• Korean Journal of Mathematics
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• v.16 no.1
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• pp.25-40
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• 2008

We are concerned with a free boundary problem for the 2D Stokes channel flows, which determines the profile of the wing for the channel, so that the given traction force is to be distributed along the wing of the channel. Using the domain embedding technique, the free boundary problem is transferred into the shape optimization problem through the compliant formulation by releasing the traction condition along the variable boundary. The justification of the formulation will be discussed.

• Computational Structural Engineering
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• v.9 no.3
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• pp.169-177
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• 1996

The focus of this study is on the problem of the design of structure of undetermined topology. This problem has been regarded as being the most challenging of structural optimization problems, because of the difficulty of allowing topology to change. Conventional approaches break down when element sizes approach to zero, due to stiffness matrix singularity. In this study, a novel nonlinear programming formulation of the topology problem is presented. Its main feature is the ability to account for topology variation through zero element sizes. Stiffness matrix singularity is avoided by embedding the equilibrium equations as equality constraints in the optimization problem. Although the formulation is general, two dimensional plane elasticity examples are presented. The design problem is to find minimum weight of a plane structure of fixed geometry but variable topology, subject to constraints on stress and displacement. Variables are thicknesses of finite elements, and are permitted to assume zero sizes. The examples demonstrate that the formulation is effective for finding at least a locally minimal weight.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.04a
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• pp.182-189
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• 1996

The focus of this study is on the problem of the design of structure of undetermined topology. This problem has been regarded as being the most challenging of structural optimization problems, because of the difficulty of allowing topology to change. Conventional approaches break down when element sizes approach to zero, due to stiffness matrix singularity. In this study, a novel nonlinear Programming formulation of the topology Problem is developed and examined. Its main feature is the ability to account for topology variation through zero element sizes. Stiffness matrix singularity is avoided by embedding the equilibrium equations as equality constraints in the optimization problem. Although the formulation is general, two dimensional plane elasticity examples are presented. The design problem is to find minimum weight of a plane structure of fixed geometry but variable topology, subject to constraints on stress and displacement. Variables are thicknesses of finite elements, and are permitted to assume zero sizes. The examples demonstrate that the formulation is effective for finding at least a locally minimal weight.

• IE interfaces
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• v.21 no.1
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• pp.1-7
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• 2008

In this paper we study the Minimum Edge Addition Problem(MEAP) to decrease the diameter of a graph. MEAP can be used for improving the serviceability of telecommunication networks with a minimum investment. MEAP is an NP-hard optimization problem. We present two mathematical programming models : One is a multi-commodity flow formulation and the other is a path partition formulation. We propose a branch-and-price algorithm to solve the path partition formulation to the optimality. We develop a polynomial time column generation sub-routine conserving the mathematical structure of a sub problem for the path partition formulation. Computational experiments show that the path partition formulation is better than the multi-commodity flow formulation. The branch-and-price algorithm can find the optimal solutions for the immediate size graphs within reasonable time.

• Computers and Concrete
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• v.19 no.2
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• pp.127-131
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• 2017

This paper presents a generalized formulation for optimizing the design of concrete beam reinforced with glass fiber reinforced polymer bar. The optimization method is formulated to find the design variables leading to the minimum weight of concrete beam with constraints imposed based on ACI code provisions. A simple genetic algorithm is utilized to solve the optimization task. The weights of concrete and glass fiber reinforced polymer bar are included in the formulation of the objective function. The ultimate limit states and the serviceability limit states are included in formulation of constraints. The results of illustrated example demonstrate the efficiency of the proposed method to reduce the weight of beam as well as to satisfy the above requirement. The application of the optimization based on the most economical design concept have led to significant savings in the amount of the component materials to be used in comparison to classical design solutions.

