Patent Publication Number: US-2021191692-A1

Title: Optimization apparatus and method of controlling optimization apparatus

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation application of International Application PCT/JP2018/033992 filed on Sep. 13, 2018, and designated the U.S., the entire contents of which are incorporated herein by reference. 
    
    
     FIELD 
     The disclosures herein relate to an optimization apparatus and a method of controlling an optimization apparatus. 
     BACKGROUND 
     An optimization problem is the problem of finding a point (i.e., solution) belonging to search space that minimizes the value of an objective function defined in the search space. When the search space is a discrete set having a finite number of elements, the minimum value can be found in an exhaustive manner by comparing objective function values that are calculated at all the points belonging to the search space. As the number of dimensions of the search space increases, the number of elements in the set increases explosively, which makes it substantially impossible to perform an exhaustive search. 
     RELATED-ART DOCUMENTS 
     Patent Document 
     [Patent Document 1] Japanese Patent Application Publication No. H7-141323 
     [Patent Document 2] Japanese Patent Application Publication No. H7-249023 
     SUMMARY 
     According to an aspect of the embodiment, an optimization apparatus includes hardware circuits configured to function as a random number generator configured to operate either in a first operation mode in which to generate a random number sequence after performing an initialization or in a second operation mode in which to generate a random number sequence without performing the initialization, an annealing calculation unit configured to perform an annealing process by use of random numbers generated by the random number generator, and an operation instruct unit configured to cause the random number generator to start operating in the first operation mode when the annealing calculation unit starts the annealing process, to cause the random number generator to stop operating when the annealing calculation unit suspends the annealing process, and to cause the random number generator to restart operating in the second operation mode when the annealing calculation unit restarts the annealing process. 
     The object and advantages of the embodiment, will be realized and attained by means of the elements and combinations particularly pointed out in the claims. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the invention, as claimed. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a drawing illustrating an example of the configuration of an optimization apparatus. 
         FIG. 2  is a drawing illustrating an example of the configuration of a random number generator embedded in a random-number-generation-&amp;-initial-value-setting unit. 
         FIG. 3  is a drawing illustrating another example of the configuration of the random number generator embedded in the random-number-generation-&amp;-initial-value-setting unit. 
         FIG. 4  is a drawing illustrating a synchronous relationship in step counts between an annealing process and a random number generation process in the case in which the iterations of the annealing process are continuously performed. 
         FIG. 5  is a drawing illustrating a synchronous relationship in step counts between an annealing process and a random number generation process in the case in which the annealing process is temporarily suspended and restarted. 
         FIG. 6  is a flowchart illustrating an example of the operation of the optimization apparatus illustrated in  FIG. 1 . 
         FIG. 7  is a drawing illustrating an example of the more detailed configuration of the optimization apparatus. 
         FIG. 8  is a flowchart illustrating an example of the operation of the optimization apparatus illustrated in  FIG. 7 . 
         FIG. 9  is a state transition diagram illustrating the transition of an operation state of the optimization apparatus illustrated in  FIG. 7  in the normal operation mode. 
         FIG. 10  is a state transition diagram illustrating the transition of an operation state of the optimization apparatus illustrated in  FIG. 7  in the continuation operation mode. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Simulated annealing mimics a metal annealing process that yields a crystal structure with few defects by gradually cooling a metal. Each point belonging to the search space corresponds to a respective state of physical phenomena, and the objective function corresponds to the energy of the system at each state. The concept of temperature is introduced to the probability of occurrence of each state. A probability distribution is then configured such that at any given temperature, the smaller the energy at a state is, the higher the probability of occurrence of the state is, and such that the lower the temperature is, the greater the ratio between the probabilities of occurrences of two states having different energies is. Lowering temperature at a sufficiently slow rate, while creating successive states with gradual state changes such as to realize the above-noted probability distribution, may allow the state to be converged on an optimum solution having the smallest energy value. 
     When a change from the energy of a current state to the energy of a next state is denoted as ΔE, the probability P of a transition from the current state to the next state is calculated as the value of a function having ΔE and temperature as variables. Lowering temperature at a sufficiently slow rate, while performing state transitions with the probability P, allows the state to be converged on an optimum solution having the smallest energy value. In an annealing process, generally, a uniform random number r (0&lt;r&lt;1) is used in order to achieve the act of making a transition to a next state with the probability P. State transition is controlled such that, upon comparison of the uniform random number r with the probability P, a result of P&gt;r causes a state transition, and a result of P≤r does not cause a state transition. 
     A true random number is difficult to generate by use of a circuit. Typically, a pseudo random number is used chat is generated by deterministic calculations performed by a pseudo random number generator such as a linear feedback shift register or a Mersenne twister. In the case of using such a pseudo random number, upon determining an initial value setting (i.e., the seed), the sequence of random numbers generated thereafter is a deterministic sequence responsive to the seed. As a result, two random number sequences having the same seed are completely the same random number sequence. 
     In an optimization apparatus, there may be a need in some cases to check intermediate statuses during an annealing process for the purpose of tuning the annealing process or the like. For example, parameters such as spin values and energy values may be read out from the optimization apparatus at every 100-th iteration with respect to a problem in which a state may converge on a solution close to the optimum solution after 1000 iterations (i.e., 1000 state transitions). In order to read out the parameters, the annealing process by the optimization apparatus is temporarily suspended, and, then, the parameters are read from the internal registers of the apparatus to the outside. 
