• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.1
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• pp.112-123
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• 1997

The optimization techniques have been applied to versatile engineering problems for reducing manufacturing cost and for automatic design. The deterministic approaches or op5imization neglect the effects on uncertainties of design variables. The uncertainties include variation or perturbation such as tolerance band. The optimum may be useless when the constraints considering worst cases of design variables can not be satisfied, which results from constraint variation. The variation of design variables can also give rise to drastic change of performances. The two issues are related to constraint feasibility and insensitive performance. Robust design suggested in the present study is developed to gain an optimum insensitive to variation on design variables within feasible region. The multiobjective function is composed to the mean and the standard deviation of original objective function, while the constraints are supplemented by adding penalty term to original constraints. This method has a advantage that the second derivatives of the constraints are not required. A mathematical problem and several standard problems for structural optimization are solved to check out the usefulness of the suggested method.

• The Mathematical Education
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• v.28 no.1
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• pp.41-45
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• 1989

Subdifferentiability of a vector-valued set function is defined first. Then in terms of zero-like functions, a perperly efficient solution of a convex programming problem with set functions will be characterized.

• International Journal of Control, Automation, and Systems
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• v.5 no.6
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• pp.691-700
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• 2007

This paper proposes a simple but effective design method of PID control using a numerical optimization method. In order to achieve both stability and performance, gain and phase margins and performance indices of step response directly compose of the cost function. Hence, the proposed approach is a multiobjective optimization problem. The main effectiveness of this approach results from the strong capability of the used optimization method. A one-dimensional example concerning gain margin illustrates the practical applicability of the optimization method. The present approach has many degrees of freedom in controller design by only adjusting related weight constants. The attained PID controller is compared with Wang#s and Ho#s methods, IAE, and ISE for a high-order process, and the simulation result for various design targets shows that the proposed approach achieves desired time-domain performance with a guarantee of frequency-domain stability.

• Proceedings of the KIEE Conference
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• 2011.07a
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• pp.1966-1967
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• 2011

본 연구에서는 방사형 기저 함수를 이용한 다항식 신경회로망(Polynomial Neural Network) 분류기를 제안한다. 제안된 모델은 PNN을 기본 구조로 하여 1층의 다항식 노드 대신에 다중 출력 형태의 방사형 기저 함수를 사용하여 각 노드가 방사형 기저 함수 신경회로망(RBFNN)을 형성한다. RBFNN의 은닉층에는 fuzzy 클러스터링을 사용하여 입력 데이터의 특성을 고려한 적합도를 사용하였다. 제안된 분류기는 입력변수의 수와 다항식 차수가 모델의 성능을 결정함으로 최적화가 필요하며 본 논문에서는 Multiobjective Particle Swarm Optimization(MoPSO)을 사용하여 모델의 성능뿐만 아니라 모델의 복잡성 및 해석력을 고려하였다. 패턴 분류기로써의 제안된 모델을 평가하기 위해 Iris 데이터를 이용하였다.

• Journal of the Korean Operations Research and Management Science Society
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• v.8 no.1
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• pp.41-59
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• 1983

The purpose of this paper is to present a method of multi-objective, stochastic optimization in water resources system which investigates the development of potential non-normal deterministic equivalents for subsequent use in multiobjective stochastic programming methods, Given probability statement involving a function of several random variables, it is often possible to obtain a deterministic equivalent of it that does not include any orginal random variables. A Stochastic trade-off technique-MSTOT is suggested to help a decision maker achieve satisfactory levels for several objective functions. This makes use of deterministic equivalents to handle random variables in the objective functions. The emphasis is in the development of non-normal deterministic equivalents for use in multiobjective stochastic techniques.

• Structural Engineering and Mechanics
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• v.72 no.2
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• pp.181-190
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• 2019

Topology optimization of structures seeking the best distribution of mass in a design space to improve the structural performance and reduce the weight of a structure is one of the most comprehensive issues in the field of structural optimization. In addition to structures stiffness as the most common objective function, frequency optimization is of great importance in variety of applications too. In this paper, an efficient multi-objective Bi-directional Evolutionary Structural Optimization (BESO) method is developed for topology optimization of frequency and stiffness in continuum structures simultaneously. A software package including a Matlab code and Abaqus FE solver has been created for the numerical implementation of multi-objective BESO utilizing the weighted function method. At the same time, by considering the weaknesses of the optimized structure in single-objective optimizations for stiffness or frequency problems, slight modifications have been done on the numerical algorithm of developed multi-objective BESO in order to overcome challenges due to artificial localized modes, checker boarding and geometrical symmetry constraint during the progressive iterations of optimization. Numerical results show that the proposed Multiobjective BESO method is efficient and optimal solutions can be obtained for continuum structures based on an existent finite element model of the structures.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.5
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• pp.819-827
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• 1997

