Abstract
The augmented Lagrangian penalty formulation and four different coordination strategies are used to examine the nu- merical 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.
Highlights
A complex optimization problem may be decomposed into two or more subsystems with partitioned design variables and separate objective functions and design constraints
The numerical behavior of the analytical target cascading (ATC) method was investigated for multilevel optimization of hierarchical systems based on different solution strategies
Three example problems were used to examine the effects of penalty parameter updating coefficient β and convergence tolerance τ on the computational cost and solution accuracy
Summary
A complex optimization problem may be decomposed into two or more subsystems with partitioned design variables and separate objective functions and design constraints. The scaled tolerance formulation [3] was used in [7] to investigate the numerical behavior of the ATC methodology and the local convergence properties of different coordination strategies They examined the effects of linking variables, subproblem solution accuracy, and the number of significant digits on numerical stability. An iterative method was presented in [8] for finding the minimal penalty weight factors that provide converged solutions within user-specified inconsistency tolerances, and its effectiveness was demonstrated with several examples This method contains an inner and an outer loop. By means of the ALP relaxation, ill-conditioning is reduced for the inner loop because accurate solutions can be obtained for smaller weight factors This formulation was later adopted in [16] that used Diagonal Quadratic Approximation (DQA) and Truncated DQA (TDQA) for parallelization of ATC. The effects of the penalty parameter updating coefficient in the outer loop and the initial guessed values for the decision variables to start the multilevel optimization process are examined by solving three example problems
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