• East Asian mathematical journal
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• 제30권2호
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• pp.149-172
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• 2014

The problems of optimization addressed in the high school curriculum are usually posed in real-life contexts. However, because of the instructional purposes, problems are artificially constructed to suit computation, rather than to reflect real-life problems. Those problems have thus limited use for teaching 'practicalities', which is one of the goals of mathematics education. This study, by utilizing 'GeoGebra', suggests the optimization problem solving related to the quadratic curve, using the contour-line method which contemplates the quadratic curve changes successively. By considering more realistic situations to supplement the limit which deals only with numerical and algebraic approach, this attempt will help students to be aware of the usefulness of mathematics, and to develop interests in mathematics, as well as foster students' integrated thinking abilities across units. And this allows students to experience a variety of math.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.685-692
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• 2009

We consider the linearized (approximated) problem for differentiable vector optimization problem, and then we establish equivalence results between a differentiable vector optimization problem and its associated linearized problem under the proper efficiency.

• 대한기계학회논문집
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• 제18권2호
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• pp.313-322
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• 1994

Structural optimization has been developed by two methods. One is the direct method which applies the Nonlinear Programming (NLP) algorithm directly to the structural optimization problem. This method is known to be very excellent mathematically. However, it is very expensive for large-scale problems due to the one-dimensional line search. The other method is the approximation method which utilizes the engineering senses very well. The original problem is approximated to a simple problem and an NLP algorithm is adopted for solving the approximated problems. Practical solutions are obtained with low cost by this method. The two methods are compared through standard structural optimization problems. The Finite element method with truss and beam elements is used for the structural and sensitivity analyses. The results are analyzed based on the convergence performances, the number is function calculations, the quality of the cost functions, and etc. The applications of both methods are also discussed.

• 대한기계학회논문집
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• 제16권2호
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• pp.236-247
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• 1992

Optimization has been developed to minimize the cost function while satisfying constraints. Nonlinear Programming method is used as a tool for the optimization. Usually, cost and constraint function calculations are required in the engineering applications, but those calculations are extremely expensive. Especially, the function and sensitivity analyses cause a bottleneck in structural optimization which utilizes the Finite Element Method. Also, when the functions are quite noisy, the informations do not carry out proper role in the optimization process. An algorithm called "Second-order Approximation Method" has been proposed to overcome the difficulties recently. The cost and constraint functions are approximated by the second-order Taylor series expansion on a nominal points in the algorithm. An optimal design problem is defined with the approximated functions and the approximated problem is solved by a nonlinear programming numerical algorithm. The solution is included in a candidate point set which is evaluated for a new nominal point. Since the functions are approximated only by the function values, sensitivity informations are not needed. One-dimensional line search is unnecessary due to the fact that the nonlinear algorithm handles the approximated functions. In this research, the method is analyzed and the performance is evaluated. Several mathematical problems are created and some standard engineering problems are selected for the evaluation. Through numerical results, applicabilities of the algorithm to large scale and complex problems are presented.presented.

• 경영정보학연구
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• 제5권2호
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• pp.203-217
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• 2003

제약식 프로그래밍과 최적화 솔버는 공통된 문제를 풀기 위한 해법으로서 서로 다른 영역에서 발전되어왔다. 특히 제약식 확산법과 선형 계획법은 두 영역의 주된 기법으로서 조합 최적화 문제를 푸는데 함께 사용될 수 있는 통합가능한 보완 기법들이다. 지금까지 이를 통합하기 위한 시도는 주로 한 기법을 다른 기법의 모형 틀안에 포함시키는 것이었다. 본 논문은 둘의 통합을 통한 잇점들은 충분히 사용하기 위해서는 모형 역시 통합될 필요가 있음과 그 모형 통합의 틀을 보이고 그 틀 안에서 어떻게 두 기법의 솔버의 수준으로 통합되어 새로운 혼합 솔버를 구축할 수 있는지를 보인다.

• 한국소음진동공학회논문집
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• 제18권11호
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• pp.1118-1127
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• 2008

The position and size of holes in the partition of a double cavity are known to strongly affect the eigenfrequency of the longitudinal eigenmodes of the double cavity. To maximize or minimize the eigenfrequency of the hole-partitioned double cavity, two acoustical topology optimization problems are formulated and solved. While two sub-cavities are filled with air, a partition between them is assumed to consist of sub-partitions of variable acoustical properties. One design variable is assigned to each sub-partition, whose material properties are interpolated as those of an intermediate material between air and a rigid body. The penalty parameter of the used interpolation function is adjusted to obtain a distinct air and rigid body distribution at the converged stage in each acoustical topology optimization problem. A special attention is paid to the selection of initial values of design variables to obtain solutions as close to global optimum and symmetric as possible. To show numerical characteristics of these optimization problems, the formulated problems are first solved for the one-dimensional partition design domain and then for the two-dimensional partition design domain.

• Structural Engineering and Mechanics
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• 제7권5호
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• pp.485-502
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• 1999

Using the continuous Hopfield network model as the basis to solve the general crisp and fuzzy constrained optimization problem is presented and examined. The model lies in its transformation to a parallel algorithm which distributes the work of numerical optimization to several simultaneously computing processors. The method is applied to different structural engineering design problems that demonstrate this usefulness, satisfaction or potential. The computing algorithm has been given and discussed for a designer who can program it without difficulty.

• 대한산업공학회지
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• 제34권1호
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• pp.13-22
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• 2008

This paper gives reviews on current research status in telecommunication network design. Two problems are identified as major research issues. One is the WDM network design problem, where traffic grooming, virtual topology design and routing and wavelength assignment problems are considered. The other is the OSPF weight setting problem which was proposed as a practical method to implement traffic engineering capability in IP networks. After presenting surveys on those problems, we discuss potential challenging research issues in telecommunication network design.

• Management Science and Financial Engineering
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• 제3권1호
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• pp.75-88
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• 1997

Tabu search (TS) has been successfully applied for solving many complex combinatorial optimization problems in the areas of operations research and production control. However, TS is for single-objective problems in its present form. In this article, a TS-based heuristic is developed to determine Pareto-efficient solutions to a multi-objective combinatorial optimization problem. The developed algorithm is then applied to the discrete optimal design problem in statistics to demonstrate its usefulness.

• 대한수학회논문집
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• 제28권2호
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• pp.419-423
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• 2013

In this paper we present a robust duality theory for generalized convex programming problems under data uncertainty. Recently, Jeyakumar, Li and Lee [Nonlinear Analysis 75 (2012), no. 3, 1362-1373] established a robust duality theory for generalized convex programming problems in the face of data uncertainty. Furthermore, we extend results of Jeyakumar, Li and Lee for an uncertain multiobjective robust optimization problem.