• 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.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.379-390
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• 2005

In this paper, optimality conditions for multiobjective programming problems having F-convex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function. Furthermore, an F-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of a saddle point are given.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.837-847
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• 2005

We consider multiobjective fractional programming problems with generalized invexity. An equivalent multiobjective programming problem is formulated by using a modification of the objective function due to Antczak. We give relations between a multiobjective fractional programming problem and an equivalent multiobjective fractional problem which has a modified objective function. And we present modified vector saddle point theorems.

• Journal of Korean Institute of Industrial Engineers
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• v.31 no.3
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• pp.180-193
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• 2005

This paper deals with a multiobjective process planning problem of flexible assembly systems(FASs). The FAS planning problem addressed in this paper is an integrated one of the assignment of assembly tasks to stations and the determination of assembly routing, while satisfying precedence relations among the tasks and flexibility capacity for each station. In this research, we consider two objectives: minimizing transfer time of the products among stations and absolute deviation of workstation workload(ADWW). We place emphasis on finding a set of diverse near Pareto or true Pareto optimal solutions. To achieve this, we present a new multiobjective coevolutionary algorithm for the integrated problem here, named a multiobjective symbiotic evolutionary algorithm(MOSEA). The structure of the algorithm and the strategies of evolution are devised in this paper to enhance the search ability. Extensive computational experiments are carried out to demonstrate the performance of the proposed algorithm. The experimental results show that the proposed algorithm is a promising method for the integrated and multiobjective problem.

• Journal of the Korean Mathematical Society
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• v.40 no.5
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• pp.883-899
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• 2003

In this paper, we will introduce the general concepts of generalized multiobjective game, generalized weight Nash equilibria and generalized Pareto equilibria. Next using the fixed point theorems due to Idzik [5] and Kim-Tan [6] , we shall prove the existence theorems of generalized weight Nash equilibria under general hypotheses. And as applications of generalized weight Nash equilibria, we shall prove the existence of generalized Pareto equilibria in non-compact generalized multiobjective game.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.506-511
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• 1998

In this paper we consider multiobjective linear programming problems with coefficients of the objective functions specified by possibility distributions. Possibly and necessarily efficient solution sets are defined as funny solution sets whose membership grades represent possibility and necessity degrees to which a feasible solution is efficient. Considering efficiency condition and its dual condition in ordinary multiobjective linear programming problem, we propose efficiency test methods based on an extreme ray generation method. Since the proposed methods can be put in the part of a bi-section method, we can develop calculation and methods of the degree of possible and necessary efficiency for feasible solutions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.2
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• pp.101-108
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• 2009

In this paper, we introduce generalized multiobjective fractional programming problem with two kinds of inequality constraints. Kuhn-Tucker sufficient and necessary optimality conditions are given. We formulate a generalized multiobjective dual problem and establish weak and strong duality theorems for an efficient solution under generalized convexity conditions.

• Journal of Korean Institute of Industrial Engineers
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• v.23 no.2
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• pp.307-321
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• 1997

In this paper, we consider the expert's ambiguity and the decision maker's fuzzy goals which are incorporated into multiobjective nonlinear programming problems in order to find a compensatory solution. The proposed method can be applied to all cases of multiobjective problems with fuzzy parameters since the interactive process with a decision maker is simple, various uncertainties involved in decision making are eliminated and all the objectives are well balanced. An illustrative numerical example for nonlinear programming problems with fuzzy parameters is demonstrated along with the corresponding computer output.

• Proceedings of the IEEK Conference
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• 2000.07b
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• pp.677-680
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• 2000

The technique of reinforcement learning algorithm is extended to solve the multiobjective control problem for uncertain dynamic systems. A multiobjective adaptive critic structure is proposed in order to realize a max-min method in the reinforcement learning process. Also, the proposed reinforcement learning technique is applied to a multiobjective satisfactory fuzzy logic controller design in which fuzzy logic subcontrollers are assumed to be derived from human experts. Some simulation results are given in order to show effectiveness of the proposed method.

• East Asian mathematical journal
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• v.5 no.2
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• pp.209-213
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• 1989

The efficiency(Pareto optimum) is a type of solutions for multiobjective programs. We formulate duality relations for multiobjective nonlinear programs by using the concept of efficiency. The results are the weak and strong duality relations for a vector dual of the Wolfe type involving invex functions.