AU2020465147B2 - Information processing system and optimal solution search processing method - Google Patents

Abstract

The purpose of the present invention is to provide a means for determining how to solve a complex optimization problem involving various constraints by a mixed binary quadratic programming problem.　One preferable aspect of the present invention is an information processing system comprising a computation device and a calculator for controlling the computation device. The calculator comprises: a pre-processing unit that generates solution candidates for an optimization problem including a plurality of constraints, extracts a solution candidate satisfying at least some of the constraints from among the solution candidates, and generates a mixed integer quadratic programming problem on the basis of the extracted solution candidate; and an interaction computation execution unit that inputs data based on the mixed integer quadratic programming problem to the computation device and causes the computation device to execute computation. The computation device performs computation for updating variables in the mixed integer quadratic programming problem and outputs the variables which result in a target function becoming a maximum or a minimum value as a solution.

Description

Technical Field

[0001]

The present invention relates to an information

processing device, a computation device, an information

processing method, and the like. More specifically, the

present invention relates to a technique for executing an

optimal solution search process.

Background

[0002]

Patent Literature 1 discloses "a semiconductor device

that includes a plurality of unit units each having a first

memory cell that stores a value representing one spin of an

Ising model by three or more states, a second memory cell

that stores an interaction coefficient representing

interaction from a different spin exerting the interaction

on the one spin, and a logic circuit that decides a next

state of the one spin on the basis of a value representing

a state of the different spin and a function having, as a

constant or a variable, the interaction coefficient".

[0003]

Patent Literature 2 describes a method by which all

spins are updated probabilistically simultaneously with

respect to an Ising model having arbitrary connections

while a theoretical background required by Markov Chain

Monte Carlo methods is satisfied, thereby achieving optimal

solution search.

[0004]

Patent Literature 3 discloses obtaining means for

obtaining candidate information that is information of a

candidate of a subset in a set partitioning problem, and

generation means for generating a Hamiltonian equation in

an Ising model corresponding to the set partitioning

problem on the basis of the candidate information obtained

by the obtaining means.

Patent Literature

[0005]

PTL 1: Japanese Patent Application Laid-Open No. 2016

51314

PTL 2: WO 2019/216277

PTL 3: Japanese Patent Application Laid-Open No. 2017

151810

Non-Patent Literature

[0006]

NPTL 1: Okuyama, T., Sonobe, T., Kawarabayashi, K. I.,

& Yamaoka, M. (2019). Binary optimization by momentum

annealing. Physical Review E, 100(1), 012111.

NPTL 2: Botev, Z. I. (2017). The normal law under

linear restrictions: simulation and estimation via minimax tilting. Journal of the Royal Statistical Society: Series

B (Statistical Methodology), 79(1), 125-148.

NPTL 3: Neal, R. M. (1998). Suppressing random walks

in Markov chain Monte Carlo using ordered overrelaxation.

In Learning in graphical models (pp. 205-228). Springer,

Dordrecht.

[0007]

Many of physical phenomena and social phenomena can be

represented by an interaction model. The interaction model

is defined by a plurality of nodes configuring the model,

interaction between the nodes, and further a coefficient

acting on each node, if necessary. In the fields of

physics and social science, various models including the

Ising model are proposed, but any of them can be

interpreted as one form of the interaction model.

[0008]

It is important in the solution of a social problem to

calculate a node state that minimizes or maximizes an index

related to this interaction model. For example, there are

given a problem of detecting the clique of a social network

and the portfolio optimization problem of the financial

field. In the field of operations and research, these are

roughly divided into an unconstrained binary quadratic

programming problem and a mixed binary quadratic programming problem.

[0009]

When a traveling salesman problem, a path search

problem, or the like, as the mixed binary quadratic

programming problem is solved as the ground state search

problem of the interaction model, the energy function

thereof is typically represented by the linear sum of a

plurality of terms, such as penalty terms representing

constraints. Since the optimal value of the weight of each

term is typically unknown, a solution is searched for while

the weight is changed, thereby obtaining an exact solution

or a good quality approximation solution.

[0010]

The optimization problem can be calculated in a short

time and with saved power when the problem to be solved can

be represented once by the interaction model. However, the

complex constraints are often imposed in the optimization

problem that is actually required in society, and it is

difficult to represent all of these penalty terms by the

interaction model.

[0011]

It is desired to address or ameliorate one or more

disadvantages or limitations associated with the prior art,

or to at least provide a useful alternative.

Summary

[0012]

In one embodiment, the present invention provides an

information processing system that includes a computation

device and a calculator that controls the computation

device. The calculator includes a pre-processing unit that

generates solution candidates for an optimization problem

including a plurality of constraints, extracts a solution

candidate satisfying at least some of the constraints from

among the solution candidates, and generates a mixed

integer quadratic programming problem on the basis of the

extracted solution candidate, and an interaction

computation execution unit that inputs data based on the

mixed integer quadratic programming problem to the

computation device and causes the computation device to

execute computation. The computation device performs

computation for updating variables in the mixed integer

quadratic programming problem, and outputs the variables

which result in a target function becoming a maximum or a

minimum value as a solution.

[0013]

The pre-processing unit creates a candidate list by

excluding, from intermediate input data including a set of

an array, a portion of the array and generates a mixed

integer quadratic programming problem from the candidate list. The computation device includes a variable memory that stores a value indicating a state of the variable of the mixed integer quadratic programming problem, a state transition calculation block that calculates a next state of the value indicating the state of the variable, a non linear coefficient memory that stores a non-linear coefficient of the state transition calculation block, a linear coefficient memory that stores a linear coefficient of the state transition calculation block, a weight input line that receives a weight signal of the state transition calculation block, and a temperature input line that receives a temperature signal of the state transition calculation block. The state transition calculation block includes a difference calculation block that calculates difference calculation by using the weight signal, the non linear coefficient, and the linear coefficient. It also includes a sampling block that randomly performs sampling from a probability distribution with section constraints by using the weight signal, the temperature signal, and the output value of the difference calculation block. It further includes a next state decision block that calculates the next state of the variable by using the value read from the variable memory.

[0014] [DELETED]

[0015]

According to at least some embodiments of the present

invention, the complex optimization problem having various

constraints can be solved by the mixed binary quadratic

programming problem.

Brief Description of Drawings

[0016]

One or more embodiments of the present invention are

hereinafter described, by way of example only, with

reference to the accompanying drawings, in which:

Figure 1 is a conceptual diagram illustrating the

relationship between the variable array and the target

function value of an optimization problem.

Figure 2 is a diagram provided for the description of

an example.

Figure 3 is a diagram provided for the description of

the example.

Figure 4 is a block diagram illustrating the schematic

configuration of an information processing device.

Figure 5 is a block diagram of a computation circuit.

Figure 6 is a functional block diagram illustrating

main functions included in the information processing

device.

Figure 7 is a flowchart describing an optimal solution

search process.

Figure 8 is a detailed block diagram of the

computation circuit.

Figure 9 is a block diagram of a unit configuring the

computation circuit.

Figure 10 is a diagram conceptually describing the

meaning of a pre-process S710.

Figure 11 is a table diagram illustrating an example

of a candidate list 620.

Detailed Description

[0017]

An embodiment will be described below in detail with

reference to the drawings. It should be noted that in the

following description, the same or similar configurations

may be denoted by shared reference numerals to omit the

overlapped description thereof. Also, when there are a

plurality of elements having the same or similar functions,

the same reference numerals may be denoted by different

subscripts for description. Also, when the plurality of

elements are not required to be distinguished from each

other, the subscripts may be omitted for description.

