• Journal of Korean Society for Quality Management
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• v.32 no.3
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• pp.234-243
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• 2004

In this paper, we study the optimality of 2-level resolution V minimal fractional factorial designs which can be constructed by using a partially balanced array. Moreover the relative efficiencies of such designs are compared in the sense of three optimality criteria such as determinant(D)-optimality, trace(A)-optimality, and eigenvalue(E) -optimality criterion.

• Communications for Statistical Applications and Methods
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• v.16 no.1
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• pp.195-208
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• 2009

A conventional single design optimality criterion has been used to select an efficient experimental design. But, since an experimental design is constructed with respect to an optimality criterion pre specified by investigators, an experimental design obtained from one optimality criterion which is superior to other designs may perform poorly when the design is evaluated by another optimality criterion. In other words, none of these is entirely satisfactory and even there is no guarantee that a design which is constructed from using a certain design optimality criterion is also optimal to the other design optimality criteria. Thus, it is necessary to develop certain special types of experimental designs that satisfy multiple design optimality criteria simultaneously because these multi-optimal designs (MODs) reflect the needs of the experimenters more adequately. In this article, we present a heuristic approach to construct second-order response surface designs which are more flexible and potentially very useful than the designs generated from a single design optimality criterion in many real experimental situations when several competing design optimality criteria are of interest. In this paper, over cuboidal design region for $3\;{\leq}\;k\;{\leq}\;5$ variables, we construct multi-optimal designs (MODs) that might moderately satisfy two famous alphabetic design optimality criteria, G- and IV-optimality criteria using a GA which considers a certain amount of randomness. The minimum, average and maximum scaled prediction variances for the generated response surface designs are provided. Based on the average and maximum scaled prediction variances for k = 3, 4 and 5 design variables, the MODs from a genetic algorithm (GA) have better statistical property than does the theoretically optimal designs and the MODs are more flexible and useful than single-criterion optimal designs.

• Journal of the Korean Mathematical Society
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• v.40 no.2
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• pp.287-305
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• 2003

Second order necessary optimality condition for properly efficient solutions of a twice differentiable vector optimization problem is given. We obtain a nonsmooth version of the second order necessary optimality condition for properly efficient solutions of a nondifferentiable vector optimization problem. Furthermore, we prove a second order necessary optimality condition for weakly efficient solutions of a nondifferentiable vector optimization problem.

• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.667-677
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• 2001

We consider a nonsmooth multiobjective opimization problem(PE) involving locally Lipschitz functions and define gen-eralized invexity for locally Lipschitz functions. Using Fritz John type optimality conditions, we establish Fritz John type sufficient optimality theorems for (PE) under generalized invexity.

• Journal of Ecology and Environment
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• v.31 no.3
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• pp.177-181
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• 2008

Recently, the evolutionary study of human psychology and behavior has undergone rapid growth, diversifying into a few distinct sub-disciplines. One fundamental issue over which researchers in Human Behavioral Ecology and Evolutionary Psychology (EP) have different views is the role of formal optimality modeling for making hypotheses and deriving predictions about human adaptations. The study of EP typically rests on informal inferences and rarely uses optimality modeling, a strategy which human behavioral ecologists have severely criticized. Here I argue that EP researchers have every reason to make extensive use of optimality modeling as its research method. I show that optimality modeling can play an integral role in identifying the functional organization of human psychological adaptations.

• Journal of the Korean Statistical Society
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• v.27 no.1
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• pp.133-152
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• 1998

The central composite design is widely used in the response surface analysis, because it can fit the second order model with small experimental points. In practice, the experimental data are not always obtained on all the points. When there are missing observations, many problems due to the missing cells can occur. In this paper, the influence of a missing cell on the central composite design is discussed. First, the influences of a missing cell on the variances of estimated regression coefficents are compared as $\alpha$ varies. Second, how the average predition variance is affected by a missing sell is discussed. And the influence on rotatability is investigated. Third, the influence of a missing cell on optimality, especially on D-optimality and A-optimality, is examined.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.89-96
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• 2005

Numerical procedure of design optimality evaluation is studied for caisson structural systems. Two kinds of evaluation methods can be considered; mathematical optimality criteria method (MOCM) and numerical optimization method (NOM). The choice of the method depends on the available information of the system MOCM can be used only when the information of all function values, gradients and Lagrange multipliers is available, which may not be realistic in practice. Therefore, in this study, NOMs are applied for the structural optimality evaluation, where only design variables are necessary. To this end, Metropolis genetic algorithm (MGA) is advantageously used and applied for a standard optimization model of caisson composite breakwater. In the numerical example, cost and constraint functions are assumed to be changed from the orignal design situation and their effects are evaluated for optimality. From the theoretical consideration and numerical experience, it is found that the proposed optimality evaluation procedure with MGA-based NOM is efficient and practically applicable.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.597-610
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• 2010

For a class of nonlinear bilevel programming problems in which the follower's problem is linear, the paper develops a genetic algorithm based on the optimality conditions of linear programming. At first, we denote an individual by selecting a base of the follower's linear programming, and use the optimality conditions given in the simplex method to denote the follower's solution functions. Then, the follower's problem and variables are replaced by these optimality conditions and the solution functions, which makes the original bilevel programming become a single-level one only including the leader's variables. At last, the single-level problem is solved by using some classical optimization techniques, and its objective value is regarded as the fitness of the individual. The numerical results illustrate that the proposed algorithm is efficient and stable.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.287-301
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• 2014

In this paper, we prove a necessary optimality theorem for a nonsmooth optimization problem in the face of data uncertainty, which is called a robust optimization problem. Recently, the robust optimization problems have been intensively studied by many authors. Moreover, we give examples showing that the convexity of the uncertain sets and the concavity of the constraint functions are essential in the optimality theorem. We present an example illustrating that our main assumptions in the optimality theorem can be weakened.

• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.55-63
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• 1995

The characteristics of $I{\lambda}$-optimality are investigated with repsect to other experimental design's criteria, D-and G-optimality. The comparisons are based on D- and G-, and $I{\lambda}$-efficiencies using the Beta(p, q) distribution as a weighting function for $I{\lambda}$-optimality. Results indicate that serious consideration should be given to the $I{\lambda}$-optimality criterion especially when the error variance function is not homogeneous.