• 대한수학회보
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• 제50권1호
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• pp.73-81
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• 2013

In this paper, an efficient hybrid nonlinear conjugate gradient method is proposed to solve general unconstrained optimization problems on the basis of CD method [2] and DY method [5], which possess the following property: the sufficient descent property holds without any line search. Under the Wolfe line search conditions, we proved the global convergence of the hybrid method for general nonconvex functions. The numerical results show that the hybrid method is especially efficient for the given test problems, and it can be widely used in scientific and engineering computation.

• 디지털콘텐츠학회 논문지
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• 제11권1호
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• pp.39-45
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• 2010

본 논문에서는 기울기 기반 빠른 정상점 탐색 방법론을 제시하고 시뮬레이션 결과를 제시한다. 제안하는 방법론은 유한 구간에서 단봉 그래프를 가지는 함수의 정상점(최대치)을 최대한 적은 수의 함수값을 참조하여 찾는 문제에 대한 솔루션으로, 대표적인 적용분야로는 자동초점이 있다. 우리는 정상점 탐색을 위해 주기적 탐색, 기울기 기반 탐색, 상세 탐색과 같이 세가지 탐색 전략을 통해 정상점을 찾는다. 노이즈가 첨가된 가우시안 함수를 발생시켜 시뮬레이션 한 결과 대략 8번탐색 횟수와 1.04의 오차를 보임을 알 수 있었다.

• ETRI Journal
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• 제45권1호
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• pp.119-130
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• 2023

We propose a quantized gradient search algorithm that can achieve global optimization by monotonically reducing the quantization step with respect to time when quantization is composed of integer or fixed-point fractional values applied to an optimization algorithm. According to the white noise hypothesis states, a quantization step is sufficiently small and the quantization is well defined, the round-off error caused by quantization can be regarded as a random variable with identically independent distribution. Thus, we rewrite the searching equation based on a gradient descent as a stochastic differential equation and obtain the monotonically decreasing rate of the quantization step, enabling the global optimization by stochastic analysis for deriving an objective function. Consequently, when the search equation is quantized by a monotonically decreasing quantization step, which suitably reduces the round-off error, we can derive the searching algorithm evolving from an optimization algorithm. Numerical simulations indicate that due to the property of quantization-based global optimization, the proposed algorithm shows better optimization performance on a search space to each iteration than the conventional algorithm with a higher success rate and fewer iterations.

• 한국생물공학회:학술대회논문집
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• 한국생물공학회 2002년도 생물공학의 동향 (X)
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• pp.539-542
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• 2002

We propose new encoding method for numerical data in DNA using temperature gradient. To represent numerical values in DNA sequences, we introduce melting temperature. Since DNA strands representing smaller values have a lower Tm, they tend to denature with ease and also easily amplified by denaturation temperature gradient PCR. We also implement a local search molecular algorithm using temperature gradient, which is contrasted to conventional exhaustive search molecular algorithms. The proposed methods are verified by solving an instance of the travelling salesman problem. We could effectively amplify the correct solutions and the use of temperature gradient made the detection of solutions easier.

• 한국유체기계학회 논문집
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• 제2권1호
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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.

• 대한건축학회논문집:구조계
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• 제33권12호
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• pp.53-62
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• 2017

Many gradient-based mathematical methods have been developed and are in use for structural size optimization problems, in which the cross-sectional areas or sizing variables are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. The main objective of this paper is to propose an efficient optimization method for structures with discrete-sized variables based on the harmony search (HS) meta-heuristic algorithm that is derived using penalty function. The recently developed HS algorithm was conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. In this paper, a discrete search strategy using the HS algorithm with a static penalty function is presented in detail and its applicability using several standard truss examples is discussed. The numerical results reveal that the HS algorithm with the static penalty function proposed in this study is a powerful search and design optimization technique for structures with discrete-sized members.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2000년도 하계종합학술대회 논문집(4)
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• pp.47-49
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• 2000

In this paper we propose the multiple local search method(MLSM) based on the motion information of the neighbor blocks. In the proposed method motions are estimated from the multiple searches of many candidate local search regions. To reduce the additional search points we avoid to search the same candidate regions previously visited using the distance from the initial search point to the recently found vector points. In the simulation the proposed method shows more excellent results than that of other gradient based method especially in the search of motion boundary.

• 대한수학회지
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• 제47권1호
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• pp.63-70
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• 2010

In this paper, we develop a nonmonotone spectral memory gradient method for unconstrained optimization, where the spectral stepsize and a class of memory gradient direction are combined efficiently. The global convergence is obtained by using a nonmonotone line search strategy and the numerical tests are also given to show the efficiency of the proposed algorithm.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2005년도 춘계 학술발표회 논문집
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• pp.359-366
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• 2005

Most engineering optimization are based on numerical linear and nonlinear programming methods that require substantial gradient information and usually seek to improve the solution in the neighborhood of a starting point. These algorithm, however, reveal a limited approach to complicated real-world optimization problems. If there is more than one local optimum in the problem, the result may depend on the selection of an initial point, and the obtained optimal solution may not necessarily be the global optimum. This paper describes a new harmony search(HS) meta-heuristic algorithm-based approach for structural size optimization problems with continuous design variables. This recently developed HS algorithm is conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. Two classical space truss optimization problems are presented to demonstrate the effectiveness and robustness of the HS algorithm. The results indicate that the proposed approach is a powerful search and optimization technique that may yield better solutions to structural engineering problems than those obtained using current algorithms.

• Smart Structures and Systems
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• 제23권1호
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• pp.45-60
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• 2019

This paper is devoted to proposing a new approach for damage detection of structures. In this technique, the biconjugate gradient method (BCG) is employed. To remedy the noise effects, a new preconditioning algorithm is applied. The proposed preconditioner matrix significantly reduces the condition number of the system. Moreover, based on the characteristics of the damage vector, a new direct search algorithm is employed to increase the efficiency of the suggested damage detection scheme by reducing the number of unknowns. To corroborate the high efficiency and capability of the presented strategy, it is applied for estimating the severity and location of damage in the well-known 31-member and 52-member trusses. For damage detection of these trusses, the time history responses are measured by a limited number of sensors. The results of numerical examples reveal high accuracy and robustness of the proposed method.