value in the local solution in which the energy is minimized so as to be larger than that in the case where the energy is not minimized.

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

  In one aspect, the present invention can reduce computation time without compromising convergence.

It is a figure which shows the structural example of the transition control part of the pseudo | simulation annealing method in this invention. It is a figure which shows the operation | movement flow of the transition control part in this invention. It is a figure which shows an example of a circuit structure of the transition control part in the optimization apparatus of 1st Embodiment. It is a state transition diagram which shows an example of the state transition of generation | occurrence | production of a pulse signal. It is a figure which shows an example of the truth value table of the logic circuit which generate | occur | produces a pulse signal. It is a figure which shows an example of the state machine which generate | occur | produces a pulse signal. It is a figure which shows an example of the software simulation result of the pseudo | simulation annealing method implement | achieved using the transition control part of FIG. It is a figure which shows an example of a circuit structure of the transition control part in the optimization apparatus of 2nd Embodiment. It is a figure which shows an example of the software-simulation result of the pseudo | simulation annealing method implement | achieved using the transition control part of FIG. It is a figure which shows an example of the optimization apparatus using the transition control part of FIG. It is a figure which shows an example of a circuit structure of the transition control part in the optimization apparatus of 3rd Embodiment. It is a figure which shows an example of the software-simulation result of the pseudo | simulation annealing method implement | achieved using the transition control part of FIG. It is a figure which shows the notional structure of the optimization apparatus by a pseudo | simulation annealing method. It is a block diagram of the circuit level of the example of composition of the operation part required for the transition control part in a prior art example, especially an availability judgment part. It is a figure which shows the operation | movement flow of the transition control part in a prior art example. It is a figure which shows the concept of the occupancy probability of the state in a pseudorandom number method.

  FIG. 1 shows an example of the configuration of the transition control unit of the pseudo annealing method provided with the function of promoting escape from the local solution proposed in the present invention. The same components as those of the transition control unit 14 shown in FIG. 14 are denoted by the same reference numerals.

  As shown in FIG. 1, the transition control unit 20 has an offset addition circuit 21 and an offset control circuit 22 added to the circuit portion that realizes the function of the availability determination unit 14b shown in FIG. The other parts are the same as the transition control unit 14 shown in FIG.

The offset addition circuit 21 functions as an offset addition circuit that adds the offset value y to the energy change value (−ΔE) accompanying the state transition. In the example of the circuit of FIG. 1, the offset addition circuit 21 is a subtractor 21a. Therefore, in the example of FIG. 1, instead of adding the offset value y to the energy change value (−ΔE), the product Tf ⁻¹ (u) (the thermal excitation energy corresponds to the product of the temperature value T to be compared and the random value). And the offset value y is reduced, but the same is true for either.

  The offset control circuit 22 controls the offset value y in the local solution (solution in which the energy is minimized) to be larger than that in the case where it is not the local solution. In the example of FIG. 1, the offset control circuit 22 is an accumulator 22a having a reset terminal R. The accumulator 22a sets the offset value y to 0 when the transition availability f input to the reset terminal R indicates that state transition is permitted (that is, when state transition occurs). The accumulator 22a also has an input terminal and a clock terminal. The accumulator 22a outputs an offset value y every time a pulse signal (not shown) is input to the clock terminal when the transition availability f indicates that the state transition is not permitted (that is, when the state transition does not occur). The offset increment value Δy input to the input terminal is added.

A pulse signal (not shown) is supplied by, for example, a state machine described later. The offset increment value Δy is stored, for example, in a register not shown.
Such a transition control unit 20 adds the offset value y held in the accumulator 22 a to the energy change value (−ΔE) selected by the selector 14 b 2 −ΔE + y is a temperature value T and a random number value The state transition is allowed when it is larger than the product Tf ⁻¹ (u) of

  Then, the accumulator 22a changes the offset value y as follows. If there is an allowed state transition and a state transition occurs, the accumulator 22a resets the offset value y to zero. If there is no permitted transition and no state transition occurs, the accumulator 22a increases the offset value y by the offset increment value Δy.

FIG. 2 summarizes the operation flow for determining whether this state transition is possible.
The operation flow is a step of selecting one state transition as a candidate (S10), comparing the sum of the energy change value (-.DELTA.E) and the offset value y for the state transition, and comparing the product of the temperature value T and the random value Of determining whether or not to Furthermore, the operation flow has a step (S12) of adopting the state transition if the state transition is possible, clearing the offset value y, and disapproving the state value, if not, (S12).

