KR101593681B1 - Method and device for optimization design based on hybrid type - Google Patents

Abstract

According to an embodiment of the present invention, there is provided a method of optimizing a hybrid system, comprising: obtaining a temporary optimal solution for an optimal design based on multiple initial points in a global optimization unit of an optimum design apparatus; And searching for a global optimal solution for the optimal design using the temporary optimal solution as an initial point, in a local optimization unit of the optimum design apparatus.

Description

METHOD AND APPARATUS FOR OPTIMIZATION DESIGN BASED ON HYBRID TYPE < RTI ID = 0.0 >

Embodiments of the present invention relate to an optimal design method and apparatus, and more particularly, to a hybrid optimization method and apparatus for sequentially utilizing a pattern search technique and a local optimization technique using multiple initial points .

The efficient global optimization method considering existing constraints proceeds in two steps. In the first step, the objective function is generated as a Kriging model, which is an interpolation technique among various meta models, and an optimization process is performed by applying SVM (Support Vector Machine) in order to add sampling considering constraints.

Based on the new experimental points derived from the first step, we select the auxiliary samples in the second step to update the Kriging model, which is an approximate model of the objective function, and the SVM, which is an approximate model of the constraint. This two-step process is repeated until the convergence condition or the maximum number of iterations defined by the user is satisfied.

In case of global optimization problem, unconstrained optimization problem and constrained optimization problem can be categorized.

Conventional global optimization techniques are very limited to apply to constrained problems. This is because constraints can not be taken into account when adding additional sampling. Therefore, there is a disadvantage that the global optimum solution is likely to violate the constraint.

In addition, the accuracy of the approximate model is very important for performing global optimization. However, in the case of the conventional technique, a single fidelity meta-model using only one model, for example, kriging, radial basis function (RBF) Respectively.

In this case, there is a drawback that the efficiency of the global optimization technique is lowered due to the necessity of performing additional sampling work in order to secure the accuracy of the approximate model. In addition, when choosing additional sampling to take account of constraints, the choice of the number of design variables leads to a further increase in the analysis time for the additional sampling, resulting in lower efficiency.

On the other hand, there are generally various global optimizers for finding the optimal solution. In the case of the pattern search method, which is a global optimizer that determines the initial point, the initial point is determined by the designer's know-how, experience, or arbitrary design.

However, in the case of a pattern search method using a single point, there is a problem in that an accurate global optimum solution can not be found or an optimal local optimum is found according to the influence of the initial point.

Therefore, there is a desperate need for an optimal design technique of a hybrid method in which a global optimization is accurately and efficiently performed by performing local optimization using an optimal solution derived from a pattern search technique as an initial point.

As related prior art, there is registered patent publication No. 10-0393847 entitled " Multi-discipline integrated optimum design method using inter-disciplinary variable processing and optimum sensitivity information, registered on July 24, 2003.

One embodiment of the present invention provides a hybrid method optimal design method and apparatus capable of efficiently and precisely locating a global optimum solution by sequentially using a multiple initial point-based pattern search technique and a local optimization technique.

The problems to be solved by the present invention are not limited to the above-mentioned problem (s), and another problem (s) not mentioned can be clearly understood by those skilled in the art from the following description.

According to an embodiment of the present invention, there is provided a method of optimizing a hybrid system, comprising: obtaining a temporary optimal solution for an optimal design based on multiple initial points in a global optimization unit of an optimum design apparatus; And searching for a global optimal solution for the optimal design using the temporary optimal solution as an initial point, in a local optimization unit of the optimum design apparatus.

The step of obtaining the temporary optimal solution may include the step of applying the multiple initial points to the pattern search method to obtain the temporary optimal solution.

Wherein the step of obtaining the temporary optimal solution includes: generating the multiple initial points through an experimental design method; Defining a pattern for global search for the entire design area; Calculating a response value for the multiple initial points in each of the patterns by globally searching the pattern based on the multiple initial points; Deriving the best response value among the response values in each of the patterns; And determining the derived response value as the temporary optimal solution if the derived response value satisfies the convergence condition.

Wherein the step of obtaining the temporary optimal solution defines a new pattern for global search for the entire design area and performs the global search if the derived response value does not satisfy the convergence condition, And repeating the process of deriving the best response value.