     The purpose is to know the intermediate statuses leading to the final result that will be obtained after performing 1000 iterations. Because of this, the final result and intermediate statuses are preferably identical between the case in which 1000 iterations are continuously performed and the case in which 1000 iterations are intermittently performed by running 100 iterations at a time. In a conventional optimization apparatus, however, a random number generator continues functioning to keep generating random numbers during other operations of the optimization apparatus in addition to an annealing process, such as during the reading of parameters. Namely, a random number generation process by the random number generator is being performed independently of the running and suspending of an annealing process. As a result, a random number sequence used in an annealing process is different between the case in which 1000 iterations are continuously performed and the case in which 1000 iterations are intermittently performed by running 100 iterations at a time. This gives rise to a problem that the final result and intermediate statuses differ. 
     In the following, embodiments of the invention will be described with reference to the accompanying drawings. 
       FIG. 1  is a drawing illustrating an example of the configuration of an optimization apparatus. In  FIG. 1  and the subsequent similar drawings, boundaries between functional or circuit blocks illustrated as boxes basically indicate functional boundaries, and may not correspond to separation in terms of physical positions, separation in terms of electrical signals, separation in terms of control logic, etc. Each functional or circuit block may be a hardware module that is physically separated from other blocks to some extent, or may indicate a function in a hardware module in which this and other blocks are physically combined together. 
     The optimization apparatus illustrated in  FIG. 1  includes a control unit  10  and an annealing unit  20 . The control unit includes an operation instruct unit  11 , an initial value transmitting unit  12 , and a control data storage unit  13 . The annealing unit  20  includes a random-number-generation-&amp;-initial-value-setting unit  21  and an annealing calculation unit  22 . 
     The annealing calculation unit  22  of the annealing unit  20  performs an annealing process by successively changing a state stored in an internal register. The annealing calculation unit  22  calculates an evaluation function value responsive to each state as the energy of each state, and controls a transition from a current state to a next state based on the evaluation function value and current temperature. 
     Specifically, the annealing calculation unit  22  calculates the evaluation function value E of the current state S, and also calculates the evaluation function value E′ of a candidate next state S′ that has a slight change from the current state S, followed by calculating a difference ΔE (=E′−E). In the case in which the Boltzmann distribution is used to represent the probability distribution of a state S and the Metropolis method is used, for example, probability P with which a transition to the next state S′ occurs may be defined by the following formula. 
         P =min[1, exp(−βΔ E )]  (1)
 
     Here, β is thermodynamic beta (i.e., the reciprocal of absolute temperature T), and is equal to 1/T. The function min[1, x] assumes a value of 1 or a value of x, whichever is smaller. According to the above formula, a transition to the next state occurs with probability “1” in the case of ΔE≤0, and a transition to the next state occurs with probability P (=exp(−βΔE)) in the case of 0&lt;ΔE. The Metropolis method is a non-limiting example, and other transition control algorithms such as Gibbs sampling may alternatively be used. 
     The form of the evaluation function is not limited to a particular form, and may be an energy function based on an Ising model, for example, as shown below. 
         E ( S )=−ΣΣ W   ij   x   i   x   j   −Σb   i   x   i    (2)
 
     Here, Σ represents a sum with respect to the suffix i or j from 1 to M (M: positive integer). The state S is a state having M spins as follows. 
         S   i =( x   1   , x   2   , . . . , x   M )   (3)
 
     Each spin assumes a value of −1 or +1. W ij  is a weighting factor for the coupling between spins, and may be such that W ij =0. Further, b i  is a bias. 
     The probability P defined by the formula (1) and the evaluation function E defined by the formula (2) are examples only. The probability and evaluation function used for an annealing process are not limited to the noted probability and evaluation function. Further, the annealing unit  20  may be such that a plurality of annealing calculation units  22  calculate state transitions in a plurality of systems in parallel, rather than a single annealing calculation unit  22  calculating a state transition in a single system. 
     In an annealing process performed by the annealing calculation unit  22 , a uniform random number r (0&lt;r&lt;1) generated by the random-number-generation-&amp;-initial-value-setting unit  21  is used in order to achieve the act of making a transition to a next state with the probability P. State transition is controlled such that, upon comparison of the uniform random number r with the probability P, a result of P&gt;r causes a state transition, and a result, of P≤r does not cause a state transition. For example, the probability P i  of inversion with respect to each of the spins x i  (i=1 to M) in the above-noted formula (3) may be calculated as the probability P defined by the formula (1) with respect to an inversion of the spin of interest. Then, inversion rules may be such that the spin can be inverted when P i &gt;r, and should not be inverted when P i ≤r. In this case, one of the spins for which the rules allow spin inversion is randomly selected, and is inverted to achieve a state transition. 
     Each time the annealing calculation unit  22  compares the probability P with the uniform random number r, this uniform random number r may be a random number newly generated by the random-number-generation-&amp;-initial-value-setting unit  21 . The random-number-generation-&amp;-initial-value-setting unit  21  generates random numbers in synchronization with the advancement of an annealing process, and also sets the initial values of a state S (i.e., the initial values of respective spins), the weighting factors W ij  for coupling between the spins, the biases bi, and temperature values in the annealing calculation unit  22  at the start of the annealing process. 