Other operations may be the same as the normal pseudo annealing method.
The effects of the transition control unit 20 having the offset addition circuit 21 and the offset control circuit 22 as described above will be described below.

  When the current state is caught by the local solution and can not escape easily, the energy change value for all state transitions is a large positive value. The allowable probability for each state transition at this time is approximately expressed by an exponential function as shown in the following equations 4-1 and 4-2, regardless of whether it is the Metropolis method or the Gibbs method.

Assuming that the offset value y is added to the energy change value {−ΔE _i } and the determination is performed in all the state transition determinations, the allowable probabilities of all the state transitions are as shown in Equation 5 below, and all states It can be seen that the transition probability of probability increases at the same scaling factor e ^{y / T.}

  As described above, if it is possible to increase the absolute value of the permissible probability while maintaining the relative ratio of the permissible probability of all the state transitions, the residence time in the local solution without changing the branching ratio of the subsequent state transitions Can be shortened. Therefore, by using the offset value y, promotion of escape from the local solution can be expected. However, if the offset value y is not properly controlled, the acceleration effect may not be sufficient or the convergence may be deteriorated.

  First, when the current state is not a local solution, the transition probability can not be approximated by an exponential function because there is a state transition in which the energy decreases. Therefore, if there is an offset value y, the branching ratio is changed. For this reason, when not a local solution, it is desirable that the offset value y be 0 or sufficiently small.

  If the offset value y when the current state is a local solution is a constant value, although there is an acceleration effect, it is not always sufficient. The transition probability remains very small even if the offset value y is given if the increase in energy accompanying the state transition is only large. If a local solution can not be easily escaped even if the offset value y is given, it is desirable to use a larger offset value y.

  In order to solve this, the offset control circuit 22 of FIG. 1 is configured to gradually increase the offset value y when no state transition occurs, and reset the offset value y to 0 when a state transition occurs. .

  If the state remains in the local solution, the offset value y gradually increases, so it can always escape someday. In addition, when the state is not a local solution, the reset accompanying the state transition frequently occurs, so the offset value y is 0 or a small value, and it is possible to prevent the branch ratio from being greatly affected.

  It is desirable to properly select the offset increment value Δy. If the offset increment value Δy is increased, the local solution can be quickly exited. However, if it is too large, the state transition does not necessarily occur every time even if it is not a local solution, and therefore it may be affected by the offset value y. In addition, even in the local solution, the offset value y may become large before a state transition that should increase the energy relatively little and have a high allowable probability as a candidate, and the branch ratio may deviate from the correct value. In order not to greatly affect the branching ratio, it seems to be preferable to make the average stay time in the local solution be several times the average stay time when it is not the local solution.

  From the above, it can be understood that if the offset increment value Δy is appropriately selected, the residence time in the local solution can be shortened without adversely affecting the convergence, and the calculation time of the optimization can be shortened. .

The verification by software simulation of this effect will be described later together with the embodiment shown below.
By the way, the present invention shortens the calculation time by adding the above-described new functional block to the transition control unit 14 of FIG. 13 which realizes the pseudo annealing method as described above, and more specifically, the availability determination unit 14b. The There is no need to change the other parts. Therefore, the present invention can be applied without any dependence on the set of state transitions that can be permitted for the current state, the function form giving the change of energy accompanying the state transition, the calculation method thereof, and the like. Therefore, the specific circuit configuration method of these parts will not be described in detail.

  However, with regard to the pseudo-annealing method in the case where the energy to be optimized is expressed by the Ising model below, and in the optimization in the Boltzmann machine which is almost equivalent to it, calculation of the change of energy accompanying transition occurrence and state transition I will explain the law briefly.

The Ising model is a model representing a system of N spins interacting with each other, and each spin s _i has a binary value of ± 1. The energy of the system is represented by the following equation 6.

In Equation 6, J _{i, j} represents an interaction coefficient between spin s _i and spin s _j , and h _i represents an external magnetic field coefficient which is a bias value of the system.
Candidates for state transition from the current state to the next state are inversions of one spin, and there are N ways. Therefore, as a transition candidate, a set of spin numbers or a plurality of spin numbers to be inverted may be generated.

  And the change of the energy accompanying the i-th spin inversion is represented by the following formula 7.

Here, F _i in the following equation 8 is called a local field value, and represents the rate of energy change due to the inversion of each spin.