• Journal of Distribution Science
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• v.15 no.2
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• pp.15-20
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• 2017

Purpose - This paper aims to suggest a delivery constrained internet shopping optimization problem (DISOP) which must be solved for online recommendation system to provide a customized service considering cost and delivery conditions at the same time. Research design, data, and methodology - To solve a (DISOP), we propose a multi-objective formulation and a solution approach. By using a commercial optimization software (LINDO), a (DISOP) can be solved iteratively and a pareto optimal set can be calculated for real-sized problem. Results - We propose a new research problem which is different with internet shopping optimization problem since our problem considers not only the purchasing cost but also delivery conditions at the same time. Furthermore, we suggest a multi-objective mathematical formulation for our research problem and provide a solution approach to get a pareto optimal set by using numerical example. Conclusions - This paper proposes a multi-objective optimization problem to solve internet shopping optimization problem with delivery constraint and a solution approach to get a pareto optimal set. The results of research will contribute to develop a customized comparison and recommendation system to help more easy and smart online shopping service.

• Archives of Pharmacal Research
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• v.23 no.5
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• pp.507-512
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• 2000

This study set out to improve the physical and pharmaceutical characteristics of the present formulation using an appropriate experimental design. The work described here concerns the formulation of the dispersible tablet applying direct compression method containing roxithromycin in the form of coated granules. In this study $2^3$ factorial design was used as screening test model and Central Composite Design (CCC) associated with response surface methodology was used as optimization study model to develop and to optimize the proper formulation of roxithromycin dispersible tablet. The three independent variables investigated were functional excipients like binder (X1), disintegrant (X2) and lubricant (X3). The effects of these variables were investigated on the following responses: hardness (Y1), friability (Y2) and disintegration time (Y3) of tablet. Three replicates at the center levels of the each design were used to independently calculate the experimental error and to detect any curvature in the response surface. This enabled the best formulations to be selected objectively. The effect order of each term to all response variable was X3> X2> Xl> X1＊X2> X2＊X2> X2＊X3> X3＊X3> Xl＊X3> Xl＊Xl and model equations on each response variables were generated. Optimized compositions of formula were accordingly computed using those model equations and confirmed by following demonstration study. As a result, this study has demonstrated the efficiency and effectiveness of using a systematic formulation optimization process to develop the tablet formulation of roxithromycin dispersible tablet with limited experiment.

• Structural Engineering and Mechanics
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• v.52 no.1
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• pp.205-220
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• 2014

This paper is concerned with the modification of multidisciplinary feasible formulation for MDO problems using the integrated coupled approximate models. A drawback of conventional MDFs is the numerical difficulty in decomposing the design variables and deriving the coupled equations of state. To overcome such a drawback of conventional methods, the coupling in analysis and design is resolved by approximating the state variables in each discipline by the response surface method and by modifying the optimization formulation using the corresponding integrated coupled approximate models. The validity, reliability and effectiveness of the proposed method are illustrated and verified through two optimization problems, a mathematical MDF problem and the multidisciplinary optimum design of suspension unit of wheeled armored vehicle.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.10
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• pp.157-165
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• 1995

The new formulation of designing the two degree of freedom(TDF) robust controller is proposed using $H_{\infty}$optimization and model matching method. In this formulation the feedback controller and feedforward controller are designed in a single step using $H_{\infty}$optimization procedure. Roughly speaking, the feedback controller is designed to meet robust stability and disturbance rejection specifications, while the feedforward controller is used to improve the robust model matching properties of the closed loop system. The proposed formulation will be illustrated and evaluated on a seeker scan-loop. And the performances of TDF robust controller are compared with those of the $H_{\infty}$ controller designed using Loop Shaping Design Procedure proposed by McFarlane and Glover.lover.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.8
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• pp.779-785
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• 2009

This paper is concerned with a computational approach for topology optimization of geometrically nonlinear structures following specific load-displacement trajectories. In our previous works, attention was paid to stabilize topology optimization involving large displacement and a method called the element connectivity parameterization was developed. Here, we aimed to extend the element connectivity parameterization method to find an optimal geometrically nonlinear structure yielding a specific load-displacement trajectory. In contrast to designing a stiffest structure, the trajectory design problem requires special consideration in topology optimization formulation and solution procedure. Some numerical problems were considered to test the developed element connectivity parameterization based formulation.