Frederik Rehbach

Thomas Bartz-Beielstein, Marcel Dröscher, Alpar Gür et al.

Crises like the COVID-19 pandemic pose a serious challenge to health-care institutions. They need to plan the resources required for handling the increased load, for instance, hospital beds and ventilators. To support the resource planning of local health authorities from the Cologne region, BaBSim.Hospital, a tool for capacity planning based on discrete event simulation, was created. The predictive quality of the simulation is determined by 29 parameters. Reasonable default values of these parameters were obtained in detailed discussions with medical professionals. We aim to investigate and optimize these parameters to improve BaBSim.Hospital. First approaches with "out-of-the-box" optimization algorithms failed. Implementing a surrogate-based optimization approach generated useful results in a reasonable time. To understand the behavior of the algorithm and to get valuable insights into the fitness landscape, an in-depth sensitivity analysis was performed. The sensitivity analysis is crucial for the optimization process because it allows focusing the optimization on the most important parameters. We illustrate how this reduces the problem dimension without compromising the resulting accuracy. The presented approach is applicable to many other real-world problems, e.g., the development of new elevator systems to cover the last mile or simulation of student flow in academic study periods.

Thomas Bartz-Beielstein, Frederik Rehbach, Olaf Mersmann et al.

We present a resource-planning tool for hospitals under special consideration of the COVID-19 pandemic, called babsim.hospital. It provides many advantages for crisis teams, e.g., comparison with their own local planning, simulation of local events, simulation of several scenarios (worst / best case). There are benefits for medical professionals, e.g, analysis of the pandemic at local, regional, state and federal level, the consideration of special risk groups, tools for validating the length of stays and transition probabilities. Finally, there are potential advantages for administration, management, e.g., assessment of the situation of individual hospitals taking local events into account, consideration of relevant resources such as beds, ventilators, rooms, protective clothing, and personnel planning, e.g., medical and nursing staff. babsim.hospital combines simulation, optimization, statistics, and artificial intelligence processes in a very efficient way. The core is a discrete, event-based simulation model.

Frederik Rehbach, Martin Zaefferer, Boris Naujoks et al.

Surrogate-based optimization relies on so-called infill criteria (acquisition functions) to decide which point to evaluate next. When Kriging is used as the surrogate model of choice (also called Bayesian optimization), one of the most frequently chosen criteria is expected improvement. We argue that the popularity of expected improvement largely relies on its theoretical properties rather than empirically validated performance. Few results from the literature show evidence, that under certain conditions, expected improvement may perform worse than something as simple as the predicted value of the surrogate model. We benchmark both infill criteria in an extensive empirical study on the `BBOB' function set. This investigation includes a detailed study of the impact of problem dimensionality on algorithm performance. The results support the hypothesis that exploration loses importance with increasing problem dimensionality. A statistical analysis reveals that the purely exploitative search with the predicted value criterion performs better on most problems of five or higher dimensions. Possible reasons for these results are discussed. In addition, we give an in-depth guide for choosing the infill criteria based on prior knowledge about the problem at hand, its dimensionality, and the available budget.

Thomas Bartz-Beielstein, Martin Zaefferer, Frederik Rehbach

The performance of optimization algorithms relies crucially on their parameterizations. Finding good parameter settings is called algorithm tuning. The sequential parameter optimization (SPOT) package for R is a toolbox for tuning and understanding simulation and optimization algorithms. Model-based investigations are common approaches in simulation and optimization. Sequential parameter optimization has been developed, because there is a strong need for sound statistical analysis of simulation and optimization algorithms. SPOT includes methods for tuning based on classical regression and analysis of variance techniques; tree-based models such as CART and random forest; Gaussian process models (Kriging), and combinations of different meta-modeling approaches. Using a simple simulated annealing algorithm, we will demonstrate how optimization algorithms can be tuned using SPOT. The underling concepts of the SPOT approach are explained. This includes key techniques such as exploratory fitness landscape analysis and sensititvity analysis. Many examples illustrate how SPOT can be used for understanding the performance of algorithms and gaining insight into algorithm's behavior. Furthermore, we demonstrate how SPOT can be used as an optimizer and how a sophisticated ensemble approach is able to combine several meta models via stacking. This article exemplifies how SPOT can be used for automatic and interactive tuning.