  Since whether to allow state transition is determined by the change in energy, it is basically sufficient to calculate the change in energy from the local field value without calculating the energy itself. When using the state for the lowest energy obtained as the output, the energy can be determined by calculating the change of the energy from the local field value and accumulating it.

  further,

Therefore, it is not necessary to recalculate the local field values by matrix operation every time, and it is sufficient to add only the change due to the spin that has been inverted along with the state transition.
Also, the Boltzmann machine used for the neural network is the same as the pseudo annealing method of the Ising model except that the state variable takes two values of (0, 1). Therefore, almost the same configuration can be made. The equations representing energy, energy change value, and local field value are as in the following Equation 10, Equation 11, and Equation 12.

In Boltzmann machines, what is equivalent to the spin of Ising model is often called a neuron, but for simplicity it is called a spin below.
Therefore, the state holding unit 11 shown in FIG. 13 can be configured using an N-bit register holding values of N spins, an adder, and a relatively simple arithmetic circuit such as an exclusive OR.

  As described above, since the pseudo annealing method using the Ising model and the pseudo annealing method using the Boltzmann machine are equivalent and can be mutually converted, in the following, it is assumed that the Boltzmann machine which easily corresponds to 0 or 1 of the logic circuit. To explain.

  In the Boltzmann machine (and pseudo annealing of Ising model), there is only one state variable that changes with the state transition, and the energy change value for that can be calculated in advance using the local field value. Therefore, in the following embodiment, an implementation in which the energy change value calculated in advance is selected according to the generation of the transition candidate is described as an example. However, when it is not a Boltzmann machine, since there may be cases in which transitions in which a plurality of state variables change are considered, an implementation that calculates an energy change value necessary after the occurrence of a transition candidate may be advantageous.

Hereinafter, three embodiments of an optimization apparatus assuming a Boltzmann machine will be described.
First Embodiment
FIG. 3 is a diagram showing an example of a circuit configuration of the transition control unit in the optimization device of the first embodiment. The same elements as those of the transition control unit 20 shown in FIG. 1 are denoted by the same reference numerals. The transition control unit 20a of FIG. 3 is basically the same as the transition control unit 20 of FIG. 1, but in FIG. 3 the configuration of the accumulator 22a is shown a little more concretely.

The accumulator 22a includes an adder 22a1, a selector 22a2, and a register 22a3.
The adder 22a1 outputs a sum obtained by adding the offset increment value Δy and the offset value y output from the register 22a3.

  The selector 22a2 selects and outputs 0 when the transition availability f indicates that the state transition is permitted, and selects the addition result output from the adder 22a1 when the transition availability f indicates that the state transition is not permitted. Output.

The register 22a3 takes in the value output from the selector 22a2 in synchronization with the pulse signal supplied to the clock terminal, and outputs it as an offset value y.
The bit widths of the adder 22a1 and the register 22a3 are appropriately set. The bit width may be about the same as the bit width of the energy change value (−ΔE). For example, assuming that the bit width of the interaction coefficient is 16 and the number of spins is 1024, the energy change value (-.DELTA.E) is 27 bits at maximum, so it is sufficient to use this bit width. In practice, it is almost always sufficient if there is less than this. The bit width of the output of the noise table 14b3 may be equal to or less than the bit width of the energy change value (-.DELTA.E).

  The pulse signal supplied to the clock terminal of the register 22a3 is supplied from a state machine that controls repetitive operations in the circuit operation, and is controlled to become active only once after determining whether the state transition in one repetitive operation is possible. Ru.

  Since the number of cycles of the clock signal necessary for the determination of availability and the subsequent updating of each parameter changes depending on the result of availability determination, it is necessary to generate a pulse signal so as to match the number of cycles.

In the following, a method of generating a pulse signal will be described by taking as an example the case of entering the next repetition in 5 cycles if there is an update of the state and 1 cycle if there is not.
FIG. 4 is a state transition diagram showing an example of state transition of pulse signal generation.

  As shown in FIG. 4, a transition is made between five states of 0-4. At the time of state 0, if the transition possibility f is 0, a pulse signal is generated. In this case, transition from state 0 is not performed. When the transition possibility f is 1 at the state 0, the transition to the state 1 is made. In FIG. C. Indicates don't care. That is, from state 1, regardless of the value of transition possibility f, the state transitions to states 2, 3 and 4 in synchronization with the clock signal CLK, and the state returns to state 0. Then, upon returning from state 4 to state 0, a pulse signal is generated.

