• Journal of the Earthquake Engineering Society of Korea
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• v.10 no.6 s.52
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• pp.19-28
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• 2006

Most conventional model updating methods must use mathematical objective function with experimental modal matrices and analytical system matrices or must use information about the gradient or higher derivatives of modal properties with respect to each updating parameter. Therefore, most conventional methods are not appropriate for complex structural system such as bridge structures due to stability problem in inverse analysis with ill-conditions. Sometimes, moreover, the updated model may have no physical meaning. In this paper, a new FE model updating method based on a hybrid optimization technique using genetic algorithm (GA) and Holder-Mead simplex method (NMS) is proposed. The performance of hybrid optimization technique on the nonlinear problem is demonstrated by the Goldstein-Price function with three local minima and one global minimum. The influence of the objective function is evaluated by the case study of a simulated 10-dof spring-mass model. Through simulated case studies, finally, the objective function is proposed to update mass as well as stiffness at the same time. And so, the proposed hybrid optimization technique is proved to be an efficient method for FE model updating.

• Journal of the Earthquake Engineering Society of Korea
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• v.12 no.6
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• pp.13-23
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• 2008

In this study, a finite element (FE) model updating method based on the hybrid genetic algorithm (HGA) is proposed to improve the grillage FE model for plate girder bridges. HGA consists of a genetic algorithm (GA) and direct search method (DS) based on a modification of Nelder & Mead's simplex optimization method (NMS). Fitness functions based on natural frequencies, mode shapes, and static deflections making use of the measurements and analytical results are also presented to apply in the proposed method. In addition, a multi-objective function has been formulated as a linear combination of fitness functions in order to simultaneously improve both stiffness and mass. The applicability of the proposed method to girder bridge structures has been verified through a numerical example on a two-span continuous grillage FE model, as well as through an experimental test on a simply supported plate girder skew bridge. In addition, the effect of measuring error is considered as random noise, and its effect is investigated by numerical simulation. Through numerical and experimental verification, it has been proven that the proposed method is feasible and effective for FE model updating on plate girder bridges.

• Journal of KIISE:Computer Systems and Theory
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• v.32 no.3
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• pp.133-147
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• 2005

Various types of ray-tracing methods are used to predict the quantity measures of radiation illumination, the uniformity of illumination, radiation performance of LCD BLU(Hack-Light Unit). The uniformity of radiation illumination is one of the most important design factor of BLU and is usually controlled by the diffusive-ink pattern printed on the bottom of light-guide panel of BLU. Therefore it is desirable to produce an improved (ideally, the optimal) ink pattern to achieve the best uniformity of radiation illumination. In this paper, we applied the Welder-Mead simplex-search method among various direct search method to compute the optimal ink pattern. Direct search methods are widely used to optimize the functions which are often highly nonlinear, unpredictably discontinuous, and nondifferentiable, The ink-pattern controlling the uniformity of radiation illumination is one type of these functions. In this paper, we found that simplex search methods are well suited to computing the optimal diffusive-ink pattern. In extensive numerical testing, we have found the simplex search method to be reasonably efficient and reliable at computing the optimal diffusive-ink pattern. The result also suggests that optimization can improve the functionality of simulation tools which are used to design LCD BLU.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.1
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• pp.59-70
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• 1992

Quadratic programming problems(QP) have been widely used as a direction-finding subproblem in the engineering and structural design optimization. To develop an efficient solution algorithm for the QP subproblems, theoretical aspects and numerical behavior of mathematical programming methods that can be used as QP solver are studied and compared. For the solution of both primal and dual QP, Simplex, gradient projection(GRP), and augmented Lagrange multiplier algorithms are investigated and coded. From the numerical study, it is found that the primal GRP algorithm with potential constraint strategy and the dual Simplex algorithm are more attractive and effective than the others. They have theoretical robustness as well. Moreover, primal GRP algorithm is preferable in case the number of constraints is larger than the number of design variables. Favorable features of GRP and Simplex algorithm are merged into a combined algorithm, which is useful in the structural design optimization.

• Journal of the military operations research society of Korea
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• v.11 no.1
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• pp.79-86
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• 1985

A multi-interchange simplex method is presented. This method tries to cut almost half of the set of convex combinations which generate all decreasing feasible directions. Analysis of this method indicates high possibility of the existence of polynomial-time simplex-type methods.

