Multiblock polymers are a fascinating class of soft materials owing to their spontaneous self-assembly into a variety of ordered mesophases at the nanoscale. However, controlling the ordering and hence the properties is difficult due to a vast number of design parameters including the choice of monomer species, block sequence, block molecular weights and dispersity, polymer architecture, and binary interaction parameters. Navigating through this design space in order to find an optimal formulation for a target property requires an approach that efficiently searches through the countless parameter combinations in an automated fashion. We report on an inverse design strategy to target bulk morphologies utilizing particle swarm optimization (PSO) as a global optimizer and self consistent-field theory (SCFT) as a forward prediction engine. To avoid metastable states in the forward prediction, we utilize pseudospectral variable cell SCFT initiated from a library of defect-free seeds of known block copolymer morphologies. We demonstrate that our approach allows for a robust identification of block copolymers and copolymer alloys that self-assemble into a targeted structure, optimizing parameters such as block fractions, blend fractions, and Flory chi parameters.