A state machine for realizing such state transition may be a circuit satisfying the following truth table.
FIG. 5 is a diagram showing an example of a truth table of a logic circuit that generates a pulse signal.

FIG. 6 is a diagram showing an example of a state machine that generates a pulse signal.
The state machine 50 has a 3-bit flip flop 51, an increment circuit 52, an AND circuit 53, a selector 54, and AND circuits 55 and 56. The truth table of FIG. 5 shows the relationship between the output values Q1, Q2 and Q3 of the 3-bit flip-flop 51 in each state and the input values D1, D2 and D3.

  Of the 3-bit values output from the increment circuit 52, the upper 2 bits ([d0: d1]) of the 3-bit flip-flop 51 and the values output from the selector 54 are supplied as input values D1 to D3. . The 3-bit flip-flop 51 takes in the input values D1 to D3 at timings synchronized with the clock signal CLK, and outputs them as output values Q1 to Q3.

  The increment circuit 52 adds 1 to the 3-bit output values Q1 to Q3 output from the 3-bit flip-flop 51. For example, when the output values Q1 to Q3 are "001" (that is, Q1 = Q2 = 0, Q3 = 1), the increment circuit 52 outputs "010".

The AND circuit 53 inputs a value obtained by inverting the logic level of each bit of the output values Q1 to Q3 and outputs the logical product of them as an output value.
The least significant bit (d2) of the 3-bit value output from the increment circuit 52 is supplied to one input terminal of the selector 54, and the transition availability f is supplied to the other input terminal. Then, the selector 54 outputs the transition availability f if the output value of the AND circuit 53 is 1, and outputs d3 if the output value of the AND circuit 53 is 0.

The AND circuit 55 inputs a value obtained by inverting the logic level of each bit of the output values Q1 to Q3 ([q1: q3]), and outputs the logical product of them as an output value.
The AND circuit 56 outputs a logical product of the clock signal CLK and the output value output from the AND circuit 55 as a pulse signal.

The pulse signal can be generated by the state machine 50 as described above.
An operation example of the optimization apparatus according to the first embodiment will be described below.
The random number generation circuit 14b1 generates the number of the state transition candidate (transition number N) one by one according to the random number value in each repetition described above. The selector 14 b 2 selects and outputs the energy change value (−ΔE) accompanying the state transition. Further, the multiplier 14b4 multiplies the temperature value T by the value obtained by performing conversion by the noise table 14b3 based on random numbers which are uniform random numbers, thereby generating thermal excitation energy in the metropolis method or Gibbs method. . Then, the subtractor 21a subtracts the offset value y output from the accumulator 22a from the thermal excitation energy. The comparator 14b5 compares the subtraction result output from the subtractor 21a with the energy change value (-ΔE) selected and output by the selector 14b2 to determine whether the state transition is possible.

  The offset value y is reset to 0 by the accumulator 22a when a state transition is adopted, and the offset increment value Δy increment is added when the state transition is not adopted and remains in the current state. Thus, the offset value y is controlled to monotonically increase with respect to the staying time in the current state.

A standard for determining the offset increment value Δy is given as follows.
As mentioned above, in order to obtain the acceleration effect without adversely affecting the convergence, it is better to select the offset increment value Δy so that the residence time of the local solution will be several times that of the non-local solution. Be When one state transition candidate occurs in each iteration as in the present embodiment, the probability that each state transition is a candidate is the inverse of the number of all state transitions. Taking this into consideration, the offset increment value Δy is such that the offset value y becomes the energy of the height of the mountain necessary to escape from the local solution when the staying time becomes several times the number of all state transitions. It is considered that it is better to

  FIG. 7 is a diagram showing an example of a software simulation result of the pseudo annealing method realized by using the transition control unit of FIG. The problem to be optimized is the traveling salesman problem of 32 cities formulated by Ising model (Boltzmann machine). The horizontal axis represents the number of iterations, and the vertical axis represents the rate at which the optimal solution was obtained (percent correct answer (%)). The result 60 shows the relationship between the number of iterations and the correct answer rate when the transition control unit 20a of FIG. 3 is used, and the result 61 is the number of iterations when the transition control unit 14 shown in FIG. 14 is used. Indicates the relationship with the correct answer rate.