The searching for the global optimal solution may include searching for the global optimal solution through a local optimizer whose initial point is the temporary optimal solution.

Wherein the searching for the global optimal solution comprises: defining the temporary optimal solution as the initial point; Determining an optimization search direction and a length based on the initial point; deriving a solution based on the optimization search direction and the length; And determining the optimal solution when the derived solution satisfies the convergence condition.

The searching for the global optimal solution may further include repeating the process of determining the optimization search direction and the length again using the derived solution as an initial point if the derived solution does not satisfy the convergence condition .

The hybrid optimal design apparatus according to an embodiment of the present invention includes a global optimizer for obtaining a temporary optimal solution for an optimal design through a pattern search technique based on multiple initial points; And a local optimizer for searching a global optimal solution for the optimal design through local optimization with the temporary optimal solution as an initial point.

The details of other embodiments are included in the detailed description and the accompanying drawings.

According to an embodiment of the present invention, the global optimal solution can be efficiently and accurately found by sequentially utilizing the multiple initial point-based pattern search technique and the local optimization technique.

According to one embodiment of the present invention, the global optimal solution can be found without depending on the know-how and experience of the designer.

According to an embodiment of the present invention, since it is not necessary to spend a lot of analysis time to consider the number of various cases, the optimum search time can be minimized.

According to an embodiment of the present invention, it is possible to apply the present invention regardless of the number of design variables and constraint conditions in the search for an optimal solution.

FIG. 1 is a block diagram illustrating a hybrid optimum design apparatus according to an embodiment of the present invention. Referring to FIG.
FIG. 2 is a block diagram illustrating a detailed configuration of the global optimizer of FIG. 1. FIG.
3 is a block diagram illustrating a detailed configuration of the local optimizer of FIG.
FIG. 4 is a flowchart illustrating a method of optimizing a hybrid method according to an embodiment of the present invention. Referring to FIG.
5 is a flowchart illustrating an optimization process using a pattern search technique according to an embodiment of the present invention.
FIG. 6 is a flowchart illustrating a process of searching for a global optimal solution through local optimization according to an embodiment of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS The advantages and / or features of the present invention, and how to accomplish them, will become apparent with reference to the embodiments described in detail below with reference to the accompanying drawings. It should be understood, however, that the invention is not limited to the disclosed embodiments, but is capable of many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, To fully disclose the scope of the invention to those skilled in the art, and the invention is only defined by the scope of the claims. Like reference numerals refer to like elements throughout the specification.

Various optimizers In general, various global optimizers are used to find the optimum in a problem. However, the existing various global optimizations are affected by the initial point and have a characteristic that it is time-consuming to find an accurate global optimal solution.

Also, even if the dimension of the design variable is high or the response value represented by the actual phenomenon is an optimization problem in which the nolinear is very large, it is very difficult to find the exact solution with various optimizations, Even time is costly and expensive.

Accordingly, in an embodiment of the present invention, in order to accurately and efficiently search for an optimal solution, a pattern search method, which is a global optimization using multiple initial points, and a local optimizer are sequentially used We propose a method and an apparatus to find the optimal solution accurately and efficiently through the hybrid technique.

An embodiment of the present invention can be applied to design problems to improve performance in all industries such as various mechanical parts and electronic equipments such as mechanical equipments, and furthermore, it is possible to design a computer aided engineering (CAE) The design is applicable to all industrial sectors that want to improve the performance of all industrial products.

The pattern search technique applied to an embodiment of the present invention is not applicable to a continuous function or a differentiable function because it does not require gradient information during the optimization process . Therefore, the pattern search method can be referred to as a direct search method or a derivative-fee method.

The pattern search method determines a mesh size that distinguishes an initial point from an initial design area in an initial state. The algorithm proceeds through the initial point and the mesh size. In this pattern search technique, a search is made for each mesh point that is more advanced than the initial point based on the initial point. Since the pattern search technique is widely used in the optimization process, detailed description thereof will be omitted herein.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

FIG. 1 is a block diagram illustrating a hybrid optimum design apparatus according to an embodiment of the present invention. Referring to FIG.

Referring to FIG. 1, an apparatus 100 for optimizing a hybrid scheme according to an embodiment of the present invention may include a global optimizer 110, a local optimizer 120, and a controller 130.