     The control unit  10  controls the operation of the annealing unit  20 . The initial value transmitting unit  12  of the control unit  10  transmits the initial parameters set from an external source (i.e., the initial values of a state S, the weighting factors W ij  for coupling between the spins, the biases bi, temperature values, and the like) to the random-number-generation-&amp;-initial-value-setting unit  21  of the annealing unit  20 . The control data storage unit  13  of the control unit  10  stores therein control data set from an external source (i.e., an iteration count limit and data indicative of an operation mode). The operation instruct unit  11  of the control unit  10  controls the random number generation process of the random-number-generation-&amp;-initial-value-setting unit  21  and the annealing process of the annealing calculation unit  22  based on the control data stored in the control data storage unit  13 . 
     The portion (i.e., random number generator) of the random-number-generation-&amp;-initial-value-setting unit  21  operates either in a first operation mode in which to generate a random number sequence after performing an initialization or in a second operation mode in which to generate a random number sequence without performing such an initialization. In general, a random number generator performs initialization such as setting a seed value and initializing memory areas before performing a process of generating a random number sequence. In the first operation mode, such an initialization is performed, followed by performing a process of generating a random number sequence. In the second operation mode, such an initialization is not performed, and a process of generating a random number sequence is performed based on the existing status of internal registers, memories, and the like at that point in time. Accordingly, use of the second operation mode at the time of restarting a random number generation process after temporarily suspending a random number generation process makes it possible to generate the same random number sequence as in the case in which a random number generation process is continuously performed without any interruptions. 
     At the time the annealing calculation unit  22  suspends an annealing process, the random number generator may suspend its operation, and may retain the internal states existing at the time of suspension. At the time the annealing calculation unit  22  restarts the annealing process, the random number generator may restart its operation from the internal states existing at the time of suspension, without performing initialization. This arrangement reliably generates the same random number sequence as in the case in which a random number generation process is continuously performed without any interruptions. 
     In the following description, for the sake of ease of understanding, the first operation mode is referred to as a normal operation mode, and the second operation mode is referred to as a continuation operation mode. 
     Which one of the operation modes is used for the operation of the random number generator is determined by the operation instruct unit  11  based on the control data supplied from the control data storage unit  13 . The operation instruct unit  11  causes the random number generator to start operating in the normal operation mode when causing the annealing calculation unit  22  to perform an annealing process from the initial state. In order to cause the random number generator to operate in the normal operation mode, a user may set data in the control data storage unit  13  which provides an express indication of the normal operation mode from outside the optimisation apparatus. Alternatively, the number of iterations that have been performed in a particular annealing process may be kept of record, and the random number generator may be controlled to operate in the normal operation mode when the number is zero at the start or restart of the particular annealing process. 
     The operation instruct unit  11  stops the operation of the random number generator when the annealing calculation unit  22  suspends an annealing process upon completing the execution of a predetermined number of iterations. The number of iterations is the number of state transitions performed by the annealing calculation unit  22 . 
     The operation instruct unit  11  causes the random number generator to restart its operation in the continuation operation mode when causing the annealing calculation unit  22  to resume the annealing process. In order to cause the random number generator to operate in the continuation operation mode, a user may set data in the control data storage unit  13  from outside the optimization apparatus at the restart of the annealing process, and the data provides an express indication of the continuation operation mode Alternatively, the number of iterations that have been performed in a particular annealing process may be kept of record, and the random number generator may be controlled to operate in the continuation operation mode when the number is not zero at the start or restart of the particular annealing process. 
       FIG. 2  is a drawing illustrating an example of the configuration of the random number generator embedded in the random-number-generation-&amp;-initial-value-setting unit  21 . The random number generator illustrated in  FIG. 2  which is a linear feedback shift register includes  16  flip-flops  30 - 1  through  30 - 16 ,  16  selectors  31 , and XOR gates  32  through  34 . 
     The flip-flops  30 - 1  through  30 - 16  are connected in series such that a data output Q is coupled to a data input D, thereby constituting a shift register which operates in synchronization with a clock signal CLK. The XOR gates  32  through  34  calculate an exclusive OR of the 11-th, 13-th, 14-th, and 16-th flip-flops, and the calculated outcome is applied as a feedback input to the first flip-flop  30 - 1  of the shift register. This feedback input, achieves a linear feedback shift register. 
     The selectors  31  are provided in one-to-one correspondence with the flip-flops  30 - 1  through  30 - 16  to select either the input for shift operations or a seed value SEED (16 bits) for initialization. The values selected by the selectors  31  are loaded into the flip-flops  30 - 1  through  30 - 16  in synchronization with the clock signal CLK. At the time of initialization, an initialization signal INISET may be set to 1, for example. In response to this, the 16 selectors  31  select the 16 respective bits of the seed value SEED. The 16 respective bits of the seed value SEED are then stored in the 16 flip-flops  30 - 1  through  30 - 16 . At the time of shift operations, the initialization signal INISET may be set to 0, for example. In response to this, the selectors  31  select the inputs for shift operations (i.e., the outputs of the preceding flip-flops or the feedback input). The selected values are then stored in the 16 flip-flops  30 - 1  through  30 - 16 . 
     After setting the seed value at the initialization, shift operations are successively performed in synchronization with the clock signal CLK, so that the linear feedback shift register generates a random number sequence. Outputting an N-bit random number as a uniform random number r is achieved by consolidating N successive outputs of the XOR gate  32  as a uniform random number r. Alternatively, an XOR gate may be provided to calculate an XOR of the outputs Q of a two or more predetermined number of flip-flops among the flip-flops  30 - 1  through  30 - 16 . N successive outputs of the XOR gate may then be output as a uniform random number r. 
