Laurent Krähenbühl

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 manly 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.

Effective dielectric constant of periodic composite materials

We presentcomputer 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.

Thin layers in electrical engineering-example of shell models in analysing eddy-currents by boundary and finite element methods

During last years, several numerical formulations have been developed by us to modelize physical problems like: conducting film effects over the surface of insulators (pollution) [1], high frequency eddy-currents [2], earth field effects on the hull of a ship [3]. The physical effects being at stake are completely different, but in each of these examples, they originate from a region thin in regard with the other geometrical dimensions. An efficient numerical approach consists on using a surfacic representation with special boundary conditions expressing the solution inside the thin region. We propose in that paper a didactical approach to thin regions in electromanetics and, as an example, the boundary conditions and surfacic equation for eddy currents flowing inside a thin ferromagnetic shell. The numerical tests are done using the BEM software PH13D, but the results could easily be transposed in a FEM context. The practical applications may concern the computation of losses (shield of electrical machines or transformers) or low frequency electromagnetic perturbations (screen effects, EMC) as well as special domains like optimization of the induction heating of pans (french art culinaire).

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 e1=3−0.03i or e1=30−0.3i 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 r...

A multiobjective methodology for evaluating genetic operators

This paper is concerned with the problem of evaluating genetic algorithm (GA) operator combinations. Each GA operator, like crossover or mutation, can be implemented according to several different formulations. This paper shows that: 1) the performances of different operators are not independent and 2) different merit figures for measuring a GA performance are conflicting. In order to account for this problem structure, a multiobjective analysis methodology is proposed. This methodology is employed for the evaluation of a new crossover operator (real-biased crossover) that is shown to bring a performance enhancement. A GA that was found by the proposed methodology is applied in an electromagnetic (EM) benchmark problem.

Treating constraints as objectives in multiobjective optimization problems using niched Pareto genetic algorithm

In this paper, the constraints, in multiobjective optimization problems, are treated as objectives. The constraints are transformed in two new objectives: one is based on a penalty function and the other is made equal to the number of violated constraints. To ensure the convergence to a feasible Pareto optimal front, the constrained individuals are eliminated during the elitist process. The treatment of infeasible individuals required some relevant modifications in the standard Parks and Miller elitist technique. Analytical and electromagnetic problems are presented and the results suggest the effectiveness of the proposed approach.

A boundary integral equation method for the calculation of the effective permittivity of periodic composites

We present a numerical method based upon the resolution of boundary integral equations for the calculation of the effective permittivity of a lossless composite structure consisting of a two component mixture, each with its own dielectric and shape characteristics. The topological arrangements considered are periodic lattices of inhomogeneities. Our numerical simulations are compared to the effective medium approach and with results of previous works.

Genetic algorithm coupled with a deterministic method for optimization in electromagnetics

In this paper, a hybrid technique for global optimization based on the genetic algorithm and a deterministic method is presented. A potential advantage of the hybrid method compared to the genetic algorithm is that global optimization can be performed more efficiently. An intrinsic problem of the hybrid techniques is related to the moment of stopping the stochastic routine to launch the deterministic one. This is investigated using some natural criteria for the commutation between the two methods. The results show that it is possible to gain in efficiency and in accuracy but the criterion is usually problem dependent. Finally, to show the solution of a real problem, the hybrid algorithm is coupled to a 2D code based on the boundary element method to optimize a connector of 145 kV GIS.

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. Index terms-Genetic algorithms, niching methods, sharing, crowding, clearing, shape optimization, magnetizer.

Computation of electric fields and potential on polluted insulators using a boundary element method

The authors present a calculation method for electric fields and potential applicable in the case of a polluted insulator. This method, based on boundary integral equations, is suitable for 3-D geometries and polluted layers. Results obtained by this method are compared with analytical solutions (potential, currents) and with measured values (potential, leakage current). >