Numerical Comparison of Multi-Level Optimization Techniques

Multi-level or multi-disciplinary design optimization techniques rely on a decomposition of the optimization problem into separate levels or subsystems. In this overview we distinguished six established approaches. Namely, Optimization by Linear Decomposition (OLD), Concurrent SubSpace Optimization (CSSO), Collaborative Optimization (CO), Bi-Level Integrated System Synthesis (BLISS), Analytical Target Cascading (ATC) and Quasi-separable Subsystem Decomposition (QSD). The methods were compared on the basis of a structural two-bar truss optimization problem. Convergence curves towards the solution, the number of local and multi-level iterations were compared with respect to an All-in-One optimization. This study showed that, CO with an inexact penalty method and ATC performed equally well in terms of number of function calls. OLD, BLISS and QSD were more expensive, due to costly approximations. CSSO did not converge. In future work we plan to integrate CO and ATC into a multi-scale analysis method, while adapting certain approximation concepts of the other multi-level techniques.