• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.5
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• pp.748-754
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• 2008

The general capacitor placement problem is a combinatorial optimization problem having an objective function composed of power losses and capacitor installation costs subject to bus voltage constraints. In this paper, a global optimization technique, which employing the chaos search algorithm, is applied to solve optimal capacitor placement problem with reducing computational effort and enhancing global optimality of the solution. Chaos method in optimization problem searches the global optimal solution on the regularity of chaotic motions and easily escapes from local or near optimal solution than stochastic optimization algorithms. The chaos optimization method is tested on 9 buses and 69 buses system to illustrate the effectiveness of the proposed method.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.893-906
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• 2023

In this article, we are devoted to study the problem of the existence, uniqueness and positivity of the global solutions of the 3 × 3 reaction-diffusion systems with the total mass of the components with time. We also suppose that the nonlinear reaction term has a critical growth with respect to the gradient. The technique that we used to prove the global existence is the method of the compact semigroup.

• Korean Journal of Optics and Photonics
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• v.20 no.6
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• pp.319-327
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• 2009

We introduce a new design technique by treating a two-group zoom lens system with a wide angle of view. First, the concept of the global optimization is introduced in the initial design stage, and from this, the global design technique is completed by analyzing and summarizing large quantities of modern design data. That is, we define the global structure function to achieve a new conceptual design technique for global optimization. And the function is put in a simple form by referring lots of patent data, manipulated with other algebraic equations, and solved finally such that we obtain the global solution region. The global solution region corresponds to the global optimization and suggests insightful systematized directions for the design of two-group zoom lens systems. These directions are attractive compared to global optimization.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.81-87
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• 1998

In this paper, a global acoustic design sensitivity analysis (DSA) of field point pressure with respect to structural sizing design variables is developed. Firstly acoustic sensitivity is formulated and implemented numerically. And it is combined with continuum structural sensitivity to obtain the global acoustic, design sensitivity. For this procedure, GASA (global acoustic design sensitivity analyzer) has been developed. A half scale of automobile cavity model is considered in this paper. In order to confirm accuracy of the results of global acoustic DSA obtained by GASA, it is compared with the result of central finite difference method. In order to reduce computation time, Rayleigh approximated solution is evaluated and compared with the solution which used every nodal velocities. Also the acoustic optimization procedure is performed using design sensitivities. From these numerical studies, it can be shown that global acoustic DSA is a useful tool to improve acoustic problems.

• Korean Journal of Computational Design and Engineering
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• v.15 no.1
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• pp.24-32
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• 2010

This paper introduces a B-spline based branch & bound algorithm for global optimization. The branch & bound is a well-known algorithm paradigm for global optimization, of which key components are the subdivision scheme and the bound calculation scheme. For this, we consider the B-spline hypervolume to approximate an objective function defined in a design space. This model enables us to subdivide the design space, and to compute the upper & lower bound of each subspace where the bound calculation is based on the LHS sampling points. We also describe a search tree to represent the searching process for optimal solution, and explain iteration steps and some conditions necessary to carry out the algorithm. Finally, the performance of the proposed algorithm is examined on some test problems which would cover most difficulties faced in global optimization area. It shows that the proposed algorithm is complete algorithm not using heuristics, provides an approximate global solution within prescribed tolerances, and has the good possibility for large scale NP-hard optimization.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1161-1178
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• 2018

In this paper, we consider the Cauchy problem for a class of nonlinear sixth-order wave equation. The global existence and the finite time blow-up for the problem are proved by the potential well method at both low and critical initial energy levels. Furthermore, we present some sufficient conditions on initial data such that the weak solution exists globally at supercritical initial energy level by introducing a new stable set.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.223-240
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• 2011

In this paper, the problem on periodic solutions of the bidirectional associative memory neural networks with both periodic coefficients and periodic time-varying delays is discussed. By using degree theory, inequality technique and Lyapunov functional, we establish the existence, uniqueness, and global asymptotic stability of a periodic solution. The obtained results of stability are less restrictive than previously known criteria, and the hypotheses for the boundedness and monotonicity on the activation functions are removed.

• Communications of the Korean Mathematical Society
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• v.29 no.4
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• pp.505-518
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• 2014

Considered here is the first initial boundary value problem for the two-dimensional g-Navier-Stokes equations in bounded domains. We first study the long-time behavior of strong solutions to the problem in term of the existence of a global attractor and global stability of a unique stationary solution. Then we study the long-time finite dimensional approximation of the strong solutions.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.579-600
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• 2017

In this paper we consider a semilinear pseudoparabolic equation with polynomial nonlinearity and infinite delay. We first prove the existence and uniqueness of weak solutions by using the Galerkin method. Then, we prove the existence of a compact global attractor for the continuous semigroup associated to the equation. The existence and exponential stability of weak stationary solutions are also investigated.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.623-632
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• 1997

In this paper, the nonexistence of the global solutions of semilinear wave equations with damping terms in the boundary conditions is investigated.