[0018]

The denotations of the "first", "second", "third", and

the like in this specification and the like are given for

identifying components, and do not always limit the number, order, or contents thereof. Also, numbers for identifying the components are used for each context, and the numbers used in one context do not always indicate the same configuration in other contexts. Also, the component identified by a certain number is not prevented from serving as the functions of the components identified by other numbers.

[0019]

An example described below is a computation circuit

that includes a variable memory that stores a value

indicating the state of the variable of a mixed integer

quadratic programming problem, a non-linear coefficient

memory that stores the non-linear coefficient of a state

transition calculation block in response to the variable

memory, a linear coefficient memory that stores the linear

coefficient of the state transition calculation block in

response to the variable memory, a weight input line that

receives the weight signal of the state transition

calculation block, a temperature input line that receives

the temperature signal of the state transition calculation

block, a difference calculation block that calculates

difference calculation by using the weight signal of the

state transition calculation block, the non-linear

coefficient of the state transition calculation block, and

the linear coefficient of the state transition calculation block, a sampling block that randomly performs sampling from a probability distribution with section constraints by using the weight signal of the state transition calculation block, the temperature signal of the state transition calculation block, and the output value of the difference calculation block, and a next state calculation block that calculates the next state of the variable by using the output value of the sampling block and the value read from the variable memory.

[0020]

Typically, an integer programming problem refers to an

optimization problem including an integer variable. Also,

when a variable taking an integer value and a variable

taking a real number value are mixed, the integer

programming problem refers to a mixed integer programming

problem. The mixed integer programming problem that

becomes a quadratic programming program refers to a mixed

integer quadratic programming problem. In this

specification, in particular, the mixed integer quadratic

programming problem in which a variable taking a binary

value and a variable taking a real number value are mixed

is called a mixed binary quadratic programming problem.

First, the meaning of the mixed binary quadratic

programming problem will be described.

[0021]

Depending on the optimization problem to be solved, a

binary value variable and a continuous variable may be

mixed. For example, in the problem of the financial field,

the purchasing rate of a financial product may be 0% or 10%

to 100%. For example, this is the case where when the

financial product is not purchased, the purchasing rate is,

of course, 0%, and when the financial product is purchased,

the purchasing rate is 10% or more of the minimum unit. At

this time, by using the binary value variable xE{-1, 1} and

the continuous variable yE[-1, 1] indicating whether the

financial product is purchased or not, the purchasing rate

r can be expressed by r={(1+x)/2}X{0.1+0.9X(1+y))/2}.

[0022]

The continuous variable y can also be discretely

represented by a plurality of binary value variables, but

the number of variables is required to be only one by

enabling the continuous variable to be handled. Thus, by

enabling the continuous variable to be handled by the

calculator system, the number of variables of the

optimization problem can be reduced to increase the problem

scale that can be handled by the calculator resources.

Also, when a certain problem is solved, it can be expected

to shorten the calculation time since the number of

variables is reduced.

[0023]

On the other hand, although the problem can also be

handled only by the continuous variable, the continuous

variable allows the value of 0.3 or the like with respect

to the variable in which only -1 or +1 is to be recognized

as the value. In this case, when the constraint "the

variable x is -1 or +1" is added to the target function,

for example, as the penalty function (x2 -1) 2 , the variable x

can also be handled as the continuous variable, but this

cannot provide a quadratic equation. Also, there is a

problem that for example, the target function becomes

complex and it is thus difficult to find the optimal

solution. Thus, there is a merit of the configuration such

that when the quadratic programming problem is created, the

domain of the predetermined variable is made to have, from

the beginning, the binary value or the discrete value,

which can be handled by the calculator. In this

specification, hereinafter, when referred to only as the

optimization problem, the mixed binary quadratic

programming problem is represented.

[0024]

There are N variables si, ... , sN of the optimization

problem (here, the meaning of the mixed binary quadratic

programming problem). Then, the domain Di of each variable

is one of the binary value {-1, +1} and the continuous

value [-1, +1]. Which of the two is decided for each problem. Then, the target function H of the optimization problem is expressed by the following equation 1. That is, the target function H is expressed by the quadratic equation of the variable s.

[0025]

[Mathematical 1]

H(s) sTJs -hs (1) 2

[0026]

In the equation 1, an N-dimensional vector of s=[si,...,

SN], J is an NXN symmetric matrix, and h is an N

dimensional vector. As described above, since the domain

is different for each variable, the mixed binary quadratic

programming problem can be expressed as in the following

equation 2.

[0027]

[Mathematical 2]

min H (s) (2)

[0028]

Here, the index sets Ab, Ac will be defined as in the

equation 3.

[Mathematical 3]

A ={l Di = -1 1} (3)

[0029]

The set Smixed={1sEDi} will be defined. When these

denotations are used, the equation 2 can also be expressed

as the equation 4.

[0030]

[Mathematical 4]

min H (s) (4) BESmixed

[0031]

Hereinafter, the element of the ith row and the ith

column of the matrix J is 0 with respect to all iEAb. This

is because this conversion does not change the optimal

solution of the equation 2.

[0032]

If Dj={-1, +1}, this optimization problem is a

combination optimization problem called a ground state

search problem of an Ising model. In this embodiment, in

the optimization problem also including the ground state search of the Ising model, the optimal solution or the approximation solution is searched for by an algorithm that utilizes Markov Chain Monte Carlo methods (hereinafter, called MCMC (Markov Chain Monte Carlo methods)).

[0033]

Figure 1 is a conceptual diagram illustrating the

landscape of the target function value with respect to the

variable array. The horizontal axis of the graph is the

variable array s, and the vertical axis of the graph is the

target function H(s). The MCMC repeats probabilistic

transition from the current state s to the certain state s'

near the state s. The probability of the transition from

the state s to the state s' is called the transition

probability P (s, s'). Examples of the transition

probability P include a Metropolis method and a heat-bath

method (heat-bath algorithm).

[0034]

The transition probability has a parameter called a

temperature, and this represents the easiness of the

transition between the states. When the MCMC is executed

while the temperature is gradually decreased from the large

value, the target function value is asymptotically

converged to the lowest state. A method for calculating

the optimal solution or the approximation solution of the

minimization problem by using this is simulated annealing

(hereinafter, called SA (Simulated Annealing)) and momentum

annealing (hereinafter, called MA (Momentum Annealing))

proposed in NPTL 1.

[0035]

In solving the minimization problem expressed in the

equation 4, it is considered that instead, the minimization

problem of the following equation 5 is solved. It should

be noted that the set Sreiaxed{5ssiE [-l, +1] }

.

[0036]

[Mathematical 5]

min H (s) (5) ESrelaxed

[0037]

The optimal solution of the equation 5 is expressed as

s*=[s1*, ... , sN*] . Although the proof is omitted, s+=[si+,

sN+] calculated by the following equation 6 is one of the

optimal solutions of the equation 4. The aim of the

example represented in this application is the optimal

solution search of the equation 2, but even when the

conversion of the equation 6 is obtained after the optimal

solution s* of the equation 5 is solved, the desired

solution s+ can be obtained. It should be noted that the

function sgn is a function in which the function sgn returns +1 when the argument is 0 or more, and returns -1 when the argument is other than that.

[0038]

[Mathematical 6]

sgn(s*) (iEAb) si =)(6) s*( Ac)

[0039]

Here, the N-dimensional vector v=[vi, ... , VN] is

introduced to define the function H' expressed by the

equation 7.

[Mathematical 7]

H'(s, v) = H(s) + V(v) (7)

[0040]

It should be noted that the function V(v) is as

defined in the equation 8.

