An SLP filter algorithm for probabilistic analytical target cascading

Decision-making under uncertainty is particularly challenging in the case of multidisciplinary, multilevel system optimization problems. Subsystem interactions cause strong couplings, which may be amplified by uncertainty. Thus, effective coordination strategies can be particularly beneficial. Analytical target cascading (ATC) is a deterministic optimization method for multilevel hierarchical system design that has been extended to probabilistic formulations. Solving the probabilistic optimization problem requires propagation of uncertainty, namely, evaluating or estimating the output distributions, a task that is computationally expensive for highly nonlinear functions. This article presents the use of sequential linear programming (SLP) for probabilistic ATC. By linearizing and solving a problem successively, the strategy takes advantage of the simplicity and ease of uncertainty propagation for a linear system under the assumption that inputs are normally distributed or can be transformed into equivalent normal distributions. A suspension strategy, developed for a deterministic SLP coordination strategy for ATC, is applied to reduce computational cost by suspending the analyses of subsystems that do not need considerable redesign. The accuracy and effectiveness of the proposed coordination strategy is demonstrated with several numerical examples.