Managing approximation models in collaborative optimization

Collaborative optimization (CO), one of the multidisciplinary design optimization techniques, has been credited with guaranteeing disciplinary autonomy while maintaining interdisciplinary compatibility due to its bi-level optimization structure. However, a few difficulties caused by certain features of its architecture have been also reported. The architecture, with discipline-level optimizations nested in a system-level optimization, leads to considerably increased computational time. In addition, numerical difficulties such as the problem of slow convergence or unexpected nonlinearity of the compatibility constraint in the system-level optimization are known weaknesses of CO. This paper proposes the use of an approximation model in place of the disciplinary optimization in the system-level optimization in order to relieve the aforementioned difficulties. The disciplinary optimization result, the optimal discrepancy function value, is modeled as a function of the interdisciplinary target variables, and design variables of the system level. However, since this approach is hindered by the peculiar form of the compatibility constraint, it is hard to exploit well-developed conventional approximation methods. In this paper, neural network classification is employed as a classifier to determine whether a design point is feasible or not. Kriging is also combined with the classification to make up for the weakness that the classification cannot estimate the degree of infeasibility. In addition, for the purpose of enhancing the accuracy of the predicted optimum, this paper also employs two approximation management frameworks for single-objective and multi-objective optimization problem in the system-level optimization. The approximation is continuously updated using the information obtained from the optimization process. This can cut down the required number of disciplinary optimizations considerably and lead to a design (or Pareto set) near to the true optimum (or true Pareto set) of the system-level optimization.