     In the normal operation mode described above, the initialization signal INISET may be set to 1, for example, to set the seed value SEED to the flip-flops  30 - 1  through  30 - 16  in synchronization with the clock signal CLK to perform initialization. After the initialization, the initialization signal INISET may be set to 0, for example, to perform shift operations successively in synchronization with the clock signal CLK, thereby generating a random number sequence. 
     In order to suspend a random number generation process, the pulses of the clock signal CLK may be stopped from being supplied so as to retain the bit values stored in the flip-flops  30 - 1  through  30 - 16 . The initialization signal INISET is kept, in the state in which it is set to 0. 
     In the continuation operation mode previously described, while keeping the state in which the initialization signal INISET is set to 0, the pulses of the clock signal CLK are supplied again to perform shift operations successively in synchronization with the clock signal CLK, thereby generating a random number sequence. Namely, shift operations are successively performed to generate a random number sequence as a continuation from the state in which the values stored in the flip-flops  30 - 1  through  30 - 16  are the same as at the time of suspension. 
     Use of a linear feedback shift register as illustrated in  FIG. 2  as a random number generator enables the generation of pseudo-random numbers by use of a simple, small-scale circuit configuration. In the case of the linear feedback shift register illustrated in  FIG. 2 , the period of pseudo-random numbers is 65535. 
       FIG. 3  is a drawing illustrating another example of the configuration of the random number generator embedded in the random-number-generation-&amp;-initial-value-setting unit  21 . The random number generator illustrated in  FIG. 3  which is a Mersenne twister includes an initialization block  40 , a memory circuit  41 , a selector circuit  42 , a combinatorial logic circuit  43 , an address counter  44 , and a flip-flop  45 . 
     The memory circuit  41  has addresses 1 through 624, each of which stores therein 1-word (i.e., 32 bits) data. At the time of initialization, the initialization signal INISET may be set to 1, for example, to place the selector circuit  42  in such a state as to select the output value of the initialization block  40 . The initialization block  40  performs predetermined arithmetic operations based on a seed value SEED such as multiplication, addition, and bit shifts so as to calculate and output values that are to be stored in the respective addresses of the memory circuit  41 . The output values calculated by the initialization block  40  are successively stored via the selector circuit  42  in the respective addresses 1 through 624 of the memory circuit  41  in the first cycle to the 624-th cycles of the initialization process. In so doing, the address value indicated by the address counter  44  successively increases from 1 to 624 in synchronization with the clock signal CLK. In the first cycle of the initialization process, the initialization block  40  calculates an output value by performing a predetermined arithmetic operation on the seed value SEED. The output value calculated by the initialization block  40  is stored in the memory circuit  41  and also stored in the flip-flop  45 . In the second cycle through the 624-th cycle, the initialization block  40  calculates output values by performing predetermined arithmetic operations on the value stored in the flip-flop  45 . 
     As a further initialization process following after the above-described process, the initialization signal INISET may be set to 0, for example, to place the selector circuit  42  in such a state as to select the output value of the combinatorial logic circuit  43 . The combinatorial logic circuit  43  may then perform arithmetic operations on the values stored at the respective addresses of the memory circuit  41 . Specifically, the stored values may be retrieved from the memory circuit  41  in response to the address value indicated by the address counter  44 , and, then, the combinatorial logic circuit  43  performs arithmetic operations inclusive of bit shifts, EXOR, multiplication, and addition, followed by writing the result of the operation back to the memory circuit  41 . With this, the initialization process comes to an end. 
     At the time of a random number generation process following the initialization, the initialization signal INISET may be set to 0, for example, to place the selector circuit  42  in such a state as to select the output value of the combinatorial logic circuit  43 . The address counter  44  outputs addresses in synchronization with the clock signal CLK so that the stored values are retrieved from the memory circuit  41  in response to these addresses. The combinatorial logic circuit  43  performs predetermined arithmetic operations inclusive of AND, OR, bits shifts, XOR, and the like on the received retrieved values. The calculated values are then stored via the selector circuit  42 , at the addresses in the memory circuit  41  indicated by the address counter  44 . At the (624n+1)-th random number generation (n: integer greater than or equal to 0), a process is performed that updates the values stored in the respective addresses 1 through 624 in the memory circuit  41  as described above. The address counter  44  thereafter outputs an address that is successively increased from 1 to 624, and the stored values are retrieved from such addresses in the memory circuit  41 . Random numbers are generated by performing predetermined arithmetic operations inclusive of bit shifts, AND, and XOR on the retrieved values. In this manner, (624n+m)-th random number generations (m: integer from 1 to 624) are performed. Thereafter, the process described above is repeated multiple times. 
     In the normal operation mode described above, the initialization signal INISET may be set to 1, for example, to set initial values to the respective addresses 1 through 624 in the memory circuit  41  in synchronization with the clock signal CLK to perform initialization. After the initialization, the initialization signal INISET may be set to 0, for example, to perform retrieval from the memory circuit  41  and arithmetic: operations by the combinatorial logic circuit  43  successively in synchronization with the clock signal CLK, thereby generating a random number sequence. 
     In order to suspend a random number generation process, the pulses of the clock signal CLK may be stopped from being supplied so as to retain the values stored in the memory circuit  41 . Further, the internal state of the address counter  44  (i.e., the output address value) may also be retained. Moreover, the initialization signal INISET may be kept in the state in which it is set to 0. 
