Reaction Diffusion equations (RDE) (e.g. Meinhardt: The Algorithmic Beauty of Sea Shells) have been formulated for achieving the stable generation of patterns. General rules exist on the relation of parameters in these differential equations to achieve stable patterns, e.g. local instability (autocatalysis) plus global stabilization (fast diffusion). Target of the project is to use evolutionary algorithms (e.g. ES or EP) to optimize the parameters of the RDE for achieving stable patterns of a certain type (large dots, small dots, etc.) In the later stage of the project, more recently suggested dynamical systems for pattern formation can be explored, e.g. Basu et al. Nature 434, page.1130, 2005.
The exploration of the search space can be as useful in many applications as the identification of optima. E.g. in aerodynamic design optimization , the identification of interesting and new flow phenomena can be as important to the engineer as the pure performance of the design. It is known that an analysis of the genotype space can be used to direct the search towards unexplored regions. In this project, we want to use the analysis of the phenotype in order to direct the search towards interesting phenomena. The project will start with the optimization of Reaction Diffusion Equations for pattern generation. The target is to analysis the 2D pattern in such a way as to explore parameter settings that produce particularly unique and novel patterns compared to a set of already identified patterns which are stored in an archive. In the summer project the target can be extended during a stay at Honda towards the 2D analysis of the flow field of a turbine blade optimization in order to produce a set of blade designs that produce particular novel and unique flow fields while not performing worse than a given lower threshold.
The choice of an efficient representation for a given geometry in an evolutionary design optimization is very important. A good representation provides a well-balanced trade-off between high design flexibility and a low number of parameters. For the optimization of aerodynamic designs deformation methods have been favored as they allow an adequate rocess flow for design generation and evaluation. In this project, Free Form Deformation (FFD) is applied for generating coupled designs, a top layer and a bottom layer design. Whereas the evolutionary algorithm interacts directly with the top layer design, the bottom layer design is generated by pre-defined transfer functions. In this project, different variants of the transfer functions have to be analyzed with respect to their influence on the fitness landscape. The characteristics of different transfer functions have to be highlighted and suggestions have to be made for different optimization settings.
The process of developing innovative and aesthetical designs with the support of computational algorithms is very challenging. In this project, ways of generating and applying measures for aesthetic should be evaluated. After studying related literature on the concepts for measuring design aesthetical qualities, a test system has to be implemented which contributes to a systematic developmental process of designs. As a starting point we think of using data mining algorithms on user preferred design schemes for estimating possible aesthetic qualities of novel/unknown design regions. A possible sketch for a test scenario may look as follows: In the first phase of the framework, various geometrical shapes are presented to different human users who decide (spontaneously) on their aesthetical value and/or interestingness. Based on the database of inputs data mining algorithms are applied for the extraction of shape features and calculation of clusters according to their quality values. In a third phase, the user interacts with the system by creating new shapes and presenting them to the system. The generated shapes are analyzed by the software with respect to the local or global aesthetic/interestingness quality and feedback is provided to the user. This feedback enables the user to reshape and modify the created design towards a desired development.
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