KR20180046172A - System and method for searching optimal solution based on multi-level statistical machine learning - Google Patents

Abstract

Provided are a system to search for an optimal solution based on multilevel statistical machine learning and a method thereof. According to an embodiment of the present invention, the system includes: a generating part generating a first regression model about at least one objective function and a second regression model about at least one limit condition by using learning data; a first calculating part calculating the uncertainty of each area in a searching space through the first regression model and calculating the fracture probability of each area through the second regression model; an adjusting part adjusting the size of each area by estimating a reliable area in the searching space through the uncertainty of each area; a second calculating part calculating an entropy index of each adjusted area; and a preprocessing part conducting preprocessing for searching for an optimal solution by using at least one among the uncertainty, the fracture probability, and the entropy index.

Description

Field of the Invention < RTI ID = 0.0 > [0001] < / RTI &

Embodiments of the present invention relate to Numerical Optimization techniques.

Numerical optimization technique refers to a technique of mathematically obtaining an optimal solution by formulating an objective function, constraints, design variables, etc. of a machine, a circuit, a schedule, a performance, and a quality factor. The objective of this numerical optimization technique is to search for an equivalent solution with a small number of test points or to search for a better optimal solution with the same number of test points. When the product, system, service, etc. are designed using the numerical optimization technique, design time and cost can be greatly reduced.

However, the conventional numerical optimization technique has a limitation in that it can not utilize the accumulated accumulated learning data at all during the optimization process. (X1 = 0.051, x2 = 0.052) having similar values may require different new data that are numerically different from each other, resulting in completely different results. Therefore, conventionally, the optimization process has to be always performed using new data. Thus, there is a problem that accumulated learning data of several hundreds of billions to a few tanks are left unchanged.

Korean Patent Registration No. 10-1337499 (Nov. 29, 2013)

Embodiments of the present invention are for performing an optimization process using previously accumulated learning data.

According to an exemplary embodiment of the present invention, there is provided an apparatus for generating a first regression model for one or more objective functions and a second regression model for one or more constraints using learning data; A first calculation unit for calculating an uncertainty for each region in the search space using the first regression model and calculating a probability of failure for each region using the second regression model; An adjustment unit for adjusting a size of each region by estimating a trust region in the search space using the uncertainty for each region; A second calculation unit for calculating an adjusted entropy index for each region; And a preprocessing unit for performing preprocessing for an optimal solution search using at least one of the calculated uncertainty, the failure probability, and the entropy index.

The generator may generate the first regression model by combining a plurality of regression models for each of the objective functions, and generate the second regression model by combining a plurality of regression models for each of the constraints.

The first calculation unit may calculate the uncertainty for each of the regions using the variation amount of the objective function.

The adjustment unit may estimate the reliability region by enlarging, reducing, dividing, or integrating the confidence region according to the uncertainty, and may adjust the size of each region by dividing the region other than the confidence region to a predetermined size.

The second calculation unit may calculate the adjusted value probability index for each area using at least one of the calculated uncertainty, the failure probability, and the entropy index.

The preprocessor may set an area having the maximum value probability index as a search start point and perform an experiment for searching the optimal solution from the search start point.

The second calculator may calculate the adjusted value probability index for each area using the following equation.

V _TR = λ ₁ I _TR - λ ₂ Pr _TR + λ ₃ M

(Where V _TR is the value probability index, I _TR is the entropy index, Pr _TR is the failure probability, M is the uncertainty, and λ ₁ , λ ₂ , and λ ₃ are the value probability coefficients)

The pre-processing unit may perform an experiment for the optimal solution search for an area where the entropy index is equal to or greater than a first threshold value.

And a learning unit for learning new data acquired according to the performance of the experiment, wherein the generation unit can regenerate the first regression model and the second regression model using the learning data and the new data.

The preprocessing unit may give an approximate inferred value derived from the first regression model and the second regression model for a region where the uncertainty is less than a second threshold value and an area where the failure probability exceeds a third threshold value.

According to another exemplary embodiment of the present invention, there is provided a method for generating a first regression model for at least one objective function and a second regression model for at least one constraint using learning data, Calculating an uncertainty for each region in the search space using the first regression model in a first calculation unit; Calculating a failure probability for each of the areas using the second regression model in the first calculation unit; Adjusting a size of each of the areas by estimating a reliability area in the search space using the uncertainty of each area in the adjustment part; Calculating an entropy index for each region adjusted in the second calculation unit; And performing a pre-processing for an optimal solution search using at least one of the calculated uncertainty, the failure probability, and an entropy index in the preprocessing unit.

Wherein the step of generating the first regression model and the second regression model includes the steps of generating a first regression model by combining a plurality of regression models for each of the objective functions and generating a plurality of regression models The second regression model can be generated.

The step of calculating the uncertainty may calculate the uncertainty of each of the regions using the variance of the objective function.

Wherein the step of adjusting the size of each of the regions comprises: estimating the confidence region by expanding, reducing, dividing, or integrating the confidence region according to the uncertainty; dividing the region other than the confidence region into a set size, You can adjust the size.

The optimal solution search method may further include calculating, by the second calculation unit, the adjusted value probability index of each region using at least one of the calculated uncertainty, the failure probability, and the entropy index before the step of performing the pre- The method comprising the steps of:

The pre-processing may set an area having the maximum value probability index as a search start point, and perform an experiment for searching the optimal solution from the search start point.

