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Complex System Optimization & Analysis

 

Search strategies

Biologically inspired search strategies like Evolutionary Algorithms are powerful mechanisms, which demonstrate their full potential for complex and nonlinear problems. At the same time, it is necessary to carefully consider the needs and constraints of each problem separately. We develop and apply global stochastic algorithms taking the system robustness against perturbations of the environment as well as the possibility of further development of the system into account. Both aspects are not only important in classical design optimization, but also for the creation of optimal network and process structures, where the inherent time dependency of the system plays a crucial role.

The optimal choice of the search strategy depends on the problem. In our research, we typically have to cope with high dimensional solution spaces with a large number of criteria embedded into a multi-physics simulation environment. The consideration of full working ranges and uncertainties during the search is necessary to ensure the practical usability of the optimized systems. The integration of uncertainties can significantly change not only the resulting system but also the topology of the search landscape.

System modelling

Data-driven system modelling is widely applied in design optimization in order to reduce the necessary time and computational requirements of the algorithm. However, for complex systems it is necessary to account for a high number of design parameters. Therefore, models of high-dimensional spaces are necessary in order to apply system modelling technqiues to problems like full vehicle simulation and optimization (structural and aerodynamic) or to the optimization of processes like production systems. In addition to their predictive capability, data-driven system models can also be used to explore novel search paradigms like e.g. the search for innovative solutions, which reveal alternative system structures that are unqiue compared to already existing solutions.

Representations and transformations determine the topology of the search space

The choice of an adequate representation of a shape, structure or a system in general is a necessary first step in any design or optimization process. This parametric description encodes an instantiation of a system, which is evaluated against a set of quality measures. As a result, the mapping between the parametric space and the objective space is determined by both the representation and the quality measure.  A thorough understanding of the properties of specific representations, like e.g. deformation methods for shape optimization, is essential for formulating efficient search strategies.
In our research, we demonstrated that it is often not possible to generate representations that are equally optimal for all phases of the search. Therefore, it is necessary to change and to adapt the mapping itself during the optimization process. These adaptations can range from changing the underlying parametric description (the representation) to the quality evaluation of the system (e.g from coarse to fine). The success of the optimisation often requires a time-continuous adaptation of the problem formulation to the constraints that govern different search phases.

 

Robustness and evolvability

Robustness describes the property of a system to maintain its functionality under perturbations either of the system itself or of environmental parameters. Whereas biological systems are inherently robust against a large variety of perturbations, it requires considerable effort to realize robustness in technical systems. Evolutionary design methods allow to incorporate robustness effi ciently into the optimization process. We apply such a framework successfully to a wide spectrum of applications. The importance to consider robustness early in the system optimization process can be demonstrated even for simple test functions for which the topology of the search space changes with the variance of the expected variations.

 

Whereas robustness describes the invariance of the system, evolvability describes a seemingly opposing property, i.e. the fl exibility of the system to change and to adapt to new constraints and criteria. Current research analyses the correlation and inter-dependency of these properties and how both can be achieved in practical optimization. The observation that often robustness of a system is necessary to achieve evolvability indicates that concurrent optimization of both criteria is possible. 

Data mining and knowledge retrieval

Dependencies and interactions between system parts are not only challenging for design optimization, but are also the biggest obstacles for the analysis and for a detailed understanding of the generated systems. We research engineering data analystics and knowledge retrieval methods in order to support the analysis of complex systems.


Active sampling as well as the utilization of data from different sources (e.g. design optimization experiments or design processes by engineers) are the basis for data mining algorithms acting on various properties like surface representations, flow field pressure gradients and general network structures. In this way, we are able to detect global sensitivities, modules and interactions of multiple parameters determining the design properties. Besides providing important information for an improved understanding of the system, the analysis can also reveal necessary information to adapt the representation or algorithmic parameters for future design optimizations.