Robust optimization with convex model considering bounded constraints on performance variation

In robust optimization, double-looped structures are often adopted where the outer loop is used to seek for the optimal design and the optimization performed in the inner loop is for the robustness assessment of the candidate solutions. However, the double-looped techniques usually will lead to a significant increase in computational efforts. Therefore, in this paper, a new robustness index is developed to handle bounded constraints on performance variation where no optimization run is required for the robustness evaluation work in the inner loop. The computation of this new index is based on the sensitivity Jacobian matrix of the system performances with respect to the uncertainties and it can quantitatively measure the maximal allowable magnitude of system variations. By introducing this index, the robust design problem can be reformulated as a deterministic optimization with robustness indices requirements. Two numerical examples are tested to show the effectiveness and efficiency of the proposed approach, whose solutions and computational efforts are compared to those from a double-looped approach proposed in previous literature.