A framework for multi-objective topology optimization is presented with the purpose to simultaneously optimize both fluid flow and acoustic quantities. The proposed method uses a coupled approach on fixed grids with immersed solid boundaries. For the fluid flow part the incompressible Navier-Stokes equations are solved and the immersed boundaries are modeled with a Brinkman penalization method. The acoustic field is computed by an acoustic/viscous splitting technique and the solution of the resulting linearized Euler equations. The reflecting boundaries are modeled by a mismatch in the acoustic impedance between solid and fluid. To describe the geometry of the boundaries a NURBS-based approach is introduced. Two test cases are investigated to validate the immersed boundary method for the fluid flow problem and the acoustics, respectively. Finally, the capability for topological changes of the proposed method is shown with a multi-objective optimization test case, which is solved with the gradient-free evolutionary algorithm NSGA-II