The step of calculating the value probability index may calculate the adjusted value probability index for each area using the following equation.

V _TR = λ ₁ I _TR - λ ₂ Pr _TR + λ ₃ M

(Where V _TR is the value probability index, I _TR is the entropy index, Pr _TR is the failure probability, M is the uncertainty, and λ ₁ , λ ₂ , and λ ₃ are the value probability coefficients)

The pre-processing may perform an experiment for searching the optimal solution for an area where the entropy index is equal to or greater than a first threshold value.

The optimal solution search method may further include: learning new data obtained in the learning unit according to the execution of the experiment, after performing the preprocessing; And regenerating the first regression model and the second regression model using the learning data and the new data in the generation unit.

The pre-processing may include applying an approximate inference value derived from the first regression model and the second regression model to a region where the uncertainty is less than a second threshold and an area where the failure probability exceeds a third threshold .

According to the embodiments of the present invention, optimization is performed using previously accumulated learning data, thereby maximizing search efficiency and minimizing optimization time. Particularly, according to embodiments of the present invention, an optimum search start point is derived to perform an experiment from the search start point, and then an experiment is selectively performed only on a specific region in consideration of an uncertainty and a failure probability, thereby minimizing unnecessary experiments And the time required for the experiment can be shortened.

Further, according to the embodiments of the present invention, by updating the regression model every time new data is learned, the optimal solution can be efficiently searched with less experimentation.

1 is a block diagram showing a detailed configuration of an optimal solution search system according to an embodiment of the present invention;
2 illustrates an example of a regression model according to an embodiment of the present invention
3 illustrates an example of a regression model according to an embodiment of the present invention
4 illustrates an example of a regression model according to an embodiment of the present invention.
5 is a view for explaining a process of calculating an uncertainty according to an embodiment of the present invention;
6 is a diagram for explaining a process of calculating a failure probability according to an embodiment of the present invention;
FIG. 7 is a view for explaining a process of calculating a failure probability according to an embodiment of the present invention; FIG.
FIG. 8 is a view for explaining a process of calculating a failure probability according to an embodiment of the present invention; FIG.
9 is a diagram for explaining a process of estimating a confidence region according to an embodiment of the present invention.
10 is a view for explaining a process of estimating a reliability region according to an embodiment of the present invention;
11 is a diagram illustrating an example of an entropy index for each region according to an embodiment of the present invention.
12 is a diagram for explaining a process of calculating a value probability index according to an embodiment of the present invention;
13 is a diagram for explaining a process of calculating a value probability index according to an embodiment of the present invention;
14 is a block diagram illustrating and illustrating a computing environment including a computing device suitable for use in the exemplary embodiments
15 is a flowchart for explaining an optimal solution searching method according to an embodiment of the present invention.

Hereinafter, specific embodiments of the present invention will be described with reference to the drawings. The following detailed description is provided to provide a comprehensive understanding of the methods, apparatus, and / or systems described herein. However, this is merely an example and the present invention is not limited thereto.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. In the following description, well-known functions or constructions are not described in detail since they would obscure the invention in unnecessary detail. The following terms are defined in consideration of the functions of the present invention, and may be changed according to the intention or custom of the user, the operator, and the like. Therefore, the definition should be based on the contents throughout this specification. The terms used in the detailed description are intended only to describe embodiments of the invention and should in no way be limiting. Unless specifically stated otherwise, the singular forms of the expressions include plural forms of meanings. In this description, the expressions "comprising" or "comprising" are intended to indicate certain features, numbers, steps, operations, elements, parts or combinations thereof, Should not be construed to preclude the presence or possibility of other features, numbers, steps, operations, elements, portions or combinations thereof.

1 is a block diagram showing a detailed configuration of an optimal solution search system 100 according to an embodiment of the present invention. 1, an optimal solution search system 100 according to an embodiment of the present invention includes an optimization engine 102, a learning data database 104, a generation unit 106, a first calculation unit 108, A second calculation unit 112, a preprocessing unit 114, a learning unit 116, and a new data database 118. The control unit 110 includes a control unit 110, a second calculation unit 112,

The optimization engine 102 is an engine for detecting an optimal solution using a numerical optimization technique, and may be equipped with optimization performing software such as a numerical optimizer. The optimization engine 102 may search for an optimal solution by performing iterative calculations through various mathematical techniques such as, for example, the Conjugated Gradient method, the Gauss-Newton method, and the like. In the present embodiments, the optimal solution is a value indicating a point on a search space that satisfies the constraint condition and maximizes or minimizes the value of the objective function. Here, the search space means a set of points that can be a solution. In addition, the objective function is a function used to obtain an optimal solution for the design object (Y ₁ , Y ₂ , Y ₃ , etc.), and the design target (or dependent variable) ₁ , X ₂ , X ₃ , etc.). In this case, the design subject may be, for example, flow performance, noise, vibration, etc. The design variable may be a variable that may affect the design target, for example, a dimension, a thickness, a radius, and the like. In addition, the constraint means a condition indicating an area which should not be searched in the search space.

