Comparison of optimization by response surface methodology with neurofuzzy methods

Malik, Zahid Yaqoob; Rashid, Kashif

doi:10.1109/20.822535

Cited by 31 publications

(14 citation statements)

References 31 publications

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“…The first method is the DE/ES/MQ strategy shown in Sect. 3 while the second strategy (see [33] and [34] for details) is based on neuro-fuzzy system for the interpolation, on a GA followed by a Sequential quadratic programming algorithm for the search on interpolated functions [33,34]. At a reduction of one magnitude order in the objective function f the number of true objective function calls is 40 time smaller.…”

Section: Single Objective Problemmentioning

confidence: 99%

Linked interpolation-optimization strategies for multicriteria optimization problems

Farina

Amato

2003

Soft Computing

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Despite the huge amount of methods available in literature, the practical use of multiobjective optimization tools in industry is still an open issue. A strategy to reduce objective function evaluations is essential, at a fixed degree of Pareto optimal front (F P ) approximation accuracy. To this aim, an extension of single objective Generalized response surface (GRS) methods to F P approximation is proposed. Such an extension is not at all straightforward due to the usually complex shape of the Pareto optimal set (S P ) as well as the non-linear relation between the F P and the S P . As a consequence of such complexity, it is extremely difficult to identify a multiobjective analogue of single objective current optimum region. Consequently, the design domain search space zooming strategy around the current optimum region, which is the core of a GRS method, has to be carefully reconsidered when F P approximation is concerned. In this paper, a GRS strategy for multiobjective optimization is proposed. This strategy links the optimization (based on evolutionary computation) to the interpolation (based on Neural Networks). The strategy is explained in detail and tested on various test cases. Moreover, a detailed analysis of approximation errors and computational cost is given together with a description of real-life applications.Keywords Evolutionary multiobjective optimization, Neural networks interpolation, Response surface methods IntroductionEvolutionary multiobjective optimization has now come to full maturity, both in terms of methodologies [1, 2] and algorithm development [3][4][5][6][7][8][9].Nevertheless, the application of the wide variety of available methods to problems arising from industrial design (in particular electromagnetic devices shape design [10-15] and optimal controllers design), is still not completely straightforward, due to the computational cost needed to evaluate the objective function. In fact, it is often either a (non-linear or coupled) Finite Element Method, or a long time-domain full-system simulation.Two alternative (to available MOEAs) approaches have been considered by the authors and colleagues in previous papers, being specifically devoted to the reduction of objective function calls. They are useful and meaningful when the following constraint and requirement hold.-On one hand (the constraint), the number of objective function calls that can be afforded from the point of view of an industrially practical computational cost is much smaller than the threshold number required for convergence of available powerful MOEAs. -On the other hand (the requirement) the few affordable solutions should converge towards the F P and be diverse each other. In other words this means that solutions are to be few (due to the computational cost) but distributed all along the F P (in order to me meaningful).The two approaches can be summarized as follows:-Build specific MOEAs for tiny populations.-Reconsider a particular preference function method with hybrid global-evolutionary and local-determinist...

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Section: Single Objective Problemmentioning

confidence: 99%

Linked interpolation-optimization strategies for multicriteria optimization problems

Farina

Amato

2003

Soft Computing

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“…The motivations of the present paper are in connection with recent works (Malik and Rashid 2000;Kim and Park 2001;Crino and Brown 2007), where the performances of the polynomial approximators that result from the applications of response surface methods (RSMs) are compared with neural networks. With this respect, the contribution of our research consists in pointing out the theoretical background that may justify the performances obtained by the different classes of approximators and in comparing such performances in two case studies.…”

Section: Introductionmentioning

confidence: 98%

Nonparametric nonlinear regression using polynomial and neural approximators: a numerical comparison

Alessandri

Mosca

2008

Comput Manag Sci

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The solution of nonparametric regression problems is addressed via polynomial approximators and one-hidden-layer feedforward neural approximators. Such families of approximating functions are compared as to both complexity and experimental performances in finding a nonparametric mapping that interpolates a finite set of samples according to the empirical risk minimization approach. The theoretical background that is necessary to interpret the numerical results is presented. Two simulation case studies are analyzed to fully understand the practical issues that may arise in solving such problems. The issues depend on both the approximation capabilities of the approximating functions and the effectiveness of the methodologies that are available to select the tuning parameters, i.e., the coefficients of the polynomials and the weights of the neural networks. The simulation results show that the neural approximators perform better than the polynomial ones with the same number of parameters. However, this superiority can be jeopardized by the presence of local minima, which affects the neural networks but does not regard the polynomial approach

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“…To reconstruct a function on the basis of its values at a set of sample points in terms of some basis in IMLS, a local approximation of it at each point is firstly defined as (1) The basis functions satisfy the following conditions (1) . (2) .…”

Section: A Brief Introduction Of Imlsmentioning

confidence: 99%

“…However, the excessive demand for computer resources with these algorithms often renders these optimal methods inefficient or impractical for some practical design problems that require, for example, repetitive usages of finite element (FE) solutions. To circumvent this problem, the response surface methodology (RSM) has been introduced to reduce the number of function evaluations that involve time consuming computer simulations without sacrificing the quality of the numerical solutions [1]- [6]. So far the most popular RSMs are those based on globally supported radial basic functions (RBF) because of their good interpolating power in dealing with both grid and scattered data.…”

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confidence: 99%

An Adaptive Interpolating MLS Based Response Surface Model Applied to Design Optimizations of Electromagnetic Devices

Yang

et al. 2007

IEEE Trans. Magn.

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A response surface model (RSM) based on a combination of interpolating moving least squares and multistep method is proposed. The proposed RSM can automatically adjust the supports of its weight functions according to the distribution of the sampling points when it is used to reconstruct a computationally heavy design problem. Numerical examples are given to demonstrate the feasibility and efficiency of the proposed method for solving inverse problems.Index Terms-Hierarchical interpolation, interpolating moving least squares approximation, response surface model.

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Comparison of optimization by response surface methodology with neurofuzzy methods

Cited by 31 publications

References 31 publications

Linked interpolation-optimization strategies for multicriteria optimization problems

Linked interpolation-optimization strategies for multicriteria optimization problems

Nonparametric nonlinear regression using polynomial and neural approximators: a numerical comparison

An Adaptive Interpolating MLS Based Response Surface Model Applied to Design Optimizations of Electromagnetic Devices

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