     In the continuation operation mode previously described, while keeping the state in which the initialization signal INISET is set to 0, the pulses of the clock signal CLK are supplied again to perform retrieval from the memory circuit  41  and arithmetic operations successively in synchronization with the clock signal CLK, thereby generating a random number sequence. Namely, retrieval from the memory circuit  41  and arithmetic operations are successively performed to generate a random number sequence as a continuation from the state in which the output address value of the address counter  44  and the stored values of the memory circuit  41  are the same as at the time of suspension. 
     Use of a Mersenne twister as illustrated in  FIG. 3  as a random number generator enables the generation of high-quality pseudo-random numbers. In the case of the Mersenne twister illustrated in  FIG. 3 , the period of pseudo-random numbers is 2 19337 −1, which is an extremely long length. 
       FIG. 4  is a drawing illustrating a synchronous relationship in step counts between an annealing process and a random number generation process in the case in which the iterations of the annealing process are continuously performed. As illustrated in  FIG. 4 , when the iterations of an annealing process are continuously performed from the first round to the 200-th round, the step count of a random number generation process also increases in synchronization with increases in the number of iterations of the annealing process (i.e., the step count illustrated in  FIG. 4 ). Here, the step count of a random number generation process is a number obtained by counting, as one step, a random number generation process that generates a number of random numbers used in a single iteration of the annealing process. 
       FIG. 5  is a drawing illustrating a synchronous relationship in step counts between an annealing process and a random number generation process in the case in which the annealing process is temporarily suspended and restarted. As illustrated in  FIG. 5 , when the iterations of an annealing process are suspended after 100 rounds, the step count of a random number generation process also stops after successively increasing from 1 to 100, in synchronization with the stopping of the step count of the annealing process upon successively increasing from 1 to 100. After the suspension, the values of the internal registers of the annealing calculation unit  22  are read from the outside by taking 500 clock cycles, for example. Thereafter, the annealing process restarts from the 101-th iteration. In synchronization with the step count of the annealing process that stops upon successively increasing from 101 to 200, the step count of the random number generation process also stops upon successively increasing from 1 to 100. 
     In the optimization apparatus of the present disclosures, the operations in “synchronization”, regarding the annealing process and the random number generation process that operate in synchronization with each other when starting, suspending, and restarting their operations, does not have to be operations that are synchronized with a common clock signal used across the entirety of the optimization apparatus. For example, the phrase “suspend the operations in synchronization” does not have to refer to the suspension of operations of the annealing process and the random number generation process at the same cycle of a common clock signal. It suffices for the operations “in synchronization” to be operations that can maintain conditions in which random numbers generated by the random number generation process are in one-to-one correspondence to random numbers used in the annealing process. Namely, the condition is satisfactory if the one-to-one correspondence does not collapse as in the cases in which the random number generation process generates excessive random numbers that are not used by the annealing process, or in which a random number generated by the random number generation process is used twice erroneously by the annealing process. 
     In other words, it suffices for one-to-one correspondence to be kept, without an excess or a deficit, between the random numbers generated by the random number generator and the random numbers utilized by the annealing calculation unit both before and after the annealing calculation unit suspends and resumes the annealing process. With this arrangement, synchronization is established on a step-by-step basis or on a random-number-by-random-number basis, even if synchronization is not established on a clock-pulse-by-clock-pulse basis. As a result, the objective to generate the same annealing results between continuous execution and intermittent execution is more readily achieved. 
     The optimization apparatus illustrated in  FIG. 1  is provided with the normal operation mode and the continuation operation mode for a random number generation process as previously described, and may selectively use one of these. As a result, when the annealing process and the random number generation process are synchronized both before and after a suspension as illustrated in  FIG. 5 , a random number sequence can be generated that is the same as when the annealing process is continuously performed as illustrated in  FIG. 4 . The final calculation results and intermediate statuses obtained by the annealing calculation unit can thus be completely matched between the continuous execution of the annealing process and the intermittent execution of the annealing process. 
       FIG. 6  is a flowchart illustrating an example of the operation of the optimization apparatus illustrated in  FIG. 1 . This example illustrates the operation of the optimization apparatus when a user specifies an operation mode as appropriate. 
     In  FIG. 6  and the subsequent flowcharts, an order in which the steps illustrated in the flowchart are performed is only an example. The scope of the disclosed technology is not limited to the disclosed order. For example, a description may explain that an A step is performed before a B step is performed. Despite such a description, it may be physically and logically possible to perform the B step before the A step while it is possible to perform the A step before the B step. In such a case, all the consequences that affect the outcomes of the flowchart may be the same regardless of which step is performed first. It then follows that, for the purposes of the disclosed technology, it is apparent, that the B step can be performed before the A step is performed. Despite the explanation chat the A step is performed before the B step, such a description is not intended to place the obvious case as described above outside the scope of the disclosed technology. Such an obvious case inevitably falls within the scope of the technology intended by this disclosure. 
     In step S 1 , the user of the optimization apparatus selects an operation mode. For an annealing process that is started for the first time in the optimization apparatus, the user selects the normal operation mode, which causes data indicative of the normal operation mode to be stored in the control data storage unit  13  of the optimization apparatus. 
