Sequential linearization in analytical target cascading for optimization of complex multilevel systems

Abstract

Large-scale design problems are high dimensional and deeply coupled in nature. The complexity of such large-scale systems prevents designers from solving them as a whole. Analytical target cascading (ATC) provides a systematic approach in solving decomposed large-scale systems that has solvable subsystems. By coordinating between subsystems, ATC can obtain the same optima as they were undecomposed. However, a convergent coordination requires series of ATC iterations that may hinder the efficiency of ATC. In this research, a sequential linearization technique is proposed to improve the efficiency of ATC. The proposed linearization technique is applied to each ATC iteration, and therefore each iteration has all linear subsystems that can be solved with high efficiency. The global convergence of this approach is ensured by a filter to determine the acceptance of the optima at each iteration and the corresponding trust region. One further motivation of the proposed strategy is its perceived potential in handling multilevel problems with random design variables. As previously studied, the sequential linear programming (SLP) algorithm provides a good balance between efficiency, accuracy, and convergence for single-level design optimization under random design variables. The proposed linearization technique can integrate with the SLP algorithm for multilevel systems. In this work, a geometric programming example is used to demonstrate the efficiency of the proposed method over standard ATC solution process without loss of accuracy.