Cooperative Multi-objective Topology Optimization Using Clustering and Metamodeling

Topology optimization optimizes material layout in a design space for a given objective, such as crash energy absorption, and a set of boundary conditions. In industrial applications, multi-objective topology optimization requires expensive simulations to evaluate the objectives and generate multiple Pareto-optimal solutions. So, it is more economical to identify preferred regions on the Pareto front and generate only the desired solutions. Clustering methods, a widely used subclass of machine learning methods, provide an unsupervised approach to summarize the dataset, which eases the identification of the preferred set of designs. However, generating solutions similar to the preferred designs based on different metrics is a challenging task. In this paper, we present an interactive method to generate designs similar to a preferred set using one of the state-of-the-art weighted-sum approaches called scaled energy weighting - hybrid cellular automata (SEW-HCA). To avoid unnecessary computations, metamodels are used to predict the desired weight vectors needed by SEW-HCA. We evaluate an application of our method for cooperative topology optimization using a cantilever multi-load-case problem and a crashworthiness optimization problem. Using the proposed method, we could successfully generate designs that are similar to preferred solutions based on geometry and performance. We believe that this is a crucial component that will improve the usefulness of multi-objective topology optimization in real-world applications.