• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.6
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• pp.1041-1049
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• 2003

In this paper, a new local two-point approximation method which is based on the exponential intervening variable is proposed. This new algorithm, called the Two-Point Convex Approximation(TPCA), use the function and design sensitivity information from the current and previous design points of the sequential approximate optimization to generate a sequence of convex, separable subproblems. This paper describes the derivation of the parameters associated with the approximation and the numerical solution procedure. In order to show the numerical performance of the proposed method, a sequential approximate optimizer is developed and applied to solve several typical design problems. These optimization results are compared with those of other optimizers. Numerical results obtained from the test examples demonstrate the effectiveness of the proposed method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.4
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• pp.431-437
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• 2003

In this paper, an approximate optimization program based on GUI(graphic user interface) environment is developed. This program is coded by using Fortran and Visual basic. Fortran is used to Progress approximate optimization process. Visual basic is used to make user environment for user to use conveniently. Inside of this program, it uses two independent programs. One is commercial program, ANSYS, and the other is optimization program, PLBA(Pshenichny-Lim-Belegundu Arora). The former is used to obtain approximate equation of stress and displacement of a structure. The latter is used to solve approximate optimization. This algorithm uses second-order information of a function and active set strategy. This program is connecting ANSYS and PLBA. And it progress the process repeatedly until it obtain optimum value. As a method of approximate optimization, sequential design domain(SDD) is introduced. SDD starts with a certain range which is offseted from midpoint of an initial design domain and then SDD of the next step is determined by optimal point of a prior step.

• Journal of Mechanical Science and Technology
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• v.15 no.9
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• pp.1257-1267
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• 2001

For efficient mechanical system optimization, a new two-point approximation method is presented. Unlike the conventional two-point approximation methods such as TPEA, TANA, TANA-1, TANA-2 and TANA-3, this introduces the shifting level into each exponential intervening variable to avoid the lack of definition of the conventional exponential intervening variables due to zero-or negative-valued design variables. Then a new quadratic approximation whose Hessian matrix has only diagonal elements of different values is proposed in terms of these shifted exponential intervening variables. These diagonal elements are determined in a closed form that corrects the typical error in the approximate gradient of the TANA series due to the lack of definition of exponential type intervening variables and their incomplete second-order terms. Also, a correction coefficient is multiplied to the pre-determined quadratic term to match the value of approximate function with that of the previous point. Finally, in order to show the numerical performance of the proposed method, a sequential approximate optimizer is developed and applied to solve six typical design problems. These optimization results are compared with those of TANA-3. These comparisons show that the proposed method gives more efficient and reliable results than TANA-3.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.12
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• pp.3040-3052
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• 2000

For effective construction of second-order response surface models, an efficient quad ratic approximation method is proposed in the context of trust region model management strategy. In the proposed method, although only the linear and quadratic terms are uniquely determined using 2n+1 design points, the two-factor interaction terms are mathematically updated by normalized quasi-Newton formula. In order to show the numerical performance of the proposed approximation method, a sequential approximate optimizer is developed and solves a typical unconstrained optimization problem having 2, 6, 10, 15, 30 and 50 design variables, a gear reducer system design problem and two dynamic response optimization problems with multiple objectives, five objectives for one and two objectives for the other. Finally, their optimization results are compared with those of the CCD or the 50% over-determined D-optimal design combined with the same trust region sequential approximate optimizer. These comparisons show that the proposed method gives more efficient than others.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.1
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• pp.31-38
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• 2004

Mechanical design process is generally accomplished by design, analysis, and test. Designers use programs fitting purpose, and obtain repeatedly a response of a simulation program, a sub-program for optimization. In this paper, shape optimization using approximate optimization technique is carried out with sequential design domain(SDD). In addition, algorithm executing Pro/Engineer and ANSYS automatically are adopted in the approximate optimization program by SDD. It is difficult for design problem to be approximated accurately for the whole range of design space. However, more or less accurate approximation is constructed if SDD is applied to that case. SDD starts with a certain range which is off-seted from midpoint of an initial design domain and then SDD of the next step is determined by a move limited. Convergence criterion is defined such that optimal point must be located within SDD during the two steps. Also, the PLBA(Pshenichny-Lim-Belegundu-Arora) algorithm is used to solve approximate optimization problems. This algorithm uses the second-order information and the active set strategy, in order to seek the direction of design variables.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.4
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• pp.317-324
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• 2008

