## 5 Experiments and Results
### Results on Open-Source Dataset  
The dataset originates from a multi-stage continuous-flow manufacturing process featuring both parallel and series configurations. Measurement machines within the system  
Figure 5: Visualization of the RL agent’s performance on the pinion manufacturing dataset. The plot displays the true target values, the agent’s predicted outcomes based on the suggested control parameters, and the optimal point (red cross) in the radius–thickness design space.  
are anonymized using numerical identifiers. In the initial stage, machines M1-M33 operate in parallel and feed into a combiner. At this point, the combined output is measured at 15 discrete locations along the outer surface of the material. Measurement values of 0.0 indicate missing data at specific positions. Due to the high frequency of missing values, only the top five measurement points with the highest data availability were selected for optimization. The primary objective was to identify optimal control parameters that minimize the deviation of measured outputs from their respective setpoints. This dataset reflects the complexity of a real-world, multi-stage manufacturing system and serves as a robust testbed for evaluating the generalization capability and performance of the proposed RL-based optimization framework. It comprises over 14,000 records, each containing sensor readings, control variable settings, system states, and output measurements across various production stages. Setpoints are provided and serve as targets for the multi-objective optimization.  
Table 4 categorizes the dataset parameters. Motor-related features, such as average and RPM, were selected as control parameters due to their direct influence on the manufacturing process and real-time adjustability. These variables are typically monitored and adjusted in operational environments, making them both logically relevant and practically implementable for an RL-based control strategy. Furthermore, their consistent presence in the dataset supports reliable model training and evaluation. Other parameters were treated as either uncontrollable or static.  
Model performance is reported in terms of reward values obtained on a hold-out validation set after training. High reward scores were observed across all selected measurement points, indicating effective alignment with optimization objectives. Table 5 summarizes the RL rewards for two different control parameter configurations. The limited reward control setup is a subset of the extended control configuration, enabling comparative analysis of the optimization model's effectiveness under varying degrees of control freedom. Appendix A provides further detail on limited and extended control configuration for this dataset.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Anonymized Parameter Category** & **Count** \\ \hline Ambient Conditions & 2 \\ Raw Material & 15 \\ Temperature & 15 \\ Pressure & 3 \\ Motor & 6 \\ Combiner Operation & 3 \\ Total Input Parameters & 44 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Categorization and count of input parameters used in the continuous-flow manufacturing dataset, grouped by their functional role in the process.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Target** & **Process Model \(\mathbf{r^{2}}\)-Score** & **Reward Limited Control** & **Reward Extended Control** \\ \hline Measurement 1 & 0.94 & 0.73 & 0.69 \\ Measurement 2 & 0.92 & 0.55 & 0.86 \\ Measurement 3 & 0.93 & 0.78 & 0.86 \\ Measurement 4 & 0.79 & 0.88 & 0.91 \\ Measurement 5 & 0.95 & 0.78 & 0.88 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Performance of individual surrogate model and mean obtained reward on test split for open-source dataset.