Theories and algorithms of structural optimization considering uncertain parameters and loading conditions have become an important frontier research field of computational mechanics. This project aims to investigate the probability/non-probability modeling theory for structural optimization problems with multi-sourced bounded uncertainties, solvable optimization formulations and convergible algorithms for bi-level nested mathematical programming problems. Correlated multi-sourced bounded uncertainties that can not be easily described by probabilistic models will be treated with convex set/probability hybrid models. An objective measure for characterizing the structural safety margin and the corresponding non-deterministic structural optimization model will be established. Convex programming formulations for problems with certain mathematical and mechanical nature and the behaviors of the solutions will be studied. It is envisaged that the project will achieve progress in the field of structural optimization studies using multi-sourced non-probabilistic uncertainty models and thus strengthens the non-deterministic structural optimization theories and methods.