  An important issue during an engineering design process is to develop an
understanding which design parameters have the most influence on the
performance. Especially in the context of optimization approaches this
knowledge is crucial in order to realize an efficient design process and
achieve high-performing results. Information theory provides powerful tools to
investigate these relationships because measures are model-free and thus also
capture non-linear relationships, while requiring only minimal assumptions on
the input data. We therefore propose to use recently introduced
information-theoretic methods and estimation algorithms to find the most
influential input parameters in optimization results. The proposed methods are
in particular able to account for interactions between parameters, which are
often neglected but may lead to redundant or synergistic contributions of
multiple parameters. We demonstrate the application of these methods on
optimization data from aerospace engineering, where we first identify the most
relevant optimization parameters using a recently introduced
information-theoretic feature-selection algorithm that accounts for
interactions between parameters. Second, we use the novel partial information
decomposition (PID) framework that allows to quantify redundant and synergistic
contributions between selected parameters with respect to the optimization
outcome to identify parameter interactions. We thus demonstrate the power of
novel information-theoretic approaches in identifying relevant parameters in
optimization runs and highlight how these methods avoid the selection of
redundant parameters, while detecting interactions that result in synergistic
contributions of multiple parameters.