     In step S 2 , the optimization apparatus starts operating, and the operation instruct unit  11  refers to the data indicative of an operation mode stored in the control data storage unit  13  to determiiie whether the operation mode setting is the continuation operation mode. When it is found that the operation mode setting is not the continuation operation mode, the procedure proceeds to step S 3 . 
     In step S 3 , the operation instruct unit  11  instructs the random-number-generation-&amp;-initial-value-setting unit  21  to start generating random numbers in the normal operation mode. In response to this instruction, the random number generator of the random-number-generation-&amp;-initial-value-setting unit  21  first performs initialization. At step S 4 , the random number generator checks whether the initialization is completed. The check in step S 4  is repeated until the initialization is completed. Upon completion of the initialization, the procedure proceeds to step S 5 , in which the operation instruct unit  11  instructs the annealing calculation unit  22  to start an annealing process. The annealing calculation unit  22  starts an annealing process, and the random number generator generates a random number sequence used in the annealing process. 
     When it is found in step S 2  that the operation mode setting is the continuation operation mode, the procedure proceeds to step S 6 . In step S 6 , the operation instruct unit  11  instructs the annealing calculation unit  22  to perform an annealing process, and also instructs the random-number-generation-&amp;-initial-value-setting unit  21  to generate random numbers. In response to these instructions, the annealing calculation unit  22  restarts the annealing process, and the random number generator of the random-number-generation-&amp;-initial-value-setting unit  21  generates a random number sequence used in the annealing process. The annealing process by the annealing calculation unit  22  and the random number generation process by the random number generator are controlled to proceed in synchronization with each other. 
     In step S 7 , the annealing calculation unit  22  performs the annealing process until a termination condition is satisfied. The termination condition may be an iteration count limit stored in the control data storage unit  13 . When the termination condition is satisfied, the annealing process by the annealing calculation unit  22  is brought, to an end. In synchronization with the end of the annealing process, the random number generation process by the random number generator of the random-number-generation-&amp;-initial-value-setting unit  21  is also brought to an end. 
     The synchronization control in step S 6  and step S 7  may be achieved by communication between the annealing calculation unit  22  and the random-number-generation-&amp;-initial-value-setting unit  21 , or may be achieved by an instruction from the operation instruct unit  11  (e.g., an instruction to perform an iteration on an iteration-by-iteration basis). Alternatively, the random number generator may have been notified of a predetermined iteration count limit by the operation instruct unit  11  in advance, and stops the random number generation process after generating a predetermined number of random numbers corresponding to the predetermined iteration count limit. How to achieve synchronization control is not limited to a particular method. 
     In step S 8 , the annealing calculation unit  22  and the random-number-generation-&amp;-initial-value-setting unit  21  retain their internal states existing in the condition in which the operations are suspended The annealing calculation unit  22  may retain all the values stored in the internal registers, such as the spin values of the current state, the values of coupling factors, temperature, the evaluation function value, and the like. Alternatively, the value of the internal registers of the annealing calculation unit  22  may be temporarily evacuated to the random-number-generation-&amp;-initial-value-setting unit  21 , so that parameters regarding the annealing process are stored in the registers of the random-number-generation-&amp;-initial-value-setting unit  21 . The random number generator of the random-number-generation-&amp;-initial-value-setting unit  21  may retain the internal states regarding random number generation (e.g., the stored values of the flip-flops of a linear feedback shift register or the stored values of the memory circuit of a Mersenne twister). 
     In step S 9 , the results of calculation by the annealing calculation unit  22 , i.e., the parameter values (the spin values of the current state and the evaluation function value) stored in the internal registers, are sent to the outside. Based on the results of calculation sent to the outside, the user determines whether to continue the annealing process. In the case of continuing the annealing process, the user sets data indicative of the continuation operation mode in the control data storage unit  13  of the optimization apparatus. 
     In step S 10 , the operation instruct unit  11  checks whether the operation mode setting has been changed. When the normal operation mode is kept, without a change, the procedures comes to an end. When the operation mode setting has been changed to the continuation operation mode, the user gives instruction to the optimization apparatus in step S 11  to restart the annealing process in the continuation operation mode. Thereafter, the procedure returns to step S 2 , from which the subsequent processes are repeated. 
       FIG. 7  is a drawing illustrating an example of the more detailed configuration of the optimization apparatus. The optimization apparatus illustrated in  FIG. 7  includes the control unit  10  and the annealing unit  20 . 
     The control unit includes the operation instruct unit  11 , the initial value transmitting unit  12 , the control data storage unit  13 , and a seed storage unit  14 . The operation instruct unit  11  includes an annealing initial value indicating unit  51 , a random number generation instruct unit  52 , and an annealing process instruct unit  53 . The control data storage unit  13  includes an iteration count limit storage unit  54  and an operation mode storage unit  55 . 
     The annealing unit  20  includes the random-number-generation-S-initial-value-setting unit  21  and the annealing calculation unit  22 . The random-number-generation-&amp;-initial-value-setting unit  21  includes a random number generator  60 , an input select unit  64 , and an initial value storage unit  65 . The random number generator  60  includes an operation control unit  61 , a generation unit  62 , and a register  63 . The annealing calculation unit  22  includes an arithmetic unit  71  and a register  72 . 
