• Management Science and Financial Engineering
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• v.22 no.1
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• pp.5-12
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• 2016

We consider a time-cost tradeoff problem with multiple milestones under a chain precedence graph. In the problem, some penalty occurs unless a milestone is completed before its appointed date. This can be avoided through compressing the processing time of the jobs with additional costs. We describe the compression cost as the convex or the concave function. The objective is to minimize the sum of the total penalty cost and the total compression cost. It has been known that the problems with the concave and the convex cost functions for the compression are NP-hard and polynomially solvable, respectively. Thus, we consider the special cases such that the cost functions or maximal compression amounts of each job are identical. When the cost functions are convex, we show that the problem with the identical costs functions can be solved in strongly polynomial time. When the cost functions are concave, we show that the problem remains NP-hard even if the cost functions are identical, and develop the strongly polynomial approach for the case with the identical maximal compression amounts.

• Journal of the Korean Data and Information Science Society
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• v.27 no.6
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• pp.1653-1660
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• 2016

Smoothly clipped absolute deviation (SCAD) penalty is known to satisfy the desirable properties for penalty functions like as unbiasedness, sparsity and continuity. In this paper, we deal with the regression function estimation and variable selection based on SCAD penalized censored regression model. We use the local linear approximation and the iteratively reweighted least squares algorithm to solve SCAD penalized log likelihood function. The proposed method provides an efficient method for variable selection and regression function estimation. The generalized cross validation function is presented for the model selection. Applications of the proposed method are illustrated through the simulated and a real example.

• Journal of Navigation and Port Research
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• v.30 no.2
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• pp.137-143
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• 2006

The optimum grillage design belongs to nonlinear constrained optimization problem. The determination of beam scantlings for the grillage structure is a very crucial matter out of whole structural design process. The performance of optimization methods, based on penalty functions, is highly problem-dependent and many methods require additional tuning of some variables. This additional tuning is the influences of penalty coefficient, which depend strongly on the degree of constraint violation. Moreover, Binary-coded Genetic Algorithm (BGA) meets certain difficulties when dealing with continuous and/or discrete search spaces with large dimensions. With the above reasons, Real-coded Micro-Genetic Algorithm ($R{\mu}GA$) is proposed to find the optimum beam scantlings of the grillage structure without handling any of penalty functions. $R{\mu}GA$ can help in avoiding the premature convergence and search for global solution-spaces, because of its wide spread applicability, global perspective and inherent parallelism. Direct stiffness method is used as a numerical tool for the grillage analysis. In optimization study to find minimum weight, sensitivity study is carried out with varying beam configurations. From the simulation results, it has been concluded that the proposed $R{\mu}GA$ is an effective optimization tool for solving continuous and/or discrete nonlinear real-world optimization problems.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.1 no.1
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• pp.1-34
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• 1997

In this study, various available meshless methods are briefly reviewed and the connection among them is investigated. The objective of meshless methods is to eliminate some difficulties which are originated from reliance on a mesh by constructing the approximation entirely in terms of nodes. Especially, focusing on Element Free Galerkin Method(EFGM) based on moving least square interpolants(MLSI), a new implementation is developed based on a variational principle with penalty function method were used to enforce the essential boundary condition. In addition, the weighted orthogonal basis functions are constructed to overcome disadvantage of MLSI.

• Structural Engineering and Mechanics
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• v.23 no.4
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• pp.387-407
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• 2006

A Genetic Algorithm (hereinafter GA) based optimum design algorithm and program for plane steel frames with partially restrained connections is presented. The algorithm was incorporated with the refined plastic hinge analysis method, in which geometric nonlinearity was considered by using the stability functions of beam-column members and material nonlinearity was considered by using the gradual stiffness degradation model that included the effects of residual stress, moment redistribution by the occurrence of plastic hinges, partially restrained connections, and the geometric imperfection of members. In the genetic algorithm, a tournament selection method and micro-GAs were employed. The fitness function for the genetic algorithm was expressed as an unconstrained function composed of objective and penalty functions. The objective and penalty functions were expressed, respectively, as the weight of steel frames and the constraint functions which account for the requirements of load-carrying capacity, serviceability, ductility, and construction workability. To verify the appropriateness of the present method, the optimum design results of two plane steel frames with fully and partially restrained connections were compared.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.8C
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• pp.786-794
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• 2006

We proposed a novel preconditioner based PCG(Preconditioned Conjugate Gradient) method for super resolution image reconstruction. Compared with the conventional block circulant type preconditioner, the proposed preconditioner can be more effectively applied for objective functions that include roughness penalty functions. The effectiveness of the proposed method was shown by simulations and experiments.

• Communications of the Korean Mathematical Society
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• v.4 no.1
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• pp.5-15
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• 1989

• Journal of Korean Society of Steel Construction
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• v.16 no.2 s.69
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• pp.201-213
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• 2004

A GA-based optimum design algorithm and a program for plane steel frame structures with semi-rigid connections are presented. The algorithm is incorporated with the refined plastic hinge analysis method wherein geometric nonlinearity is considered by using the stability functions of beam-column members, and material nonlinearity, by using the gradual stiffness degradation model that includes the effects of residual stresses, moment redistribution through the occurrence of plastic hinges, semi-rigid connections, and geometric imperfection of members. In the genetic algorithm, the tournament selection method and micro-GAs are employed. The fitness function for the genetic algorithm is expressed as an unconstrained function composed of objective and penalty functions. The objective and penalty functions are expressed as the weight of steel frames and the constraint functions, respectively. In particular, the constraint functions fulfill the requirements of load-carrying capacity, serviceability, ductility, and construction workability. To verify the appropriateness of the present method, the optimal design results of two plane steel frames with rigid and semi-rigid connections are compared.

• Structural Engineering and Mechanics
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• v.23 no.1
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• pp.29-42
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• 2006

This paper describes the design scheme of the three-dimensional structures based on the concept of the cellular automata simulation. The cellular automata simulation is performed according to the local rule. In this paper, the local rule is derived in the mathematical formulation from the optimization problem. The cell density is taken as the design variable. Two objective functions are defined for reducing the total weight of the structure and obtaining the fully stressed structure. The constraint condition is defined for defining the local rule. The penalty function is defined from the objective functions and the constraint condition. Minimization of the penalty function with respect to the design parameter leads to the local rule. The derived rule is applied to the design of the three-dimensional structure first. The final structure can be obtained successfully. However, the computational cost is expensive. So, in order to reduce the computational cost, the material parameters $c_1$ and $c_2$ and the value of the cell rejection criterion (CRC) are changed. The results show that the computational cost depends on the parameters and the CRC value.

• Structural Engineering and Mechanics
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• v.82 no.1
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• pp.41-53
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• 2022

We developed an accurate and simple vibration model to calculate the natural frequencies and their corresponding vibration modes for multi-span beam bridges with non-uniform cross-sections. A closed set of characteristic functions of a single-span beam was used to construct the vibration modes of the multi-span bridges, which were considered single-span beams with multiple constraints. To simplify the boundary conditions, the restraints were converted into spring constraints. Then the functional of the total energy has the same form as the penalty method. Compared to the conventional penalty method, the penalty coefficients in the proposed approach can be calculated directly, which can avoid the iteration process and convergence problem. The natural frequencies and corresponding vibration modes were obtained via the minimum total potential energy principle. By using the symmetry of the eigenfunctions or structure, the matrix size can be further reduced, which increases the computational efficiency of the proposed model. The accuracy and efficiency of the proposed approach were validated by the finite element method.