It can be seen from FIG. 7 that the correct answer is reached more quickly in the case of using the transition control unit 20 a of the first embodiment than in the case of using the transition control unit 14. The transition control unit according to the first embodiment is 4.3 × 10 ¹⁰ in the case where the transition control unit 14 is used in comparison with the number of iterations N ₉₉ by which the correct answer is obtained with the probability of 99% expressed by the following equation 13: In the case of using 20a, it was 7.7 × 10 ⁹ and it was shown that the speed was improved about five times.

However, in Equation 13, n is the number of iterations, and η (n) is the correct answer rate at that number.
Second Embodiment
FIG. 8 is a diagram showing an example of a circuit configuration of the transition control unit in the optimization device of the second embodiment. In FIG. 8, the circuit that generates random numbers is not shown.

  Hereinafter, the transition control unit 20b in FIG. 8 is described as all bit inversions (changes in spin value) as state transition candidates, but it is also possible to use only a part of each bit inversion as state transition candidates. It is possible. In the following description, random numbers used for thermal excitation are independent for each transition candidate, but may be common for several state transition candidates.

The transition control unit 20 b includes an accumulator 22 a as in the case of the transition control unit 20 a of FIG. 3, and further includes a thermal excitation energy generation unit 70, a subtractor 71, a comparator 72, and a selector 73.
The thermal excitation energy generation unit 70 has a noise table (storage unit) that converts the independent random number value {ui} into the value of the above-described inverse function f ⁻¹ (u) for each transition candidate. Furthermore, the thermal excitation energy generation unit 70 outputs a product of the value output from the noise table and the temperature value T as thermal excitation energy in the Metropolis method or Gibbs method.

The subtractor 71 subtracts the offset value y output from the accumulator 22a from the thermal excitation energy generated for each transition candidate.
The comparator 72 compares transition results of the subtractor 71 with the energy change value {−ΔE _i } to output transition availability {fi} indicating availability of each state transition. Note that the operation of the comparator 72 is as follows: each of the sum of the energy change value {−ΔE _i } calculated for each of the plurality of state transitions and the offset value y; and a plurality of multiplications (thermal excitation energy) It corresponds to outputting the comparison result with each of.

  If there are a plurality of permitted state transitions, the selector 73 randomly selects one of the state transitions using random number values based on the transition availability {fi}. Then, the selector 73 outputs the number (transition number N) of the selected state transition candidate, and outputs 1 as the transition possibility f. When no state transition occurs, the transition availability f is zero.

An operation example of the optimization device of the second embodiment will be described below.
In each iteration described above, the thermal excitation energy generation unit 70 receives random value {ui} which is an independent uniform random number equal to the number of state transition candidates, and performs conversion using a noise table. Then, the thermal excitation energy generation unit 70 generates thermal excitation energy in the metropolis method or Gibbs method by multiplying the value obtained by the conversion by the common temperature value T.

From the thermal excitation energy generated for each transition candidate, the subtractor 71 subtracts the offset value y output from the accumulator 22a, and the comparator 72 reduces each subtraction result output from the subtractor 71, and changes in energy The value {−ΔE _i } is compared. The comparator 72 outputs transition availability {fi} indicating availability of each state transition based on the comparison result. When there are a plurality of permitted state transitions, the selector 73 randomly selects one from among them using random number values.

  The offset value y is reset to 0 by the accumulator 22a when the permitted state transition exists and the state changes (when the transition possibility f is 1). When all the candidate state transitions are not permitted and remain in the current state (when transition possibility f is 0), the accumulator 22a adds the offset increment value Δy to the offset value y to obtain the current state. The offset value y is controlled to increase monotonically with respect to the staying time in

  The offset increment value Δy escapes from the local solution when the residence time becomes several times, considering that all the state transitions are candidates and the state transition occurs in almost one iteration when not a local solution. It is considered good to set the energy necessary for

  FIG. 9 is a view showing an example of a software simulation result of the pseudo annealing method realized by using the transition control unit of FIG. The problem to be optimized is formulated by using the Ising model (Boltzmann machine) for the traveling saleman problem in 32 cities. The horizontal axis represents the number of iterations, and the vertical axis represents the rate at which the optimal solution was obtained (percent correct answer (%)). The result 60a shows the relationship between the number of iterations and the correct answer rate when the transition control unit 20b of FIG. 8 is used, and the result 61a is when the subtractor 71 and the accumulator 22a are removed from the transition control unit 20b. Shows the relationship between the number of iterations and the correct answer rate.

