Within the classical design of, for example, bridges and airplane structures, optimization approaches generally focus primarily on adjusting large-scale (macroscopic) parameters and are therefore neglecting the influence of small-scale (microscopic) parameters on the large-scale behavior. The main reason is because of numerical efficiency. In literature various multi-level optimization appproaches are described in which six main approaches can be distinguished, Optimization by Linear Decomposition, Collaborative Optimization, Concurrent SubSpace Optimization, Bi-Level Integrated System Synthesis, Analytical Target Cascading and the method of Quasi-separable Subsystem Decomposition. This paper provides an overview of these methods, where the main interest lies in how these methods handle coupled analysis between the levels of the hierarchy. In this paper a multi-level notation is introduced, in order to make a clear distinction between the aspects of optimization and analysis of multi-level design. It emphasizes the handling of inconsistencies between subsystems and their solution. The proposed notation enables a clear comparison of the multi-level methods on the basis of their treatment of interdisciplinary consistency contraints. Furthermore, the multi-level optimization framework is illustrated for structural optimization by applying the notations to a classical two bar truss example. The work here is part of a larger ongoing effort towards integrating multi-scale mechanics and multi-level optimization. The two bar truss example is in this context a suited example. It contains relevant characteristics of multi-scale mechanics and multi-level optimization and its simplicity helps to capture the essence of multi-level design approaches. In future work we aim to describe multi-scale mechanics in a similar fashion, which is expected to open up possibilities of exploiting synergy effects through further integration of the two formulations.@en

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.@en

Multi-level optimization and multi-disciplinary optimization are areas of research that are concerned with developing efficient analysis and optimization techniques for complex systems that are made up of coupled elements (components). Within the field of multi-level optimization and multi-disciplinary optimization a large number of techniques have been developed for efficient analysis and optimization of complex systems. This paper presents an unified overview of main stream approaches that were found in the literature. Four general steps are distinguished in both multi-level optimization and multi-disciplinary optimization: physical coupling, optimization problem coupling, coordination and solution sequence. Via these four steps approaches are classified and possibilities for combining aspects of different methods are given. Finally, advantages and disadvantages of approaches applied to engineering problems are discussed and directions for further research are given. Keywords: multi-level, multi-disciplinary, optimization, decomposition, coordination, overview.@en