Despite some recent efforts towards multi-objective design optimization of multilevel converters, design optimization of solid-state-transformers (SSTs) are not presented much in the literature mainly because of the lack of computationally feasible techniques. This paper is dedicated towards a computational feasibility study of multi-objective design optimization techniques for medium-voltage (MV) grid-connected SSTs. After defining the application and scope of SST design optimization problem, a brief description of the possible solution techniques are discussed which shows the merits of semi-numerical/hybrid design optimization techniques. Subsequently, a machine learning (ML) aided hybrid optimization technique is executed for a 15 kVA single-stage SiC-based SST design. Suitable component modelling is presented and a strong agreement is observed between theoretical optimization and experimental results. Finally, a comparative evaluation of the analytical, numerical, standalone hybrid and ML-aided hybrid optimization techniques (deployed for the same 15 kVA SiC-based SST design) reveals that the ML-aided hybrid strategy is best suited for SST design optimization as it requires feasible computational time for <5% error. © 2021 IEEE.