It can be seen that the correct solution is reached faster in the case of using the transition control unit 20b of the second embodiment than in the case of not having the subtractor 71 and the accumulator 22a in FIG. 5.3 × 10 ⁷ is in the absence of accumulator 22a and the subtractor 71 compared with the number of iterations _{N 99} the resulting correct 99% probability, the case of using the transition control portion 20b of the second embodiment It was 1.1 × 10 ⁷ and was shown to be about 5 times faster.

Hereinafter, an example of the optimization apparatus using the transition control unit 20b of FIG. 8 will be described.
FIG. 10 is a diagram showing an example of an optimization apparatus using the transition control unit of FIG.
The optimization device 80 includes energy calculation units 81a1, ..., 81ai, ..., 81an, a transition control unit 82, and a state update unit 83.

Energy calculation unit 81a1~81an is an example of an energy calculation unit 12 shown in FIG. 13, the energy change value _{(-ΔE 1, ..., -ΔE i} , ..., -ΔE n ( the aforementioned {-ΔE _i} Equivalent)) to calculate and output.

  For example, the energy calculation unit 81 ai includes a register 81 b, selectors 81 c and 81 d, a multiplier 81 e, an adder 81 f, a register 81 g, a selector 81 h, and a multiplier 81 i.

Register 81b, the interaction coefficients _{J i, 1, J i,} 2 in equation 10 like the foregoing, _{..., J i,} stores _n.
The interaction coefficients J _{i, 1 to} J _{i, n} are calculated in advance according to the problem to be calculated, for example, by a control device (not shown) in the optimization device 80 or a device outside the optimization device 80. , And stored in the register 81 b. Note that the interaction coefficients J _{i, 1 to} J _{i, n} as described above may be stored in a memory such as a RAM.

The selector 81 c selects and outputs one of the interaction coefficients J _{i, 1 to} J _{i, n} stored in the register 81 b based on the transition number N output from the transition control unit 82.
For example, when N = n is input to the selector 81 c, the selector 81 c selects the interaction coefficient J _{i, n} .

The selector 81 d implements the calculation of 1−2s _i of Expression 11, and selects and outputs 1 or −1 based on the value of the updated spin s _N output from the state updating unit 83. When the updated value is 0, the selector 81d selects and outputs -1, and when the updated value is 1, the selector 81d selects and outputs 1.

The multiplier 81 e outputs a product obtained by multiplying the interaction coefficient output from the selector 81 c and the value output from the selector 81 d.
The adder 81 f outputs the sum of the multiplication result output from the multiplier 81 e and the value stored in the register 81 g.

The register 81g takes in the value output from the adder 81f in synchronization with a clock signal (not shown). The register 81 g is, for example, a flip flop. The value stored in the register 81 g is the local field value F _i in Equation 12.

The selector 81 _h outputs 1 when the value of the spin s _i after change is 0, and outputs −1 when it is 1. The output of the selector 81h corresponds to 1-2s _i of Equation 11.
The multiplier 81i outputs a product obtained by multiplying the local field value F _i output from the register 81 g and the value output from the selector 81 _h as an energy change value (−ΔE _i ).

The transition control unit 82 includes circuit units 82a1, ..., 82ai, ..., 82an, a selector 82b, and an offset control circuit 82c.
The circuit units 82a1 to 82an divide the functions of the thermal excitation energy generation unit 70, the subtractor 71, and the comparator 72 of the transition control unit 20b shown in FIG. 82 b corresponds to the selector 73 shown in FIG. The offset control circuit 82c corresponds to the accumulator 22a shown in FIG.

Therefore, transition control unit 82 performs the same operation as transition control unit 20b shown in FIG.
The state update unit 83 has the function of the state holding unit 11 shown in FIG. 13, and based on the transition availability f and the transition number N output from the transition control unit 14, the values of the retained spins s _{1 to} s _n And output the combination (State) of the values. The state updating unit 83 outputs the spin updated values (labeled s _N in the example of FIG. 11).

The transition control units 20b and 82 according to the second embodiment are applicable to the optimization apparatus 80 as described above.
Third Embodiment
FIG. 11 is a diagram showing an example of a circuit configuration of the transition control unit in the optimization device of the third embodiment. In FIG. 11, the circuit for generating the random number is not shown. The same elements as those of the transition control unit 20b shown in FIG. 8 are denoted by the same reference numerals.

  Hereinafter, the transition control unit 20 c in FIG. 11 is described as all bit inversions (changes in spin value) as state transition candidates, but it is also possible to use only a part of each bit inversion as state transition candidates. It is possible.

