A Quadratic Exterior Penalty Function Based Probabilistic Analytical Target Cascading Method

Probabilistic Analytical Target Cascading (PATC) is developed for hierarchical multi-disciplinary design optimization under random uncertainty. In this method, to let all parts of the designed system work well together, coordination strategies should be used. Traditionally, consistency constraints (equality constraints) are formulated as inequality constraints by adding corresponding parameters which are considered as design variables, and the object is to minimize deviations from the propagated targets and thus achieve intersystem compatibility, because of the additional variables, it always takes a lot of time to find the results fulfill all the optimizations. In order to relax the consistency constraints without increasing the number of design variables, the Quadratic Exterior Penalty Function (QEPF) method is introduced into PATC, and the consistency constraints become a part of the object with a dynamic weighting coefficient. This proposed method QEPF-PATC is tested on a geometric programming problem. And the accuracy and efficiency are demonstrated by comparing QEPF-PATC results to those obtained by using Probabilistic All-In-One (PAIO) and PATC.