     The random number generation instruct unit  52  of the operation instruct unit  11  causes the random number generator  60  to operate in an indicated operation mode that is either the normal operation mode or the continuation operation mode, based on the data indicative of an operation mode setting supplied from the operation mode storage unit  55 . The random number generation instruct unit  52  causes the random number generator to operate in the normal operation mode when the annealing process instruct unit  53  causes the annealing calculation unit  22  to perform an annealing process from the initial state. Specifically, under the control of the operation control unit  61 , the generation unit  62  performs initialization based on the seed value supplied from the seed storage unit  14 , followed by performing the process of generating a random number sequence. The random numbers generated by the generation unit  62  are successively stored in the register  63 . 
     The annealing initial value indicating unit  51  causes the input select unit  64  to select the initial parameters supplied from the initial value transmitting unit  12  in the case in which the operation mode storage unit  55  indicates the normal operation mode, i.e., in the case in which an annealing process is performed from the initial state As a result, the input select unit  64  outputs the initial parameters from the initial value transmitting unit  12 , and these initial parameters are stored in the initial value storage unit  65 . 
     Based on the data indicative of the iteration count limit supplied from the iteration count limit storage unit  54 , the annealing process instruct unit  53  causes the annealing calculation unit  22  to perform an indicated number of iterations of an annealing process. Specifically, after the initial parameters from the initial value storage unit  65  are stored in the register  72 , the arithmetic unit  71  advances the iterations of the annealing process while controlling state transitions by use of random numbers supplied from the register  63  of the random number generator  60 . As the annealing process advances, the parameters stored in the register  72  keep being updated. When the annealing calculation unit  22  suspends the annealing process upon completing the execution of a predetermined number of iterations, the random number generation instruct unit  52  causes the random number generator  60  to stop operating in synchronization with the suspension of the annealing process. Upon the occurrence of suspension, the parameter values of the current state stored in the register  72  may be read out to the outside of the optimization apparatus. 
     When the annealing process instruct unit  53  causes the annealing calculation unit  22  to restart the annealing process after the suspension of the annealing process, the setting in the operation mode storage unit  55  may be the continuation operation mode. At the time of restarting the annealing process, the random number generation instruct unit  52  causes the random number generator  50  to operate in the continuation operation mode based on the data indicative of the continuation operation mode supplied from the operation mode storage unit  55 . Specifically, under the control of the operation control unit  61 , the generation unit  62  resumes the operation of generating a random number sequence from the current internal state without performing initialization. The random numbers generated by the generation unit  62  are successively stored in the register  63 . 
     The annealing initial value indicating unit  51  causes the input select unit  64  to select the parameters as existed in the suspended state supplied from the register  72  of the annealing calculation unit  22  in the case in which the operation mode storage unit  55  indicates the continuation operation mode, i.e., in the case in which the annealing process is restarted from the suspended state. As a result, the input select unit  64  outputs the parameters as existed in the suspended state supplied from the register  72 , and these parameters are stored in the initial value storage unit  65 . 
     Similarities exist between the case of restarting after the suspension and the case of starting from the initial state, such that the data indicative of the iteration count limit supplied from the iteration count limit storage unit  54  is used as a basis for the annealing process instruct unit  53  to cause the annealing calculation unit  22  to perform an indicated number of iterations of an annealing process. Specifically, after the parameters from the initial value storage unit  65  are stored in the register  72 , the arithmetic unit  71  advances the iterations of the annealing process while controlling state transitions by use of random numbers supplied from the register  63  of the random number generator  60 . As the annealing process advances, the parameters stored in the register  72  keep being updated. 
       FIG. 8  is a flowchart illustrating an example of the operation of the optimization apparatus illustrated in  FIG. 7 . 
     In step S 21 , the user selects the normal operation mode, and gives instruction to the optimization apparatus to start an annealing process. In so doing, the user sets the initial parameters in the initial value transmitting unit  12 , and also sets the iteration count limit and the normal operation mode in the control data storage unit  13 . 
     In step S 22 , the initial parameters transmitted from the initial value transmitting unit.  12  of the control unit  10  are stored in the initial value storage unit  65  via the input select unit  64  of the annealing unit  20 . In step S 23 , the random number generation instruct unit  52  of the control unit  10  instructs the random number generator  60  to perform initialization. In response, the random number generator  60  performs initialization. 
     In step S 24 , the annealing calculation unit  22  performs an annealing process. Specifically, the annealing process instruct unit  53  of the control unit  10  instructs the annealing calculation unit  22  to start an annealing process. In response to this instruction, the annealing calculation unit  22  receives the initial parameters from the initial value storage unit  65 , and then performs the annealing process while controlling state transitions based on a random number sequence supplied from the random number generator  60 . 
     In step S 25 , the annealing process instruct unit  53  or the annealing calculation unit  22  checks whether the state has been updated a number of times equal to the predetermined iteration count limit. The annealing calculation unit  22  performs the annealing process until the predetermined iteration count limit, is reached. Upon reaching the predetermined iteration count limit, the procedure proceeds to step S 26 . 
     In step S 26 , the annealing calculation unit  22  stops the annealing process, and, in synchronization therewith, the random number generator  60  temporarily stops the random number generation process. This synchronization control may be achieved by direct communication between the annealing calculation unit  22  and the random number generator  60 , or may be achieved by a stop instruction sent to the random number generator  60  from the operation instruct unit  11  which monitors and controls the operation of the annealing calculation unit  22 . Alternatively, the operation control unit  61  of the random number generator  60  may have been notified of a predetermined iteration count limit by the random number generation instruct unit  52  in advance, and stops the random number generation process after generating a predetermined number of random numbers corresponding to the predetermined iteration count limit. How to achieve synchronization control is not limited to a particular method. 
