Ch. Magele

Pareto optimality and particle swarm optimization

Real-world optimization problems often require the minimization/maximization of more than one objective, which, in general, conflict with each other. These problems (multiobjective optimization problems, vector optimization problems) are usually treated by using weighted sums or other decision-making schemes. An alternative way is to look for the pareto-optimal front. In this paper, the particle swarm algorithm is modified to detect the pareto-optimal front.

SMES Optimization Benchmark Extended: Introducing Pareto Optimal Solutions Into TEAM22

In 1996, a superconducting magnetic energy storage arrangement was selected to become a benchmark problem for testing different optimization algorithms, both deterministic and stochastic ones. Since the forward problem can be solved semianalytically by Biot-Savarts law, this benchmark became quite popular. Nevertheless, the demands on optimization software have increased dramatically since then. To give an example, methods looking for Pareto-optimal points rather than for a single solution only have been introduced by several groups. In this paper, a proposal for an extended version of the benchmark problem will be made and some results will be presented.

Utilizing feedforward neural networks for acceleration of global optimization procedures [SMES problems]

Global optimization in electrical engineering usually requires an enormous amount of CPU time to evaluate the objective function when stochastic methods are used. Approximating the objective function can drastically reduce the computational demands. The use of feedforward neural networks is proposed in this paper and its application is investigated using an unconstrained and a constrained version of the TEAM Workshop problem 22.

Optimization of SMES solenoids with regard to their stray fields

Solenoidal SMES (Superconducting Magnetic Energy Storage) usually suffer form their remarkable stray field. A certain arrangement was devised that should reduce the extension of the far ranging stray field. Hence, a second solenoid was placed outside the SMES device with a current flowing in the opposite direction compared to the inner coil. Configurations with both coils in a single plane were regarded only. As an important factor the minimum energy to be stored was given. In a first step calculation, methods have been found that reveal data for the minimum geometrical dimensions of the SMES device in an analytical way. It was shown that the stray field, compared to a single coil arrangement could be reduced remarkably. Evolution strategies and a conjugate gradient method were used to improve the quality of the above solution. >

Evolution strategy and hierarchical clustering

In most real world optimization problems, one tries to determine the global among some or even numerous local solutions within the feasible region of parameters. Nevertheless, it could be worthwhile to investigate some of the local solutions as well. A most desirable behavior would be that the optimization strategy behaves globally and yields additional information about local minima detected on the way to the global solution. In this paper, a clustering algorithm has been implemented into an extended higher order evolution strategy in order to achieve these goals. Multimodal two-dimensional test problems, namely, Rastrigins function and the 4-parameter die mold press benchmark problem (Takahashi, 1996), are solved using this approach.

Shape design with great geometrical deformations using continuously moving finite element nodes

In this paper design sensitivity analysis is applied to solve the TEAM workshop problem 25. In order to justify the use of a gradient method, it is necessary to assume a continuously differentiable dependence of the stiffness matrix on the design parameters. Since design sensitivity analysis is mainly applicable to optimization problems, where the geometrical parameters undergo small changes only - which is not the case for the problem investigated in this paper-a procedure is proposed, which allows this method to be applied also when the changes in geometry are significant.

Approximation of the objective function: multiquadrics versus neural networks

Global optimization in electrical engineering using stochastic methods requires usually a large amount of CPU time to locate the optimum, if the objective function is calculated either with the finite element method (FEM) or the boundary element method (BEM). One approach to reduce the number of FEM or BEM calls using neural networks and another one using multiquadric functions have been introduced recently. This paper compares the efficiency of both methods, which are applied to a couple of test problems and the results are discussed.

Optimal design of a disk type magneto-rheologic fluid clutch

SummaryTo transmit a continuously adjustable torque from the main shaft to the move shaft electromagnetic clutches can be used in cars. In contrast to friction clutches, electromagnetic clutches transmit rotation by a magneto-rheologic fluid consisting of a base fluid mixed with numerous ferro-magnetic micro-sized particles. In the absence of a magnetic field a small basic torque is passed on only. Once the flux density is increased, the micro-sized particles start to form firmly tied chains increasing the transmitted torque. The magnitude of the torque can be regulated by the application of an appropriate magnetic field which is simulated by the Finite-Element-Method. The optimal design of the clutch requires a certain torque being transmitted while keeping the weight as small as possible. This task of multi-objective optimization is performed using a higher order Evolution Strategy, a stochastic optimization method.ZusammenfassungZur Übertragung eines stufenlos regelbaren Moments in einem Getriebe kann man elektromagnetische Kupplungen verwenden. Anders als bei normalen Druckkupplungen wird in diesem Fall das Moment mittels einer magneto-rheologischen Flüssigkeit übertragen. Diese besteht aus einer Trägerflüssigkeit, die mit unzähligen Mikropartikeln versetzt ist. Ist kein Magnetfeld vorhanden, überträgt die Kupplung lediglich ein geringes Grundmoment. Sobald allerdings die Flussdichte erhöht wird, beginnen die Mikropartikel, feste Ketten zu bilden. Damit erhöht sich auch das übertragene Moment. Das für die Übertragung verantwortliche Magentfeld wird mittels der Methode der Finiten Elemente simuliert. Ein optimales Design der Kupplung soll ein gegebens maximales Moment übertragen und dabei ein möglichst geringes Gewicht aufweisen. Diese Optimierungsaufgabe, einander widersprechende Ziele zu erfüllen, wird mit einer Evolutionsstrategie, einem stochastischen Optimierungsverfahren, gelöst.

Reconstruction of the anisotropic complex conductivity distribution in 3D

Purpose – The aim of the work is to reconstruct the anisotropic complex conductivity distribution with the common Gauss‐Newton algorithm.Design/methodology/approach – A cubic region with anisotropic material properties is enclosed by a larger cube with isotropic material properties. Numerical simulations are done with tetrahedral nodal finite elements of second‐order.Findings – It can be shown that it is possible to reconstruct anisotropic complex conductivity distribution if the starting values are chosen sufficiently close to the true values of the complex conductivity.Originality/value – In this paper, the anisotropic electric conductivity and the anisotropic permittivity are reconstructed in 3D.

Geometric multigrid to accelerate the solution of the quasi-static electric field problem by tetrahedral finite elements

The acceleration of the solution of the quasi-static electric field problem considering anisotropic complex conductivity simulated by tetrahedral finite elements of first order is investigated by geometric multigrid.