An Empirical Accuracy and Computational Cost Study of Different Methods in Analytical Target Cascading

Abstract

This paper examines the numerical behavior of the analytical target cascading (ATC) for multilevel optimization of hierarchical systems based on the Augmented Lagrangian Penalty (ALP) formulation and four different solution strategies. The strategies considered include Augmented Lagrangian using the method of multipliers (AL) and alternating direction method of multipliers (AL-AD), Diagonal Quadratic Approximation method (DQA), and Truncated Diagonal Quadratic Approximation method (TDQA). Properties examined include computational cost or efficiency and solution accuracy based on the selected values for the different parameters that appear in each formulation. The different strategies are implemented using two- and three-level example problems. While the results show the interaction between the selected ATC formulation and the values of associated parameters, they clearly highlight the impact they could have on both the solution accuracy and efficiency.