The optimization engine 102 can search the optimal solution in cooperation with the preprocessing unit 114. [ Specifically, the optimization engine 102 requests an experiment for an optimal solution search to the preprocessor 114, and the preprocessor 114 can perform experiments according to the request. The optimization engine 102 also receives the new data obtained according to the performance of the experiment from the learning unit 116 and receives the approximate speculation value provided by the preprocessing unit 114 from the preprocessing unit 114 . The optimization engine 102 may search for an optimal solution using the new data and the approximate inference values. The optimization techniques according to the present embodiments can be utilized in various fields such as, for example, a process system, job scheduling, traffic simulation, and the like.

,

), 최적해 계산을 위한 수학식 데이터(F)(

,

) 등이 될 수 있다. 상기 실험 데이터(E) 및 수학식 데이터(F)는 아래와 같이 표현될 수 있다.The learning data DB 104 is a storage for storing accumulated learning data. In the present embodiments, the learning data includes, for example, experimental data E obtained through experiments performed beforehand (

,

), The equation data F for calculating the optimal solution (

,

) And the like. The experimental data (E) and the equation data (F) can be expressed as follows.

≪ Experimental data (E) >

≪ Equation data (F) >

Here, Y designates, for example, flow performance, noise, vibration, and the like. Also, X is a variable that may affect the design target, and may be, for example, a dimension, a thickness, a radius, and the like.

) 및 제2 회귀 모델(

)을 생성한다. 생성부(106)는 학습 데이터를 이용하여 하나 이상의 목적 함수에 대한 제1 회귀 모델(

)을 생성하고, 학습 데이터를 이용하여 하나 이상의 제한 조건에 대한 제2 회귀 모델(

)을 생성할 수 있다. 상기 제1 회귀 모델(

) 및 제2 회귀 모델(

)은 학습 데이터 예측 모델(또는 근사 모델, 메타 모델, 대체 모델 등으로도 표현 가능함)로서, 다중 회귀 분석법(Multiple Regression Analysis)에 기반하여 생성될 수 있다. 다중 회귀 분석법은 Y = [y₁…y_i], X = [x₁…x_n] 데이터를 수학식으로 표현하는 분석법으로서, 예를 들어 2차 근사 모델은 아래와 같은 수학식으로 표현될 수 있다.The generation unit 106 generates a first regression model (hereinafter referred to as " first regression model ") using the learning data stored in the learning data DB 104

) And the second regression model (

). The generating unit 106 generates a first regression model for one or more objective functions

And using the learning data to generate a second regression model for one or more constraints

Can be generated. The first regression model (

) And the second regression model (

) Can be generated based on a multiple regression analysis as a learning data prediction model (or an approximate model, a metamodel, an alternative model, etc.). The multiple regression method is Y = [y ₁ ... y _i ], X = [x ₁ ... x _n ] data as an equation, for example, a quadratic approximation model can be expressed by the following equation.

<Second approximation model example>

(Where x ₁ and x ₂ are variables, y is a result, A ₀ to A ₅ are multiple regression coefficients, and? And? Are constants)

) 및 제2 회귀 모델(

)을 생성할 수 있다.The generating unit 106 generates a first regression model (for example, a first regression model) using a polynomial regression model, a kriging model, and an artificial neural network (ANN)

) And the second regression model (

Can be generated.

) 및 제2 회귀 모델(

)을 재생성(즉, 업데이트)할 수 있다. As described later, the learning unit 116 may learn new data acquired according to the execution of the experiment and store the new data in the new data DB 118. When the new data is newly learned Using the learning data and the new data,

) And the second regression model (

Can be regenerated (i.e., updated).

)을 생성하고, 제한 조건 각각에 대한 복수의 회귀 모델(

)을 생성할 수 있다. 일 예시로서, 목적 함수가 4개인 경우, 생성부(106)는 목적 함수 각각에 대한 회귀 모델

,

,

,

를 각각 생성할 수 있다. 또한, 제한 조건이 3개인 경우, 생성부(106)는 제한 조건 각각에 대한 회귀 모델

,

,

를 각각 생성할 수 있다. For this purpose, the generating unit 106 generates a plurality of regression models (

), And a plurality of regression models (

Can be generated. As an example, when there are four objective functions, the generator 106 generates a regression model

,

,

,

Respectively. In addition, when there are three constraint conditions, the generation unit 106 generates a regression model

,

,

Respectively.

)을 생성하고, 상기 제한 조건 각각에 대한 복수의 회귀 모델을 합성하여 제2 회귀 모델(

)을 생성할 수 있다. 위 예시에서, 생성부(106)는 회귀 모델

,

,

,

를 합성하여 제1 회귀 모델(

)을 생성하고, 회귀 모델

,

,

를 합성하여 제2 회귀 모델(

)을 생성할 수 있다. 이때, 생성부(106)는 제1 회귀 모델(

) 및 제2 회귀 모델(

)의 생성시, 합성되는 회귀 모델 각각에 아래와 같이 가중치(w_i, w'_i)를 각각 부여할 수 있다.Thereafter, the generating unit 106 synthesizes a plurality of regression models for each of the objective functions,

), Synthesizes a plurality of regression models for each of the constraint conditions, and generates a second regression model

Can be generated. In the above example, the generation unit 106 generates a regression model

,

,

,

And the first regression model

), And the regression model

,

,

And the second regression model

Can be generated. At this time, the generation unit 106 generates the first regression model (

) And the second regression model (

), Weights w _i and w ' _i can be given to the respective regression models to be synthesized as follows.