Similar to the transition control unit 20a of FIG. 3, the transition control unit 20c includes an accumulator 22a, and further includes a thermal excitation energy generation unit 70a, a subtractor 71a, a comparator 72a, and a selector 73.
The thermal excitation energy generation unit 70a has a noise table for converting the common random number value u (uniform random number) for each transition candidate into the value of the inverse function f ⁻¹ (u) described above, and The product multiplied by the temperature value T is output as thermal excitation energy in the Metropolis method or Gibbs method.

The subtractor 71a subtracts the offset value y common to all state transition candidates from the thermal excitation energy.
The comparator 72a compares the subtraction result output from the subtractor 71 with the energy change value {−ΔE _i } due to each state transition to output transition availability {fi} indicating whether each state transition is possible.

  If there are a plurality of permitted state transitions, the selector 73 randomly selects one of the state transitions using random numbers based on the transition availability {fi}. Then, the selector 73 outputs the number (transition number N) of the selected state transition candidate, and outputs 1 as the transition possibility f. When no state transition occurs, the transition availability f is zero.

An operation example of the optimization device of the third embodiment will be described below.
In each iteration described above, the thermal excitation energy generation unit 70a receives a random value u which is a uniform random number common to each bit inversion, and performs conversion using a noise table. Then, the thermal excitation energy generating unit 70a generates thermal excitation energy in the metropolis method or Gibbs method by multiplying the temperature value T by the value obtained by the conversion.

The offset value y output from the accumulator 22a is reduced by the subtractor 71a from the generated thermal excitation energy, and the subtraction result output from the subtractor 71a and the energy change value {-ΔE _i are reduced by the comparator 72a. } Is compared. The comparator 72a outputs transition availability {fi} indicating availability of the state transition of each state transition based on the comparison result. When there are a plurality of permitted state transitions, the selector 73 randomly selects one from among them using random number values.

The offset value y is controlled in the same manner as the transition control unit 20b of the second embodiment.
FIG. 12 is a diagram showing an example of a software simulation result of the pseudo annealing method realized by using the transition control unit of FIG. The problem to be optimized is formulated by using the Ising model (Boltzmann machine) for the traveling saleman problem in 32 cities. The horizontal axis represents the number of iterations, and the vertical axis represents the rate at which the optimal solution was obtained (percent correct answer (%)). The result 60b shows the relationship between the number of iterations and the correct answer rate when the transition control unit 20c of FIG. 11 is used, and the result 61b is when the subtractor 71a and the accumulator 22a are removed from the transition control unit 20c. Shows the relationship between the number of iterations and the correct answer rate.

It can be seen that the correct solution is reached more quickly in the case where the transition control unit 20c of the third embodiment is used from FIG. 12 than in the case where the subtractor 71a and the accumulator 22a are not provided. When the subtractor 71a and the accumulator 22a do not have the number of iterations N ₉₉ at which the correct answer is obtained with a probability of 99%, 3.4 × 10 ⁷ in the absence of the accumulator 22a, the transition control unit 20c of the third embodiment is used. In this case, it was 1.0 × 10 ⁷ and it was shown to be about 3 times faster.

Further, in the transition control unit 20c of the third embodiment, the circuit area can be reduced as compared with the transition control unit 20b of the second embodiment since the common random number u is used in each state transition.
As mentioned above, although one aspect of a control method of an optimization device and an optimization device of the present invention was explained based on an embodiment, these are only examples and are not limited to the above-mentioned statement.

14b1 random number generation circuit 14b2 selector 14b3 noise table 14b4 multiplier 14b5 comparator 20 transition control unit 21 offset addition circuit 21a subtractor 22 offset control circuit 22a accumulator

Claims (9)

