• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1157-1165
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• 2011

The Karush-Kuhn-Tucker (KKT) necessary optimality conditions for nonlinear differentiable programming problems are also sufficient under suitable convexity assumptions. The KKT conditions in multiobjective programming problems with interval-valued objective and constraint functions are derived in this paper. The main contribution of this paper is to obtain the Pareto optimal solutions by resorting to the sufficient optimality condition.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.2
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• pp.268-275
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• 2003

Generally, structural optimization is carried out based on external static loads. All forces have dynamic characteristics in the real world. Mathematical optimization with dynamic loads is extremely difficult in a large-scale problem due to the behaviors in the time domain. The dynamic loads are often transformed into static loads by dynamic factors, design codes, and etc. Therefore, the optimization results can give inaccurate solutions. Recently, a systematic transformation has been proposed as an engineering algorithm. Equivalent static loads are made to generate the same displacement field as the one from dynamic loads at each time step of dynamic analysis. Thus, many load cases are used as the multiple leading conditions which are not costly to include in modern structural optimization. In this research, it is mathematically proved that the solution of the algorithm satisfies the Karush-Kuhn-Tucker necessary condition. At first, the solution of the new algorithm is mathematically obtained. Using the termination criteria, it is proved that the solution satisfies the Karush-Kuhn-Tucker necessary condition of the original dynamic response optimization problem. The application of the algorithm is discussed.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.46 no.2
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• pp.109-115
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• 2023

This paper studied the problem of determining the optimal inventory level to meet the customer service target level in a situation where the customer demand for each branch of a nationwide retailer is uncertain. To this end, ISR (In-Stock Ratio) was defined as a key management indicator (KPI) that can be used from the perspective of a nationwide retailer such as Samsung, LG, or Apple that sells goods at branches nationwide. An optimization model was established to allow the retailer to minimize the total amount of inventory held at each branch while meeting the customer service target level defined as the average ISR. This paper proves that there is always an optimal solution in the model and expresses the optimal solution in a generalized form using the Karush-Kuhn-Tucker condition regardless of the shape of the probability distribution of customer demand. In addition, this paper studied the case where customer demand follows a specific probability distribution such as a normal distribution, and an expression representing the optimal inventory level for this case was derived.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.2246-2251
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• 2003

This paper proposes shape design of frame structures for vibration suppression and weight reduction. The $H_{\infty}$ norm of the transfer function from disturbance sources to the output points where vibration should be suppressed, is adopted as the performance index to represent the magnitude of vibration transfer. The design parameters are the node positions of the frame structure, on which constraints are imposed so that the structure achieves given tasks. For computation of Pareto optimal solutions to the two-objective design problem, a number of linear combinations of the $H_{\infty}$ norm and the total weight of the structure are considered and minimized. For minimization of the scalared objective function, a Lagrange function is defined by the objective function and the imposed constraints on the design parameters. The solution for which the Lagrange function satisfies the Karush-Kuhn-Tucker condition, is searched by the sequential quadratic programming (SQP) method. Numerical examples are presented to demonstrate the effectiveness of the proposed design method.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.19 no.5
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• pp.27-37
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• 2020

Structural optimization problems with discrete design variables require more function calculations (or finite element analyses) than those in the continuous design space. In this study, a method to find an optimal solution in the discrete design of the truss structure is presented, reducing the number of function calculations. Because a continuous optimal solution is the Karush-Kuhn-Tucker point that satisfies the optimality condition, it is assumed that the discrete optimal solution is around the continuous optimum. Then, response values such as weight, displacement, and stress are predicted using approximate models-referred to as hybrid metamodels-within specified design ranges. The discrete design method using the hybrid metamodels is used as a post-process of the continuous optimization process. Standard truss design problems of 10-bar, 25-bar, 15-bar, and 52-bar are solved to show the usefulness of this method. The results are compared with those of existing methods.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.2
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• pp.673-694
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• 2021

In this paper, we intend to study the energy efficiency (EE) optimization for a simultaneous wireless information and power transfer (SWIPT)-based distributed antenna system (DAS). Firstly, a DAS-SWIPT model is formulated, whose goal is to maximize the EE of the system. Next, we propose an optimal resource allocation method by means of the Karush-Kuhn-Tucker condition as well as an ergodic method. Considering the complexity of the ergodic method, a suboptimal scheme with lower complexity is proposed by using an antenna selection scheme. Numerical results illustrate that our suboptimal method is able to achieve satisfactory performance of EE similar to an optimal one while reducing the calculation complexity.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.1
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• pp.48-54
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• 2004

Generally, structural optimization is carried out based on external static loads. All forces have dynamic characteristics in the real world. Mathematical optimization with dynamic loads is extremely difficult in a large-scale problem due to the behaviors in the time domain. In practical applications, it is customary to transform the dynamic loads into static loads by dynamic factors, design codes, and etc. But the optimization results with the unreasonably transformed loads cannot give us good solutions. Recently, a systematic transformation has been proposed as an engineering algorithm. Equivalent static loads are made to generate the same displacement field as the one from dynamic loads at each time step of dynamic analysis. Thus, many load cases are used as the multiple loading conditions which are not costly to include in modem structural optimization. In this research, the proposed algorithm is applied to the optimization of flexible multibody dynamic systems. The equivalent static load is derived from the equations of motion of a flexible multibody dynamic system. A few examples that have been solved before are solved to be compared with the results from the proposed algorithm.

• Journal of Institute of Control, Robotics and Systems
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• v.21 no.7
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• pp.595-601
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• 2015

This paper presents an unified chassis control with electronic stability control (ESC) and active front steering (AFS) under lateral force constraint on AFS. When generating the control yaw moment, an optimization problem is formulated in order to determine the tire forces, generated by ESC and AFS. With Karush-Kuhn-Tucker optimality condition, the optimum tire forces can be algebraically calculated. On low friction road, the lateral force in front wheels is easily saturation. When saturated, AFS cannot generate the required control yaw moment. To cope with this problem, new constraint on the lateral tire force is added into the original optimization problem. To check the effectiveness of the propose method, simulation is performed on the vehicle simulation package, CarSim.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.2
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• pp.109-117
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• 2004

Optimization has been successfully applied to systems with a single discipline. As many disciplines are involved in coupled fashion, MDO (multidisciplinary design optimization) technology has been developed. MDO algorithms are trying to solve the coupled aspects generated from interdisciplinary relationship. In a general MDO algorithms, a large design problem is decomposed into small ones which can be easily solved. Although various methods have been proposed for MDO, the research is still in the early stage. This research proposes a new MDO method which is named as MDOIS (Multidisciplinary Design Optimization Based on Independent Subspaces). Many real engineering problems consist of physically separate components and they can be independently designed. The inter-relationship occurs through coupled physics. MDOIS is developed for such problems. In MDOIS, a large system is decomposed into small subsystems. The coupled aspects are solved via system analysis which solves the coupled physics. The algorithm is mathematically validated by showing that the solution satisfies the Karush-Kuhn-Tucker condition.