     In step S 27 , the parameters indicative of the results of calculation is sent from the register  72  of the annealing calculation unit  22  to the outside of the optimization apparatus. Based on these results of calculation, in step S 28 , the user determines whether the result of the annealing process is satisfactory. In the case of the result of the annealing process being satisfactory, the procedure comes to an end. In the case of the result of the annealing process being not satisfactory, the procedure proceeds to step S 29 . 
     In step S 29 , the user sets either the normal operation mode or the continuation operation mode in the control data storage unit  13  of the control unit  10 . For example, the initial parameters may be modified to perform a next annealing process under different conditions than in this time&#39;s annealing process. In such a case, the normal operation mode is chosen to be set. When this time&#39;s annealing process is to be resumed from the suspended state without any change, the continuation operation mode is chosen to be set. 
     In step S 30 , the random number generation instruct unit  52  of the control unit  10  determines whether the operation mode setting is the continuation operation mode. In the case of the setting being not the continuation operation mode (i.e., in the case of the setting being the normal operation mode), the procedure returns to step S 22 , in which initial parameters are set again, followed by repeating the subsequent processes. In the case of the setting being the continuation operation mode, in step S 31 , the annealing process instruct unit  53  instructs the annealing calculation unit  22  to perform (i.e., resume) the annealing process, and the random number generation instruct unit  52  instructs the random number generator  60  to resume the random number generation (i.e., random number generation in the continuation operation mode). In response, the annealing process by the annealing calculation unit  22  and the random number generation by the random number generator  60  are resumed in synchronization with each other. Thereafter, the procedure proceeds to step S 24 , and the subsequent steps will be repeated 
     Specifically, under the control of the operation control unit  61 , the generation unit  62  resumes the operation of generating a random number sequence from the current internal state without performing initialization. The random numbers generated by the generation unit  62  are successively stored in the register  63 . The parameters as existed in the suspended state have been stored in the initial value storage unit  65  from the register  72  via the input select unit  64 , so that the annealing calculation unit  22  stores the parameters from the initial value storage unit  65  in the register  72  as a first thing after restarting the operation. Thereafter, the arithmetic unit  71  advances the iterations of the annealing process while controlling state transitions by use of random numbers supplied from the register  63  of the random number generator  60 . As the annealing process advances, the parameters stored in the register  72  keep being updated. 
       FIG. 9  is a state transition diagram illustrating the transition of an operation state of the optimization apparatus illustrated in  FIG. 7  in the normal operation mode. As the optimization apparatus is powered on in the power-off state ST- 1 , the operation state of the optimization apparatus makes a transition to an input receiving state ST- 2 . The input receiving state ST- 2  is the state in which the optimization apparatus receives inputs for settings given from an external source, such as the initial parameters (i.e., the spin values of a state, coupling factors, temperature, and the like), an iteration count limit, and an operation mode (i.e., the normal operation mode or the continuation operation mode). The input receiving state ST- 2  is also the state in which the optimization apparatus receives instructions input thereto such as an operation start instruction. 
     As the optimization apparatus receives an operation start instruction in the input receiving state ST- 2 , the operation state makes a transition to an initialization state ST- 3 . The initialization state ST- 3  is the state in which the random number generator  60  performs initialization in the optimization apparatus. This initialization stores a seed value in the flip-lops of the shift register in the case of a linear feedback shift register, and sets initial values in the respective addresses in the memory circuit in the case of a Mersenne twister. As a predetermined number of clock cycles pass to complete the initialization in the initialization state ST- 3 , the operation state of the optimization apparatus makes a transition to an annealing state ST- 4 . 
     The annealing state ST- 4  is the state in which the annealing calculation unit  22  of the optimization apparatus performs an annealing process, with the random number generator  60  generating a random number sequence for use in the annealing process. The state transitions illustrated in  FIG. 9  correspond to the case of the normal operation mode, so that the annealing calculation unit  22  receives the initial parameters from the initial value storage unit  65 , and, then, performs the annealing process while controlling state transitions based on a random number sequence supplied from the random number generator  60 . As execution of a predetermined number of iterations is completed, the operation state of the optimization apparatus makes a transition to the input receiving state ST- 2 . 
       FIG. 10  is a state transition diagram illustrating the transition of an operation state of the optimization apparatus illustrated in  FIG. 7  in the continuation operation mode. As the optimization apparatus receives an operation start instruction in the input receiving state ST- 2 , the operation state makes a transition directly to the annealing state ST- 4  in the case of the continuation operation mode. The state transitions illustrated in  FIG. 10  correspond to the case of the continuation operation mode, so that the annealing calculation unit  22  receives the parameters as existed in the suspended state from the initial value storage unit  65 , and, then, performs the annealing process while controlling state transitions based on a random number sequence supplied from the random number generator  60 . As execution of a predetermined number of iterations is completed, the operation state of the optimization apparatus makes a transition to the input receiving state ST- 2 . 
     According to at least one embodiment, an optimization apparatus is configured such that a random number generator generates proper random numbers during an intermittent execution of an annealing process. 
     All examples and conditional language recited herein are intended for pedagogical purposes to aid the reader in understanding the invention and the concepts contributed by the inventor to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions, nor does the organization of such examples in the specification relate to a showing of the superiority and inferiority of the invention. Although the embodiment(s) of the present inventions have been described in detail, it should be understood that the various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention.