1996
DOI: 10.1109/20.497458
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A multiquadrics-based algorithm for the acceleration of simulated annealing optimization procedures

Abstract: A procedure to significantly reduce the computational cost of the simulated annealing optimization algorithm coupled with analysis methods is proposed for EM devices. The chosen approach relies on the application of the simulated annealing method to an analytical approximation of the true objective function, expressed in the form of a multiquadric expansion. The algorithm is fully described, its potential advantages are pointed out and some test cases showing the effectiveness of the implemented strategy are r… Show more

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Cited by 36 publications
(30 citation statements)
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“…RBF described by equation (9) is for coefficient b ¼ 0.5 called a multiquadric (MQ) function. Using MQ function for interpolating the objective function can be written as follows (Alotto et al, 1996):…”
Section: Compel 305mentioning
confidence: 99%
“…RBF described by equation (9) is for coefficient b ¼ 0.5 called a multiquadric (MQ) function. Using MQ function for interpolating the objective function can be written as follows (Alotto et al, 1996):…”
Section: Compel 305mentioning
confidence: 99%
“…Considering a polynomial basis , the approximation of a function is given by: (1) where is the number of vectors of the polynomial basis and are the coordinates of the approximation point. The coefficients are calculated by minimizing the quadratic error : (2) where are the coordinates of the node , is the nodal value of this node, and is a weighting function centered at node , with a limited support [4].…”
Section: A the Shape Functionsmentioning
confidence: 99%
“…[1], [2]. More recently, the application of the Diffuse Element Approximation (DEA) has been given very interesting results [3], with the possibility of avoiding some usual problems found in others methods: parameters adjust and full matrix resolution, for example.…”
Section: Introductionmentioning
confidence: 99%
“…The computation of discrete field values would require rather high effort, if applied to a large number of parameter vectors. Hence, the procedure of the maximum assessment is carried out using the multiquadric approximation [9,10] of magnetic field. The approximation is determined by an expression:…”
Section: Multiquadric Approximationmentioning
confidence: 99%
“…The stochastic optimization method shows the well-known advantages over the gradient-based methods, namely: (i) the parallel global minimum search technique, (ii) the simplified set-up of optimization task and (iii) the ability to find global minimum. The optimization procedure is carried out using the multiquadric approximation [9,10] of magnetic field, since the computed values are distributed in a set of discrete points through the volume of interest. The approximation based on radial basis functions is capable to handle multidimensional multiminima functions by interpolating their discrete data accurately.…”
Section: Introductionmentioning
confidence: 99%