• Journal of the Society of Naval Architects of Korea
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• v.42 no.6 s.144
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• pp.654-665
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• 2005

In this paper, we present a non-linear integer programming by genetic algorithm (GA) for available sizes of stiffener or thickness of plate in a job site. GA can rapidly search for the approximate global optimum under complicated design environment such as ship. Meanwhile it can handle the optimization problem involving discrete design variable. However, there are many parameters have to be set for GA, which greatly affect the accuracy and calculation time of optimum solution. The setting process is hard for users, and there are no rules to decide these parameters. In order to overcome these demerits, the optimization for these parameters has been also conducted using GA itself. Also it is proved that the parameters are optimal values by the trial function. Finally, we applied this method to compass deck of ship where the vibration problem is frequently occurred to verify the validity and usefulness of nonlinear integer programming.

• Structural Engineering and Mechanics
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• v.5 no.1
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• pp.59-68
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• 1997

A two-step method is presented for the optimum design of trusses with available sections under stress and Euler buckling constraints. The shape design of the truss is used as a means to convert the discrete solution into a continuous one. In the first step of the method, a continuous solution is obtained by sizing and shape design using an approximate polynomial expression for the buckling coefficients. In the second step, the member sizes obtained are changed to the nearest available sections and the truss is reconfigured by using the exact values for the buckling coefficients. The optimizer used is based on the sequential quadratic programming and the gradients are evaluated in closed form. The method is illustrated by two numerical examples.

• Journal of Korean Society of Steel Construction
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• v.10 no.4 s.37
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• pp.657-666
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• 1998

This study presents an effective dual algorithm for the optimal design of steel structures with displacement constraints. The dual method can replace a primary optimization problem with a sequence of approximate explicit subproblems with a simple algebraic structure. Since being convex and separable, each subproblem can be solved efficiently by the dual method. Specifically, this study uses the principle of virtual work to obtain the displacement constraint equations with an explicit form and adds the linear regression equation expressing the relationships between the cross-section properties to the dual algorithm to reduce the number of design variables. Furthermore, this study deals with the discrete optimization problem to select members with the standard steel sections. Through numerical analyses, the proposed method will be compared with the conventional optimality criteria method.

• Steel and Composite Structures
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• v.8 no.5
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• pp.343-359
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• 2008

In the present study, an efficient method for the optimum design of three-dimensional (3D) steel framed structures is proposed. In this method, in addition to choosing the best position of columns based on architectural requirements, the optimum cross-sectional dimensions of elements are determined. The preliminary design variables are considered as the number of columns in structural plan, which are determined by a direct optimization method suitable for discrete variables, without requiring the evaluation of derivatives. After forming the geometry of structure, the main variables of the cross-sectional dimensions are evaluated, which satisfy the design constraints and also achieve the least-weight of the structure. To reduce the number of finite element analyses and the overall computational time, a new third order approximate function is introduced which employs only the diagonal elements of the higher order derivatives matrices. This function produces a high quality approximation and also, a robust optimization process. The main feature of the proposed techniques that the higher order derivatives are established by the first order exact derivatives. Several examples are solved and efficiency of the new approximation method and also, the proposed method for the best position of columns in 3D steel framed structures is discussed.

• Journal of Korean Association for Spatial Structures
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• v.4 no.2 s.12
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• pp.89-97
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• 2004

The objective of this study is the development of a scheme and discrete optimum design algorithm, which is based on the genetic algorithm. The algorithm can perform both scheme and size optimum designs of plane trusses. The developed Scheme genetic algorithm was implemented in a computer program. For the optimum design, the objective function is the weight of structures and the constraints are limits on loads and serviceability. The basic search method for the optimum design is the genetic algorithm. The algorithm is known to be very efficient for the discrete optimization. However, its application to the complicated structures has been limited because of the extreme time need for a number of structural analyses. This study solves the problem by introducing the size & scheme genetic algorithm operators into the genetic algorithm. The genetic process virtually takes no time. However, the evolutionary process requires a tremendous amount of time for a number of structural analyses. Therefore, the application of the genetic algorithm to the complicated structures is extremely difficult, if not impossible. The scheme genetic algorithm operators was introduced to overcome the problem and to complement the evolutionary process. It is very efficient in the approximate analyses and scheme and size optimization of plane trusses structures and considerably reduces structural analysis time. Scheme and size discrete optimum combined into the genetic algorithm is what makes the practical discrete optimum design of plane fusses structures possible. The efficiency and validity of the developed discrete optimum design algorithm was verified by applying the algorithm to various optimum design examples: plane pratt, howe and warren truss.