Hybrid evolutionary approach for level set topology optimization

Although Topology Optimization is widely used in many industrial applications, it is still in the initial phase of development for highly nonlinear, multimodal and noisy problems, where the analytical sensitivity information is either not available or difficult to obtain. For these problems, including the highly relevant crashworthiness optimization, alternative approaches, relying not solely on the gradient, are necessary. One option are Evolutionary Algorithms, which are well-suited for this type of problems, but with the drawback of considerable computational costs. In this paper we propose a hybrid evolutionary optimization method using a geometric Level-Set Method for an implicit representation of mechanical structures. Hybrid optimization approach integrates gradient information in stochastic search to improve convergence behavior and global search properties. Gradient information can be obtained from structural state as well as approximated via equivalent state or any known heuristics. In order to evaluate the proposed methods, a minimum compliance problem for a standard cantilever beam benchmark case is considered. These results show that the hybridization is very beneficial in terms of convergence speed and performance of the optimized designs.