Multitask Shape Optimization Using a 3-D Point Cloud Autoencoder as Unified Representation

The choice of design representations, as of search operators, is central to the performance of evolutionary optimization algorithms, in particular, for multitask problems. The multitask approach pushes further the parallelization aspect of these algorithms by solving simultaneously multiple optimization tasks using a single population. During the search, the operators implicitly transfer knowledge between solutions to the offspring, taking advantage of potential synergies between problems to drive the solutions to optimality. Nevertheless, in order to operate on the individuals, the design space of each task has to be mapped to a common search space, which is challenging in engineering cases without clear semantic overlap between parameters. Here, we apply a 3-D point cloud autoencoder to map the representations from the Cartesian to a unified design representation: the latent space of the autoencoder. The transfer of latent space features between design representations allows the reconstruction of shapes with interpolated characteristics and maintenance of common parts, which potentially improves the performance of the designs in one or more tasks during the optimization. Compared to traditional representations for shape optimization, such as free-form deformation, the latent representation enables more representative design modifications, while keeping the baseline characteristics of the learned classes of objects. We demonstrate the efficiency of our approach in an optimization scenario where we minimize the aerodynamic drag of two different car shapes with common underbodies for cost-efficient vehicle platform design.