The global optimizer 110 obtains a temporary optimal solution for an optimal design based on multiple initial points. At this time, the global optimizer 110 may apply the multiple initial points to a pattern search method to obtain the temporary optimal solution.

In the conventional pattern search method, since a single initial point is used, an accurate global optimum solution can not be found according to the influence of the initial point, or a local optimal solution may be found.

On the other hand, in the pattern search technique applied to the embodiment of the present invention, a more accurate global optimal solution can be found because multiple initial points are used.

At this time, the multiple initial points can be generated through an experimental design method. The Design of Experiments (DOE) is an application field of statistics that aims to design efficient experimental methods and analyze the results properly.

The experimental design method is to plan an experimental method to collect information from existing variables. Such an experimental design method is a publicly known technology widely used throughout the industry, so a detailed description thereof will be omitted.

Hereinafter, the global optimizer 110 will be described in more detail with reference to FIG. 2 is a block diagram illustrating a detailed configuration of the global optimizer 110 of FIG.

2, the global optimizer 110 may include an initial point generator 210, a pattern defining unit 220, a pattern search unit 230, and an optimal solution determining unit 240 .

The initial point generating unit 210 generates the multiple initial points through the experimental design method.

The pattern definition unit 220 defines a pattern for global search for the entire design area. Here, the pattern defining unit 220 may define the pattern in consideration of a design parameter of the product.

For example, the pattern definition unit 220 may define a predetermined pattern according to a design parameter such as a structure, function, and shape of a product, or may define one pattern that is most suitable among predetermined patterns.

The pattern search unit 230 searches for a pattern defined by the pattern definition unit 220 on the basis of multiple initial points generated by the initial point generation unit 210, The response values for multiple initial points can be calculated.

The optimal solution determining unit 240 derives the best response value among the response values calculated by the pattern search unit 230 and, when the derived response value satisfies the convergence condition, It can be judged as an optimal solution.

On the other hand, if the derived response value does not satisfy the convergence condition, the optimal solution determination unit 240 defines a new pattern for global search for the entire design area, performs the global search, It is possible to repeat the process of deriving the best response value until it is satisfied.

Referring back to FIG. 1, the local optimizer 120 searches for a global optimal solution for an optimal design based on the temporary optimal solution derived by the global optimizer 110 as an initial point.

At this time, the local optimizer 120 may search for the global optimal solution through a local optimizer using the temporary optimal solution as an initial point.

Hereinafter, the local optimizer 120 will be described in more detail with reference to FIG. 3 is a block diagram illustrating a detailed configuration of the local optimizer 120 of FIG.

3, the local optimization unit 120 may include an initial point definition unit 310, an optimization search element determination unit 320, and an optimal solution determination unit 330. [

The initial point defining unit 310 defines the temporary optimal solution as the initial point.

The optimization search element determination unit 320 may determine an optimization search direction and a length based on the initial point defined by the initial point definition unit 310. [

That is, the optimization search element determination unit 320 may determine the optimization search direction and the optimization search length based on the temporary optimal solution.

The optimal solution determining unit 330 may derive a solution based on the optimization search direction and the length determined by the optimization search element determining unit 320. [

The optimal solution determining unit 330 may determine the derived solution as an optimal solution when the derived solution satisfies the convergence condition.

On the other hand, if the derived solution does not satisfy the convergence condition, the optimal solution determination unit 330 may repeat the process of determining the optimization search direction and the length again using the derived solution as an initial point.

At this time, the iterative process can be continued until the convergence condition is satisfied.

1, the controller 130 controls the operation of the hybrid optimizing apparatus 100 according to an embodiment of the present invention, that is, the operations of the global optimizer 110, the local optimizer 120, Can be controlled as a whole.

FIG. 4 is a flowchart illustrating a method of optimizing a hybrid method according to an embodiment of the present invention. Referring to FIG.

1 and 4, in step 410, the global optimizer 110 of the optimum design apparatus 100 determines a temporary optimal solution for optimal design through optimization through a pattern search technique based on multiple initial points .

Next, in step 420, the local optimizer 510 of the optimum design apparatus 100 searches for a global optimal solution for the optimum design through local optimization using the temporary optimal solution as an initial point.

5 is a flowchart illustrating an optimization process using a pattern search technique according to an embodiment of the present invention.

