• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.6
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• pp.491-496
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• 2002

Multi-objective Optimization Problems(MOPs) are occur more frequently than generally thought when we try to solve engineering problems. In the real world, the majority cases of optimization problems are the problems composed of several competitive objective functions. In this paper, we introduce the definition of MOPs and several approaches to solve these problems. In the introduction, established optimization algorithms based on the concept of Pareto optimal solution are introduced. And contrary these algorithms, we introduce theoretical backgrounds of Nash Genetic Algorithm(Nash GA) and Evolutionary Stable Strategy(ESS), which is the basis of Co-evolutionary algorithm proposed in this paper. In the next chapter, we introduce the definitions of MOPs and Pareto optimal solution. And the architecture of Nash GA and Co-evolutionary algorithm for solving MOPs are following. Finally from the experimental results we confirm that two algorithms based on Evolutionary Game Theory(EGT) which are Nash GA and Co-evolutionary algorithm can search optimal solutions of MOPs.

• Journal of Electrical Engineering and Technology
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• v.5 no.1
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• pp.70-78
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• 2010

Elitist nondominated sorting genetic algorithm (NSGA-II) is adopted and improved for multiobjective optimal reactive power flow (ORPF) problem. Multiobjective ORPF, formulated as a multiobjective mixed integer nonlinear optimization problem, minimizes real power loss and improves voltage profile of power grid by determining reactive power control variables. NSGA-II-based ORPF is tested on standard IEEE 30-bus test system and compared with four other state-of-the-art multiobjective evolutionary algorithms (MOEAs). Pareto front and outer solutions achieved by the five MOEAs are analyzed and compared. NSGA-II obtains the best control strategy for ORPF, but it suffers from the lower convergence speed at the early stage of the optimization. Several problem-specific local search strategies (LSSs) are incorporated into NSGA-II to promote algorithm's exploiting capability and then to speed up its convergence. This enhanced version of NSGA-II (ENSGA) is examined on IEEE 30 system. Experimental results show that the use of LSSs clearly improved the performance of NSGA-II. ENSGA shows the best search efficiency and is proved to be one of the efficient potential candidates in solving reactive power optimization in the real-time operation systems.

• The Transactions of the Korean Institute of Power Electronics
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• v.27 no.6
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• pp.507-514
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• 2022

This study proposes an optimal design process for a high-frequency transformer that has a large leakage inductance for dual-active-bridge converters. Notably, conventional design processes have large errors in designing leakage transformers because mathematically modeling the leakage inductance of such transformers is difficult. In this work, the geometric parameters of a shell-type transformer are identified, and finite element analysis(FEA) simulation is performed to determine the magnetization inductance, leakage inductance, and copper loss of various shapes of shell-type transformers. Regression models for magnetization and leakage inductances and copper loss are established using the simulation results and the machine learning technique. In addition, to improve the regression models' performance, the regression models are tuned by adding featured parameters that consider the physical characteristics of the transformer. With the regression models, optimal high-frequency transformer designs and the Pareto front (in terms of volume and loss) are determined using NSGA-II. In the Pareto front, a desirable optimal design is selected and verified by FEA simulation and experimentation. The simulated and measured leakage inductances of the selected design match well, and this result shows the validity of the proposed design process.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.4B
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• pp.346-353
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• 2011

Routing schemes that service applications with various delay times, maintaining the long network life time are required in wireless sensor & actor networks. However, it is known that network lifetime and hop count of trees used in routing methods have the tradeoff between them. In this paper, we propose a Pareto Ant Colony Optimization algorithm to find the Pareto tree set such that it optimizes these both tradeoff objectives. As it enables applications which have different delay times to select appropriate routing trees, not only satisfies the requirements of various multiple applications but also guarantees long network lifetime. We show that the Pareto tree set found by proposed algorithm consists of trees that are closer to the Pareto optimal points in terms of hop count and network lifetime than minimum spanning tree which is a representative routing tree.

• 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.

• Management Science and Financial Engineering
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• v.13 no.2
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• pp.1-27
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• 2007

This paper presents a fuzzy-goal programming(FGP) approach for Bi-Level Linear Multiple Objective Decision Making(BLL-MODM) problem in a large hierarchical decision making and planning organization. The proposed approach combines the attractive features of both fuzzy set theory and goal programming(GP) for MODM problem. The GP problem has been developed by fixing the weights and aspiration levels for generating pareto-optimal(satisfactory) solution at each level for BLL-MODM problem. The higher level decision maker(HLDM) provides the preferred values of decision vector under his control and bounds of his objective function to direct the lower level decision maker(LLDM) to search for his solution in the right direction. Illustrative numerical example is provided to demonstrate the proposed approach.

• The KSFM Journal of Fluid Machinery
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• v.14 no.5
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• pp.31-38
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• 2011

Optimization using a hybrid multi-objective evolutionary algorithm coupled with response surface approximation has been performed to improve the performance of a transonic axial compressor with circumferential casing grooves. In order to optimize the operating stability and peak adiabatic efficiency of the compressor with circumferential casing grooves, tip clearance, angle distribution at blade tip and the depth of the circumferential casing grooves are selected as design variables. Three-dimensional Reynolds-averaged Navier-Stokes equations with the shear stress transport turbulence model are discretized by finite volume approximations. The trade-off between two objectives with the interaction of blade and casing treatment is determined and discussed with respect to the representative clusters in the Pareto-optimal solutions compared to the axial compressor without the casing treatment.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.24 no.2
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• pp.192-197
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• 2015

In many fields, the importance of reducing weight is increasing. A product should be designed such that it is profitable, by lowering costs and exhibiting better performance than other similar products. In this study, the mass and deflection of steel structures have to be reduced as objective functions under constraint conditions. To reduce computational analysis time, central composite design(CCD) and D-Optimal are used in design of experiments(DOE). The accuracy of approximate models is evaluated using the $R^2$ value. In this study, the objective functions are multiple, so the non-dominant sorting genetic algorithm(NSGA-II), which is highly efficient, is used for such a problem. In order to verify the validity of Pareto solutions, CAE results and Pareto solutions are compared.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.32 no.1
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• pp.72-78
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• 2009

This paper considers a multiagent scheduling problem under public information where a machine is shared by multiple agents. Each agent has a local objective among the minimization of total completion time and the minimization of maximum. In this problem, it is assumed that scheduling information is public. Therefore an agent can access to complete information of other agents and pursue efficient schedules in a centralized manner. We propose an enumeration scheme to find Pareto optimal schedules and a multiobjective genetic algorithm as a heuristic approach. Experimental results indicate that the proposed genetic algorithm yields close-to Pareto optimal solution under a variety of experimental conditions.

• Journal of the Korea Society for Simulation
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• v.6 no.1
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• pp.71-84
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• 1997

For many optimization problems where some of the system components are stochastic, the objective functions cannot be represented analytically. Therefore, modeling by computer simulation is one of the most effective means of studying such complex systems. Many, if not most, simulation optimization problems have multiple aspects. Historically, multiple aspects have been combined ad hoc to form a scalar objective function, usually through a linear combination (weighted sum) of the multiple attributes, or by turning objectives into constraints. The genetic algorithm (GA), however, is readily modified to deal with multiple aspects. In this paper we propose a MAGA (Multiple Aspects-based Genetic Algorithm) as an algorithm for finding the Pareto optimal set. We demonstrate its ability to find and maintain a diverse "Pareto optimal population" on two problems.