• Journal of the Korea Society of Computer and Information
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• v.21 no.9
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• pp.91-100
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• 2016

In this research, emergency vehicle dispatching problems faced with in the wake of massive natural disasters are considered. Here, the emergency vehicle dispatching problems can be regarded as a single machine stochastic scheduling problems, where the processing times are independently and identically distributed random variables, are considered. The objective of minimizing the expected number of tardy jobs, with distinct job due dates that are independently and arbitrarily distributed random variables, is dealt with. For these problems, optimal static-list policies can be found by solving corresponding assignment problems. However, for the special cases where due dates are exponentially distributed random variables, using a proposed dynamic programming approach is found to be relatively faster than solving the corresponding assignment problems. This so-called Pivot Dynamic Programming approach exploits necessary optimality conditions derived for ordering the jobs partially.

• Korean Journal of Mathematics
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• v.23 no.2
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• pp.293-312
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• 2015

We deal with a boundary control problem for the vorticity minimization, in which the ow is governed by the time-dependent two dimensional incompressible Navier-Stokes equations. We derive a mathematical formulation and a process for an appropriate control along the portion of the boundary to minimize the vorticity motion due to the ow in the fluid domain. After showing the existence of an optimal solution, we derive the optimality system for which optimal solutions may be determined. The differentiability of the state solution in regard to the control parameter shall be conjunct with the necessary conditions for the optimal solutions.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.413-428
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• 2012

Every contingent claim is unable to be replicated in the incomplete markets. Shortfall risk is considered with some risk exposure. We show how the dynamic optimization problem with the capital constraint can be reduced to the problem to find an optimal modified claim $\tilde{\psi}H$ where$\tilde{\psi}H$ is a randomized test in the static problem. Convex and coherent risk measures defined in the Orlicz hearts spaces, $M^{\Phi}$, are used as risk measure. It can be shown that we have the same results as in [21, 22] even though convex and coherent risk measures defined in the Orlicz hearts spaces, $M^{\Phi}$, are used. In this paper, we use Fenchel duality Theorem in the literature to deduce necessary and sufficient optimality conditions for the static optimization problem using convex duality methods.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.299-306
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• 2006

Using a level set method and topological derivatives, a topological shape optimization method that is independent of an initial design is developed for linearly elastic structures. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. The 'Hamilton-Jacobi (H-J)' equation and computationally robust numerical technique of 'up-wind scheme' lead the initial implicit boundary to an optimal one according to the normal velocity field while minimizing the objective function of compliance and satisfying the constraint of allowable volume. Based on the asymptotic regularization concept, the topological derivative is considered as the limit of shape derivative as the radius of hole approaches to zero. The required velocity field to update the H -J equation is determined from the descent direction of Lagrangian derived from optimality conditions. It turns out that the initial holes is not required to get the optimal result since the developed method can create holes whenever and wherever necessary using indicators obtained from the topological derivatives. It is demonstrated that the proper choice of control parameters for nucleation is crucial for efficient optimization process.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.32 no.7
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• pp.76-82
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• 2004

A method of designing a state feedback gam achieving a specified insensitivity of the closed-loop trajectory by the singularly perturbed unified system using the operators is proposed. The order of system is reduced by the singular perturbation technique by ignoring the fast mode in it. The proposed method takes care of the actual trajectory variations over the range of the singular perturbation parameter. Necessary conditions for optimality are also derived. The previous study was done in the continuous time system The present paper extends the previous study to the discrete system and the ${\delta}-operating$ system that unifies the continuous and discrete systems. Advantages of the proposed method are shown in the numerical example.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.1256-1261
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• 2004

Nonlinear Response Optimization using Equivalent Static Loads (NROESL) method/algorithm is proposed to perform optimization of non-linear response structures. It is more expensive to carry out nonlinear response optimization than linear response optimization. The conventional method spends most of the total design time on nonlinear analysis. Thus, the NROESL algorithm makes the equivalent static load cases for each response and repeatedly performs linear response optimization and uses them as multiple loading conditions. The equivalent static loads are defined as the loads in the linear analysis, which generates the same response field as those in non-linear analysis. The algorithm is validated for the convergence and the optimality. The function satisfies the descent condition at each cycle and the NROESL algorithm converges. It is mathematically validated that the solution of the algorithm satisfies the Karush-Kuhn-Tucker necessary condition of the original nonlinear response optimization problem. The NROESL algorithm is applied to two structural problems. Conventional optimization with sensitivity analysis using the finite difference method is also applied to the same examples. The results of the optimizations are compared. The proposed method is very efficient and derives good solutions.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.1
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• pp.9-16
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• 2014

Using a level set method and topological derivatives, a topological shape optimization method that is independent of an initial design is developed for linearly elastic structures. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. The "Hamilton-Jacobi(H-J)" equation and computationally robust numerical technique of "up-wind scheme" lead the initial implicit boundary to an optimal one according to the normal velocity field while minimizing the objective function of compliance and satisfying the constraint of allowable volume. Based on the asymptotic regularization concept, the topological derivative is considered as the limit of shape derivative as the radius of hole approaches to zero. The required velocity field to update the H-J equation is determined from the descent direction of Lagrangian derived from optimality conditions. It turns out that the initial holes are not required to get the optimal result since the developed method can create holes whenever and wherever necessary using indicators obtained from the topological derivatives. It is demonstrated that the proper choice of control parameters for nucleation is crucial for efficient optimization process.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.559-567
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• 2012

A level set based topological shape optimization method for nonlinear structure considering hyper-elastic problems is developed. To relieve significant convergence difficulty in topology optimization of nonlinear structure due to inaccurate tangent stiffness which comes from material penalization of whole domain, explicit boundary for exact tangent stiffness is used by taking advantage of level set function for arbitrary boundary shape. For given arbitrary boundary which is represented by level set function, a Delaunay triangulation scheme is used for current structure discretization instead of using implicit fixed grid. The required velocity field in the actual domain to update the level set equation is determined from the descent direction of Lagrangian derived from optimality conditions. The velocity field outside the actual domain is determined through a velocity extension scheme based on the method suggested by Adalsteinsson and Sethian(1999). The topological derivatives are incorporated into the level set based framework to enable to create holes whenever and wherever necessary during the optimization.