Representation concepts in evolutionary algorithm-based structural optimization

This thesis investigatos several aspects of numerical optimization in the world of structural engineering. In particular the representation of structural parts as aprerequisite for any optimization process is of great importance. Typically, the representation intensively interacts with the applied optimization algorithrn and decisively contributes to the gcneration of superior design solutions. Moreover, the qualities of the optimization algorithrn also heavily influence the convergence behavior of the optimization process. The dcvelopment of CFRP racing motorcycle rims is presented, whereas EAs and a constant-length vector genetype are applied during the development process. The application of optimization methods provides optimum staeking sequences which lead to decisively lighter roar and front rirns compared to state-of-thc-art rnagncsium alloy rirns. The identified needs for further research in terms of the performance of the optimization algorithm arid the representation concept are addressed in this thesis. AORCEA an Adaptive Operator-Rate Controllecl Evolutionary Algorithrn is devcloped which changcs the operatot rates of the variation operators based on thc search state of the optimization algorithm. A success and a relative diversity measure are applied which are used as an indicator for the adjustrnent of thc variation operator rates, AORCEA is tcstcd on several well-known numerical benchmark functions as well as on the optimization of a steel trellis motorbike frame. The adaptive strategies always perform superior or at least equal to a reference EA with constant variation operator rates. In particular in thc field of composite laminatc optimization the representation of the stacking sequcnce is a eritical issue, A patch concept treating single laminate layers as design entity is the basis for a variablelength representation concept. The optimization of a simple eigenfrequency problem indicates that this variable-length representation concopt may lead to superior solutions with less evaluations. Furthermore. the optimization of a hockcy stick is presented as an example for an engineering application. Besides the traditional vector representation also mathematical graphbased representation concepts are investigated within this thesis, Tho optimization of truss structures is investigatecl due to the obvious similarity between trusses and rnathematical graphs. The nodes and members are encodecl as vertices and edges of a graph, respectively, and a rnajor aclvantage is the inclepenclency from ground structures which are the basis of rnally of the popular truss optimization methods. Moreover, an important advantage of graph-based representations is the possibility of concurrent optimization of topology, shape, and sizing what today is most often strictly separated. The graph-based approach leads to novel solutions which hardly could be found with traditional mcthods. A graph-based representation concept is also developecl for global laminate optimization. Such laminate structures are most often evaluatod by FE-simulations. The underlying FE-mesh which typically consists of layered shell elements is ideally suited für a representation concept. The finite elements are represented in a mathematical graph which further grollpS them to zones. The staeking sequenees of a11 zones are optimizcd and the zone layout allows for loeal reinforcements ancl the incorporation of domain knowledge. Modern CAD systems are essential for product development processes because they offer a parametric-associative representation of meehanical structures, A generie EC framewerk is established which provides all required functionalities to optimize topology and shape of such mechanical structures. The CAD package CATIA V5 and its C++ interface CAA V5 are ideally suited for the implementation of an optimization framework because the mechanical structures are represented by specification trocs, This specification tree is interpreted as mathematical graph which allows for traditional shape but also topology optimization , i.e., the generation of structures with a variable nurnber of design entities is rendered possible. For all these graph-based representation concepts appropriate variation operators are developed and the concepts are validatr«] with illustrative applications which lead to convincing results.