• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.31-40
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• 2017

In this paper, we consider a nonsmooth multiobjective robust optimization problem with more than two locally Lipschitz objective functions and locally Lipschitz constraint functions in the face of data uncertainty. We prove a nonsmooth sufficient optimality theorem for a weakly robust efficient solution of the problem. We formulate a Wolfe type dual problem for the problem, and establish duality theorems which hold between the problem and its Wolfe type dual problem.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.699-704
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• 2000

The present paper deals with a multiobjective optimization method based on the co-evolutionary genetic strategy. The co-evolutionary strategy carries out the multiobjective optimization in such way that it optimizes individual objective function as compared with each generation's value while there are more than two genetic evolutions at the same time. In this study, the designs that are out of the given constraint map compared with other objective function value are excepted by the penalty. The proposed multiobjective genetic algorithms are distinguished from other optimization methods because it seeks for the optimized value through the simultaneous search without the help of the single-objective values which have to be obtained in advance of the multiobjective designs. The proposed strategy easily applied to well-developed genetic algorithms since it doesn't need any further formulation for the multiobjective optimization. The paper describes the co-evolutionary strategy and compares design results on the simple structural optimization problem.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.597-602
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• 2013

In this paper, Mond-Weir type duality results for a uncertain multiobjective robust optimization problem are given under generalized invexity assumptions. Also, weak vector saddle-point theorems are obtained under convexity assumptions.

• Structural Engineering and Mechanics
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• v.6 no.1
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• pp.17-30
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• 1998

The method of pairwise comparison inherently contains information of ambiguity, fuzziness and conflict in design goals for a multiobjective structural design. This paper applies the principle of paired comparison so that the vaguely formulated problem can be modified and a set of numerically acceptable weight would reflect the relatively important degree of multiple objectives. This paper also presents a fuzzy global criterion method ($FGCM_{\lambda}$) included fuzzy constraints that coupled with the objective weighting rank obtained from the modified pairwise comparisons for fuzzy multiobjective optimization problems. Descriptions in sequence of this combined method and problem solving experiences are given in the current article. Multiobjective design examples of truss and mechanical spring structures illustrate this optimization process containing the revising judgement techniques.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.53 no.5
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• pp.325-331
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• 2004

The multiobjective optimization (MO) problem usually includes the conflicting objectives and the use of conventional optimization algorithms for MO problem does not so good approach to obtain an effective optimal solution. In this paper, genetic algorithm (GA) as an effective method is used to solve such MO problem of brushless DC motor (BLDCM). 3D equivalent magnetic circuit network (EMCN) method which enables us to reduce the computational burden is also used to consider the 3D structure of BLDCM. In order to effectively obtain a set of Pareto optimal solutions in MO problem, ranking method proposed by Fonseca is applied. The objective functions are decrease of cogging torque and increase of torque respectively. The airgap length, teeth width and magnetization angle of PM are selected for the design variables. The experimental results are also shown to confirm the validity of the optimization results.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.110.4-110
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• 2002

In practical control area, there are many examples with multiple objectives which may conflict or compete with each other like overhead crane control, automatic train operation, and refuse incinerator plant control, etc. These kinds of control problems are called multiobjective control problems, where it is difficult to provide the desired performance with control strategies based on single-objective optimization. Because the conventional control theories usually treat the control problem as the single objective optimization problem , the methods are not adequate to treat the multiobjective control problems. Particularly, in case of large scale systems or ill-defined systems, the multiple obj..

• Journal of the Korean Institute of Gas
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• v.1 no.1
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• pp.33-40
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• 1997

An optimization system, APROGA II using genetic algorithm, was developed to solve multi-modal and multiobjective problems. To begin with, Multi-Niche Crowding(MNC) algorithm was used for multi-modal optimization problem. Secondly, a new algorithm was suggested for multiobjective optimization problem. Pareto dominance tournaments and Sharing on the non-dominated frontier was applied to it to obtain multiple objectives. APROGA II uses these two algorithms and the system has three search engines(previous APROGA search engine, multi-modal search engine and multiobjective search engine). Besides, this system can handle binary and discrete variables. And the validity of APROGA II was proved by solving several test functions and case study problems successfully.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.6
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• pp.987-992
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• 2002

In an attempt to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands the user to have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Pareto-optimal points, instead of a single point. In this paper, pareto-based Continuous Evolutionary Algorithms for Multiobjective Optimization problems having continuous search space are introduced. This algorithm is based on Continuous Evolutionary Algorithms to solve single objective optimization problems with a continuous function and continuous search space efficiently. For multiobjective optimization, a progressive reproduction operator and a niche-formation method fur fitness sharing and a storing process for elitism are implemented in the algorithm. The operator and the niche formulation allow the solution set to be distributed widely over the Pareto-optimal tradeoff surface. Finally, the validity of this method has been demonstrated through a numerical example.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.7
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• pp.869-874
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• 2007

In searching for solutions to multiobjective optimization problem, we find that there is no single optimal solution but rather a set of solutions known as 'Pareto optimal set'. To find approximation of ideal pareto optimal set, search capability of diverse individuals at population space can determine the performance of evolutionary algorithms. This paper propose the method to maintain population diversify and to find non-dominated alternatives in Game model based Co-Evolutionary Algorithm.