) 및 제2 회귀 모델(

)의 예시><First Regression Model (

) And the second regression model (

) Example of>

=

+

+

+

(단, 가중치의 합은 1)

=

+

+

+

(The sum of the weights is 1)

=

+

+

(단, 가중치의 합은 1)

=

+

+

(The sum of the weights is 1)

The weight value may be a value arbitrarily set by the administrator, but is not limited thereto. For example, a regression model based on new data may have a relatively large weight, and a regression model based on learning data (experimental data, mathematical data) may have a relatively small weight.

)을 이용하여 탐색 공간 내 각 영역별 불확실도(uncertainty)를 계산하고, 제2 회귀 모델(

)을 이용하여 상기 각 영역별 파괴 확률(probability of failure)을 계산한다. 이를 위해, 제1 계산부(108)는 탐색 공간을 설정된 크기로 분할하여 복수 개의 영역을 생성할 수 있다. 이후, 제1 계산부(108)는 상기 각 영역별 불확실도 및 파괴 확률을 계산할 수 있다. The first calculation unit 108 calculates a first regression model

) Is used to calculate uncertainty for each region in the search space, and the second regression model

) Is used to calculate the probability of failure for each area. To this end, the first calculation unit 108 may divide the search space into a predetermined size to generate a plurality of regions. Then, the first calculation unit 108 may calculate the uncertainty and the failure probability for each of the areas.

)에서 목적 함수의 분산 변화량을 이용하여 상기 각 영역별 불확실도를 계산할 수 있다. 일 예시로서, 제1 계산부(108)는 학습 데이터에 대해 3σ, 6σ, 9σ 거리당 몬테-카를로 샘플링(MCS)을 수행하여 각 영역별 목적 함수의 분산 변화량을 계산하고, 분산 변화량이 클수록 해당 영역의 불확실도가 높은 것으로 판단할 수 있다. 이에 대해서는 도 5를 참조하여 구체적으로 후술하기로 한다.In the present embodiments, the uncertainty (or flatness) is a degree of insufficient data or information necessary to derive an optimal solution in a specific region in the search space. It is difficult to predict the influence due to the data of the region in a region of high uncertainty, The necessity of searching for the area is increased. The first calculation unit 108 calculates, for example, a first regression model (

), The uncertainty of each region can be calculated using the variance of the variance of the objective function. As an example, the first calculation unit 108 calculates Monte Carlo sampling (MCS) for 3σ, 6σ, and 9σ distances for the learning data to calculate the variance of the objective function for each area, It can be judged that the uncertainty of the region is high. This will be described later in detail with reference to FIG.

Also, in the present embodiments, the failure probability is a probability that a specific region in the search space will violate the restriction condition (i.e., a probability that the specific region in the search space reaches the restriction region out of the restriction condition) The possibility increases and the necessity of searching for the corresponding area is reduced. That is, when the area reaches the restricted area, it is defined as a failure state, and the probability that the area reaches the destruction state can be referred to as the destruction probability. The restriction condition and the restriction area may be preset in advance. The first calculation unit 108 may calculate a failure probability for each of the regions by applying a limit state function to the second regression model, for example. This will be described later in detail with reference to FIGS. 6 to 8. FIG.

The adjustment unit 110 estimates the reliability region in the search space using the calculated uncertainty for each region, and adjusts the size of each region according to the estimated confidence region. In the present embodiments, the trust region refers to a set of data or a region to which these data belong, from which a result value having a degree of similarity higher than a set value is derived. As an example, when a result value having substantially the same value (having a degree of similarity higher than a set value) is derived for each of x ₁ = 0.051 and x ₂ = 0.052, x ₁ and x ₂ can be regarded as belonging to the same trust area. Also, if different result values (with similarity less than a set value) are derived for each of x ₃ = 0.071 and x ₄ = 0.072, x ₃ and x ₄ can be regarded as belonging to different trust regions.

The adjustment unit 110 may set each of the first divided regions as one confidence region and newly estimate the confidence region using the calculated uncertainty of each region. Specifically, the adjustment unit 110 may enlarge, reduce, divide, or integrate the confidence region according to the uncertainty of each region. As an example, the adjustment unit 110 may enlarge or integrate the confidence region (i.e., the region where the result value does not significantly change due to the data in the confidence region) in the case of the confidence region where the uncertainty is less than the set value . In addition, the adjustment unit 110 can reduce or divide the confidence region in the case of a confidence region whose uncertainty is greater than or equal to a predetermined value (i.e., a region in which the result value greatly varies due to data in the confidence region). The adjustment unit 110 can repeat the above-described process each time new data is learned, thereby allowing the reliability region to be updated repetitively. Then, the adjustment unit 110 can adjust the size of each divided region by dividing the region other than the confidence region into a set size. As an example, the adjusting unit 110 may re-divide an area other than the trust area based on a minimum-size trust area. As this process is repeatedly performed, the size of each area in the search space can be changed dynamically.

The second calculation unit 112 calculates an entropy index for each region adjusted by the adjustment unit 110. In the present embodiments, the entropy index is an index indicating how much the learning data is distributed for each adjusted area, and can be expressed by the following equation.

