Numerical investigation of non-hierarchical coordination for distributed multidisciplinary design optimization with fixed computational budget

This paper presents a numerical investigation of the non-hierarchical formulation of Analytical Target Cascading (ATC) for coordinating distributed multidisciplinary design optimization (MDO) problems. Since the computational cost of the analyses can be high and/or asymmetric, it is beneficial to understand the impact of the number of ATC iterations required for coordination and the number of iterations required for disciplinary feasibility on the quality of the obtained MDO solution. At each “outer” ATC iteration, the disciplinary optimization subproblems are solved for a predefined maximum number of “inner” loop iterations. The numerical experiments consider different numbers of maximum outer iterations while keeping the total computational budget of analyses constant. Solution quality is quantified by optimality (objective function value) and consistency (violation of coordination-related consistency constraints). Since MDO problems are typically simulation-based (and often blackbox) problems, we compare implementations of the mesh-adaptive direct search optimization algorithm (a derivative-free method with convergence properties) to the gradient-based interior-point algorithm implementation of the popular Matlab optimization toolbox. The impact of the values of two parameters involved in the alternating directions updating scheme of the augmented Lagrangian penalty functions (aka method of multipliers) on solution quality is also investigated. Numerical results are provided for a variety of MDO test problems. The results indicate consistently that a balanced modest number of outer and inner iterations is more effective; moreover, there seems to be a specific combination of parameter value ranges that yield better results.