• Journal of Korean Association for Spatial Structures
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• v.4 no.4 s.14
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• pp.91-98
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• 2004

Genetic algorithm is one of the best ways to solve a discrete variable optimization problem. This method is an unconstrained optimization technique, so the constraints are handled in an implicit manner. The most popular way of handling constraints is to transform the original constrained problem into an unconstrained problem, using the concept of penalty function. I present the 3 fitness functions which represent the reject strategy, the penalty strategy, and the combined strategy. I make the design program using the 3 fitness Auctions and it is applied to the design problem of a gable frame and a 2 story 3 span frame.

• The Transactions of the Korea Information Processing Society
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• v.3 no.6
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• pp.1355-1364
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• 1996

A complex object model is one of the value based data model which extends the existing relational data model for supporting complex structured data. This paper studies a method for designing algebra for the complex object model. For this some others' algebra supporting complex objects are compared and analysed in terms of the applicability of a algebraic optimization strategics. The complex object algebra is designed, based on four principles, simple and clear definitions, no restriction on input data, single specification system. The central nature of this paper is to keep the basis of algebraic optimization method through simplicity, safety and the applicability of algebraic optimization strategy. Finally, it shown that the designed algebra has the equivalent or enhanced expressability with other's algebra.

• Journal of Korean Society of Steel Construction
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• v.12 no.5 s.48
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• pp.515-525
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• 2000

The purpose of this paper was to develop size & shape optimization programming algorithm of plane trusses. The optimum techniques applied in this study were extended penalty method of Sequential Unconstrained Minimization Techniques(SUMT) and direct search method with multi-variables proposed by Hooke & Jeeves. Upper mentioned two methods were used iteratively at each level of size and shape optimization routines. The design variables of size optimization were circular steel tube(structural member) diameter and thickness, those of shape optimization were joint coordinates, and the objective function was represented as total weight of truss. During the optimum design, two level procedures of size and shape optimization were interacted iteratively until the final optimum values were attained. At the previous studies about shape optimization of truss, the member sectional areas and coordinates were applied as design variables. So that they could not apply the buckling effect of compression member. In this paper, actual sizes of member and nodal coordinates are used as design variables to consider the buckling effect of compression member properly.

• Journal of Korean Society of Steel Construction
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• v.16 no.1 s.68
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• pp.123-134
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• 2004

In this research, a multilevel decomposition technique to enhance the efficiency of the configuration optimization of truss structures was proposed. On the first level, the nonlinear programming problem was formulated considering cross-sectional areas as design variables, weight, or volume as objective function and behavior under multiloading condition as design constraint. Said nonlinear programming problem was transformed into a sequential linear programming problem. which was effective in calculation through the approximation of member forces using behavior space approach. Such approach has proven to be efficient in sensitivity analysis and different form existing shape optimization studies. The modified method of feasible direction (MMFD) was used for the optimization process. On the second level, by treating only shape design variables, the optimum problem was transformed into and unconstrained optimal design problem. A unidirectional search technique was used. As numerical examples, some truss structures were applied to illustrate the applicability. and validity of the formulated algorithm.

• Journal of Korean Society of Steel Construction
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• v.15 no.4 s.65
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• pp.389-401
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• 2003

The purpose of this study is to develop an algorithm, which can be designed the optimal sections of the composite framed structures constituted with the beams and the columns consisted of H type of steel section and concrete considering the reliability index. The optimized problem or the composite framed structures is formulated with the objective function and the constraints taking the section sizes as the design variables. The objective functions are constituted by the total costs of constructions. Also, the constraints are derived by considering the reliability index of section stress and allowable stress. The algorithm optimized the section of the composite framed structures utilizes the SUMT method using the modified Newton-Raphson direction method. The optimizing algorithm developed in this study is applied to the numerical examples with respecting a one-bay, one-story composite framed structure and a one-bay five-story one for the practical utilization of design on the composite framed structures using the reliability indices$({\beta})$ three and zero. In addition, their numerical results are compared and analyzed to examine the possibility of optimization the applicability, and the convergence this algorithm.

• Magazine of the Korea Concrete Institute
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• v.1 no.1
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• pp.87-94
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• 1989

철근콘크리트 뼈대구조와 같이 설계변수가 과다하고, 제약조건식이 복잡한 구조물의 최적화를 위하여는 구조물을 여러개의 부분구조물로 분할하여 최적해를 구하는 분할법이 많이 사용되고 있다. 그러나 기존의 분할법에 의한 최적화는 구조해석과정과 고정된 부재력에대한 단면설계변수의 부분최적화 과정만으로 이루어지기 때문에, 최적해를 구하려면 반복적인 재해석과정만을 수행하지 않으면 안된다. 따라서 본 연구에서는 다단계분할법에 의하여 철근콘크리트 뼈대구조의 최적화 문제를 3단계로 형성하고, 분할된 부분최적화문제의 최적화시 전체구조의 강성 및 부재력 변화가 반영되어 부분 구조물의 결합을 유지시킬 수 있는 최적화 알고리즘을 제안하였다. 최적화 문제에서 설계변수로는 단면의 크기, 철근량, 모멘트 재분배율등을 취하고,목적함수는 경비함수, 제약조건으로는 강도설계법에 의한 부재강도, 시방서의 요구사항등을 고려하여 문제를 형성하였다. 본 연구에서 개발한 다단계 최적화과정의 첫째 단계에서는 탄성해석에 의하여 재분배모멘트의 설계공간을 형성한다. 이 때 부재력변화량추정(forece approximation technique)에 의하여 단면치수의 변화에 따른 부재력의 변화를 제약조건식 내에 포함시킬 수 있도록 하였다. 둘째 단면에서는 첫째 단계에서 구한 부재력변화량추정이 포함된 제약조건식 내에서 무제약최소화기법에 의하여 단면치수를 최적화하도록 하였다. 셋째 단계에서는 재분배 모멘트를 최적화하였으며, 이 때 재분배모멘트의 변화에 따른 단면설계 변수의 변화는 둘째 단계에서 구한 설계민감도(design sensitivity)를 이용하여 반영시키도록 하였다. 제안된 알고리즘을 1층 2경간 및 2층 1경간 뼈대구조에 적용하여 알고리즘의 타당성과 효율성을 입증하였다. 따라서 본 연구의 알고리즘은 철근 콘크리트 뼈대구조의 최적설계에 안정성있게 적용할 수 있을 것으로 판단된다.