[Mathematical 8]

1 V() = - (J+ 2W) v (8) 2

[0041]

The matrix W=diag(wi, ... , WN) is an arbitrary diagonal

matrix, and vi is a real number moving in [-1, +1]. In

place of the minimization problem represented in the

equation 5, the equation 9 that is the minimization problem

of the H'(s, v) is introduced.

[0042]

[Mathematical 9]

min H (s) + min V (V) (9) $GE[-1,1]N ,,G [_1 N

[0043]

Two N-dimensional vectors x=s+v, y=s-v will be defined.

The target function of the optimization problem to be

originally solved is only H, but by introducing the

function of V here, the function that can be parallel

updated by the MCMC can be newly obtained. Then, the

function H' can be rewritten as the equation 10.

[0044]

[Mathematical 10]

h X+Y H =-{ 1 -o Jy-hT(x-Py)+(-yTwxY} y (X - y)TW(X - y) (10) (0 2 2

[0045]

That is, the minimization problem of the equation 5

can be restated as the minimization problem of the equation

11 (and may be handled as the maximization problem).

[0046]

[Mathematical 11]

T(ox- y)Wx-y min G(x, y) := -xTJy - hT (X + y) + (11) lXil+lYils2 2

[0047]

When the optimal solution of the equation 11 is

expressed as x*, y*, an equality equation s*=(x*+y*)/2 is

established. These discussions can be established even

when W is a zero matrix.

[0048]

From the above, the optimal solution of the mixed

binary quadratic programming problem expressed by the

equation 2 can be calculated from the solution of the

quadratic programming problem with the constraints

represented in the equation 11. To calculate this solution,

the MCMC is utilized.

[0049]

Figure 2 is a graphical model representing the

relationship between the respective variables in the target

function G in the equation 11. The relationship between the respective variables in the function G can be represented by a complete bipartite graph. The variables in the function G by which the variable xi is multiplied are only yi, ... , yN and xi. When the variable value is updated probabilistically, the MCMC uses the value of the variable related to the variable. That is, when the value of the variable xi is updated, yi, ... , yN and Xi are calculated, and the variables other than those (here, X2,...

XN) are not referred to. This is ditto for the update of

other variables, for example, the value of X2. Thus, when

the values of the variable array y are constant, the

theoretical requirement of the MCMC is not violated even

when each value of the array x is updated probabilistically

independently simultaneously.

[0050]

Likewise, the variables by which the variable yi is

multiplied are only xi, ... , XN and yi. Thus, under the state

where the value of the variable array x is constant, each

value of the array y can be updated probabilistically

independently simultaneously.

[0051]

From the above, by executing the MCMC configured by

the procedure that repeats "the simultaneous update of xi,

... , xN" and "the simultaneous update of yi, ... , yN", the

arrays x, y minimizing the function G can be searched for while the advantage of increased speed by parallelization can be obtained.

[0052]

It should be noted that in the discussion of this

example, no constraints are provided for the matrix J. For

example, also when none of the elements of the matrix J is

zero, the above discussion can be established, so that the

parallel update is enabled.

[0053]

Figure 3 is an example of a fully connected graph. On

the other hand, when the MCMC is directly applied to the

minimization problem of the equation 2 that is the original

problem, the way of relating of the variable array s is

represented by the fully connected graph as illustrated in

Figure 3, so that only one variable can be updated

probabilistically at a time, which is limited to sequential

update.

[0054]

From here, the procedure of the probabilistic update

with respect to each variable will be described. The

variable to be updated is xi. Under the state where the

values of the variables yi, ... , yN are constant, the

existence probability p(xi) of the variable xi in the

Boltzmann distribution at the temperature T satisfies the

equation 12.

[0055]

[Mathematical 12]

p(Xj) oceC2 i W (12)

[0056]

It should be noted that the variable Ai is the value

calculated by the equation 13.

[Mathematical 13]

Ai =hi + wjy + Jiyy (13)

[0057]

Since the variables xi and yi are Ixil+Iyil 2, the range

in which xi can move is -(2-|yil) or more and (2-|yil) or less.

Thus, for the variable xi, the next state of the xi should

be sampled on the basis of the truncated normal

2 distribution in which -( -|yil) or more and (2-yil) or less

is a domain in the normal distribution having average Ai/wi

and distribution T/wi. In this method, the next state is

decided without depending on the current state of xi. This

is ditto for yi. In this specification, when the variables

of x and y are not distinguished from each other, s may be

denoted.

[0058]

The random number according to the standard normal

distribution can be generated by a Box-Muller method. Here,

since the domain is limited, the algorithm represented in

NPTL 2 should be used.

[0059]

The optimal solution search is regarded as sampling

from the equilibrium state at a temperature of 0. For that,

to achieve the good quality solution search, the

convergence to the equilibrium state in a short time is

preferable. To increase the convergence properties to the

equilibrium state, various techniques are proposed in the

MCMC, and these can also be utilized. For example, NPTL 3

proposes an overrelaxation method. This samples, as the

candidates of the next state, not only one state, but also

K states, from the Boltzmann distribution at the

temperature T. Then, a total of (K+1) states are

rearranged to be represented as xco ... <xcr=x± xcK. That is,

the current state is the (r+1)th from the smaller of the

(K+1) values. Then, xcK+1-r is adopted to the next state. In

this method, the next state depends on the current state of

Xi.

[0060]

In light of the above, the configuration of the

information processing device that achieves the present invention is illustrated in Figures 4 to 6.

[0061]

Figure 4 is an example of the information processing

device that searches for the optimal solution of the mixed

binary quadratic programming problem. As illustrated in

the drawing, an information processing device 10 includes a

processor 11, a main storage device 12, an auxiliary

storage device 13, an input device 14, an output device 15,

a communication device 16, one or more computation devices

20, and a system bus 5 that communicatably connect these

devices. For example, the information processing device 10

may be achieved partially or wholly by using virtual

information processing resources, such as a Cloud Server

provided by a Cloud System. Also, for example, the

information processing device 10 may be achieved by a

plurality of information processing devices that are

communicatably connected to each other and are operated to

cooperate with each other.

[0062]

For example, the processor 11 is configured by using a

CPU (Central Processing Unit) and an MPU (Micro Processing

Unit). The main storage device 12 is a device that stores

a program and data, and is, for example, a ROM (Read Only

Memory), an SRAM (Static Random Access Memory), an NVRAM

(Non Volatile RAM), a mask ROM (Mask Read Only Memory), a

PROM (Programmable ROM) and the like), a RAM (Random Access

Memory), (a DRAM (Dynamic Random Access Memory) and the

like), and the like. The auxiliary storage device 13 is a

hard disk drive (Hard Disk Drive), a flash memory (Flash

Memory), an SSD (Solid State Drive), an optical storage

device (a CD (Compact Disc), a DVD (Digital Versatile Disc),

and the like), and the like. The program and data stored

in the auxiliary storage device 13 are read into the main

storage device 12, as needed.

[0063]

The input device 14 is a user interface that receives

the input of information from the user, and is, for example,

a keyboard, a mouse, a card reader, a touch panel, and the

like. The output device 15 is a user interface that

provides information to the user, and is, for example, a

display device (an LCD (Liquid Crystal Display), a graphic

card, and the like) that visualizes various information, an

audio output device (speaker), a printing device, and the

like. The communication device 16 is a communication

interface that communicates with other devices, and is, for

example, an NIC (Network Interface Card), a wireless

communication module, a USB (Universal Serial Interface)

module, a serial communication module, and the like.

