Novel collaborative optimization method based on geometric analysis

Geometric analysis of collaborative optimization (CO) algorithm is presented, based on which a new system-level optimization model is constructed. Compared with the algebraic analysis, the geometric analysis is more intuitive and concise, which shows that in the discipline-level optimization the optimal design point is the closest point to the target point provided by the system-level optimization. Moreover, the gradient of the active constraint boundary at the optimal design point can also be obtained through the geometric analysis. As a result, a linear approximation of the discipline-level active constraint can be constructed, which will then be passed to the system-level optimization to serve as system-level constraint. As the iteration goes on, more linear constraints will be added to the system-level optimization and the combination of these linear constraints can gradually approximate the feasible region of the original optimization problem. A gear reducer design problem is solved by using both the presented CO method and the conventional CO method, which shows that the presented method is more computationally efficient than the conventional one.