# Optimized Scheduling of IoT Devices in Healthcare Facilities: Balancing Cost and Quality of Care
## 4 Results
### Experimental Campaign
A qualitative comparison suggests NSGA-II performs better. It produced fewer dominated solutions (one crossed blue marker vs. three crossed red ones at cost values of 250, 270, and 350). Moreover, NSGA-II contributes five solutions to the convex hull, compared to just two from SCIP 2-OBJ (at the extreme left and right). This is further supported by the hypervolume measure, where NSGA-II dominates a larger area. Overall, these results indicate that NSGA-II is more effective at identifying well-balanced, high-performance solutions. Numerical confirmation is provided in row 1 of Table 6.  
The second experiment (see row 2 in Tables 5 and 6), which scaled the number of patients and devices, along with the time limit, to double the initial values, reinforced the findings from the first experiment. Although 'SCIP 2-OBJ' generated a larger set of Pareto-optimal solutions, these solutions exhibited a lower overall quality, as evidenced by the reduced number of solutions in the convex hull and hypervolume. In contrast, NSGA-II effectively identified a more selective set of higher-quality solutions. This disparity in performance is attributed to the sampling methodology inherent in the 'SCIP 2-OBJ' \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Exp. ID** & **No. Patients** & **No. Devices** & **Time Limit (s)** \\ \hline
1 & 2 & 4 & 60 \\
2 & 4 & 8 & 120 \\
3 & 5 & 10 & 240 \\
4 & 10 & 30 & 360 \\
5 & 20 & 30 & 600 \\
6 & 20 & 40 & 900 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experimental campaign. constraint approach, compounded by the time limit, which prevented the algorithm from fully converging to certified optimal solutions. The results of the third experiment (Tables 5 and 6, row 3), which increased complexity and doubled the time limit, showed that the exact approach, despite generating more solutions, failed to produce any of high quality, as none were within the convex hull. Our proposed approach, in contrast, effectively produced a slightly larger number of solutions with significantly higher quality, as demonstrated by the improved convex hull representation and hypervolume. In the last three experiments, we significantly increased the complexity, which led to different observations compared to the first three experiments. Regarding the fourth experiment represented in Table 5, we observed (Table 6, row 4) that a significantly higher number of solutions from our algorithm were dominated within the final Pareto front. Despite the low number of solutions generated by the exact method, these were of higher quality, as evidenced by the small difference between our method and the exact method in convex hull participation and hypervolume value. This occurred because the sampling process of the 'SCIP 2-OBJ' method, when conducted in a very large solution space, achieved better performance by exploring the solution domain more effectively than in the previous experiments. Additionally, the 'NSGA-II' algorithm, having to search for Pareto-optimal solutions within a broader domain, faced greater difficulty in finding numerous high-quality solutions, although it still managed to achieve better results than the exact method and locate solutions in the early generations. In the fifth experiment, we doubled the number of patients while keeping the number of devices constant, attempting to simulate a common real-world situation of resource scarcity. In this case, the exact method found many more solutions compared to the previous experiment and produced results comparable to our approach, both in terms of convex hull participation and hypervolume. In the final experiment (Tables 5 and 6, row 6), we increased the number of devices compared to the previous one. In this case, the performance advantage of the heuristic became more pronounced due to the greater problem complexity, which led the NSGA-II method to quickly find many interesting solutions while the exact approach found fewer good solutions.