X-ray diffraction, Amorphous silicon, Multi-objective optimization, Monte Carlo methods. This paper addresses a difficult inverse problem that involves the reconstruction of a three-dimensional model of tetrahedral amorphous semiconductors via inversion of diffraction data. By posing the material-structure determination as a multiobjective optimization program, it has been shown that the problem can be solved accurately using a few structural constraints, but no total-energy functionals/forces, which describe the local chemistry of amorphous networks. The approach yields highly realistic models of amorphous silicon, with no or only a few coordination defects (≤1%), a narrow bond-angle distribution of width 9-11.5°, and an electronic gap of 0.8-1.4 eV. These data-driven information-based models have been found to produce electronic and vibrational properties of a-Si that match accurately with experimental data and rival that of the Wooten-Winer-Weaire models. The study confirms the effectiveness of a multiobjective optimization approach to the structural determination of complex materials, and resolves a long-standing dispute concerning the uniqueness of a model of tetrahedral amorphous semiconductors obtained via inversion of diffraction data.