Optimum design for general or complex structures are required to the need of many numbers of structural analyses. However, current computational environment with single processor is not capable of generating a high-level efficiency in structural analysis and design process for complex structures. In this paper, a virtual parallel computing system communicated by an internet of personal computers and workstation is constructed. In addition, a routine executing Pro/E, ANSYS and optimization algorithm automatically are adopted in the distributed process technique of sequential approximate optimization for the purpose of enhancing the flexibility of application to general structures. By employing the distributed processing technique during structural analysis using commercial application, total calculation time could be reduced, which will enhance the applicability of the proposed technique to the general complex structures.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.1022-1027
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• 2004

In this study, the shape of plate-fin type heat sink is numerically optimized to acquire the minimum pressure drop under the required temperature rise. To do this, a new sequential approximate optimization (SAO) is proposed and it is integrated with the computational fluid dynamics (CFD). In thermal/fluid systems for constrained nonlinear optimization problems, three fundamental difficulties such as high cost for function evaluations (i.e., pressure drop and thermal resistance), the absence of design sensitivity information, and the occurrence of numerical noise are confronted. To overcome these problems, the progressive quadratic response surface method (PQRSM), which is one of the sequential approximate optimization algorithms, is proposed and the heat sink is optimize by means of the PQRSM.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.386-391
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• 2001

This paper presents a new two-point approximation method based on the exponential intervening variable. To avoid the lack of definition of the conventional exponential intervening variables due to zero- or negative-valued design variables the shifting level into each exponential intervening variable is introduced. Then a new quadratic approximation, whose Hessian matrix has only diagonal elements of different values, is proposed in terms of these intervening variables. These diagonal elements are computed in a closed form, which correct the typical error in the approximate gradient of the TANA series due to the lack of definition of exponential type intervening variables and their incomplete second-order terms. Also, a correction coefficient is multiplied to the pre-determined quadratic term to match the value of approximate function with that of the original function at the previous point. Finally, the authors developed a sequential approximate optimizer, solved several typical design problems used in the literature and compared these optimization results with those of TANA-3. These comparisons show that the proposed method gives more efficient and reliable results than TANA-3.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.9
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• pp.1423-1431
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• 2001

Based on the exponential intervening variable, a new two-point approximation method is presented. This introduces the shifting level into each exponential intervening variable to avoid the lack of def inition of the conventional exponential intervening variables due to zero-or negative-valued design variables. Then a new quadratic approximation whose Hessian matrix has only diagonal elements of different values is proposed in terms of these intervening variables. These diagonal elements are determined in a closed form that corrects the typical error in the approximate gradient of the TANA series due to the lack of definition of exponential type intervening variables and their incomplete second-order terms. Also, a correction coefficient is multiplied to the pre-determined quadratic term to match the value of approximate function with that of the previous point. Finally, in order to show the numerical performance of the proposed method, a sequential approximate optimizer is developed and applied to solve six typical design problems. These optimization results are compared with those of TANA-3. These comparisons show that the proposed method gives more efficient and reliable results than TANA-3.

• Journal of Mechanical Science and Technology
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• v.17 no.5
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• pp.698-707
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• 2003

A new quadratic response surface modeling method is presented. In this method, the incomplete small composite design (ISCD) is newly proposed to .educe the number of experimental runs than that of the SCD. Unlike the SCD, the proposed ISCD always gives a unique design assessed on the number of factors, although it may induce the rank-deficiency in the normal equation. Thus, the singular value decomposition (SVD) is employed to solve the normal equation. Then, the duality theory is used to newly develop the conservative least squares fitting (CONFIT) method. This can directly control the ever- or the under-estimation behavior of the approximate functions. Finally, the performance of CONFIT is numerically shown by comparing its'conservativeness with that of conventional fitting method. Also, optimizing one practical design problem numerically shows the effectiveness of the sequential approximate optimization (SAO) combined with the proposed ISCD and CONFIT.