H = log (1 + K)

K = area data / total data

I = 1 - H

Here, H denotes entropy and I denotes an entropy index. Also, K represents the number of data of one region adjusted for the total number of data. The higher the entropy index, the less information there is needed to search for the area. As the adjusted entropy index for each area is calculated, the generation unit 106 can represent the secured state of the learning data by the third regression model. The third regression model, like the first regression model and the second regression model, can be generated based on a polynomial regression model, a kriging model, an ANN model, or the like.

Also, the second calculation unit 112 may calculate the value probability index of each region adjusted using at least one of the calculated uncertainty, the failure probability, and the entropy index. In the present embodiments, the value probability index is an index representing the adjusted search value of each area, and may be calculated using at least one of the uncertainty, the failure probability, and the entropy index. As an example, the second calculation unit 112 may calculate the adjusted value probability index for each area using the following equation.

V _TR = λ ₁ I _TR - λ ₂ Pr _TR + λ ₃ M

(Wherein, V _TR is the value the probability index, I _TR of the zone is the entropy index, Pr _TR of the zone is failure probability, M of the zone represents the uncertainty in the zone, the value of λ _1, λ _2, λ ₃ Probability coefficient)

The value probability coefficient may be a value arbitrarily set by the administrator, but is not limited thereto. For example, the value probability coefficient may be inferred using a map learning technique such as an artificial neural network (ANN).

The preprocessing unit 114 performs preprocessing for an optimal solution search using at least one of the calculated uncertainty, the failure probability, and the entropy index. In the present embodiments, the preprocessing is a kind of preparatory process which is performed to shorten the optimization time of the optimal solution and minimize the unnecessary experiment. For example, the preprocessing is a process of setting a search start point A process of determining whether to perform an experiment for searching for an optimal solution, and a process of applying an approximate inference value to an area in which an experiment is not performed.

As described above, the preprocessing unit 114 can perform an experiment at the request of the optimization engine 102. [ At this time, the preprocessing unit 114 sets an area where the computed value probability index is the maximum as a search start point, and performs an experiment for an optimal search from the search start point. Since the search value increases as the value probability index increases, it is possible to maximize the search efficiency and minimize the optimization time when the experiment for searching the optimal solution is performed as the search start point of the region having the highest value probability index.

In addition, the preprocessing unit 114 may use various techniques such as a Latin-Hyper Cube Sampling (LHS) technique, an Orthogonal Array (OA) technique, and a Monte-Carlo Sampling technique, And the experiment on the new experimental point can be performed. At this time, the preprocessing unit 114 may perform the experiment selectively only on a specific region, rather than performing an experiment on the entire region of the search space (or the entire new experimental point calculated).

As an example, the preprocessing unit 114 may perform an experiment for the optimal solution search for an area where the entropy index is equal to or greater than a first threshold value (e.g., 0.1). As described above, since a region having a high entropy index has a small amount of information, the need for searching for the region increases, so that the preprocessing unit 114 can perform the experiment only on the region where the entropy index is equal to or greater than the first threshold value.

As another example, the preprocessing unit 114 may perform the above-described experiments for regions where the uncertainty is less than a second threshold (e.g., 0.2) and regions where the probability of failure exceeds a third threshold (e.g., 0.5) It is possible to give an approximate reasoning value derived from the first regression model and the second regression model. It is easy to predict the influence of the data in the area with lower uncertainty, so that the necessity to search for the area is reduced, and the probability of reaching the restricted area increases as the probability of destruction increases. The need is reduced. Therefore, the preprocessing unit 114 may apply an approximate reasoning value to the region where the uncertainty is less than the second threshold value and the region where the failure probability exceeds the third threshold value, without performing another experiment. The approximate reasoning value is an inference value derived from the learning data and the regression model of the learning data. The method of deriving the approximate inference value from the regression model is generally well known in the art to which the present invention belongs. It will be omitted.

In this way, the preprocessing unit 114 derives an optimum search start point and performs an experiment from the search start point. Thereafter, the preprocessing unit 114 selectively performs an experiment only on a specific region in consideration of the uncertainty and the failure probability, Can be shortened.

) 및 제2 회귀 모델(

)을 재생성(즉, 업데이트)할 수 있다. 즉, 본 발명의 실시예들에 따르면, 신규 데이터가 학습될 때마다 회귀 모델을 업데이트함으로써, 보다 적은 실험으로 최적해를 효율적으로 탐색할 수 있다.The learning unit 116 learns new data newly obtained as the preprocessing unit 114 performs experiments. As described above, the preprocessing unit 114 can perform the experiment according to the request of the optimization engine 102, and in this case, new data according to the execution of the experiment can be generated. The learning unit 116 may learn the new data and store it in the new data DB 118. [ After that, the generation unit 106 generates a first regression model (hereinafter, referred to as &quot; first regression model &quot;

) And the second regression model (

Can be regenerated (i.e., updated). That is, according to the embodiments of the present invention, by updating the regression model every time new data is learned, the optimal solution can be efficiently searched with less experimentation.

) 및 제2 회귀 모델(

)은 다중 회귀 분석법에 기반하여 생성될 수 있다.Figures 2 to 4 are illustrations of a regression model according to one embodiment of the present invention. As described above, the first regression model (

) And the second regression model (

) Can be generated based on multiple regression analysis.