• Journal of the Korea institute for structural maintenance and inspection
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• v.12 no.1
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• pp.135-142
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• 2008

This study is concerned with the optimum design of LB-Deck plate girder bridge. The optimizing problems of the composite bridge are formulated with objective functions and constraints. The objective functions are formulated as the total cost of the concrete deck and steel girder construction and the constraints are derived by criteria with respect to the Korean Highway bridge design. The optimizing algorithm using SUMT for optimum design of the Simple span, 2-Span, 3-span LB-deck plate and general RC-steel composite girder bridges (L=60m) which act live load(DB24). And their optimum numerical results are compares and analyzed to examine the possibility of optimization, the application and convergency of this optimizing algorithm.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.3
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• pp.39-55
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• 1992

In this research, a Three Level Decomposition technique has been developed for configuration design optimization of truss structures. In the first level, as design variables, behavior variables are used and the strain energy has been treated as the cost function to be maximized so that the truss structure can absorb maximum energy. For design constraint of the optimal design problem, allowable stress, buckling stress, and displacement under multi-loading conditions are considered. In the second level, design problem is formulated using the cross-sectional area as the design variable and the weight of the truss structure as the cost function. As for the design constraint, the equilibrium equation with the optimal displacement obtained in the first level is used. In the third level, the nodal point coordinates of the truss structure are used as coordinating variable and the weight has been taken as the cost function. An advantage of the Three Level Decomposition technique is that the first and second level design problems are simple because they are linear programming problems. Moreover, the method is efficient because it is not necessary to carry out time consuming structural analysis and techniques for sensitivity analysis during the design optimization process. By treating the nodal point coordinates as design variables, the third level becomes unconstrained optimal design problems which is easier to solve. Moreover, by using different convergence criteria at each level of design problem, improved convergence can be obtained. The proposed technique has been tested using four different truss structures to yield almost identical optimum designs in the literature with efficient convergence rate regardless of constraint types and configuration of truss structures.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.2
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• pp.73-84
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• 1993

In this research, configuration design optimization of plane truss structure has been tested by using decomposition technique. In the first level, the problem of transferring the nonlinear programming problem to linear programming problem has been effectively solved and the number of the structural analysis necessary for doing the sensitivity analysis can be decreased by developing stress constraint into member stress approximation according to the design space approach which has been proved to be efficient to the sensitivity analysis. And the weight function has been adopted as cost function in order to minimize structures. For the design constraint, allowable stress, buckling stress, displacement constraint under multi-condition and upper and lower constraints of the design variable are considered. In the second level, the nodal point coordinates of the truss structure are used as coordinating variable and the objective function has been taken as the weight function. By treating the nodal point coordinates as design variable, unconstrained optimal design problems are easy to solve. The decomposition method which optimize the section areas in the first level and optimize configuration variables in the second level was applied to the plane truss structures. The numerical comparisons with results which are obtained from numerical test for several truss structures with various shapes and any design criteria show that convergence rate is very fast regardless of constraint types and configuration of truss structures. And the optimal configuration of the truss structures obtained in this study is almost the identical one from other results. The total weight couldbe decreased by 5.4% - 15.4% when optimal configuration was accomplished, though there is some difference.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.2
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• pp.95-109
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• 1993

In this study, the optimal configuration of arch structure has been tested by a decomposition technique. The object of this study is to provide the method of optimizing the shapes of both two hinged and fixed arches. The problem of optimal configuration of arch structures includes the interaction formulas, the working stress, and the buckling stress constraints on the assumption that arch ribs can be approximated by a finite number of straight members. On the first level, buckling loads are calculated from the relation of the stiffness matrix and the geometric stiffness matrix by using Rayleigh-Ritz method, and the number of the structural analyses can be decreased by approximating member forces through sensitivity analysis using the design space approach. The objective function is formulated as the total weight of the structures, and the constraints are derived by including the working stress, the buckling stress, and the side limit. On the second level, the nodal point coordinates of the arch structures are used as design variables and the objective function has been taken as the weight function. By treating the nodal point coordinates as design variable, the problem of optimization can be reduced to unconstrained optimal design problem which is easy to solve. Numerical comparisons with results which are obtained from numerical tests for several arch structures with various shapes and constraints show that convergence rate is very fast regardless of constraint types and configuration of arch structures. And the optimal configuration or the arch structures obtained in this study is almost the identical one from other results. The total weight could be decreased by 17.7%-91.7% when an optimal configuration is accomplished.