• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.8
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• pp.753-759
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• 2009

Feed-forward neural networks have been widely used as function approximation tools in the context of global approximate optimization. In the present study, a wavelet neural network (WNN) which is based on wavelet transform theory is suggested as an alternative to a traditional back-propagation neural network (BPN). The basic theory of wavelet neural network is briefly described, and approximation performance is tested using a nonlinear multimodal function and a composite rotor blade analysis problem. Laplacian of Gaussian function, Mexican function, and Morlet function are considered during the construction of WNN architectures. In addition, approximation results from WNN are compared with those from BPN.

• Journal of Mechanical Science and Technology
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• v.15 no.8
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• pp.1132-1142
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• 2001

The paper describes the construction of global function approximation models for use in design optimization via global search techniques such as genetic algorithms. Two different approximation methods referred to as evolutionary fuzzy modeling (EFM) and neuro-fuzzy modeling (NFM) are implemented in the context of global approximate optimization. EFM and NFM are based on soft computing paradigms utilizing fuzzy systems, neural networks and evolutionary computing techniques. Such approximation methods may have their promising characteristics in a case where the training data is not sufficiently provided or uncertain information may be included in design process. Fuzzy inference system is the central system for of identifying the input/output relationship in both methods. The paper introduces the general procedures including fuzzy rule generation, membership function selection and inference process for EFM and NFM, and presents their generalization capabilities in terms of a number of fuzzy rules and training data with application to a three-bar truss optimization.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.9 s.240
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• pp.1243-1252
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• 2005

A current trend of design methodologies is to make engineers objectify or automate the decision-making process. Numerical optimization is an example of such technologies. However, in numerical optimization, the uncertainties are uncontrollable to efficiently objectify or automate the process. To better manage these uncertainties, the Taguchi method, reliability-based optimization and robust optimization are being used. To obtain the target performance with the maximum robustness is the main functional requirement of a mechanical system. In this research, a design procedure for global robust optimization is developed based on the kriging and global optimization approaches. The DACE modeling, known as the one of Kriging interpolation, is introduced to obtain the surrogate approximation model of the function. Robustness is determined by the DACE model to reduce real function calculations. The simulated annealing algorithm of global optimization methods is adopted to determine the global robust design of a surrogated model. As the postprocess, the first order second-moment approximation method is applied to refine the robust optimum. The mathematical problems and the MEMS design problem are investigated to show the validity of the proposed method.

• The KIPS Transactions:PartB
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• v.14B no.5
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• pp.377-382
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• 2007

This paper proposes a training algorithm for global optimization of the parameters of radial basis function networks. Since conventional training algorithms usually perform only local optimization, the performance of the network is limited and the final network significantly depends on the initial network parameters. The proposed hybrid simulated annealing algorithm performs global optimization of the network parameters by combining global search capability of simulated annealing and local optimization capability of gradient-based algorithms. Via experiments for function approximation problems, we demonstrate that the proposed algorithm can find networks showing better training and test performance and reduce effects of the initial network parameters on the final results.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.05a
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• pp.122-125
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• 2000

The paper describes the adaptation of evolutionary fuzzy model ins (EFM) in developing global function approximation tools for use in genetic algorithm based optimization of nonlinear structural systems. EFM is an optimization process to determine the fuzzy membership parameters for constructing global approximation model in a case where the training data are not sufficiently provided or uncertain information is included in design process. The paper presents the performance of EFM in terms of numbers of fuzzy rules and training data, and then explores the EFM based sizing of automotive component for passenger protection.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.12a
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• pp.10-13
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• 2001

Nonlinear Function Approximation of Moduled Neural Network Using Genetic Algorithm Neural Network consists of neuron and synapse. Synapse memorize last pattern and study new pattern. When Neural Network learn new pattern, it tend to forget previously learned pattern. This phenomenon is called to catastrophic inference or catastrophic forgetting. To overcome this phenomenon, Neural Network must be modularized. In this paper, we propose Moduled Neural Network. Modular Neural Network consists of two Neural Network. Each Network individually study different pattern and their outputs is finally summed by net function. Sometimes Neural Network don't find global minimum, but find local minimum. To find global minimum we use Genetic Algorithm.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.3 no.2
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• pp.227-232
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• 2003

Recently, support vector learning attracts an enormous amount of interest in the areas of function approximation, pattern classification, and novelty detection. One of the main reasons for the success of the support vector machines(SVMs) seems to be the availability of global and sparse solutions. Among the approaches sharing the same reasons for success and exhibiting a similarly good performance, we have KFD(kernel Fisher discriminant) approach. In this paper, we consider the problem of function approximation utilizing both predetermined basis functions and the KFD approach for regression. After reviewing support vector regression, semi-parametric approach for including predetermined basis functions, and the KFD regression, this paper presents an extension of the conventional KFD approach for regression toward the direction that can utilize predetermined basis functions. The applicability of the presented method is illustrated via a regression example.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1999.05a
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• pp.141-146
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• 1999

A new method, so called MMA(Method of Moving Asymptotes) was applied to the optimization problems of non-linear functions and non-linear structures. In each step of the iterative process, tile MMA generates a strictly convex approximation subproblems and solves them by using the dual problems. The generation of these subproblems is controlled by so called 'moving asymptotes', which may both make no oscillation and speed up tile convergence rate of optimization process. By contrast in generalized dual function, the generated function by MMA is always explicit type. Both the objective and behaviour constraints which were approximated are optimized by dual function. As the results of some examples, it was found that this method is very effective to obtain the global solution for problems with many local solutions. Also it was found that MMA is a very effective approximate method using the original function and its 1st derivatives.

• Korean Journal of Computational Design and Engineering
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• v.5 no.2
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• pp.127-135
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• 2000

Emergent computing paradigms such as genetic algorithms have found increased use in problems in engineering design. These computational tools have been shown to be applicable in the solution of generically difficult design optimization problems characterized by nonconvexities in the design space and the presence of discrete and integer design variables. Another aspect of these computational paradigms that have been lumped under the bread subject category of soft computing, is the domain of artificial intelligence, knowledge-based expert system, and machine learning. The paper explores a machine learning paradigm referred to as teaming classifier systems to construct the high-quality global function approximations between the design variables and a response function for subsequent use in design optimization. A classifier system is a machine teaming system which learns syntactically simple string rules, called classifiers for guiding the system's performance in an arbitrary environment. The capability of a learning classifier system facilitates the adaptive selection of the optimal number of training data according to the noise and multimodality in the design space of interest. The present study used the polynomial based response surface as global function approximation tools and showed its effectiveness in the improvement on the approximation performance.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.2
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• pp.191-201
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• 2010

This paper presents a new global optimization algorithm based on the branch-and-bound principle using Bspline approximation techniques. It describes the algorithmic components and details on their implementation. The key components include the subdivision of a design space into mutually disjoint subspaces and the bound calculation of the subspaces, which are all established by a real-valued B-spline volume model. The proposed approach was demonstrated with various test problems to reveal computational performances such as the solution accuracy, number of function evaluations, running time, memory usage, and algorithm convergence. The results showed that the proposed algorithm is complete without using heuristics and has a good possibility for application in large-scale NP-hard optimization.