Referring to FIGS. 2 and 5, in step 510, the initial point generator 210 of the global optimizer 110 generates multiple initial points through an experimental design method.

Next, in step 520, the pattern defining unit 220 of the global optimizer 110 defines a pattern for global search for the entire design area.

Next, in step 530, the pattern search unit 230 of the global optimizer 110 performs global search of the pattern based on the multiple initial points to obtain a response value for the multiple initial points in each of the patterns .

Next, in step 540, the optimal solution determining unit 240 of the global optimizing unit 110 derives the best response value among the response values in each of the patterns.

Next, if the derived response value satisfies the convergence condition (the "YES" direction of 550), the optimal solution determining unit 240 of the global optimizing unit 110, in step 560, It is determined as the temporary optimal solution.

On the other hand, if the derived response value does not satisfy the convergence condition ("No" direction of 550), the process returns to step 520.

That is, the global optimizer 110 may repeat steps 520 to 550 until the derived response value satisfies the convergence condition.

FIG. 6 is a flowchart illustrating a process of searching for a global optimal solution through local optimization according to an embodiment of the present invention.

3 and 6, in step 610, the initial point defining unit 310 of the local optimizing unit 120 defines the temporary optimal solution as the initial point.

Next, in step 620, the optimization search element determination unit 320 of the local optimization unit 120 determines an optimization search direction and a length based on the initial point.

Next, in step 630, the optimal solution determining unit 330 of the local optimizing unit 120 derives a solution based on the optimization search direction and the length.

Next, if the solution obtained in step 640 satisfies the convergence condition (the "YES" direction of 640), the optimal solution determining unit 330 of the local optimizing unit 120 determines the derived solution as an optimal solution do.

If, on the other hand, the resulting solution does not satisfy the convergence condition (step 640, "no" direction), then step 620 is returned.

That is, the local optimizer 120 may repeat steps 620 to 640 until the derived solution satisfies the convergence condition.

Example

Next, the accuracy of the global optimization according to the present invention is compared through mathematical examples.

The mathematical example is as shown in Equation (1). The design variable is 10, which is a problem to find a variable that minimizes the objective function 'f' while satisfying a total of 8 constraints. The global optimum of this problem is shown in Table 1.

[Table 1]

[Equation 1]

Here, 'f' can be defined as a performance function to improve performance as an objective function. 'g' means various design requirements (conditions) to satisfy the design.

In order to compare the results of using multiple initial points and single initial points, the optimal solution was obtained by using a single initial point for all 20 initial points in the pre-design domain The results are summarized in Table 2.

Table 2 shows that when a single initial point is used, various optimal solutions are derived for each initial point. The response value of the global optimum solution is '24 .3062'. There may be a similar case for each of the following initial points, but it can be confirmed that there are many differences.

In order to derive an accurate global optimal solution, the initial point is determined by the designer's judgment. Therefore, it is very difficult to obtain an accurate optimal solution.

In order to solve this problem, in one embodiment of the present invention, an accurate global optimal solution can be obtained by using multiple initial points. This has the advantage that the designer can consider all design areas without having to define initial points.

For this, the optimal solution is obtained through the multiple initial point-based pattern search method proposed in the present invention.

Specifically, we first create multiple initial points through an experimental design method, and then define a pattern to search for the entire design area. The pattern is searched simultaneously based on the generated initial points, and the response value is calculated for each pattern, and the best response value among the response values is selected.

If the response value satisfies the convergence condition, it is determined to be the optimal solution and the optimization process is terminated. If not, a new pattern is defined and the pattern is searched based on the best response value obtained at the current step, and it is repeated until the convergence condition is satisfied.

Table 3 shows the results of the optimal solution obtained by this method.

[Table 3]

Through the multiple initial point-based pattern search method, it can be seen that there is a slight difference from '27 .3523' which is the result of finding the optimal solution and '24 .3062' which is the global optimal solution. This is not only the dimension of the design variable is high but also the number of constraints is large, so that the exact solution can not be found.

Therefore, in order to find an accurate solution, a hybrid method of finding a global optimal solution through an optimization process applying local optimization with an initial point obtained from a multiple initial point-based pattern search technique is applied to the present invention.

The local optimization method derives the optimal solution by the following method.

