• 대한기계학회논문집A
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• 제29권6호
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• pp.842-851
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• 2005

In this paper, a new method for constrained optimization of noisy functions is proposed. In approximate optimization using response surface methods, if constraints have severe noise, the approximate feasible region defined by approximate constraints is apt to include some of the infeasible region defined by actual constraints. This can cause the approximate optimum to converge into the infeasible region. In the proposed method, the approximate optimization is performed with the approximate constraints shifted by their deviations, which are calculated using a diagonal quadratic response surface method. This can prevent the approximate optimum from converging into the infeasible region. To fit the objective and constraints into diagonal quadratic models, we select the center and 4 additional points along each axis of design variables as experimental points. The deviation of each function is calculated using the differences between the real and approximate function values at the experimental points. A sequential approximate optimization technique based on the trust region algorithm is adopted to manage approximate models. The proposed approach is validated by solving some design problems. The results of the problems show the effectiveness of the proposed method.

• 대한기계학회논문집A
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• 제29권1호
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• pp.45-52
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• 2005

A general approximate optimization technique by sequential design domain(SDD) did not save response values for getting an approximate function in each step. It has a disadvantage at aspect of an expense. In this paper, previous response values are recycled for constructing an approximate function. For this reason, approximation function is more accurate. Accordingly, even if we did not determine move limit, a system is converged to the optimal design. Size and shape optimization using approximate optimization technique is carried out with SDD. Algorithm executing Pro/Engineer and ANSYS are automatically adopted in the approximate optimization program by SDD. Convergence criterion is defined such that optimal point must be located within SDD during the three steps. The PLBA(Pshenichny-Lim-Belegundu-Arora) algorithm is used to solve approximate optimization problems. This algorithm uses the second-order information in the direction finding problem and uses the active set strategy.

• 대한기계학회논문집A
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• 제34권11호
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• pp.1603-1611
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• 2010

본 논문에서는 범프 및 브레이크 하중조건 하에서 자동차 넉클의 강도설계에 관한 다양한 회귀모델 기반 근사최적화 기법 및 그 성능을 비교하고자 한다. 최적설계문제는 응력, 변형 및 진동주파수의 제한조건 하에서 중량을 최소화하여 설계변수인 단면치수가 결정되도록 정식화 된다. 비교 연구를 위해 사용된 근사화 기법은 순차적 근사최적화(SAO), 순차적 이점대각이차 근사최적화(STDQAO), 그리고 개선된 이동최소 자승법(MLSM) 기반 근사최적화 기법인 CF-MLSM 와 Post-MLSM 이다. SAO 와 STDQAO 적용을 위하여 상용 프로세스통합 설계최적화(PIDO) 코드를 사용하였다. 본 연구에 적용한 MLSM 기반 근사최적화 기법들은 제한조건의 가용성을 보장할 수 있도록 새롭게 개발되었다. 다양한 근사최적화 기법에 의한 설계결과는 설계 해의 개선 및 수렴속도 등 수치적 성능을 기준으로 실제 비근사최적화 결과와 비교검토 되었다.

• 한국전산구조공학회논문집
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• 제24권5호
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• pp.543-551
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• 2011

본 논문에서는 해양작업 상태의 하중조건을 고려한 부유식 원유생산 저장 하역장치에 설치된 라이져 보강구조의 강도설계에 관련하여 다양한 근사화 기법 기반 설계최적화 및 그 성능을 비교하고자 한다. 설계최적화 문제는 하중조건별 구조강도의 제한조건 하에서 중량을 최소화하여 설계변수인 구조 부재치수가 결정되도록 정식화된다. 비교 연구를 위해 사용된 근사화 기법은 반응표면법 기반 순차적 근사최적화(RBSAO), 크리깅 기반 순차적 근사최적화(KBSAO), 그리고 개선된 이동최소자승법(MLSM) 기반 근사최적화 기법인 CF-MLSM와 Post-MLSM이다. RBSAO와 KBSAO의 적용을 위하여 상용프로세스 통합 설계최적화(PIDO) 코드를 사용하였다. 본 연구에 적용한 MLSM 기반 근사최적화 기법들은 제한조건의 가용성을 보장할 수 있도록 새롭게 개발되었다. 다양한 근사화 모델 기반 설계최적화 기법에 의한 결과는 설계 해의 개선 및 수렴속도 등의 수치적 성능을 기준으로 실제 비근사 설계최적화 결과와 비교 검토하였다.

• 대한기계학회논문집A
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• 제29권9호
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• pp.1199-1208
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• 2005

Nowadays, it is performed actively to optimize by using an approximate model. This is called the approximate optimization. In addition, the sequential approximate optimization (SAO) is the repetitive method to find an optimum by considering the convergence of an approximate optimum. In some recent studies, it is proposed to increase the fidelity of approximate models by applying the sequential sampling. However, because the accuracy and efficiency of an approximate model is directly connected with the design area and the termination criteria are not clear, sequential sampling method has the disadvantages that could support an unreasonable approximate optimum. In this study, the SAO is executed by using trust region, Kriging model and Optimal Latin Hypercube design (OLHD). Trust region is used to guarantee the convergence and Kriging model and OLHD are suitable for computer experiment. finally, this SAO method is applied to various optimization problems of highly nonlinear mathematical functions. As a result, each approximate optimum is acquired and the accuracy and efficiency of this method is verified by comparing with the result by established method.

