• 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 Ocean Engineering and Technology
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• v.26 no.6
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• pp.80-85
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• 2012

The methods of robust design optimization (RDO) and reliability-based robust design optimization (RBRDO) were implemented in the present study. RBRDO is an integrated method that accounts for the design robustness of an objective function and for the reliability of constraints. The objective function in RBRDO is expressed in terms of the mean and standard deviation of an original objective function. Thus, a multi-objective formulation is employed. The regressive approximate models are generated via the moving least squares method (MLSM) and constraint-feasible moving least squares method (CF-MLSM), which make it possible to realize the feasibility regardless of the multimodality/nonlinearity of the constraint function during the approximate optimization processes. The regression model based RBRDO is newly devised and its numerical characteristics are explored using the design of an actively controlled ten bar truss structure.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.544-556
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• 1991

The optimization of many engineering design problems requires a nonlinear programming algorithm that is robust and efficient. A general-purpose nonlinear optimization program IDOL (Interactive Design Optimization Library) is developed based on the Augmented Lagrange Mulitiplier (ALM) method. The ideas of selecting a good initial design point, using resonable initial values for Lagrange multipliers, constraints scaling, descent vector restarting, and dynamic stopping criterion are employed for computational enhancement to the ALM method. A descent vector is determined by using the Broydon-Fletcher-Goldfarb-Shanno (BFGS) method. For line search, the Incremental-Search method is first used to find bounds on the solution, then the bounds are reduced by the Golden Section method, and finally a cubic polynomial approximation technique is applied to locate the next design point. Seven typical test problems are solved to show IDOL efficient and robust.

• Journal of the Society of Naval Architects of Korea
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• v.34 no.1
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• pp.93-101
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• 1997

Generally the traditional optimization methods have possibilities not only to give a different optimum value according to their starting point, but also to get to local optima. On the other hand, Genetic Algorithm (GA) has an ability of robust global search. In this paper, a new optimization method - the combination of traditional optimization method and genetic algorithm - is presented so as to overcome the above disadvantage of traditional methods. In order to increase the efficiency of the hybrid optimization method, a knowledge-based reasoning is adopted in the part of mathematical modeling, algorithm selection, and process control. The validation of the developed knowledge-based hybrid optimization method was examined and verified applying the method to nonlinear mathematical models.

• Korean Journal of Computational Design and Engineering
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• v.17 no.5
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• pp.375-386
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• 2012

Most engineering design problems require analyses or simulations to evaluate objective functions. However, a single simulation can take many hours or even days to finish for many real world problems. As a result, design optimization becomes impossible since they require hundreds or thousands of simulation evaluations. The surrogate-based optimization (SBO) strategy became a remedy for such computationally expensive analyses and simulations. A surrogate-based optimization strategy has been developed in this study in order to improve global optimization performance. The strategy is a heuristic algorithm and it exploits not only multiple surrogates, but also multiple optimizers. Multiple optimizations of multiple surrogate models yield multiple candidate design points of optima. During the sequential sampling process, the algorithm ranks candidate design points, selects the points as many as specified, and builds the improved surrogate model. Various mathematical functions with different numbers of design variables are chosen to compare the proposed method with the other most recent algorithm, MSEGO. The proposed method shows superior performance to the other method.

• International Journal of Control, Automation, and Systems
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• v.1 no.1
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• pp.101-110
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• 2003

This paper introduces an identification method for nonlinear models in the form of rule-based Fuzzy-Neural Networks (FNN). In this study, the development of the rule-based fuzzy neural networks focuses on the technologies of Computational Intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithms. The FNN modeling and identification environment realizes parameter identification through synergistic usage of clustering techniques, genetic optimization and a complex search method. We use a HCM (Hard C-Means) clustering algorithm to determine initial apexes of the membership functions of the information granules used in this fuzzy model. The parameters such as apexes of membership functions, learning rates, and momentum coefficients are then adjusted using the identification algorithm of a GA hybrid scheme. The proposed GA hybrid scheme effectively combines the GA with the improved com-plex method to guarantee both global optimization and local convergence. An aggregate objective function (performance index) with a weighting factor is introduced to achieve a sound balance between approximation and generalization of the model. According to the selection and adjustment of the weighting factor of this objective function, we reveal how to design a model having sound approximation and generalization abilities. The proposed model is experimented with using several time series data (gas furnace, sewage treatment process, and NOx emission process data from gas turbine power plants).

• Korean Management Science Review
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• v.24 no.2
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• pp.73-80
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• 2007

Robust Design(RD) is a cost-effective methodology to determine the optimal settings of control factors that make a product performance insensitive to the influence of noise factors. To better facilitate the robust design optimization, a dual response surface approach, which models both the process mean and standard deviation as separate response surfaces, has been successfully accepted by researchers and practitioners. However, the construction of response surface approximations has been limited to problems with only a few variables, mainly due to an excessive number of experimental runs necessary to fit sufficiently accurate models. In this regard, an innovative response surface approach has been proposed to investigate robust design optimization problems with larger number of variables. Response surfaces for process mean and standard deviation are partitioned and estimated based on the multi-level approximation method, which may reduce the number of experimental runs necessary for fitting response surface models to a great extent. The applicability and usefulness of proposed approach have been demonstrated through an illustrative example.

• Structural Engineering and Mechanics
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• v.24 no.5
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• pp.529-541
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• 2006

This work gives an application of stochastic techniques for the optimization of stiffened plates in vibration. The search strategy consists of substituting, for finite element calculations in the optimization process, an approximate response from a Rayleigh-Ritz method. More precisely, the paper describes the use of a Rayleigh-Ritz method in creating function approximations for use in computationally intensive design optimization based on genetic algorithms. Two applications are presented; their deal with the optimization of stiffeners on plates by varying their positions, in order to maximize some natural frequencies, while having well defined dimensions. In other words, this work gives the fundamental idea of using a Ritz approximation to the response of a plate in vibration instead of finite element analysis.

• Structural Engineering and Mechanics
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• v.31 no.4
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• pp.407-421
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• 2009

The present paper addresses the optimal design of composite laminates with the aim of minimizing free-edge delamination stresses. A technique involving the application of particle swarm optimization (PSO) integrated with FEM was developed for the optimization. Optimization was also conducted with the zero-order method (ZOM) included in ANSYS. The semi-analytical method, which provides an approximation of the interlaminar normal stress of laminates under in-plane load, was used to partially validate the optimization results. It was found that optimal results based on ZOM are sensitive to the starting design points, and an unsuitable initial design set will lead to a result far from global solution. By contrast, the proposed method can find the global optimal solution regardless of initial designs, and the solutions were better than those obtained by ZOM in all the cases investigated.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.19 no.5
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• pp.589-595
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• 2010

This paper presents a reliability-based shape optimization (RBSO) using the evolutionary structural optimization (ESO). An actual design involves uncertain conditions such as material property, operational load, poisson's ratio and dimensional variation. The deterministic optimization (DO) is obtained without considering of uncertainties related to the uncertainty parameters. However, the RBSO can consider the uncertainty variables because it has the probabilistic constraints. In order to determine whether the probabilistic constraint is satisfied or not, simulation techniques and approximation methods are developed. In this paper, the reliability-based shape design optimization method is proposed by utilization the reliability index approach (RIA), performance measure approach (PMA), single-loop single-vector (SLSV), adaptive-loop (ADL) are adopted to evaluate the probabilistic constraint. In order to apply the ESO method to the RBSO, a sensitivity number is defined as the change of strain energy in the displacement constraint. Numerical examples are presented to compare the DO with the RBSO. The results of design example show that the RBSO model is more reliable than deterministic optimization.