• Journal of the military operations research society of Korea
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• v.9 no.2
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• pp.57-60
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• 1983

We show that the complexity of Simplex Method for Linear Programming problem is equivalent to the complexity of finding just an adjacent basic feasible solution if exists. Therefore a simplex type method which resolves degeneracy in polynomial time with respect to the size of the given linear programming problem can solve the general linear programming problem in polynomial steps.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.37 no.8
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• pp.975-981
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• 2013

A robust optimization is only one of the ways to minimize the effects of variances in design variables on the objective functions at the preliminary design stage. To predict the variances and to formulate the probabilistic constraints are the most important procedures for the robust optimization formulation. Though several methods such as the process capability index and the six sigma technique were proposed for the prediction and formulation of the variances and probabilistic constraints, respectively, there are few attempts using a percent defective which has been widely applied in the quality control of the manufacturing process for probabilistic constraints. In this study, the robust optimization for a lower control arm of automobile vehicle was carried out, in which the design space showing the mean and variance sensitivity of weight and stress was explored before robust optimization for a lower control arm. The 2nd order Taylor expansion for calculating the standard deviation was used to improve the numerical accuracy for predicting the variances. Simplex algorithm which does not use the gradient information in optimization was used to convert constrained optimization into unconstrained one in robust optimization.

• Proceedings of the KIEE Conference
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• 2006.07a
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• pp.311-312
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• 2006

본 논문에서는 선로 전력조류제약을 고려한 경제급전(SCED : Security-Constrained economic dispatch)에 내점 선형계획법을 이용하여 최적해를 구하는 문제를 다룬다. 최적전력조류(Optimal Power Flow)식으로부터 선로의 유효전력만을 근사화하여 선로 전력조류 제약을 고려할 경제급전(SCED)의 식을 정식화한다. 선형계획법을 적용하여 최적해를 구하기 위해서 발전기출력과 유효전력, 부하, 손실과의 관계를 이용하여 경제급전의 식을 선형화 하는 알고리즘을 제시한다. 선형화 알고리즘은 목적함수로 계통 발전기의 총 연료비를 취하고 전력수급평형식으로 발전기출력증분에 대한 선로의 증분손실계수를 이용하며, 선로의 제약조건은 일반화발전 분배계수(GGDF : Generalized Generation Distribution Factor)를 이용하여 선형화한다. 최적화 기법으로서 내점법(Interior Point Method)을 적용하고자 하며 사례연구를 통하여 선형계획법 중 가장 많이 사용하는 심플렉스(Simplex)법과의 수렴특성을 비교하여 내점 법의 효용성을 확인하고자 한다.

• Proceedings of the KIEE Conference
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• 1999.07g
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• pp.2830-2832
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• 1999

신경망은 선형 시스템 뿐 만 아니라 비선형 시스템에 있어서도 탁월한 모델링 및 예측 성능을 갖고 있다. 하지만 좋은 성능을 갖는 신경망을 구현하기 위해서는 최적화 해야할 파라미터들이 있다. 은닉층의 뉴런의 수, 학습율, 모멘텀, 학습오차 등이 그것인데 이러한 파라미터들은 경험에 의해서, 또는 문헌들에서 제시하는 값들을 선택하여 사용하는 것이 일반적인 경향이다. 하지만 신경망의 전체적인 성능은 이러한 파라미터들의 값에 의해서 결정되기 때문에 이 값들의 선택은 보다 체계적인 방법을 사용하여 구하여야 한다. 본 논문은 유전 알고리즘을 이용하여 이러한 신경망 파라미터들의 최적 값을 찾는데 목적이 있다. 유전 알고리즘을 이용하여 찾은 파라미터들을 사용하여 학습된 신경망의 학습오차와 예측오차들을 심플렉스 알고리즘을 이용하여 찾은 파라미터들을 사용하여 학습된 신경망의 오차들과 비교하여 본 결과 유전 알고리즘을 이용하여 찾을 파라미터들을 이용했을 때의 신경망의 성능이 더욱 우수함을 알 수 있다.

• The KSFM Journal of Fluid Machinery
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• v.2 no.1 s.2
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• pp.29-34
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• 1999

To develop the efficient numerical optimization method for the design of an airfoil, an evaluation of various methods coupled with two-dimensional Naviev-Stokes analysis is presented. Simplex method and Hook-Jeeves method we used as direct search methods, and steepest descent method, conjugate gradient method and DFP method are used as indirect search methods and are tested to determine the search direction. To determine the moving distance, the golden section method and cubic interpolation method are tested. The finite volume method is used to discretize two-dimensional Navier-Stokes equations, and SIMPLEC algorithm is used for a velocity-pressure correction method. For the optimal design of two-dimensional airfoil, maximum thickness, maximum ordinate of camber line and chordwise position of maximum ordinate are chosen as design variables, and the ratio of drag coefficient to lift coefficient is selected as an objective function. From the results, it is found that conjugate gradient method and cubic interpolation method are the most efficient for the determination of search direction and the moving distance, respectively.