• 한국해양공학회지
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• 제35권2호
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• pp.131-140
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• 2021

The paper deals with comparative study of various surrogate models based approximate optimization in the structural design of the passive type deck support frame under design load conditions. The passive type deck support frame was devised to facilitate both transportation and installation of 20,000 ton class topside. Structural analysis was performed using the finite element method to evaluate the strength performance of the passive type deck support frame in its initial design stage. In the structural analysis, the strength performances were evaluated for various design load conditions. The optimum design problem based on surrogate model was formulated such that thickness sizing variables of main structure members were determined by minimizing the weight of the passive type deck support frame subject to the strength performance constraints. The surrogate models used in the approximate optimization were response surface method, Kriging model, and Chebyshev orthogonal polynomials. In the context of numerical performances, the solution results from approximate optimization were compared to actual non-approximate optimization. The response surface method among the surrogate models used in the approximate optimization showed the most appropriate optimum design results for the structure design of the passive type deck support frame.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.375-381
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• 2008

Boundedness for the set of all the $\epsilon$-approximate solutions for convex optimization problems are considered. We give necessary and sufficient conditions for the sets of all the $\epsilon$-approximate solutions of a convex optimization problem involving finitely many convex functions and a convex semidefinite problem involving a linear matrix inequality to be bounded. Furthermore, we give examples illustrating our results for the boundedness.

• 한국기계가공학회지
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• 제20권6호
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• pp.33-43
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• 2021

A60 class bulkhead penetration piece is a fire resistance system installed on a bulkhead compartment to protect lives and to prevent flame diffusion in a fire accident on a ship and offshore plant. This study focuses on the approximate optimization of the fire resistance design of the A60 class bulkhead penetration piece using a multi-island genetic algorithm. Transient heat transfer analysis was performed to evaluate the fire resistance design of the A60 class bulkhead penetration piece. For approximate optimization, the bulkhead penetration piece length, diameter, material type, and insulation density were considered discrete design variables; moreover, temperature, cost, and productivity were considered constraint functions. The approximate optimum design problem based on the meta-model was formulated by determining the discrete design variables by minimizing the weight of the A60 class bulkhead penetration piece subject to the constraint functions. The meta-models used for the approximate optimization were the Kriging model, response surface method, and radial basis function-based neural network. The results from the approximate optimization were compared to the actual results of the analysis to determine approximate accuracy. We conclude that the radial basis function-based neural network among the meta-models used in the approximate optimization generates the most accurate optimum design results for the fire resistance design of the A60 class bulkhead penetration piece.

• 한국산업융합학회 논문집
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• 제24권1호
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• pp.31-43
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• 2021

In this study, approximate design optimization using various meta-models was performed for the structural design of active type deck support frame. The active type deck support frame was newly developed to facilitate both transportation and installation of 20,000 ton class offshore plant topside. Structural analysis was carried out using the finite element method to evaluate the strength performance of the active type deck support frame in its initial design stage. In the structural analysis, the strength performances were evaluated for various design load conditions that were regulated in ship classification organization. The approximate optimum design problem based on meta-model was formulated such that thickness sizing variables of main structure members were determined by achieving the minimum weight of the active type deck support frame subject to the strength performance constraints. The meta-models used in the approximate design optimization were response surface method, Kriging model, and Chebyshev orthogonal polynomials. The results from approximate design optimization were compared to actual non-approximate design optimization. The Chebyshev orthogonal polynomials among the meta-models used in the approximate design optimization represented the most pertinent optimum design results for the structure design of the active type deck support frame.

• 대한기계학회논문집A
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• 제22권4호
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• pp.811-825
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• 1998

An approximate line search is presented for dynamic response optimization with Augmented Lagrange Multiplier(ALM) method. This study empolys the approximate a augmented Lagrangian, which can improve the efficiency of the ALM method, while maintaining the global convergence of the ALM method. Although the approximate augmented Lagragian is composed of only the linearized cost and constraint functions, the quality of this approximation should be good since an approximate penalty term is found to have almost second-order accuracy near the optimum. Typical unconstrained optimization algorithms such as quasi-Newton and conjugate gradient methods are directly used to find exact search directions and a golden section method followed by a cubic polynomial approximation is empolyed for approximate line search since the approximate augmented Lagrangian is a nonlinear function of design variable vector. The numberical performance of the proposed approach is investigated by solving three typical dynamic response optimization problems and comparing the results with those in the literature. This comparison shows that the suggested approach is robust and efficient.