[0064]

The computation device 20 is a device that executes a process related to the optimal solution search of the mixed binary quadratic programming problem. For example, the computation device 20 may take the form of an expansion card mounted on the information processing device 10 like a

GPU (Graphics Processing Unit). For example, the

computation device 20 is configured of hardware, such as a

CMOS (Complementary Metal Oxide Semiconductor) circuit, an

FPGA (Field Programmable Gate Array), and an ASIC

(Application Specific Integrated Circuit). The computation

device 20 includes an interface and the like to be

connected to the controller, the storage device, and the

system bus 5, and performs the transmission and reception

of a command and information between the computation device

20 and the processor 11 via the system bus 5. For example,

the computation device 20 may be communicatably connected

to other computation devices 20 via the communication line,

and be operated to cooperate with other computation devices

20. For example, the function achieved by the computation

device 20 may be achieved by causing the processor (the CPU,

the GPU, and the like) to execute the program.

[0065]

The computation device 20 illustrated in Figure 4 will

be described in Figure 5 later. One or more computation

devices 20 can be mounted.

[0066]

Figure 5 is a diagram describing the operation

principle of the communication device 20, and is a block

diagram of a circuit configuring the communication device

20 (hereinafter, called a computation circuit 500). The

computation circuit 500 achieves the function of sampling

the variable array xi, ... , XN or the variable array yi,

YN from the Boltzmann distribution at the temperature T

(the equation 12). The operation principle of the

computation device 20 will be described below together with

the drawing.

[0067]

As illustrated in the drawing, the computation circuit

500 includes a variable memory 511, a non-linear

coefficient memory 512, a liner coefficient memory 513, a

difference calculation block 514, a sampling block 515, and

a next state decision block 516.

[0068]

In the variable memory 511 of each computation circuit

500, the information representing the above variables x1,...

xN and yl, ... , yN is stored (see Figure 2)

[0069]

In the non-linear coefficient memory 512, the

information representing the matrix J is stored. The

matrix J is typically the symmetric matrix, and the usage

amount of the non-linear coefficient memory 512 can be reduced by using the symmetric properties thereof. In the linear coefficient memory 513, the information representing the vector h is stored.

[0070]

As illustrated in the drawing, the control signal EN,

the weight signal SW, and the temperature signal TE are

inputted to the communication circuit 500.

[0071]

The signal EN is a signal that periodically repeats

the values of H (high) and L (low), and represents which of

the variable arrays x and y is updated. For example, it is

determined that when the EN is H, the variable array x is

updated, and when the EN is L, the variable array y is

updated. By the signal EN, the variables xi, ... , XN are

updated simultaneously, and also, the variables yi, ... , yN

are updated simultaneously. In Figure 5, for

simplification, the signal EN is inputted only to the

sampling block 515, but is applied likewise to other

portions that require this signal, such as the variable

memory.

[0072]

The signal SW is a signal representing the vector of

the N elements representing the diagonal components of the

diagonal matrix W.

[0073]

The value of the matrix J stored in the non-linear

coefficient memory 512, the vector h stored in the linear

coefficient memory 513, the signal SW, and the variable s

(x or y) stored in the variable memory 511 are inputted to

the difference calculation block 514. The difference

calculation block 514 outputs (J+diag(wi, ... , wN))y+h when

the signal EN is H, and (J+diag(wi, ... , wN))x+h when the EN

is L. The output value corresponds to the above A±.

[0074]

The sampling block 515 receives the output of the

difference calculation block 514, the signal SW, the signal

TW that holds the value of the temperature parameter, the

signal EN, and the values of other variables. Then, as the

ith element, one or a plurality of values are outputted by

being randomly sampled from the truncated normal

distribution expressed by the equation 12 in which -(2-|yi)

or more and (2-|yil) or less is a domain when the signal EN

is H and -(2-xI) or more and (2-xI) or less is a domain

when the EN is L.

[0075]

The next state decision block 516 decides the next

state of the variable on the basis of one or a plurality of

values outputted from the sampling block 515. If the

simple heat-bath method is defined as the update rule of

the MCMC, the next state decision block 516 should receive only one output value of the sampling block 515, and write it into the variable memory 511 as-is. Also, when the known overrelaxation method is used as the update rule of the MCMC, the next state decision block 516 receives a plurality of values from the sampling block 515 and the current value of the variable to be updated from the variable memory 511, selects one according to the overrelaxation method, and writes it to the variable memory

511. As is well known, the overrelaxation method decides

the next state so that the correlation with the previous

state becomes negative.

[0076]

Figure 6 illustrates main functions (software

configurations) included in the information processing

device 10. As illustrated in the drawing, the information

processing device 10 includes a storage unit 600, a model

conversion unit 611, a model coefficient setting unit 612,

a weight setting unit 613, a variable value initialization

unit 614, a temperature setting unit 615, an interaction

computation execution unit 616, a variable value reading

unit 617, and a pre-processing unit 618. These functions

are achieved in such a manner that the processor 11 reads

and executes the program stored in the main storage device

12, or by the hardware included in the computation device

20. It should be noted that the information processing device 10 may include, in addition to the above functions, other functions such as an operating system, a file system, a device driver, and a DBMS (DataBase Management System).

[0077]

Of the above functions, the storage unit 600 stores

problem data 601, quadratic programming-type problem data

602, domain data 603, a computation device control program

604, intermediate input data 619, and a candidate list 620

into the main storage device 12 or the auxiliary storage

device 13.

[0078]

The problem data 601 is, for example, data in which

the optimization problem or the like is described in a

known predetermined description form. In this example, the

problem data 601 is created from the candidate list 620

described later by the pre-processing unit 618. For

example, analysis input data inputted by the user via the

user interface (the input device, the output device, the

communication device, and the like) is converted by the

pre-processing unit 618 to the intermediate input data 619

including the combination of the candidates. The analysis

input data is, for example, data to be analyzed, such as

personnel data and order reception data. The personnel

data is, for example, data, such as a person-in-charge's ID,

a workplace, a qualification, and an occupation field. The order reception data is, for example, data related to order reception, such as product and service contents, a place, and a delivery date. These are only an example, and the present invention is not required to be limited to this as long as the data is handled as the material of the optimization problem.

[0079]

The intermediate input data 619 is generated from the

analysis input data. The above example includes, for

example, the combination in the array of candidates

representing which person in charge takes charge of which

order reception.

[0080]

As is known, in a column generation method, the

solution is configured of formulation in which the solution

is represented by the superposition of the limited partial

solutions. The pre-processing unit 618 further generates

the candidate list 620 by excluding the predetermined

candidates that do not satisfy the constraint conditions

from the intermediate input data 619. By the pre-process,

the complex constraint is not required to be represented by

the interaction model. The pre-processing unit 618

generates the problem data 601 from the candidate list 620.

[0081]

The quadratic programming-type problem data 602 is data generated in such a manner that the model conversion unit 611 converts the problem data 601 to the data in the type matching the format of the quadratic programming problem represented by the equation 4. For this conversion, the domain of each given variable is written into the domain data 603. For example, the domain data indicates whether each variable takes the binary value or takes the real number. The computation device control program 604 is a program executed when the interaction computation execution unit 616 controls the computation device 20, or a program in which the interaction computation execution unit

616 loads the program to each computation device 20 to

cause the computation device 20 to execute it.

[0082]

As described above, the model conversion unit 611

converts the problem data 601 to the quadratic programming

type problem data 602 that is the format of the quadratic

programming problem. For this, the function of deriving

the equation 11 from the equation 1 should be implemented,

as software or hardware, on the model conversion unit 611.

The function of the model conversion unit 611 is not

necessarily required to be implemented on the information

processing device 10, and the information processing device

10 may capture the quadratic programming-type problem data

602 generated by other information processing devices and the like via the input device 14 and the communication device 16.

[0083]

The model coefficient setting unit 612 sets the matrix

J of the equation 11 based on the quadratic programming

type problem data 602 to the non-linear coefficient memory

512, and sets the vector h based on the quadratic

programming-type problem data 602 to the linear coefficient

memory 513.

