Fitness sharing and niching methods revisited

Interest in multimodal optimization function is expanding rapidly since real-world optimization problems often require the location of multiple optima in the search space. In this context, fitness sharing has been used widely to maintain population diversity and permit the investigation of many peaks in the feasible domain. This paper reviews various strategies of sharing and proposes new recombination schemes to improve its efficiency. Some empirical results are presented for high and a limited number of fitness function evaluations. Finally, the study compares the sharing method with other niching techniques

Efficient genetic algorithms for solving hard constrained optimization problems

This paper studies many Genetic Algorithm strategies to solve hard-constrained optimization problems. It investigates the role of various genetic operators to avoid premature convergence. In particular, an analysis of niching methods is carried out on a simple function to show advantages and drawbacks of each of them. Comparisons are also performed on an original benchmark based on an electrode shape optimization technique coupled with a charge simulation metho

Niching genetic algorithms for optimization in electromagnetics. I. Fundamentals

Niching methods extend genetic algorithms and permit the investigation of multiple optimal solutions in the search space. In this paper, we review and discuss various strategies of niching for optimization in electromagnetics. Traditional mathematical problems and an electromagnetic benchmark are solved using niching genetic algorithms to show their interest in real world optimization

Effective dielectric constant of random composite materials

The randomness in the structure of two-component dense composite materials influences the scalar effective dielectric constant, in the quasistatic limit. A numerical analysis of this property is developed in this paper. The computer-simulation models used are based on both the finite element method and the boundary integral equation method for two-and three-dimensional structures, respectively. Owing to possible anisotropy the orientation of spatially fixed inhomogeneities of permittivity e1, embedded in a matrix of permittivity e2, affects the effective permittivity of the composite material sample. The primary goal of this paper is to analyze this orientation dependence. Second, the effect of the components geometry on the dielectric properties of the medium is studied. Third the effect of inhomogeneities randomly distributed within a matrix is investigated. Changing these three parameters provides a diverse array of behaviors useful to understand the dielectric properties of random composite materials. Finally, the data obtained from this numerical simulation are compared to the results of previous analytical wor

Complex effective permittivity of a lossy composite material

In recent work, boundary integral equations and finite elements were used to study the (real) effective permittivity for two-component dense composite materials in the quasistatic limit. In the present work, this approach is extended to investigate in detail the role of losses. We consider the special but important case of the axisymmetric configuration consisting of infinite circular cylinders (assumed to be parallel to the z axis and of permittivity e1) organized into a crystalline arrangement (simple square lattice) within a homogeneous background medium of permittivity e2=1. The intersections of the cylinders with the x – y plane form a periodic two-dimensional structure. We carried out simulations taking e15320.03i or e1=3-0.03i and e2=1. The concentration dependence of the loss tangent of the composite material can be fitted very well, at low and intermediate concentrations of inhomogeneities, with a power law. In the case at hand, it is found that the exponent parameter depends significantly on the ratio of the real part of the permittivity of the components. We argue, moreover, that the numerical results discussed here are consistent with the Bergman and Milton theory

Effective dielectric constant of periodic composite materials

We present computer simulation data for the effective permittivity (in the quasistatic limit) of a system composed of discrete inhomogeneities of permittivity e1, embedded in a three-dimensional homogeneous matrix of permittivity e2. The primary purpose of this paper is to study the related issue of the effect of the geometric shape of the components on the dielectric properties of the medium. The secondary purpose is to analyse how the spatial arrangement in these two-phase materials affects the effective permittivity. The structures considered are periodic lattices of inhomogeneities. The numerical method proceeds by an algorithm based upon the resolution of boundary integral equations. Finally, we compare the prediction of our numerical simulation with the effective medium approach and with results of previous analytical works and numerical experiments

Commentaire de : " Transformation thermodynamics: cloaking and concentrating heat flux " - Opt. Express 20, 8207 (mars 2012).

Optics Express a publié en mars 2012 un article concernant la transposition au domaine de la thermique (équation de la chaleur) du principe de la cape d'invisibilité optique. Les auteurs y présentent en particulier la théorie bidimensionnelle d'un métamatériau en forme de disque, aux propriétés thermiques remarquables en conduction pure (équation de la chaleur), dont ils proposent ensuite une réalisation approchée, formée de dix couches d'isolant thermique séparées par dix couches de conducteurs de conductivités thermiques décroissant avec le rayon. Nous donnons ici les résultats d'une expérience numérique complémentaire, consistant à comparer le comportement thermique de la réalisation proposée de ce métamatériau à celui d'une configuration tout à fait banale à deux couches. Cette expérience montre clairement que les auteurs sont allés trop loin dans l'interprétation pratique de leurs résultats théoriques. En particulier, et conformément aux résultats habituels de la thermodynamique, la réalisation approchée qu'ils proposent pour leur matériau théorique (tout comme plus généralement toute autre réalisation, aussi soignée soit-elle), ne permet en aucun cas de protéger un objet de la chaleur mieux que ne le fait un simple isolant d'épaisseur équivalente. L'isolation qu'ils obtiennent est même moins bonne, ce qui enlève tout intérêt pratique à leur travail, qui contient par ailleurs d'autres erreurs

3D INTERFACE ELEMENTS FOR MODELING COMPLEX POTENTIAL DROPS - COMPARISON WITH A BOUNDARY ELEMENTS METHOD

International audienceVoltage drops due to complex surface impedance and/or surface current sources are modelled by a 3D Finite Elements Method. Two specific formulations are given with these special 3D curvilinear second order elements: conduction in a low frequency marine electrometer and thermoelectric Seebeck effect on a solidification front. Simultaneous normal and tangential interfacial discontinuities can be computed. The method is validated by comparison with a Boundary Elements Method and experimental values

Coins et arrondis en éléments finis - Une approche mathématique des coins et arrondis pour les solutions par éléments finis de l'équation de Laplace

La modélisation par éléments finis d'un objet technique conduit souvent à négliger certains détails de structure. C'est en particulier le cas des arêtes et des coins. Ces points particuliers jouent cependant parfois un rôle physique important : c'est le cas par exemple en électrostatique, en raison des effets de pointe. Il est donc important, après une résolution par éléments finis, de savoir estimer le champ au voisinage de ces singularités, en prenant en compte les rayons de courbure réels. Nous nous intéressons ici aux liens qui existent entre la solution singulière théorique, la solution numérique obtenue par éléments finis avec un angle vif, et celle qui est obtenue avec un maillage décrivant un arrondi. Un estimateur non local du champ sur l'arrondi est proposé. Some geometrical details like exact curvatures near edges and corners are often neglected in finite element meshes. Nevertheless they could greatly change the local solutions and the physical behavior (electric arc, ...). Therefore, it could be useful to be able to estimate the real field values near these singular points, using an adequate post-processing, which has to take into account the real curve radii. This paper presents the links between the theoretical singular solution, the numerical solution with a sharp angle, and the solutions with rounded angle. A non-local estimator for the field on the rounded edges and corners is proposed

Tolerance synthesis using bond graph inversion and fuzzy logic

International audienceIn the context of mechatronic systems design, this paper addresses a parameter tolerance synthesis with respect to specifications including output epistemic uncertainties. The methodology proposed here concerns uncertainties modelled with fuzzy logic. The procedure relies on output uncertainties propagation through an inverse model. Design parameter tolerance is then synthesized. The results are validated injecting designed parameters in the direct model. The methodology is illustrated on a linear model with specifications including combined uncertainties