## 3 Simulation Results
Figure 13 illustrates the distribution of prediction errors across various combinations of these two key factors for each cooling system. Figure 12: SHAP values for the CO\({}_{2}\) cooling system. Upon closer inspection of the sub-figures, it is evident that the prediction errors in both models generally remain within an acceptable range across most combinations of input variables. However, the largest errors occur at the extreme points. In the sub-figure related to the ammonia cooling system, these extremes correspond to situations where the the previous hour's power consumption is particularly high. Similarly, the next sub-figure related to the CO2 cooling system shows that the highest errors arise when there is very high power consumption in the previous hour, especially when accompanied by elevated water temperatures. Using the developed XGBoost models for the primary cooling systems and the technical constraints of the saltwater pre-cooling unit, the proposed BO method was applied to minimize the total power consumption while meeting operational requirements. In the Business-as-Usual (BaU) scenario, the pre-cooling system lowers the saltwater temperature to 12 \({}^{\circ}\)C before discharge into the breeding pools. However, in the optimized model, the discharge temperature is dynamically adjusted throughout the day to minimize total electricity costs. When the temperature of the water intake from the tank falls below 7 \({}^{\circ}\)C, the optimized model disables the pre-cooling process to comply with the system's safety limitations. To illustrate how the proposed model responds to seasonal variations in water temperature and electricity price, Figure 14 presents the difference between the optimized discharge temperature and the original intake temperature from the water tank for the 15 th day of each month. Figure 14: Change in discharge water temperature across hours and months in the optimized model. Figure 13: Distribution of prediction errors across various combinations of the previous hour’s power consumption and the temperature of the discharged water. As shown, during the colder months of January, February, March, and December there is no difference between the intake and discharge temperatures, as ambient conditions already meet the required thresholds. In contrast, during warmer months the model reduces the discharge temperature more significantly. The values inside each block indicate the electricity price in \(\epsilon\)/MWh at that hour. As observed, the greatest reductions in water temperature occur when electricity prices are low or negative. This demonstrates the system's flexibility to shift consumption toward low-price periods and reduce demand on the primary cooling systems, as enabled by the newly installed pre-cooling unit. Previously, we highlighted that the primary cooling units operate in a price-agnostic manner, focusing solely on maintaining the breeding pool temperature within safe limits. In contrast, the new pre-cooling unit adds responsiveness to price signals by actively cooling when electricity is cheap. This not only increases operational flexibility but also lowers the load on the primary systems, particularly in warmer months. Finally, the most significant flexibility contributions from the system occur during warm periods, when higher ambient temperatures demand more cooling effort. Figure 15 illustrates the total energy consumption and net savings achieved on the 15 th of each month after utilization of the optimized model. As expected, energy consumption increases during warmer months due to higher cooling demand. On the other hand, in colder months most energy use stems from internal heat sources such as fish metabolism and machinery. Net savings peak in June, driven by the combined effect of high intake water temperature and elevated electricity prices demonstrate the value of flexibility under these conditions. After examining seasonal trends, it is also useful to assess system behavior within a single day.