[0084]

The variable value initialization unit 614 initializes

the value of each variable stored in the variable memory

511 of the computation device 20. For example, the

variable value initialization unit 614 should decide the

value of each variable by random sampling uniformly from -1

or more and +1 or less. In that case, it should be noted

that |xil+|yil2 that is the constraint related to the

variable is satisfied. Also, it should be noted that the

value of each variable at this time is handled by the

continuous value.

[0085]

The temperature setting unit 615 sets the temperature

T used when the interaction computation execution unit 616

performs the optimal solution search.

[0086]

The interaction computation execution unit 616 causes

the computation device 20 to execute computation

(hereinafter, called interaction computation) that searches

for the variable arrays x and y minimizing the function G

expressed by the equation 11 for each temperature T set by

the temperature setting unit 615. For the interaction

computation, for example, the interaction computation

execution unit 616 changes the temperature T from the high

temperature toward the low temperature.

[0087]

The variable value reading unit 617 reads the variable

arrays x and y stored in the variable memory 511 when the

optimal solution search by the interaction computation

execution unit 616 is ended. The value read here is the

solution of the equation 11. According to the above

discussion, the N-dimensional vector s*=(x+y)/2 is

calculated. Then, the domain data 603 is read, and the

s+ vector obtained by the equation 6 is outputted, as the

final solution, to the output device 15 and the

communication device 16. That is, when the ith domain is

determined as {-1, +1} by the domain data 603, sgn (s*i) is

outputted, and when the ith domain is [-1, +1], si itself

is outputted. In this way, the solution according to the

defined value region is calculated.

[0088]

Figure 7 is a flowchart describing a process performed

by the information processing device 10 for the optimal

solution search (hereinafter, called the optimal solution

search process S700). The optimal solution search process

S700 will be described below together with the drawing. It

should be noted that in the following, the letter "S"

indicated before each of the reference numerals is the

meaning of a process step. For example, the optimal

solution search process S700 is started by receiving an

instruction and the like from the user via the input device

14.

[0089]

As illustrated in Figure 7, first, the pre-processing

unit 618 generates the intermediate input data 619 from the

analysis input data, generates the candidate list 620 from

the intermediate input data 619, and generates the problem

data 601 from the candidate list 620 (S710).

[0090]

Next, the model conversion unit 611 converts the

problem data 601 to the quadratic programming-type problem

data 602 (S711). For example, the quadratic programming

type problem data represents, in an arbitrary form, the

matrix J and the vector h in the function H expressed by

the equation 1. When the storage unit 600 has already

stored the quadratic programming-type problem data 602, the process S711 is omitted. The process of the S711 and the processes after the S712 may be respectively executed by the different devices. Also, the process of the S711 and the processes after the S712 may be executed at different timings (for example, it is considered that the process of the S711 is previously performed).

[0091]

Sequentially, the model coefficient setting unit 612

sets the values of the matrix J and the vector h to the

non-linear coefficient memory 512 and the linear

coefficient memory 513, respectively (S712). The value of

the memory can also be set or edited by the user via the

user interface (achieved by, for example, by the input

device 14, the output device 15, the communication device

16, and the like).

[0092]

Sequentially, the weight setting unit 613 decides the

value of the signal SW. As described in the above equation

8, the signal SW is allowed to take an arbitrary value for

searching for the optimal solution. For that, the signal

value may always be 0. In this case, the load of the

calculation can be reduced. Also, as represented in the

equation 3 to the equation 5 in PTL 2, the signal value may

be decided from the eigenvalue of the matrix J.

Alternatively, the signal value may be decided from the row sum of the matrix J. The calculation for the value calculation of the signal SW may be executed in the computation device 20 or by the processor 11.

Alternatively, the user may set the signal value by

himself/herself (S713).

[0093]

Sequentially, the variable value initialization unit

614 initializes the value of each variable stored in the

variable memory 511 (S714). The value stored in the

variable memory 511 is the continuous value. As described

previously, the initial value should be random. From the

above, the parameter representing the equation 11 is set.

[0094]

Sequentially, the temperature setting unit 615 sets

the sequence Tk (k=1, 2, 3, ... ) of the temperature parameter

used in the optimal solution search (S715). It should be

noted that the above index k represents the type of the

temperature T set. For a method for setting the

temperature T, for example, the method of PTL 1 can be

adopted.

[0095]

Sequentially, the interaction computation execution

unit 616 executes the probabilistic simultaneous update of

the variable array by the computation of the computation

circuit 500 illustrated in Figure 5 (S716).

[0096]

Sequentially, the interaction computation execution

unit 616 determines whether or not the stop condition has

been established (for example, whether or not the

temperature T has reached the lowest temperature that is

set previously) (S717). When the interaction computation

execution unit 616 determines that the stop condition has

been established (S717: YES), the process goes to S718. On

the other hand, when the interaction computation execution

unit 616 determines that the stop condition has not been

established (S717: NO), the process returns to the S716.

[0097]

In the S718, the variable value reading unit 617 reads

the value of the variable stored in the variable memory 511

and the domain of each variable of the quadratic

programming-type problem data 602 stored in the domain data

603. Then, the vector through the conversion based on the

equation 6 is calculated, and is outputted as the solution

of the equation 2 or the equation 4. From the above, the

optimal solution search process S700 is ended.

[0098]

As described above in detail, according to the

information processing device 10 of this embodiment, the

optimal solution search of the mixed binary quadratic

programming problem can be efficiently performed. For that, the optimization problem can be efficiently solved. It should be noted that the information processing device 10

(including the computation device 20) has a simple

configuration, and can thus be easily manufactured at low

cost.

[0099]

The computation circuit 500 may be configured of

software or may be configured of hardware as long as it

includes the function of executing the calculation solving

the already described optimization problem. Specifically,

not only hardware in which the computation circuit 500 is

mounted as an electronic circuit (such as a digital

circuit) in the annealing method, but also a method by

which the computation circuit 500 is mounted as a

superconducting circuit and the like, may be used. Also,

the computation circuit 500 may be hardware achieving the

Ising model by other than the annealing method. For

example, a laser network method (optical parametric

oscillation), a quantum neural network, and the like are

known. Also, although the way of thinking is different in

part, a quantum gate method by which the calculation

performed by the Ising model is replaced with a gate, such

as a Hadamard gate, a rotation gate, and a controlled-NOT

gate, can also be adopted as the configuration of this

example.

[0100]

As a specific mounting example of the computation

circuit 500, an example in which the computation circuit

500 is mounted as a CMOS (Complementary Metal-Oxide

Semiconductor) integrated circuit described in PTL 1 and a

logic circuit on the FPGA (Field Programmable Gate Array)

will be described.

[0101]

In the technique of PTL 1, the units to which the

technique of the SRAM (Static Random Access Memory) is

applied are disposed in an array, and the memory storing

the variable in each unit and the circuit for updating the

variable are disposed.

[0102]

Figure 8 is a block diagram illustrating a circuit

configuration example when the technique of the SRAM is

applied to the computation circuit 500 of this example. A

plurality of units 801 configure an array unit 802. The

configuration can be manufactured by applying a

semiconductor manufacturing technique.

[0103]

One unit 801 includes a multiple value memory 901 that

stores one of the variables xi, ... , xN and yi, .••, yN, and a

configuration for updating the value of the multiple value

memory 901. That is, 2N units 801 are prepared.