) 및 제2 회귀 모델(

)은 예를 들어, 다항 회귀(Polynomial Regression) 모델에 기반하여 생성될 수 있다.Referring to FIG. 2, the first regression model

) And the second regression model (

) May be generated based on, for example, a polynomial regression model.

) 및 제2 회귀 모델(

)은 예를 들어, 크리깅(Kriging) 모델에 기반하여 생성될 수 있다.Also, referring to FIG. 3, the first regression model

) And the second regression model (

) May be generated based on, for example, a Kriging model.

) 및 제2 회귀 모델(

)은 예를 들어, 인공 신경망(ANN) 모델에 기반하여 생성될 수 있다. 또한, 상기 인공 신경망은 은닉층이 3개 이상인 심층 신경망일 수 있다.Also, referring to FIG. 4, the first regression model

) And the second regression model (

May be generated based on, for example, an artificial neural network (ANN) model. Also, the artificial neural network may be a neural network having three or more hidden layers.

) 및 제2 회귀 모델(

)이 이에 한정되는 것은 아니다.However, these are merely examples, and the first regression model

) And the second regression model (

) Is not limited thereto.

)에서 목적 함수의 분산 변화량을 이용하여 상기 각 영역별 불확실도를 계산할 수 있다. 5 is a view for explaining a process of calculating an uncertainty according to an embodiment of the present invention. As described above, the first calculation unit 108 calculates the first regression model (for example,

), The uncertainty of each region can be calculated using the variance of the variance of the objective function.

As an example, the first calculation unit 108 can calculate the variance change of the objective function for each region. 5, it can be confirmed that the variation amount of the objective function in the B region is larger than the variation amount of the objective function in the A region. In this case, the uncertainty of the B region may be higher than the uncertainty of the A region. That is, the uncertainty of a particular region may be proportional to the variance of the variance of the objective function in that region.

6 to 8 are views for explaining a process of calculating a failure probability according to an embodiment of the present invention. As described above, the first calculation unit 108 can calculate the failure probability for each of the regions by applying the limit state function to the second regression model, for example.

And can represent a safe state when the limit state function is positive and a failure state when it is negative.

: 안전

: safety

: 한계 상태

: Limit state

: 파괴 상태

: Fracture state

Here, g represents the limit state function, and X ₁ , X ₂ , ... X _n Represents the random variables of the marginal state function. At this time, the limit state function g can be defined as follows.

g = _Rall - _Rp (X)

Here, _Rall denotes a tolerance and _Rp (X) denotes a constraint on the design variable X, respectively.

Referring to FIG. 6, when g (R _p , X) < 0, the fracture state is reached.

In addition, the joint probability density function for the design variable X can be expressed as shown in FIG. 7. In this case, the fracture probability (P _f ) may vary depending on the value of β.

Referring to FIG. 8, as the value β increases, the width of the hatched portion corresponding to the fracture probability (P _f ) decreases. Here, β represents the distance from the restricted region to the restricted region.

The equation for calculating the fracture probability (P _f ) is as follows.

_{Here, f Rp, X (r p} , x) represents the joint probability density function. As described above, the probability of failure is a probability that a specific region in the search space will violate the restriction condition (i.e., a probability that the specific region in the search space reaches the restriction region outside the restriction condition). So that the necessity of searching for the corresponding area is reduced.

FIG. 9 and FIG. 10 illustrate a process of estimating a confidence region according to an embodiment of the present invention.

Referring to FIG. 9, the search space may be divided into one or more areas, and the adjustment unit 110 may set each of the first divided areas as one confidence area. As an example, each lattice space in Fig. 9 may be a trust region of learning data belonging to the lattice space. Thereafter, the adjustment unit 110 may estimate (or update) the confidence region in the search space using the calculated uncertainty for each region.

Specifically, the adjustment unit 110 may expand, reduce, divide, or integrate the confidence region according to the uncertainty. As an example, the adjustment unit 110 may calculate the variance change amount a of the confidence region with respect to the variance change amount of the entire region using an Analysis of Variance technique, and if the confidence level region 0 < a < 0.01, Is integrated with an adjacent confidence region, and if the confidence level is 0.01 < a < 0.05, the confidence level is maintained as it is.

Referring to FIG. 10, the adjustment unit 110 may re-estimate the confidence region of FIG. 9 as the learning unit 116 learns new data. In this case, as shown in FIG. 10, it can be seen that the confidence region of FIG. 9 is enlarged or reduced. The adjustment unit 110 can repeat the above-described process each time new data is learned, thereby allowing the reliability region to be updated repetitively.

FIG. 11 is an exemplary diagram illustrating an entropy index (I) for each region according to an embodiment of the present invention. As described above, the adjustment unit 110 can estimate (or update) the reliability region in the search space using the calculated uncertainty for each region, and adjust the size of each region according to the estimated confidence region.

Specifically, the adjustment unit 110 can adjust the size of each divided area by dividing the area other than the reliability area into a set size.

As an example, referring to FIG. 11, the adjusting unit 110 may re-divide an area other than the trust area based on a minimum-size trust area. Accordingly, the region other than the confidence region is re-divided into the colored region size, and the second calculation unit 112 can calculate the entropy index (I) for each of the trust region and the re-divided region. As shown in Fig. 11, it can be confirmed that the entropy index (I) is calculated as 1 in the region where the learning data does not exist.