In this paper, a new modeling of a fine actuator for an optical pick-up has been proposed and multiobjective optimization of the actuator has been performed. The fine actuator is constituted of the bobbin which is supported by wire suspension, the coils which wind around the bobbin, and the magnets which cause the magnetic flux. If current flows in the coils, magnetic force is so produced as to be balanced with spring force of wire, so the bobbin is pisitioned. In this model the transfer function from input voltage to output displacementof bobbin has been obtained so that we can describe this integrated system with electromagnetic and mechanical parts. Wire suspension is regarded as a continuous Euler beam, damper as distributed viscous damping, and bobbin as a rigid body which can move up- and down- ward motion only. According to the model, the high frequency dynamic characteristics of the fine actuator can be known and the effect of damping can be investigated while the conventional second order model cannot. In multiobjective optimization, two objective functions have been chosen to maximize the fundamental frequency and the sensitivity with respect to the input voltage of the actuator so that Pareto's optimal solutions have been obtained using .epsilon.-constraint method. These objective functions will satisfy the trends which will enhance the access speed and reduce the tracking error in the optical pick-up technology of next generation. In the result of optimization, we obtain the designs of the optical pick-up fine actuator which has high speed, high sensitivity and low resonant peak. Furthermore, we offer the relation between two object functions so that the designer can make easy choice.

• International Journal of Control, Automation, and Systems
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• v.2 no.2
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• pp.247-255
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• 2004

The majority of real-world problems encountered by engineers involve simultaneous optimization of competing objectives. In this case instead of single optima, there is a set of alternative trade-offs, generally known as Pareto-optimal solutions. The use of evolutionary algorithms Pareto GA, which was first introduced by Goldberg in 1989, has now become a sort of standard in solving Multiobjective Optimization Problems (MOPs). Though this approach was further developed leading to numerous applications, these applications are based on Pareto ranking and employ the use of the fitness sharing function to maintain diversity. Another scheme for solving MOPs has been presented by J. Nash to solve MOPs originated from Game Theory and Economics. Sefrioui introduced the Nash Genetic Algorithm in 1998. This approach combines genetic algorithms with Nash's idea. Another central achievement of Game Theory is the introduction of an Evolutionary Stable Strategy, introduced by Maynard Smith in 1982. In this paper, we will try to find ESS as a solution of MOPs using our game model based co-evolutionary algorithm. First, we will investigate the validity of our co-evolutionary approach to solve MOPs. That is, we will demonstrate how the evolutionary game can be embodied using co-evolutionary algorithms and also confirm whether it can reach the optimal equilibrium point of a MOP. Second, we will evaluate the effectiveness of our approach, comparing it with other methods through rigorous experiments on several MOPs.

• Journal of Korean Society of Forest Science
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• v.89 no.3
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• pp.335-341
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• 2000

In this study, the multiobjective linear programming (MOLP) formulation was built to solve for the optimal forest management planning considering carbon sequestration and timber production simultaneously. The formulation was applied to a case study problem to investigate the trends of the optimal forest harvest schedules as the function of preference of forest management for carbon sequestration and timber production. The study site was Mt. Kari area in Hongchun. The formulation includes several site-specific constraints for non-declining yields, upper and lower bounds of cut volume and area for timber, ending inventory conditions, etc.. According to the changes of weight combinations for timber production and carbon sequestration, the joint production possibilities curve was proposed as the option for management choice.

• Journal of Mechanical Science and Technology
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• v.19 no.5
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• pp.1080-1086
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• 2005

The preliminary design optimization of multi-stage spur gear reduction units has been a subject of considerable interest, since many high-performance power transmission applications (e.g., automotive and aerospace) require high-performance gear reduction units. There are multiple objectives in the optimal design of multi-stage spur gear reduction unit, such as minimizing the volume and maximizing the surface fatigue life. It is reasonable to formulate the design of spur gear reduction unit as a multi-objective optimization problem, and find an appropriate approach to solve it. In this paper an interactive physical programming approach is developed to place physical programming into an interactive framework in a natural way. Class functions, which are used to represent the designer's preferences on design objectives, are fixed during the interactive physical programming procedure. After a Pareto solution is generated, a preference offset is added into the class function of each objective based on whether the designer would like to improve this objective or sacrifice the objective so as to improve other objectives. The preference offsets are adjusted during the interactive physical programming procedure, and an optimal solution that satisfies the designer's preferences is supposed to be obtained by the end of the procedure. An optimization problem of three-stage spur gear reduction unit is given to illustrate the effectiveness of the proposed approach.