[0104]

The configuration example of Figure 8 will be

described also with reference to the typified configuration

of Figure 5. The data stored in the non-linear coefficient

memory 512 and the liner coefficient memory 513 are set

from the model coefficient setting unit 612. The NXN

matrix J is stored in the non-linear coefficient memory 512,

but this is sharably used by all the units 801. Also, the

N-dimensional vector h is stored in the linear coefficient

memory 513, but this is sharably used by all the units 801.

To reduce the circuit scale, these memories are shared

among the respective units 801. Thus, the non-linear

coefficient memory 512 and the liner coefficient memory 513

supply the coefficients J and h to all the units 801, but

in Figure 8, the signal lines therefor are omitted. It

should be noted that in principle, the respective units 801

may each include the non-linear coefficient memory 512 and

the liner coefficient memory 513.

[01051

In a weight memory 803, the vector (wi, ... , wN) of the

N elements representing the diagonal components of the

diagonal matrix W is stored. This data is set by the

weight setting unit 613. Since the ith unit storing xi, yi

uses the ith component wi, the value of the signal SW is

required to be switched for each unit 801. In Figure 8, the signal line supplying the signal SW to the unit 801 is omitted.

[0106]

The temperature signal TE supplied from the

temperature setting unit 615 is supplied to all the units

801. The function and configuration of the temperature

signal follow the conventional art. The signal line

supplying the signal TE to the unit 801 is omitted.

[0107]

An interaction driver 804 alternately inputs, to each

unit 801, the signal allowing the update of the variable x

and the signal allowing the update of the variable y. Thus,

the variables Xi to XN are updated simultaneously, and the

variables y1 to yN are updated simultaneously.

[0108]

An SRAM interface 805 performs writing and reading

with respect to the memory storing the variable of the unit

801 created by applying the circuit configuration of the

SRAM. The variable read after the completion of the

process in the computation circuit 500 is transmitted to

the variable value reading unit 617. The variable value

reading unit 617 outputs the read variable as the

continuous value or the binary value on the basis of the

domain data 603, thereby obtaining the solution of the

mixed binary quadratic programming problem.

[0109]

A controller 806 performs the initialization of the

computation circuit 500 and the completion report of the

process by the instruction of the interaction computation

execution unit 616.

[0110]

Figure 9 is a diagram illustrating the circuit

configuration example of one unit 801. One unit includes

the multiple value memory 901 that stores any one of the

continuous variables xi, ... , xN and yl, ... , yN.

[0111]

A difference calculation circuit 902 achieves the

function of the difference calculation block 514. The

vector of (yi, ... , yN) is inputted to the difference

calculation circuit 902 when the variable stored in the

multiple value memory 901 is any one of xi, ... , xN. Also,

the vector of (x, ... , xN) is inputted when the variable

stored in the multiple value memory 901 is any one of yi,...

yN. These variable vectors are read by the SRAM interface

805 from the multiple value memory 901 of each of other

units 801, and are generated. Also, the NXN matrix J and

the N-dimensional vector h that are the coefficients are

inputted. Also, the weight wi is inputted. The difference

calculation circuit 902 outputs the value A± of the ith row

of (J+diag(wi, ... , wN))s+h (s is the variable vector of x or y) with respect to these inputs.

[0112]

A sampling circuit 903 achieves the function of the

sampling block 515. The output Ai, the signal EN, the

signal SW, the signal TE, y± when the variable stored in

the multiple value memory 901 is x±, and xi when the

variable stored in the multiple value memory 901 is yi are

inputted to the sampling circuit 903. Then, the candidate

of the next state of the variable is sampled from the

existence probability p(si) of the variable si on the basis

of the equation 12.

[0113]

A state decision circuit 904 decides the next state of

the variable on the basis of one or a plurality of

candidates outputted from the sampling circuit 903. For

example, in the case of following the overrelaxation method,

when a plurality of candidates are obtained from the

sampling circuit 903, the state decision circuit 904

decides the next state by selecting the candidate in which

the correlation with the previous state of the multiple

value memory 901 is negative. The decided next state is

stored in the multiple value memory 901.

[0114]

In the above, for the difference calculation block 514,

the sampling block 515, and the nest state decision block

516, the hardware, such as the FPGA, is assumed, but for

example, software implementation is enabled by the GPU

disposed in the unit. By including the unit 801 in an

array in this way, the parallel update of the variable is

enabled.

[0115]

Figure 10 is a diagram conceptually describing the

meaning of the pre-process S710 in the flow of Figure 7.

In the optimization problem, when the constraint conditions

become complex, it becomes difficult to represent all the

constraints by the interaction model. Accordingly, the

solution candidates of the problem to be solved are

previously generated by a general-purpose calculator, and

are divided into the set partitioning and the set covering

problems satisfying the conditions from the set of the

solution candidates. The set partitioning and the set

covering problems are equivalent to the minimization

problem (or the maximization problem) of the target

function represented by the interaction model including the

Ising model, and can be solved by the annealing technique

with respect to the interaction model, such as the quantum

annealing and the CMOS annealing. Thus, the number of

types of problems solved by the annealing technique can be

increased.

[0116]

This example will be described with an example in

which task programming determining which person in charge

processes which task is optimized. In Figure 10, analysis

input data 1001 includes personnel information, such as the

ID, qualification, address, and the like of a person in

charge to be a candidate, and order reception information,

such as the contents, place, limit time, and skill required

for response of the task. Also, the analysis input data

1001 includes an evaluation parameter and the like for

determining whether the task programming is optimal.

[0117]

In the pre-process S710, the pre-processing unit 618

of the information processing device 10 generates and

stores, for example, the intermediate input data 619 in a

table form, from the inputted analysis input data 1001 by

the intermediate input data formation S7101.

[0118]

In the pre-process S710 by the pre-processing unit 618,

the candidate list 620 is generated from the intermediate

input data 619 by the candidate list generation S7102.

[0119]

Figure 11 is an example of the candidate list 620, and

is a table diagram describing an optimization algorithm

called the column generation method. The aim of this

algorithm is to select some of a plurality of candidates.

The candidates here are formed in a predetermined array,

and the optimal combination is selected from the set of the

array under the predetermined conditions.

[0120]

In the example of Figure 11, each candidate indicates

"the task to be taken charge of by one person in charge".

For example, the candidate 1 indicates that "the person in

charge 1 takes charge of only the task 1", and the

candidate 3 indicates that "the person in charge 2 takes

charge of the task 3". The problem in which among the

combinations of the subsets including each of the

respective elements (for example, the tasks) of the given

set, the combination in which the sum of the costs becomes

minimal is called the set partitioning problem.

[0121]

The variable xi is a variable representing whether the

candidate is selected. For example, when xi=1, the

candidate 1 is adopted. When x1=0, the candidate 1 is not

adopted. The presence or absence of the skill a± is a

parameter indicating whether the person in charge of the

candidate has the skill or qualification. For example, the

parameter is represented such that when a1=1, the person in

charge has the skill, and when ai=0, the person in charge

does not have the skill. The evaluation value ci of the

candidate is the evaluation of the candidate, and its defining method is arbitrary.

[0122]

The pre-processing unit 618 combines the data of the

analysis input data 1001 by the typical program, and

creates the set of the candidates like Figure 11

automatically or by editing by the operator, so that the

set of the candidates can be the intermediate input data

619. The algorithm of the automatic program is mechanical

data combination generation. However, in the column

generation method, the selected candidates are combined to

be the answer of the entire problem, so that the candidates

1 to n that become the parts of the answer of the entire

problem are required to be originally executable.

[0123]

For example, the intermediate input data 819 has, as

the candidates, all combinations in which from 1000 tasks,

each person in charge takes charge of 1 to 1000 tasks.

However, when the description "the person in charge takes

charges of the task 1 and the task 100" is present in the

intermediate input data 619, if each task is as follows,

the one person in charge cannot take charge of both tasks.

