The ability to adjust objectives and behavior to changing operation conditions and requirements is a key feature of self-optimizing mechatronic systems.  The term self-optimization implies that adequate optimization methods are crucial. They can be applied to both the determination of objectives and the adaption of system behavior.

The main task of the project area A is to develop optimization methods for use in the cognitive operator of the operator-controller-modules, that are adequately adapted to the requirements of self-optimizing systems. We distinguish between two classes of methods, which are developed in two subprojects:

1:  Numerical methods on the basis of models of the physical behavior of the systems (SP A1)

2:  Learning and planning methods on the basis of blackbox models, which can possibly rely on experience gathered during operation (SP A2)

These two approaches complement one another. They can be applied to different kinds of problems or can be combined in a specific self-optimization process.  An example for this combination is the selection of design points from a Pareto set (provided by methods developed in the subproject A1) using planning methods (developed in the subproject A2). This cooperation will be focused in the 3rd period. Both classes are reviewed in one of the two subprojects of the project area A.

Within the framework of self-optimization it is often especially important to consider several objective functions simultaneously, so that in a natural way one is lead into the mathematical field of multiobjective optimization. Methods from multiobjective optimization can in particular be applied in the second step of the self-optimization process to generate new objectives by adjusting the priorities of the objective functions in the optimization model.

Motivated by the hierarchical structure defined by the OCM architecture, the subproject A1 focuses on hierarchical optimization problems. In particular, bi-level problems (optimization problems with two interdependent levels) are examined, and algorithms for the solution of these problems developed that take their hierarchical nature into account. In many applications one has to solve optimal control problems – for these problems the subproject A1 has developed algorithms which in the case of mechanical or differentially flat systems can also deal with several objective functionals.

Behavior-based optimization refers to optimization approaches which avoid an explicit physical modeling of the system or process that is to be optimized. Instead, they utilize a direct mapping of the relevant input variables to the corresponding output variables. A specific system or process is always handled as a blackbox. This modeling approach usually implies a discretization of the processes. The correlation between environmental states, system behavior and the achievement of objectives can be defined by the developer of the systems or can be learned by a system itself. Usually, these blackbox models have a coarser granularity than physical models, since both experts and learning methods imply a classification of environmental states and the system behavior. However, behavior-based optimization can be applied if the formulation or computation of physical models is too complex. Furthermore, behavior-based optimization can handle longer planning horizons (for instance, a travel of a RailCab from Hamburg to Munich).