Comparison of Alternative Strategies for Multilevel Optimization of Hierarchical Systems

Abstract

The augmented Lagrangian penalty formulation and four different coordination strategies are used to examine the numerical behavior of Analytical Target Cascading (ATC) for multilevel optimization of hierarchical systems. The coordination strategies considered include augmented Lagrangian using the method of multipliers and alternating direction method of multipliers, diagonal quadratic approximation, and truncated diagonal quadratic approximation. Properties examined include computational cost 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 decomposed 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 computational cost.