Task 1: Working in Tokyo from 10 o'clock to 12 o'clock

on June 25 (Thursday)

Task 100: Working in Osaka from 10 o'clock to 12

o'clock on June 25 (Thursday)

[0124]

Accordingly, to generate the executable candidate idea,

the candidate list generation S7102 generates the candidate

list 620 by excluding the inappropriate candidates on the

basis of the problem setting stored in the intermediate

input data 619. That is, in the pre-process S710, the

selection of the candidates included in the intermediate

input data 619 is performed by the condition search by the

typical information processing device, not by the

optimization calculation. Thus, the pre-process S710

generates the candidate group of the candidate list 620.

Then, the problem data 601 of the optimization calculation

is generated from the candidate list 620.

[0125]

The above is a simple example in which "the person

taking charge of the task 1 cannot take charge of the task

100", but for example, many more complex constraints, such

as the constraint "the person taking charge of the task 1

and the task 2 cannot take charge of the task 40, the task

41, and the task 43", are considered. It is simpler to

perform the process of the candidate selection under the

condition by the normal software of the general-purpose

calculator, and on the contrary, handling as the constraint

in the optimization calculation using the interaction model

and the like is troublesome.

[0126]

Also, for example, for the constraint condition in

which "the skill is required in the traveling of the task

2", when the variable at indicating the presence or absence

of the skill and the variable indicating the presence or

absence of the skill required by the task 2 of the person

in charge are compared, the candidate including the task 2

is not created for the person in charge not having the

skill, so that the candidate can be immediately selected.

[0127]

In this example, to be able to cope with the mixed

binary quadratic programming problem after generating the

problem data 601 from the candidate list 620 in the problem

generation S7103 of the pre-process S710, the pre-process

S710 further converts the problem data 601 to the quadratic

programming-type problem data 602 by the data conversion

S711 to complete the generation of the optimization problem.

[0128]

The constraint conditions given by the problem data

601 can be arbitrarily set. For example, one person in

charge selectively executes the candidate, and cannot

allocate a plurality of candidates. To satisfy this

condition, for example, for the person in charge 1, only

one of the candidate 1 and the candidate 2 is required to

be selected. For the selection, x±=1, and thus, the constraint given for this is expressed by the equality equation constraint of xl+x2=1.

Also, for example, for the operator 2, only one of the

candidate 3 to the candidate 5 is required to be selected.

The equality equation constraint given for this is

x3+x4+x5=1.

[0129]

When the constraint term P 2 of the equality equation

constraint related to the operator 2 is expressed by a

penalty method, the following is given.

[Mathematical 14]

P2 =(X3 + X4 + X - 2(14)

[0130]

Also, each operator is not necessarily required to

take charge of the task depending on the case, for example,

in Figure 11, which provides a condition in which "the

operator 1 can select up to one candidate". In this case,

the following patterns are considered.

One of the candidates 1, 2 is selected.

Neither of the candidates 1, 2 is selected.

When this is expressed by a mathematical equation, xl+x2 1.

Since the constraint Pi of the inequality equation

constraint is expressed by the penalty method, the continuous variable z moving between 0 and 1 is introduced to create the penalty term.

[0131]

For example, the penalty term in expressing the

constraint of xl+x2 1 is expressed by the equation 15.

[Mathematical 15]

P 1 = (x 1 + x2 - (1-z) )2 - (15)

[0132]

In the above description, the variable has been stated

as "the continuous variable z moving between 0 and 1".

When xl+x2 1, the equation is established when the binary is

"the binary value variable z of 0 or 1". However, when the

number of candidates is increased, the continuous variable

is required to be used.

[0133]

For example, when up to 20 candidates are selected

from among the candidate 1 to the candidate 100,

xi+x2+x3+...xioo 20 is required to be expressed in order to

optimize the number of candidates selected. In this case,

the penalty function Px expressing this inequality equation

cannot be created only by the single binary value variable

z. For that, by introducing the continuous variable z, the

equation can be expressed only by the single auxiliary

2 variable such that Px=(x1+x2+x3+...xioo-20z) . PTL 3 describes

that the Hamiltonian in the Ising model indicating the set

partitioning problem to be calculated is generated on the

basis of the obtained candidate information, but since the

continuous variable is not used, the equation cannot be

expressed only by the single auxiliary variable.

[0134]

As described above, xi is the binary value variable of

"1" or "0", and the variable z is the auxiliary variable

that takes the range of the real number of 0 or more and 1

or less. By the combination with the penalty function Pi,

the target function H of the equation 16 is obtained. This

becomes the function to be minimized. In this example, the

mixed binary quadratic optimization problem can be handled.

For that, the degree of freedom of the value that can be

selected as the auxiliary variable z is large. Also, the

real number value can also be selected as xi, and the

application range is large. It should be noted that in the

above, depending on the case, "1" can be replaced with "+1",

and "0" can be replaced with "-1".

[0135]

[Mathematical 16]

H = Zcxk + Pi --- (16) k

[0136]

It should be noted that in Figure 11, the constant ci

represents the evaluation value of each candidate, and in

this example, as ci is larger, the evaluation of the

candidate is higher. ci may be arbitrarily set by the user,

or may be automatically set. For example, as the number of

candidates of tasks to be taken charge of is larger, the

evaluation value is increased, and so forth.

[0137]

Returning to Figure 10, as already described, in the

quadratic programming-type problem data 602, the annealing

calculation is performed by the computation device 20

applied to the optimization computation, and result data

1002 is read.

[0138]

The post-process S1003 converts the answer obtained by

the annealing to, as the answer of the column generation,

the appropriate one. For example, since it is appropriate

to select only one of the candidates 3 to 5, the solution

obtained by the annealing is probabilistically obtained

although the penalty function of the equation 14 is added,

and this constraint may be violated. At this time, the

solution is forcefully adjusted so as to obtain X3+X4+X5=1.

Thus, a solution candidate 1004 is obtained.

[0139]

In the solution evaluation and selection process S1005,

the solution candidate obtained by the column generation is

evaluated. If none of the obtained solution candidates is

as expected, the reasons such as the quality of the answer

obtained by the annealing is not good and the setting of

the evaluation value ci defined for each candidate is

inappropriate are considered. Accordingly, for example,

determining whether the quality of the solution has reached

the reference anyway, and determining, if the quality of

the solution has not reached the reference, recalculation

by adjusting the magnitude of the penalty coefficient and

the evaluation value for each candidate, and the like are

included in this process. An answer 1006 is obtained from

the finally obtained solution candidate 1004.

[0140]

The present invention is not particularly limited to

whether the constraint condition of the problem is

processed in the pre-process S710 or is processed in the

optimization problem. This may be considered depending on

the case; for example, the portion that is troublesome to

be handled in the mixed binary quadratic programming

problem is processed in the S710, and so forth.

[0141]

The one embodiment has been described above in detail,

but the present invention is not limited to the above embodiment, and needless to say, various modifications can be made within the scope not departing from its purport.

For example, the above embodiment has been described in

detail for simply describing parts of the present invention,

and is not necessarily required to include all the

described configurations. Also, part of the configuration

of the above embodiment can be subjected to addition,

deletion, and replacement with respect to other

configurations.

[0142]

Also, part or all of the above respective

configurations, functioning units, processing units,

processing means, and the like may be achieved by hardware

by, for example, designing by an integrated circuit and the

like. Also, the above respective configurations, functions,

and the like may be achieved by software in such a manner

that the processor interprets and executes the program

achieving each function. The information of the program,

the table, the file, and the like achieving each function

can be placed on a recording device, such as a memory, a

hard disk, and an SSD (Solid State Drive), and a recording

medium, such as an IC card, an SD card, and a DVD.