A state holding unit for holding values of a plurality of state variables included in an evaluation function representing energy;
An energy calculator configured to calculate a change value of the energy for each of a plurality of state transitions when a state transition occurs in response to any of the values of the plurality of state variables changing;
A temperature control unit that controls a temperature value indicating the temperature;
In probabilistically determining whether to accept any of the plurality of state transitions based on the temperature value, the change value, and the random value based on the relative relationship between the change value and the thermal excitation energy. A transition control unit that adds an offset value to the change value and controls the offset value in the local solution in which the energy is minimized so as to be larger than that in the case where the energy is not minimized;
An optimization apparatus characterized by having. The transition control unit has an offset control circuit,
The offset control circuit sets the offset value to 0 when accepting any of the plurality of state transitions, and increments the offset value every first period when not accepting any of the plurality of state transitions. And monotonously increasing the offset value with respect to the staying time of the current state represented by the values of the plurality of state variables,
The optimization device according to claim 1, characterized in that: The offset control circuit further includes an accumulator having a reset terminal, and the accumulator sets the offset value to 0 when receiving a first signal indicating that any one of the plurality of state transitions is accepted. An offset increment value is added to the offset value upon receiving a second signal indicating that none of the plurality of state transitions is accepted.
The optimization device according to claim 2, characterized in that: The accumulator further has a clock terminal, and adds the offset increment value to the offset value each time a pulse signal from a state machine is input to the clock terminal.
The optimization device according to claim 3, characterized in that: The transition control unit
A selector that selects one of the change values calculated for each of the plurality of state transitions in accordance with the random number value;
A storage unit that outputs a value of an inverse function of a function indicating an allowance probability of the plurality of state transitions represented by the metropolis method or the Gibbs method according to the random value;
A multiplier for outputting the thermal excitation energy represented by a product of the value of the inverse function and the temperature value;
A state transition corresponding to the change value selected by the selector, represented by a value corresponding to a comparison result of the sum of the change value selected by the selector and the offset value and the thermal excitation energy A comparator that outputs the determination result as to whether to accept or not;
The optimization apparatus according to any one of claims 1 to 4, characterized in that The transition control unit
Outputs a plurality of inverse values of a function indicating an allowable probability of the plurality of state transitions represented by the metropolis method or the Gibbs method according to the random number values independent of one another for each of the plurality of state transitions A storage unit to
A multiplier for outputting the thermal excitation energy represented by a plurality of products obtained by multiplying each of the plurality of values by the temperature value;
A plurality of values corresponding to comparison results between each of a plurality of sums obtained by adding the change value calculated for each of the plurality of state transitions and the offset value, and each of the plurality of products A comparator for outputting a plurality of determination results as to whether or not each of the plurality of state transitions is accepted;
A selector that selects any one state transition when there are a plurality of state transitions to be accepted among the plurality of state transitions based on the plurality of determination results;
The optimization apparatus according to any one of claims 1 to 4, characterized in that The transition control unit
A memory for outputting a value of an inverse function of a function indicating an allowable probability of the plurality of state transitions represented by the metropolis method or the Gibbs method according to the random number value common to all of the plurality of state transitions Department,
A multiplier for outputting the thermal excitation energy represented by a product of the value of the inverse function and the temperature value;
Represented by a plurality of values corresponding to a comparison result of each of a plurality of sums obtained by adding the change value calculated for each of the plurality of state transitions and the offset value, and the product A comparator that outputs a plurality of determination results as to whether or not each of a plurality of state transitions is accepted;
A selector that receives one of the plurality of determination results and selects one of the state transitions to be accepted when there are a plurality of state transitions to be accepted among the plurality of state transitions;
The optimization apparatus according to any one of claims 1 to 4, characterized in that The transition control unit
A plurality of inverse functions of a function indicating an allowable probability of the plurality of state transitions represented by Metropolis method or Gibbs method according to the random number value common to two or more state transitions among the plurality of state transitions A storage unit that outputs the value of
A multiplier for outputting the thermal excitation energy represented by a plurality of products obtained by multiplying each of the plurality of values by the temperature value;
A plurality of values corresponding to comparison results between each of a plurality of sums obtained by adding the change value calculated for each of the plurality of state transitions and the offset value, and each of the plurality of products A comparator for outputting a plurality of determination results as to whether or not each of the plurality of state transitions is accepted;
A selector that selects one of the accepted state transitions when there are multiple accepted state transitions among the plurality of state transitions based on the plurality of determination results;
The optimization apparatus according to any one of claims 1 to 4, characterized in that In the control method of the optimization device,
A state holding unit included in the optimization device holds values of a plurality of state variables included in an evaluation function representing energy, respectively.
When a state transition occurs in response to a change in any of the values of the plurality of state variables, an energy calculation unit included in the optimization device calculates the change value of the energy for each of the plurality of state transitions. And
A temperature control unit of the optimization device controls a temperature value indicating a temperature;
Whether the transition control unit included in the optimization device accepts any of the plurality of state transitions according to the relative relationship between the change value and the thermal excitation energy based on the temperature value, the change value, and a random value In addition, an offset value is added to the change value, and the offset value in the local solution in which the energy is minimized is controlled to be larger than that in the case where the energy is not minimized. Do,
And controlling the optimization device.

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