• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.3
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• pp.225-242
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• 2016

The phase-type representation is strongly connected with the positive realization in positive system. We attempt to transform phase-type representation into sparse mono-cyclic positive representation with as low order as possible. Because equivalent positive representations of a given phase-type distribution are non-unique, it is important to find a simple sparse positive representation with lower order that leads to more effective use in applications. A Hypo-Feedback-Coxian Block (HFCB) representation is a good candidate for a simple sparse representation. Our objective is to find an HFCB representation with possibly lower order, including all the eigenvalues of the original generator. We introduce an efficient nonlinear optimization method for computing an HFCB representation from a given phase-type representation. We discuss numerical problems encountered when finding efficiently a stable solution of the nonlinear constrained optimization problem. Numerical simulations are performed to show the effectiveness of the proposed algorithm.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.269-279
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• 2007

This paper describes a direct search method for a class of linearly constrained optimization problem. Through research we find it can be treated as an unconstrained optimization problem. And with the decrease of dimension of the variables need to be computed in the algorithms, the implementation of convergence to KKT points will be simplified to some extent. Convergence is shown under mild conditions which allow successive frames to be rotated, translated, and scaled relative to one another.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.05a
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• pp.1023-1026
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• 2007

Optimal damping layout of the constrained viscoelastic damping layer on beam is identified with temperatures by using a gradient-based numerical search algorithm. An optimal design problem is defined in order to determine the constrained damping layer configuration. A finite element formulation is introduced to model the constrained damping layer beam. The four-parameter fractional derivative model and the Arrhenius shift factor are used to describe dynamic characteristics of viscoelastic material with respect to frequency and temperature. Frequency-dependent complex-valued eigenvalue problems are solved by using a simple resubstitution algorithm in order to obtain the loss factor of each mode and responses of the structure. The results of the numerical example show that the proposed method can reduce frequency responses of beam at peaks only by reconfiguring the layout of constrained damping layer within a limited weight constraint.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.195-204
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• 2003

Network optimization is being increasingly important and fundamental issue in the fields such as engineering, computer science, operations research, transportation, telecommunication, decision support systems, manufacturing, and airline scheduling. Networks provide a useful way to modeling real world problems and are extensively used in practice. Many real world applications impose on more complex issues, such as, complex structure, complex constraints, and multiple objects to be handled simultaneously and make the problem intractable to the traditional approaches. Recent advances in evolutionary computation have made it possible to solve such practical network optimization problems. The invited talk introduces a thorough treatment of evolutionary approaches, i.e., hybrid genetic algorithms approach to network optimization problems, such as, fixed charge transportation problem, minimum cost and maximum flow problem, minimum spanning tree problem, multiple project scheduling problems, scheduling problem in FMS.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.544-556
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• 1991

The optimization of many engineering design problems requires a nonlinear programming algorithm that is robust and efficient. A general-purpose nonlinear optimization program IDOL (Interactive Design Optimization Library) is developed based on the Augmented Lagrange Mulitiplier (ALM) method. The ideas of selecting a good initial design point, using resonable initial values for Lagrange multipliers, constraints scaling, descent vector restarting, and dynamic stopping criterion are employed for computational enhancement to the ALM method. A descent vector is determined by using the Broydon-Fletcher-Goldfarb-Shanno (BFGS) method. For line search, the Incremental-Search method is first used to find bounds on the solution, then the bounds are reduced by the Golden Section method, and finally a cubic polynomial approximation technique is applied to locate the next design point. Seven typical test problems are solved to show IDOL efficient and robust.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.411-418
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• 2004

Using a level set method we develop a shape optimization method applied to energy flow problems in steady state. The boundaries are implicitly represented by the level set function obtainable from the 'Hamilton-Jacobi type' equation with the 'Up-wind scheme.' The developed method defines a Lagrangian function for the constrained optimization. It minimizes a generalized compliance, satisfying the constraint of allowable volume through the variations of implicit boundary. During the optimization, the boundary velocity to integrate the Hamilton-Jacobi equation is obtained from the optimality condition for the Lagrangian function. Compared with the established topology optimization method, the developed one has no numerical instability such as checkerboard problems and easy representation of topological shape variations.

• Journal of Korean Society for Quality Management
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• v.9 no.1
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• pp.12-21
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• 1981

• Journal of Electrical Engineering and Technology
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• v.13 no.3
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• pp.1099-1109
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• 2018

For practical consideration, economic dispatch (ED) problems in power system have non-smooth cost functions with equality and inequality constraints that makes the problems complex constrained nonlinear optimization problems. This paper proposes a new constraint handling method for equality and inequality constraints which is employed to solve ED problems, where the incremental rate is employed to enhance the modification process. In order to prove the applicability of the proposed method, the study cases are tested based on the classical particle swarm optimization (PSO) and differential evolution (DE) algorithm. The proposed method is evaluated for ED problems using six different test systems: 6-, 15-, 20-, 38-, 110- and 140-generators system. Simulation results show that it can always find the satisfactory solutions while satisfying the constraints.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.589-594
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• 1997

We have already presented the constraint satisfaction algorithm which could solve the losed loop problem in constraint network by using local constraint propagation, variable elimination and constraint modularization. With this algorithm, we have implemented a knowledge-based system (intelligent CAD) for supporting machine design interactively. In this paper, we present newer constraint satisfaction algorithm which can solve inequalities or under-constrained problems in constraint network, interactively and efficiently. This algorithm is a hybrid type of using both declarative description (constraint represention) and optimization algorithm (Simulated Annealing), simultaneously. The under-constrained problems are represented by constraint networks and satisfied completely with this algorithm. The usefulness of our algorithm will be illustrated by the application to a gear design.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.9
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• pp.116-123
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• 1997

We have already presented the constraint satisfaction algorithm which could solve the closed loop porblem in constraint network by using local constraint propagation, variable elimination and constraint modularization. With this algorithm, we have implemented a knowledge-based system (intelligent CAD) for supporting machine design interactively. In this paper, we present newer constraint satisfaction algorithm which can solve inequalities or under-constrained problems in constraint network, interactively and effi- ciently. This algorithm is a hybrid type of using both declarative description (constraint representation) and optimization algorithm (Simulated Annealing), simultaneously. The under-constrained problems are represented by constraint networks and satisfied completely with this algorithm. The usefulness of our algorithm will be illustrated by the application to a gear design.