Soft Computing Methods for Applied Shape Optimization

Evolutionary algorithms (EA) were first introduced in the nineteen-seventies for optimizing technical devices. EA consist of operators simulating natural reproduction. According to biological principles, the reproduction consists of recombination and mutation as well as a selection process refered to as `survival of the fittest'. Rediscovered in the last decade, evolutionary algorithms proved their potential as global search algorithms with properties and qualities that can hardly be depicted by conventional gradient based methods. In multi-objective optimization, EA can be seen as superior to gradient based methods. For optimizing engineering relevant technical devices, as for instance flow geometry optimization, there is no analytical expression of the gradient available and also, a numerical approximation to the gradient is not appropriate due to its vast computational overhead. In this dissertation, EA are not only introduced as Simulated Annealing, but also used to determine system parameters necessary for setting up approximation models. These approximation models are able to depict the functional coherence between design variables and objective function and are thus able to answer the correct objective function value on even unseen design parameter combinations. As approximation models we consider the latest proposed and most capable neural network systems, the Bayesian regularization network and also the adaptive neuro-Fuzzy inference system. As an examplary problem, we consider a staggered channel, paramererized by Bezier splines. From a numerical simulation, we calculate the pressure drop of a number of distorted geometries. From these samples, the network systems are trained and, after training, used in an evolutionary algorithm where we then seek the optimum with the approximation model. As soon as an optimization problem has more than one objective function, and these are concurrenting, a set of solutions is seeked. This set of solutions can be discovered by evolutionary algorithms since they work on solution sets instead of a single solution only as most gradient based methods do. In this dissertation, we present configurations of heat exchange units which are subject to optimization according to objectives like heating performance, pressure drop, flow velocity at control spots, and covered flow field. In such problems, Pareto sets appear, these correspond to equivalent design proposals, i.e. each design of a Pareto set is equally optimal, a further problem dimension is necessary to choose a single design from this set. By considering the Pareto sets, the engineer can quantify his subjective perceptions and choose from a number of optimal solutions.