[0143]

Also, in the above respective drawings, the control

lines and the information lines that are considered to be necessary for description are illustrated, and all the controls lines and the information lines in terms of implementation are not always illustrated. For example, it may be considered that almost all the configurations are actually connected to each other.

[0144]

Also, the disposing form of various functioning units,

various processing units, and various databases of the

above-described information processing device 10 is only an

example. The disposing form of various functioning units,

various processing units, and various databases can be

changed to the optimal disposing form from the viewpoint of

the performance of the hardware and the software included

in the information processing device 10, the processing

efficiency, the communication efficiency, and the like.

[0145]

Also, the configuration of the database that stores

the above-described various data (schema and the like) can

be flexibly changed from the viewpoint of the efficient

usage of the resources, the improved processing efficiency,

the improved access efficiency, the improved search

efficiency, and the like.

Industrial Applicability

[0146]

The present invention can be used for the information

processing device, the computation device, the information

processing method, and the like.

[0146a]

Throughout this specification and the claims which

follow, unless the context requires otherwise, the word

"comprise", and variations such as "comprises" and

"comprising", will be understood to imply the inclusion of

a stated integer or step or group of integers or steps but

not the exclusion of any other integer or step or group of

integers or steps.

[0146b]

The reference in this specification to any prior

publication (or information derived from it), or to any

matter which is known, is not, and should not be taken as

an acknowledgment or admission or any form of suggestion

that that prior publication (or information derived from

it) or known matter forms part of the common general

knowledge in the field of endeavour to which this

specification relates.

Reference Signs List

[0147]

10... information processing device,

11... processor,

12... main storage device,

20... computation device,

511... variable memory,

512... non-linear coefficient memory,

513... linear coefficient memory,

514... difference calculation block,

515... sampling block,

516... next state decision block,

600... storage unit,

601... problem data,

602... quadratic programming-type problem data,

603... domain data,

604... computation device control program,

611... model conversion unit,

612... model coefficient setting unit,

613... weight setting unit,

614... variable value initialization unit,

615... temperature setting unit,

616... interaction computation execution unit,

617... variable value reading unit

Claims (11)

{THE CLAIMS DEFINING THE INVENTION ARE AS FOLLOWS:}

1. An information processing system that includes a

computation device and a calculator that controls the

computation device,

wherein the calculator includes:

a pre-processing unit that generates solution

candidates for an optimization problem including a

plurality of constraints, extracts a solution candidate

satisfying at least some of the constraints from among the

solution candidates, and generates a mixed integer

quadratic programming problem on the basis of the extracted

solution candidate; and

an interaction computation execution unit that inputs

data based on the mixed integer quadratic programming

problem to the computation device and causes the

computation device to execute computation, and

wherein the computation device performs computation

for updating variables in the mixed integer quadratic

programming problem, and outputs the variables which result

in a target function becoming a maximum or a minimum value

as a solution; and

wherein the pre-processing unit creates a candidate

list by excluding, from intermediate input data including a

set of an array, a portion of the array, and generates the mixed integer quadratic programming problem from the candidate list, and wherein the computation device includes: a variable memory that stores a value indicating a state of the variable of the mixed integer quadratic programming problem; a state transition calculation block that calculates a next state of the value indicating the state of the variable; a non-linear coefficient memory that stores a non linear coefficient of the state transition calculation block; a linear coefficient memory that stores a linear coefficient of the state transition calculation block; a weight input line that receives a weight signal of the state transition calculation block; and a temperature input line that receives a temperature signal of the state transition calculation block, and wherein the state transition calculation block includes: a difference calculation block that calculates difference calculation by using the weight signal, the non linear coefficient, and the linear coefficient; a sampling block that randomly performs sampling from a probability distribution with section constraints by using the weight signal, the temperature signal, and the output value of the difference calculation block; and a next state decision block that calculates the next state of the variable by using the value read from the variable memory.

2. The information processing system according to claim 1,

wherein the variable memory stores a continuous value

as each value xi, ... , XN and yi, .. , yN indicating the state

of the variable.

3. The information processing system according to claim 2,

wherein the information processing system includes:

a storage unit that stores a domain of the variable of

the mixed integer quadratic programming problem; and

a variable value reading unit that reads the value

from the variable memory and converts the continuous value

stored in the variable memory to a binary value on the

basis of the domain of the variable.

4. The information processing system according to claim 2,

wherein the non-linear coefficient J is an NXN matrix,

wherein the linear coefficient h is an N-dimensional

vector, and

wherein the weight signal SW is a signal representing a vector of N elements representing diagonal components wi,

... wN of a diagonal matrix W.

5. The information processing system according to claim 4,

wherein the non-linear coefficient J, the linear

coefficient h, the weight signal SW, and the value stored

in the variable memory are inputted to the difference

calculation block, and the difference calculation block

outputs (J+diag(wi, ... , wN))s+h, and

wherein it should be noted that s is one of N

dimensional vectors (x1, ... , XN) and (yi, .. , yN)•

6. The information processing system according to claim 4,

wherein the non-linear coefficient J is a symmetric

matrix.

7. The information processing system according to claim 6,

wherein an element of the ith row and the ith column

of the non-linear coefficient J is 0.

8. The information processing system according to claim 5,

wherein an output A of the difference calculation

block, the weight signal SW, the temperature signal TE, the

control signal EN, and the value stored in the variable

memory are inputted to the sampling block, wherein one or a plurality of values are outputted by being randomly sampled from a normal distribution in which

- (2-|yil) or more and (2-|yil) or less is a domain when the

control signal EN is a first value and -(2-|xil) or more and

(2-|xil) or less is a domain when the control signal EN is a

second value, and

wherein the normal distribution is formed on the basis

of the output A, the weight signal SW, and the temperature

signal TE.

9. The information processing system according to claim 8,

wherein the normal distribution is a normal

distribution having average Ai/wi and distribution T/wi, and

wherein it should be noted that Ai is the ith value of

the output A and T is the value of the temperature signal

TE.

10. The information processing system according to claim 5,

wherein the information processing system includes a

plurality of units each including a multiple value memory

that stores one of the values xi, ... , XN and yi, .••, yN

indicating the state of the variable,

wherein each of the units includes a difference

calculation circuit that executes a function of part of the

difference calculation block, a sampling circuit that executes a function of part of the sampling block, and a next state decision circuit that executes a function of part of the next state decision block, and wherein in the unit including the multiple value memory that stores one of the values xi and yi indicating the state of the variable, the difference calculation circuit receives, as inputs, the non-linear coefficient J, the linear coefficient h, the ith diagonal component wi of the diagonal matrix W, the N-dimensional vector (y, ... , yN) when the value stored in the multiple value memory of the noting unit is xi, and the N-dimensional vector (xi, ... , XN) when the value stored in the multiple value memory of the noting unit is yi, and outputs A±=h+wis±+E±jsj (where hi is the ith element of the linear coefficient h, and s represents y when the value stored in the multiple value memory of the noting unit is xi and x when the value stored in the multiple value memory of the noting unit is y).

11. The information processing system according to claim

10,

wherein the output A± of the difference calculation

circuit, the diagonal component wi, the temperature signal

TE, the control signal EN, and the value stored in the

variable memory are inputted to the sampling circuit, and

wherein one or a plurality of values are outputted by being randomly sampled from the normal distribution having the average Ai/wi and the distribution T/wi in which -(2-|yil) or more and ( 2 -|yI) or less is a domain when the control signal EN is a first value and -(2-xI) or more and (2-xI) or less is a domain when the control signal EN is a second value (it should be noted that T is the value of the temperature signal TE).