• Proceedings of the KSME Conference
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• 2003.11a
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• pp.43-48
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• 2003

In this study the optimization of plate-fin type heat sink for the thermal stability is performed numerically. The optimum design variables are obtained when the temperature rise and the pressure drop are minimized simultaneously. The flow and thermal fields are predicted using the finite volume method and the optimization is carried out by using the sequential quadratic programming (SQP) method which is widely used in the constrained nonlinear optimization problem. The results show that when the temperature rise is less than 34.6 K, the optimal design variables are as follows; $B_{1}$ = 2.468 mm, $B_{2}$ = 1.365 mm, and t = 10.962 mm. The Pareto optimal solutions are also presented for the pressure drop and the temperature rise.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.16 no.3
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• pp.293-302
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• 2004

In this study the optimization of plate-fin type heat sink for the thermal stability is peformed numerically. The optimum design variables are obtained when the temperature rise and the pressure drop are minimized simultaneously. The flow and thermal fields are predicted using the finite volume method and the optimization is carried out by using the sequential quadratic programming (SQP) method which is widely used in the constrained non-linear optimization problem. The results show that when the temperature rise is less than 34.6K, the optimal design variables are as follows; B$_1$=2.468mm, B$_2$=1.365mm, and t=10.962mm. The Pareto optimal solutions are also presented for the pressure drop and the temperature rise.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.38 no.11
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• pp.861-869
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• 1989

The optimization problems, based on Pontryagin's Maximum Principle, for minimizing (damping) Xenon spatial oscillations in Load Following operations of Pressurized Water Reactor (PWR) is presented. The optimization model is formulated as an optimal tracking problem with quadratic objective functional. The oen-group diffusion equations and Xe-I dynamic equations are defined as equality constraints. By applying the maximum principle, the original problem is decomposed into a single time problem with no constraints. The resultant subproblems are optimized by using the conjugate Gradient Method. The computational results show that the Xenon spatial oscillation is minimized, and the reactor follows the load demand of the electrical power systems while maintaining the desired power distribution.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1303-1315
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• 2018

For principal component analysis (PCA) to efficiently analyze large scale matrices, it is crucial to find a few singular vectors in cheaper computational cost and under lower memory requirement. To compute those in a fast and robust way, we propose a new stochastic method. Especially, we adopt the stochastic variance reduced gradient (SVRG) method [11] to avoid asymptotically slow convergence in stochastic gradient descent methods. For that purpose, we reformulate the PCA problem as a unconstrained optimization problem using a quadratic penalty. In general, increasing the penalty parameter to infinity is needed for the equivalence of the two problems. However, in this case, exact penalization is guaranteed by applying the analysis in [24]. We establish the convergence rate of the proposed method to a stationary point and numerical experiments illustrate the validity and efficiency of the proposed method.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.1037-1067
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• 2017

Motzkin and Straus established a close connection between the maximum clique problem and a solution (namely graph-Lagrangian) to the maximum value of a class of homogeneous quadratic multilinear functions over the standard simplex of the Euclidean space in 1965. This connection and its extensions were successfully employed in optimization to provide heuristics for the maximum clique problem in graphs. It is useful in practice if similar results hold for hypergraphs. In this paper, we develop a homogeneous multilinear function based on the structure of hypergraphs and their complement hypergraphs. Its maximum value generalizes the graph-Lagrangian. Specifically, we establish a connection between the clique number and the generalized graph-Lagrangian of 3-uniform graphs, which supports the conjecture posed in this paper.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.12
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• pp.116-123
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• 2001

An automated injection molding design methodology has been developed to optimize multiple quality attributes, which are usually in conflict with each other, in injection molded parts. For the optimization, commercial CAE simulation tools and optimization techniques are integrated into the methodology. To decal with the multiple objective problem the relative closeness computed in TOPSIS(Technique for Order Preference by Similarity to Ideal Solution) is used as a performance measurement index for optimization multiple part defects. To attain robustness against process variation, Taguchi's quadratic loss function is introduced in the TOPSIS. Also, the modified complex method is used as an optimization tool to optimize objective function. The verification of the developed design methodology was carried out on simulation software with an actual model. Applied to production this methodology will be useful to companies in reducing their product development time and enhancing their product quality.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.6
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• pp.1048-1057
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• 2008

