Investigation of Multi-Fidelity Modeling Capabilities for Surrogate Based Optimization

Kurzfassung

The main goal of this thesis is the investigation of potential solutions for an elective integration of multi-fidelity modeling techniques into a surrogate based optimization framework. During an iterative optimization procedure, the algorithm is expected to determine not only the location of the next sample but also the most elective fidelity level to sample when multiple fidelities are available. The proposed multi-fidelity algorithm's performance is evaluated on both analytic benchmark functions such as the Forrester or the Rosenbrock function, as well as in the context of aerodynamic shape optimization for a 2D airfoil. The motivation for this work is that high fidelity simulations are cost and time consuming. Surrogate models can be trained with a limited number of real simulation data sets in order to return fast and cheap predictions of the values from interest instead of running the simulation. During the subsequent optimization phase, typically, only one fidelity level of data can be incorporated and utilized to generate new data points. Expanding this capability to choose between different fidelity levels of data sources during the iterative optimization phase is expected to enhance the optimization speed or reduce the costs required to achieve the desired result. One main finding of this theses is that analytic benchmark functions are too easy to optimize and do not allow an assessment of the multi-fidelity optimization performance. In addition, most of the multi-fidelity acquisition functions available in literature are very sensitive to the problem definition, especially to the cost and correlation distribution between the fidelities. Available papers suggest potential infill criteria to allow multi-fidelity capabilities but often miss specific information on how to implement these criteria within a surrogate based optimization (SBO) framework. The technique discussed within this thesis is inspired by an approach from DiFiore et al. but significant modifications have been done in order to improve efficiency. The primary modification involves separating the decision-making process for the location and fidelity of the next sample, aiming to prevent negative interactions that may impact the overall performance of the algorithm. Overall, an improvement in optimization efficiency is achieved with the multi-fidelity technique compared to the single-fidelity method. Further research on other infill criteria and the general code structure of the algorithm is suggested because it could lead to a further increase in efficiency. This thesis is focusing on the airfoil shape optimization for the aircraft industry but also other industries like the space- or automotive-industry could profit from the improvement in efficiency for SBO when applying a multi-fidelity technique.