AbstractsMathematics

In the research domain Complex Problem Solving (CPS) in psychology, computer-supported tests are used to analyze complex human decision making and problem solving. The approach is to use computer-based microworlds and to evaluate the performance of participants in such test-scenarios and correlate it to certain characteristics. However, these test-scenarios have usually been defined on a trial-and-error basis, until certain characteristics became apparent. The more complex models become, the more likely it is that unforeseen and unwanted characteristics emerge in studies. In this thesis,we use mathematical optimization methods as an analysis and training tool for Complex Problem Solving, but also show how optimization should be used in the design stage of new complex problem scenarios in the future. We present the IWR Tailorshop, a novel test scenario with functional relations and model parameters that have been formulated based on optimization results. The IWR Tailorshop is the first CPS test-scenario designed for the application of optimization and is based on the economic framing of another famous microworld, the Tailorshop. We describe an optimization-based analysis approach and extend it to optimization-based feedback with different approaches for both feedback computation and feedback presentation. Additionally, we investigate differentiable reformulations for an unavoidable minimum expression and show the according numerical results. To address the difficulties of computing globally optimal solutions for this test-scenario, which yields non-convex mixed-integer optimization problems, we present a decomposition approach for the IWR Tailorshop. The new test-scenario has been implemented in a web-based interface together with an analysis software for collected data, which both are available as open-source software and allow for an easy adaption to other test-scenarios. In this work, we also apply our methodology in a web-based feedback study using the IWR Tailorshop in which participants are trained to control the microworld by optimization-based feedback. In this study with 148 participants, we show that such a feedback can significantly improve participants’ performance in a complex microworld with a possibly huge difference to a control group. However, the performance improvement depends on the representation of the feedback. We give a detailed analysis of the study and report on new insights about human decision making which only have been possible through the IWR Tailorshop and our optimization-based analysis and training approach. Im psychologischen Forschungsgebiet Komplexes Problemlösen (engl.: Complex Problem Solving) werden computergestützte Tests eingesetzt, um die komplexe Entscheidungsfindung und das Lösen komplexer Probleme von Menschen zu analysieren. Dazu werden üblicherweise computerbasierte Mikrowelten verwendet, in denen die Leistung von Probanden ermittelt und mit bestimmten Eigenschaften verknüpft wird. Solche Testszenarien wurden bisher im Allgemeinen in…