Predictive simulations of human motion are a precious resource for a deeper understanding of the motor control policies encoded by the central nervous system. They also have profound implications for the design and control of assistive and rehabilitation devices, for ergonomics, as well as for surgical planning. However, the potential of state-of-the-art predictive approaches is not fully realized yet, making it difficult to draw convincing conclusions about the actual optimality principles underlying human walking. In the present study we propose a novel formulation of a bilevel, inverse optimal control strategy based on a full-body three-dimensional neuromusculoskeletal model. In the lower level, prediction of walking is formulated as a principled multi-objective optimal control problem based on a weighted Chebyshev metric, whereas the contributions of candidate control objectives are systematically and efficiently identified in the upper level. Our framework has proved to be effective in determining the contributions of the selected objectives and in reproducing salient features of human locomotion. Nonetheless, some deviations from the experimental kinematic and kinetic trajectories have emerged, suggesting directions for future research. The proposed framework can serve as an inverse optimal control platform for testing multiple optimality criteria, with the ultimate goal of learning the control objectives that best explain observed human motion.