## 2 Materials and Methods
### Hyperparameter Tuning  
The goal of HPT is to optimize the hyperparameters in a way that improves the performance of an ML model. This is an important but usually difficult and computationally intensive task. The simplest approach--but also the most computationally expensive--is a manual search (or trial and error) [15].  
Common approaches include the Simple Random Search (RS), where hyperparameters are randomly and repeatedly selected for evaluation, and the grid search. Directed search methods and other model-free algorithms, such as evolution strategies [16] or pattern search [17], also play an important role. Hyperband, a multi-armed bandit strategy that dynamically allocates resources to a set of random configurations and uses successive bisections to stop configurations with poor performance [18], is also commonly used in the HPT domain. The most sophisticated and efficient approaches are Bayesian Optimization (BO) and SMBO methods, which are based on the optimization of cost functions obtained through simulations or experiments.  
Figure 3: Visualization of the slitting machine that was used to generate the data for the experiments. The image is provided by ‘Kampf Schneid- und Wickeltechnik GmbH & Co. KG’, Wiehl, Germany.  
For this article, we considered an HPT approach based on the Sequential Parameter Optimization Toolbox (SPOT) [7], which is suitable for situations where only limited resources are available. This may be due to limited availability or cost of hardware. Another reason might be that confidential data may only be processed locally, due to legal requirements. Furthermore, our approach emphasizes the importance of understanding algorithms as a key tool for transparency and explainability. This can be enabled by quantifying the contribution of ML and Deep Learning components (nodes, layers, split decisions, activation functions, etc.) and understanding the meaning of hyperparameters and their interactions. The SPOT provides statistical tools for understanding hyperparameters and their interactions. Additionally, the SPOT software code is available in the open-source _spotPython_ and _spotRiver_ packages on GitHub ([[https://github.com/sequential-parameter-optimization](https://github.com/sequential-parameter-optimization)]([https://github.com/sequential-parameter-optimization](https://github.com/sequential-parameter-optimization)), accessed on 16 October 2023), allowing for replicability of results. The SPOT is established open-source software that has been maintained for over 15 years [7]. It includes SMBO methods for tuning, based on classical regression and analysis of variance techniques, tree-based models such as CART and RF, BO (Gaussian Process Models, also known as Kriging), and combinations of different meta-modeling approaches. Any ML model in scikit-learn (_sklearn_) can be used as a meta-model.  
The loop of the model-based tuning process with the SPOT can be divided into the following steps [7]:  
* Setup: Different combinations of hyperparameter values are evaluated, in order to build an initial design.
* Evaluation: The new or initial hyperparameters are evaluated.
* Termination: The loop checks weather a termination criterion like maximum number of iteration or maximum tuning time has been reached.
* Selection: This step selects samples for building the surrogate model.
* Building Surrogate: The surrogate is built.
* Surrogate Search: The algorithm searches for the best hyperparameter settings based on the surrogate model.
* Optimal Computing Budget Allocation (OCBA): This step is used to determine the number of repeated evaluations.