The preprocessing unit 114 may perform an experiment for an optimal solution search for an area where the entropy index I is equal to or greater than a predetermined value. At this time, the preprocessing unit 114 may preferentially perform the experiment on the region where the entropy index I is the highest. If a plurality of regions having the same entropy exponent (I) exist, the preprocessing unit 114 may preferentially perform an experiment on an area having the smallest sum of the distance from the learning data within a set radius. In FIG. 11, the experiment on the colored area can be performed preferentially.

12 is a view for explaining a process of calculating a value probability index according to an embodiment of the present invention. As described above, the second calculation unit 112 can calculate the value probability index of each region adjusted by using at least one of the calculated uncertainty, the failure probability, and the entropy index. Respectively.

V _TR = λ ₁ I _TR - λ ₂ Pr _TR + λ ₃ M

(Wherein, V _TR is the value the probability index, I _TR of the zone is the entropy index, Pr _TR of the zone is failure probability, M of the zone represents the uncertainty in the zone, the value of λ _1, λ _2, λ ₃ Probability coefficient)

12), the second regression model (i.e., the Constraints Network of FIG. 12), and the third regression model (i.e., the Knowledge Network of FIG. 12) It can be deduced. Referring to FIG. 12, the first regression model and the second regression model are generated based on new data and learning data (similar data, mathematical data), and the third regression model is generated based on the acquisition state for learning data .

Referring to FIG. 13, the second calculation unit 112 may calculate the adjusted value probability index for each area. At this time, the preprocessing unit 114 sets an area having the maximum value probability index as a search start point, and performs an experiment for an optimal search from the search start point. In FIG. 13, an area having a value probability index of 0.6 may be set as a search start point, and the preprocessing unit 114 may perform an experiment for searching for an optimal solution from the search start point.

14 is a block diagram illustrating and illustrating a computing environment 10 that includes a computing device suitable for use in the exemplary embodiments. In the illustrated embodiment, each of the components may have different functions and capabilities than those described below, and may include additional components in addition to those described below.

The illustrated computing environment 10 includes a computing device 12. In one embodiment, the computing device 12 may be one or more components included in the optimal solution search system 100, or the optimal solution search system 100.

The computing device 12 includes at least one processor 14, a computer readable storage medium 16, The processor 14 may cause the computing device 12 to operate in accordance with the exemplary embodiment discussed above. For example, processor 14 may execute one or more programs stored on computer readable storage medium 16. The one or more programs may include one or more computer-executable instructions, which when executed by the processor 14 cause the computing device 12 to perform operations in accordance with the illustrative embodiment .

The computer-readable storage medium 16 is configured to store computer-executable instructions or program code, program data, and / or other suitable forms of information. The program 20 stored in the computer-readable storage medium 16 includes a set of instructions executable by the processor 14. In one embodiment, the computer-readable storage medium 16 may be any type of storage medium such as a memory (volatile memory such as random access memory, non-volatile memory, or any suitable combination thereof), one or more magnetic disk storage devices, Memory devices, or any other form of storage medium that can be accessed by the computing device 12 and store the desired information, or any suitable combination thereof.

Communication bus 18 interconnects various other components of computing device 12, including processor 14, computer readable storage medium 16.

The computing device 12 may also include one or more input / output interfaces 22 and one or more network communication interfaces 26 that provide an interface for one or more input / output devices 24. The input / output interface 22 and the network communication interface 26 are connected to the communication bus 18. The input / output device 24 may be connected to other components of the computing device 12 via the input / output interface 22. The exemplary input and output device 24 may be any type of device, such as a pointing device (such as a mouse or trackpad), a keyboard, a touch input device (such as a touch pad or touch screen), a voice or sound input device, An input device, and / or an output device such as a display device, a printer, a speaker, and / or a network card. The exemplary input and output device 24 may be included within the computing device 12 as a component of the computing device 12 and may be coupled to the computing device 102 as a separate device distinct from the computing device 12 It is possible.

15 is a flowchart illustrating an optimal solution search method according to an embodiment of the present invention. The method shown in Fig. 15 can be performed, for example, by the above-described optimal solution search system 100 described above. In the illustrated flow chart, the method is described as being divided into a plurality of steps, but at least some of the steps may be performed in reverse order, combined with other steps, performed together, omitted, divided into detailed steps, One or more steps may be added and performed.

In step S102, the generating unit 106 generates a first regression model for one or more objective functions and a second regression model for one or more constraints using the learning data.

In step S104, the first calculation unit 108 calculates the uncertainty of each area in the search space using the first regression model, and calculates the failure probability of each area using the second regression model.

In step S106, the adjustment unit 110 adjusts the size of each area by estimating the reliability area in the search space using the uncertainty of each area.

In step S108, the second calculation unit 112 calculates an adjusted entropy index for each area.

In step S110, the preprocessing unit 114 performs preprocessing for the optimal solution search using at least one of the calculated uncertainty, the failure probability, and the entropy index.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed embodiments, but, on the contrary, I will understand. Therefore, the scope of the present invention should not be limited to the above-described embodiments, but should be determined by equivalents to the appended claims, as well as the appended claims.

