Acoustic filters have a wide range of applications, yet customizing them with desired properties is difficult. Motivated by recent progress in additive manufacturing that allows for fast prototyping of complex shapes, we present a computational approach that automates the design of acoustic filters with complex geometries. In our approach, we construct an acoustic filter comprised of a set of parameterized shape primitives, whose transmission matrices can be precomputed. Using an efficient method of simulating the transmission matrix of an assembly built from these underlying primitives, our method is able to optimize both the arrangement and the parameters of the acoustic shape primitives in order to satisfy target acoustic properties of the filter. We validate our results against industrial laboratory measurements and high-quality off-line simulations. We demonstrate that our method enables a wide range of applications including muffler design, musical wind instrument prototyping, and encoding imperceptible acoustic information into everyday objects.