PurposeThe purpose of this paper is to extend a (μ/ρ, λ) evolution strategy to perform remarkably more globally and to detect as many solutions as possible close to the Pareto optimal front.Design/methodology/approachA C‐link cluster algorithm is used to group the parameter configurations of the current population into more or less independent clusters. Following this procedure, recombination (a classical operator of evolutionary strategies) is modified. Recombination within a cluster is performed with a higher probability than recombination of individuals coming from detached clusters.FindingsIt is shown that this new method ends up virtually always in the global solution of a multi‐modal test function. When applied to a real‐world application, several solutions very close to the front of Pareto optimal solutions are detected.Research limitations/implicationsStochastic optimization strategies need a very large number of function calls to exhibit their ability to reach very good local if not the global solution. Therefore, the application of such methods is still limited to problems where the forward solutions can be obtained with a reasonable computational effort.Originality/valueThe main improvement is the usage of approximate number of isolated clusters to dynamically update the size of the population in order to save computation time, to find the global solution with a higher probability and to use more than one objective function to cover a larger part of the Pareto optimal front.
To 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-ElementMethod. 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.Optimaler Entwurf einer magneto-rheologischen Flü ssigkeitskupplung. Zur Ü bertragung 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 Flü ssigkeit ü bertragen. Diese besteht aus einer Trä gerflü ssigkeit, die mit unzä hligen Mikropartikeln versetzt ist. Ist kein Magnetfeld vorhanden, ü berträ gt die Kupplung lediglich ein geringes Grundmoment. Sobald allerdings die Flussdichte erhö ht wird, beginnen die Mikropartikel, feste Ketten zu bilden. Damit erhö ht sich auch das ü bertragene Moment. Das fü r die Ü bertragung verantwortliche Magentfeld wird mittels der Methode der Finiten Elemente simuliert. Ein optimales Design der Kupplung soll ein gegebens maximales Moment ü bertragen und dabei ein mö glichst geringes Gewicht aufweisen. Diese Optimierungsaufgabe, einander widersprechende Ziele zu erfü llen, wird mit einer Evolutionsstrategie, einem stochastischen Optimierungsverfahren, gelö st. Schlü sselwö rter: nichtlineare Magnetfeldprobleme; magneto-rheologische Flü ssigkeiten; stochastische Optimierungsverfahren; multiple Zielfunktionen
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