This paper represents a design method for PID or low-order controllers cascaded with a linear plant in the unit feedback system where it is required to meet the given time response specifications such as overshoot and settling time. This problem is difficult to solve because the zeros of the controller appear in the numerator of the overall system and thus those zeros may make the time response design difficult. In this paper, we propose a new approach based on the partial model matching and the so called K-polynomial. The partial matching problem is formulated to an optimization problem in which a quadratic function of coefficient errors between a target model and the resulting closed loop system is minimized. For the sake of satisfying the closed loop stability, a set of quadratic constraints associated with the cost function is introduced. As a result, the controller designed meets both time response requirements and the closed loop stability, if any. It is shown through several examples that the present method can be easily applied to these problems.

• Journal of Electrical Engineering and Technology
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• v.3 no.1
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• pp.52-59
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• 2008

This paper describes the secant method for solving the economic dispatch (ED) problem with generator constraints and transmission losses. The ED problem is an important optimization problem in the economic operation of a power system. The proposed algorithm involves selection of minimum and maximum incremental costs (lambda values) and then the evaluation of optimal lambda at required power demand is done by secant method. The proposed algorithm has been tested on a power system having 6, 15, and 40 generating units. Studies have been made on the proposed method to solve the ED problem by taking 120 and 200 units with generator constraints. Simulation results of the proposed approach were compared in terms of solution quality, convergence characteristics, and computation efficiency with conventional methods such as lambda iterative method, heuristic methods such as genetic algorithm, and meta-heuristic methods like particle swarm optimization. It is observed from different case studies that the proposed method provides qualitative solutions with less computational time compared to various methods available in the literature.

• Transactions of the Korean Society of Automotive Engineers
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• v.19 no.1
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• pp.66-72
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• 2011

Injection pressure is an important factor in filling procedure for injection molded parts. In addition, weldlines should be avoided to successfully produce injection molded parts. In this study, we optimally obtained injection molding process parameters that minimize injection pressure. Then, we determined the thickness of the part to avoid weldlines. To solve the optimization problem proposed, we employed MAPS-3D (Mold Analysis and Plastics Solution-3 Dimension), a commercial CAE tool for injection molding analysis, and PIAnO (Process Integration, Automation, and Optimization) as a commercial PIDO (Process Integration and Design Optimization) tool. We integrated MAPS-3D into PIAnO, automated the analysis and design procedure, and performed optimization by employing PQRSM (Progressive Quadratic Response Surface Method) equipped in PIAnO. We successfully obtained optimization results, which demonstrates the effectiveness of our design method.

• Journal of Mechanical Science and Technology
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• v.18 no.9
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• pp.1590-1603
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• 2004

In this study the optimization of plate-fin type heat sink with vortex generator for the thermal stability is performed numerically. The optimum solutions in the heat sink are obtained when the temperature rise and the pressure drop are minimized simultaneously. Thermal performance of heat sink is influenced by the heat sink shape such as the base-part fin width, lower-part fin width, and basement thickness. To acquire the optimal design variables automatically, CFD and mathematical optimization are integrated. The flow and thermal fields are predicted using the finite volume method. The optimization is carried out by means of the sequential quadratic programming (SQP) method which is widely used for the constrained nonlinear optimization problem. The results show that the optimal design variables are as follows; B$_1$=2.584 mm, B$_2$=1.741 mm, and t=7.914 mm when the temperature rise is less than 40 K. Comparing with the initial design, the temperature rise is reduced by 4.2 K, while the pressure drop is increased by 9.43 Pa. The relationship between the pressure drop and the temperature rise is also presented to select the heat sink shape for the designers.