First, the optimal solution obtained through the multiple initial point-based pattern search technique is defined as an initial point. The direction and search length of the optimization search are determined based on the initial point. This leads to an improved solution. If this solution satisfies the convergence condition, it is selected as the optimal solution. However, if the convergence condition is not satisfied, the optimization search direction and length are determined again with the improved solution as the initial point.

As shown in Table 4, the global optimal solution can be found by locally optimizing the optimal solution obtained from the multiple initial point-based pattern search method.

[Table 4]

Embodiments of the present invention include computer readable media including program instructions for performing various computer implemented operations. The computer-readable medium may include program instructions, local data files, local data structures, etc., alone or in combination. The media may be those specially designed and constructed for the present invention or may be those known to those skilled in the computer software. Examples of computer-readable media include magnetic media such as hard disks, floppy disks and magnetic tape, optical recording media such as CD-ROMs and DVDs, magneto-optical media such as floppy disks, and ROMs, And hardware devices specifically configured to store and execute the same program instructions. Examples of program instructions include machine language code such as those produced by a compiler, as well as high-level language code that can be executed by a computer using an interpreter or the like.

While the present invention has been described in connection with what is presently considered to be practical exemplary embodiments, it is to be understood that the invention is not limited to the disclosed embodiments. Therefore, the scope of the present invention should not be limited to the described embodiments, but should be determined by the scope of the appended claims and equivalents thereof.

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 exemplary embodiments, but, on the contrary, Modification is possible. Accordingly, the spirit of the present invention should be understood only in accordance with the following claims, and all equivalents or equivalent variations thereof are included in the scope of the present invention.

110: Global optimization unit
120: Local optimization unit
130:
210: initial point generation unit
220: Pattern definition section
230: pattern search unit
240:
310: Initial point definition unit
320: Optimization search element determination unit
330:

Claims (8)

A method for optimizing an optimal design using an optimum design apparatus including a global optimizing unit and a local optimizing unit,
The global optimization unit of the optimum design apparatus generates multiple initial points for the entire design region through an experimental design method and performs a global search for the entire design region through a pattern search technique based on the multiple initial points Obtaining a temporary optimal solution for an optimal design; And
The local optimization unit of the apparatus for optimizing design defines the temporary optimal solution as an initial point and searches for a global optimal solution for the optimal design through local optimization based on the optimized search direction and length determined based on the initial point
And a second optimization method of the hybrid method.
The method according to claim 1,
The step of obtaining the temporary optimal solution
Applying the multiple initial points to a pattern search method to obtain the temporary optimal solution
And a second optimization method of the hybrid method.
3. The method of claim 2,
The step of obtaining the temporary optimal solution
Generating the multiple initial points through an experimental design method;
Defining a pattern for global search for the entire design area;
Calculating a response value for the multiple initial points in each of the patterns by globally searching the pattern based on the multiple initial points;
Deriving the best response value among the response values in each of the patterns; And
If the derived response value satisfies the convergence condition, determining the derived response value as the temporary optimal solution
And a second optimization method of the hybrid method.
The method of claim 3,
The step of obtaining the temporary optimal solution
If the derived response value does not satisfy the convergence condition, a new pattern for global search for the entire design area is defined and the global search is performed, and the best response value is derived until the convergence condition is satisfied Repeating the process
The method further comprising the steps of:
The method according to claim 1,
The step of searching for the global optimal solution
Searching the global optimal solution through a local optimizer with the temporary optimal solution as an initial point
And a second optimization method of the hybrid method.
6. The method of claim 5,
The step of searching for the global optimal solution
Defining the temporary optimal solution as the initial point;
Determining an optimal search direction and a length based on the initial point;
Deriving a solution based on the optimized search direction and length; And
If the solution satisfies the convergence condition,
And a second optimization method of the hybrid method.
The method according to claim 6,
The step of searching for the global optimal solution
If the derived solution does not satisfy the convergence condition, repeating the process of determining the optimization search direction and the length again using the derived solution as an initial point
The method further comprising the steps of:
Through the experimental design method, multiple initial points are generated for the entire design region, and a global search is performed for the entire design region through a pattern search technique based on the multiple initial points to obtain a temporary optimal solution for the optimum design. part; And
A local optimization unit for defining the temporary optimal solution as an initial point and searching for a global optimal solution for the optimum design through local optimization based on an optimization search direction and a length determined based on the initial point,
And a controller for controlling the hybrid system.

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