10: Computing environment
12: computing device
14: Processor
16: Computer readable storage medium
18: Communication bus
20: Program
22: I / O interface
24: input / output device
26: Network communication interface
100: Optimal solution search system
102: Optimization Engine
104: learning data DB
106: Generator
108: first calculation unit
110:
112: second calculation unit
114:
116:
118: New data DB

Claims (20)

A generating unit for generating a first regression model for one or more objective functions and a second regression model for one or more constraints using the learning data;
A first calculation unit for calculating an uncertainty for each region in the search space using the first regression model and calculating a probability of failure for each region using the second regression model;
An adjustment unit for adjusting a size of each region by estimating a trust region in the search space using the uncertainty for each region;
A second calculation unit for calculating an adjusted entropy index for each region; And
And a preprocessor for performing preprocessing for an optimal solution search using at least one of the calculated uncertainty, the failure probability, and the entropy index.
The method according to claim 1,
Wherein the generation unit generates the first regression model by synthesizing a plurality of regression models for each of the objective functions and synthesizes a plurality of regression models for each of the constraints to generate the second regression model, system.
The method according to claim 1,
Wherein the first calculation unit calculates an uncertainty for each of the regions by using a variation amount of the objective function.
The method according to claim 1,
Wherein the adjusting unit estimates the reliability area by enlarging, reducing, dividing, or integrating the reliability area according to the uncertainty, and adjusting the size of each area by dividing the area other than the reliability area by the set size, system.
The method according to claim 1,
Wherein the second calculation unit calculates the adjusted value probability index for each area using at least one of the calculated uncertainty, the failure probability, and the entropy index.
The method of claim 5,
Wherein the preprocessing unit sets an area having the maximum value probability index as a search start point and performs an experiment for searching the optimal solution from the search start point.
The method according to claim 5 or 6,
Wherein the second calculation unit calculates the adjusted value probability index for each area using the following equation.
V _TR = λ ₁ I _TR - λ ₂ Pr _TR + λ ₃ M
(Where V _TR is the value probability index, I _TR is the entropy index, Pr _TR is the failure probability, M is the uncertainty, and λ ₁ , λ ₂ , and λ ₃ are the value probability coefficients)
The method according to claim 1,
Wherein the preprocessing unit performs an experiment for searching the optimal solution for an area where the entropy index is equal to or greater than a first threshold value.
The method of claim 8,
Further comprising a learning unit for learning new data acquired according to the execution of the experiment,
And the generation unit regenerates the first regression model and the second regression model using the learning data and the new data.
The method according to claim 1,
Wherein the preprocessing unit gives an approximate reasoning value derived from the first regression model and the second regression model to a region where the uncertainty is less than a second threshold value and an area where the failure probability exceeds a third threshold value, .
Generating a first regression model for one or more objective functions and a second regression model for one or more constraints using the training data;
Calculating an uncertainty for each region in the search space using the first regression model in a first calculation unit;
Calculating a failure probability for each of the areas using the second regression model in the first calculation unit;
Adjusting a size of each of the areas by estimating a reliability area in the search space using the uncertainty of each area in the adjustment part;
Calculating an entropy index for each region adjusted in the second calculation unit; And
And performing, in the preprocessing unit, preprocessing for an optimal solution search using at least one of the calculated uncertainty, the failure probability, and the entropy index.
The method of claim 11,
Wherein the step of generating the first regression model and the second regression model includes the steps of generating a first regression model by combining a plurality of regression models for each of the objective functions and generating a plurality of regression models And generates the second regression model by synthesizing the second regression model.
The method of claim 11,
Wherein the step of calculating the uncertainty calculates an uncertainty for each of the regions using the variance of the objective function.
The method of claim 11,
Wherein the step of adjusting the size of each of the regions comprises: estimating the confidence region by expanding, reducing, dividing, or integrating the confidence region according to the uncertainty; dividing the region other than the confidence region into a set size, The optimal solution search method of size adjustment.
The method of claim 11,
Before the step of performing the preprocessing,
Further comprising calculating, at the second calculation unit, the adjusted value probability index for each area using at least one of the calculated uncertainty, the failure probability, and the entropy index.
16. The method of claim 15,
Wherein the preprocessing step sets an area where the value probability index is maximum to a search start point and performs an experiment for searching the optimal solution from the search start point.
16. The method according to claim 15 or 16,
Wherein the step of calculating the value probability index calculates the adjusted value probability index for each area using the following equation.
V _TR = λ ₁ I _TR - λ ₂ Pr _TR + λ ₃ M
(Where V _TR is the value probability index, I _TR is the entropy index, Pr _TR is the failure probability, M is the uncertainty, and λ ₁ , λ ₂ , and λ ₃ are the value probability coefficients)
The method of claim 11,
Wherein the pre-processing step performs an experiment for the optimal solution search on an area where the entropy index is equal to or greater than a first threshold value.
19. The method of claim 18,
After performing the pre-processing,
Learning in the learning unit new data acquired according to the execution of the experiment; And
Further comprising the step of regenerating the first regression model and the second regression model using the learning data and the new data in the generation unit.
The method of claim 11,
The pre-processing step may include applying an approximate inference value derived from the first regression model and the second regression model to a region where the uncertainty is less than a second threshold value and an area where the failure probability exceeds a third threshold value , An optimal solution search method.

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