• Management Science and Financial Engineering
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• v.17 no.2
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• pp.63-84
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• 2011

The ordinary multiple criteria decision making (MCDM) approach requires two types of input, alternative values and criterion weights, and employs two schemes of alternative prioritization, dominance and potential optimality. This paper allows for incomplete information on both types of input and gives rise to the dominance relationships and potential optimality of alternatives. Unlike the earlier studies, we emphasize that incomplete information frequently takes the form of strict inequalities, such as strict orders and strict bounds, rather than weak inequalities. Then the issues of rising importance include: (1) The standard mathematical programming approach to prioritize alternatives cannot be used directly, because the feasible region for the permissible decision parameters becomes an open set. (2) We show that the earlier methods replacing the strict inequalities with weak ones, by employing a small positive number or zeroes, which closes the feasible set, may cause a serious problem and yield unacceptable prioritization results. Therefore, we address these important issues and develop a useful and simple method, without selecting any small value for the strict preference information. Given strict information on both types of decision parameters, we first construct a nonlinear program, transform it into a linear programming equivalent, and finally solve it via a two-stage method. An application is also demonstrated herein.

• Computational Structural Engineering
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• v.9 no.2
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• pp.121-131
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• 1996

This work proposes an optimality criteria applicable to the optimum design of plane frames subject to multiple behavioral constraints on member stresses and lateral displacements of nodes and also to side constraints on design variables. The method makes use of a first order approximation for both deflection and stress constraints instead of the zero order approximation based on the concept of FSD (fully stressed design). A redesign algorithm is derived from a mathematically rigorous method which uses the Newton-Raphson method to solve the system of nonlinear constraint equations and reduces the design space whenever minimum size restrictions become active. When applied to worked examples it proved more accurate and efficient, and it is often found that optimum designs are not fully stressed designs. This fact suggests that this rigorous method is worth what it claims for complicated computing and thus had better replace the crude stress ratio algorithm adopted by the majority of optimality criteria approaches. This is particularly true as long as we enjoy ever-increasing computing power at negligible costs.

• Wind and Structures
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• v.14 no.6
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• pp.559-582
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• 2011

This paper presents an integrated wind-induced dynamic analysis and computer-based design optimization technique for minimizing the structural cost of general tall buildings subject to static and dynamic serviceability design criteria. Once the wind-induced dynamic response of a tall building structure is accurately determined and the optimal serviceability design problem is explicitly formulated, a rigorously derived Optimality Criteria (OC) method is to be developed to achieve the optimal distribution of element stiffness of the structural system satisfying the wind-induced drift and acceleration design constraints. The effectiveness and practicality of the optimal design technique are illustrated by a full-scale 60-story building with complex 3D mode shapes. Both peak resultant acceleration criteria and frequency dependent modal acceleration criteria are considered and their influences on the optimization results are highlighted. Results have shown that the use of various acceleration criteria has different implications in the habitability evaluations and subsequently different optimal design solutions. The computer based optimization technique provides a powerful tool for the lateral drift and occupant comfort design of tall building structures.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.183-190
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• 2001

Topology optimization. has been evolved into a very efficient conceptual design tool and has been utilized into design engineering processes in many industrial parts. In recent years, topology optimization has become the focus of structural optimization design and has been researched and widely applied both in academy and industry. Traditional topology optimization has been using homogenization method and optimality criteria method. Homogenization method provides relationship equation between structure which includes many holes and stiffness matrix in FEM. Optimality criteria method is used to update design variables while maintaining that volume fraction is uniform. Traditional topology optimization has advantage of good convergence but has disadvantage of too much convergency time and additive checkerboard prevention algorithm is needed. In one way to solve this problem, element remove method is presented. Then, it is applied to many examples. From the results, it is verified that the time of convergence is very improved and optimal designed results is obtained very similar to the results of traditional topology using 8 nodes per element.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.392-397
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• 2001

Topology optimization is applied to determine the layout of a structure whose eigenfrequency coincides with a specified frequency. The topology optimization problem is formulated to minimize the difference between the structural frequency and a given frequency using the homogenization method and the modified optimality criteria method. It turns out that the value of a weighting factor in the updating scheme plays an important role to achieve both a suitable speed and a stable convergence of an algorithm. Unlike a constant weighting factor in previous works, it is suggested that a weight factor is varied during the iteration to control the amount of the frequency change. To substantiate the proposed approach two-dimensional structural design problems are presented and the resulted topology layouts for the specified eigenfrequency are compared to layouts for maximizing the corresponding eigenfrequency.

