• 충청수학회지
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• 제30권1호
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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.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 추계학술대회논문집A
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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.

• 대한수학회논문집
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• 제28권3호
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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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• 제6권1호
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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.

• 대한전기학회논문지:전기기기및에너지변환시스템부문B
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• 제53권5호
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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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• 제5권1호
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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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• 제어로봇시스템학회 2002년도 ICCAS
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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..

• 한국가스학회지
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• 제1권1호
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• pp.33-40
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• 1997

다극 및 다목적함수 최적화 문제를 해결하기 위해서 유전 알고리듬을 이용한 일반적인 최적화 도구인 APROGA II가 개발되었다. 우선 다극 최적화를 위해서는 다중선택집합탐색 알고리듬을 이용하였다. 두 번째로 다목적함수의 최적화를 위해서는 파레토 우성 토너먼트와 공유개념을 이용한 선택방법과 선택집합을 이용한 연속적인 세대교체법을 이용하여 새로운 알고리듬을 제안하였다. 이들 알고리듬을 이용하여 3개의 탐색엔진(APROGA 탐색엔진, 다극 탐색엔진 그리고 다목적함수 탐색엔진)을 가지고, 이진 및 이산 변수를 다룰 수 있는 APROGA II 시스템이 개발되었다. 그리고 여러 가지 검토함수들과 사례연구들을 적용시켜서 다극 탐색엔진의 성공적인 적용성을 확인하였다.

• 대한기계학회논문집A
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• 제26권6호
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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.

• 한국지능시스템학회논문지
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• 제17권7호
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• pp.869-874
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• 2007

다목적 함수의 최적화 문제(Multiobjective optimization problems)의 경우에는 하나의 최적해가 존재하는 것이 아니라 '파레토 최적해 집합(Pareto optimal set)'이라고 알려진 해들의 집합이 존재한다. 이러한 이상적 파레토 최적해 집합과 가까운 최적해를 찾기 위한 다양한 해탐색 능력은 진화 알고리즘의 성능을 결정한다. 본 논문에서는 게임 모델에 기반한 공진화 알고리즘(GCEA: Game model based Co-Evolutionary Algorithm)에서 해집단의 다양성을 유지하여, 다양한 비지배적 파레토 대안해(non-dominated alternatives)들을 찾기 위한 방법을 제안한다.