Problem formulation, solution procedures and geometric modeling: Key issues in variable-topology optimization

The field of variable-topology shape design in structural optimization has been thriving over the last decade, and a wide range of tools for handling such problems has been proposed.' In this paper we classify the existing methods in an attempt to make differences and similarities transparent. Our classification depends on the way each method responds to the ill-posedness of the fundamental generalized shape optimization problem. Our classification helps to identify the strengths and weaknesses of the current methodologies, and provides a guide for future research. A central theme in our presentation is the pivotal role played by the geometric design parametrization. A raster like representation has been the most popular choice to date, but we believe future research should place greater emphasis on alternative geometric representations, especially for problems involving macroscopic topology design of structures and multi-physics applications.