A Framework for Multi-level Modeling and Optimization of Modular Hierarchical Systems

Most products and manufacturing systems (MS) have an inherent hierarchical structure. They are composed of multiple subsystems, such as machines, process components, or resources. In order to optimize the control parameters of such systems, manufacturing planners often follow a global black-box approach. The optimization, thus, neglects the hierarchical structure encoded in the model. All subsystems and their components have to meet individual constraints and show specific uncertainty in their output. By extracting the information, which modules violate the constraints, the optimization algorithm could focus on the parameters of this specific module. Moreover, the planner can define objectives evaluating the robustness or sensitivity of a specific solution based on the knowledge of the hierarchical dependencies and about the uncertainty in the outputs. To accomplish this, the structure of the optimized system must be known to the respective methods applied.In this paper, the dependencies of the subsystems are defined by means of a tree structure. Based on this structure, different possibilities to define and solve the corresponding optimization problem are introduced. In addition, a concept for addressing the robustness of an MS with regard to the uncertainty of the components within the optimization model is proposed. As a practical example, a hot compaction process for manufacturing thermoplastic composites is formalized using the tree structure. Individual nonlinear empirical models simulate the input-output behavior of each subsystem. Based on this formalization, the results of single- and multi-objective optimization methods are compared and their strengths and weaknesses are discussed.