A reduced order model is developed for low frequency, fully coupled, undamped and constantly damped structural acoustic analysis of interior cavities, backed by flexible structural systems. The reduced order model is obtained by applying a Galerkin projection of the coupled system matrices, from a higher dimensional subspace to a lower dimensional subspace, whilst preserving some essential properties of the coupled system. The basis vectors for projection are computed efficiently using the Arnoldi algorithm, which generates an orthogonal basis for the Krylov subspace containing moments of the original system. The key idea of constructing a reduced order model via Krylov subspaces is to remove the uncontrollable, unobservable and weakly controllable, observable parts without affecting the transfer function of the coupled system. The reduced order modelling technique is applied to a frame-panel two-way coupled vibro-acoustic optimization problem, with stacking sequences of the composite structure as design variables. The optimization is performed via a hybrid search strategy combining outputs from Latin Hypercube Sampling (LHS) and Mesh Adaptive Direct Search (MADS) algorithm. It is shown that reduced order modelling technique results in a very significant reduction in simulation time, while maintaining the desired accuracy of the optimization variables under investigation.