• Proceedings of the KSR Conference
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• 2002.10b
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• pp.876-883
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• 2002

Electric vehicle body has to be subjected to uniform load and requires auxiliary equipment such as air pipe and electric wire pipe. Especially, the cross beam supports the weight of passenger and electrical equipments. a lightweight vehicle body is salutary to save operating costs and fuel consumption. Therefore this study is to perform the size and the shape optimization of crossbeam fur electric vehicle using the method of topology optimization to introduce the concept of homogenization based on optimality criteria method which is efficient for the problem having the number of design variables and a few boundary condition. this provides the method to determine the optimum position and shape of circular hole in the cross beam and then can achieve the optimal design to reduce weight.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.10a
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• pp.288-295
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• 1996

This work presents an optimality criteria method applicable io the design of plane frames with I-shape sections. All kinds of constraints are treated properly to ensure the mathematical rigour of the method as ever. Among the various properties of a section, the cross-sectional area is chosen as the design variable associated with the member. Then other properties, moment of inertia and depth, are determined from the cross-sectional area using relationships established in advance from the sectional data for AISC standard W shapes. The optimality criteria established in this work is perfect in mathematical terms provided that the relationships between properties of a section are correct. A redesign algorithm is derived relying heavily on the Newton-Raphson method to solve the system of nonlinear constraint equations. A worked example is also Presented.

• Transactions of the Korean Society of Automotive Engineers
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• v.12 no.5
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• pp.85-93
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• 2004

Electric vehicle body has to be subjected to uniform load and requires auxiliary equipment such as air pipe and electric wire pipe. Especially, the cross beam supports the weight of passenger and electrical equipments. This need to use adaptive design in initial design stage to gain economy through interchangeability between many kinds of components. This study performs the topology optimization by the concept of homogenization based on optimality criteria method which is efficient for the problem with a number of boundary condition and design variable. Therefore this provides the method to determine the optimum position and the shape of circular hole in the cross beam and then can achieve the weight minimization of electric vehicle body.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.10a
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• pp.17-24
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• 1995

This work proposes an optimality criteria applicable to the optimum design of plane frames. Stress constraints as well as displacement constraints are treated as behavioural constraints and thus the first order approximation of stress constraints is adopted. The design space of practical reinforced concrete frames with discrete design variables has been found to have many local minima, and thus it is desirable to find in advance the mathematical minimum, hopefully global, prior to starting to search a practical optimum design. By using the mathematical minimum as a trial design of any search algorithm, we may not full into a local minimum but apparently costly design. Therefore this work aims at establishing a mathematically rigorous method ⑴ by adopting first-order approximation of constraints, ⑵ by reducing the design space whenever minimum size restrictions become "active" and ⑶ by the of Newton-Raphson Method.

• The Korean Journal of Applied Statistics
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• v.13 no.2
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• pp.393-405
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• 2000

Box and Draper( 19(5) listed some properties of a design that should be considered in design selection. But it is impossible that one design criterion from optimal experimental design theory reflects many potential objectives of an experiment, because the theory was originally based on the underlying model and its strict assumption about the error structure. Therefore, when it is neces::;ary to implement multi-objective experimental design. it is common practice to balance out the several optimal design criteria so that each design criterion involved benefits in terms of its relative "high" efficiency. In this study, we proposed several composite design criteria taking the case of heteroscedastic model. WVhen the heteroscedasticity is present in the model. the well known equivalence theorem between 1)- and C-optimality no longer exists and furthermore their design characteristics are sometimes drastically different. We introduced three different design criteria for this purpose: constrained design, combined design, and minimax design criteria. While the first two methods do reflect the prior belief of experimenter, the last one does not take it into account. which is sometimes desirable. Also we extended this method to the case when there are uncertainties concerning the error structure in the model. A simple algorithm and concluslOn follow.On follow.