# Optimized Scheduling of IoT Devices in Healthcare Facilities: Balancing Cost and Quality of Care
## 4 Results
### Experimental Campaign  
To validate the effectiveness of our proposed heuristic, we conducted a comprehensive experimental campaign. Our code implementation, written in Python v3.12.10 [[https://www.python.org/downloads/release/python-31210](https://www.python.org/downloads/release/python-31210)]([https://www.python.org/downloads/release/python-31210](https://www.python.org/downloads/release/python-31210)) (accessed on 17 March 2025), was executed on a macOS system (MacBook Pro with Apple M2 Pro chip and 32 GB of RAM). We evaluate and compare the performance of two multi-objective optimization algorithms (NSGA-II and SCIP 2-OBJ) by analyzing their respective Pareto-optimal solution sets. We identify dominated solutions, compute the hypervolume indicator (a widely used metric for assessing Pareto front quality), and visualize the results using scatter plots and hypervolume areas. The hypervolume metric quantifies the region of objective space dominated by a solution set relative to a reference point. This provides an intuitive measure of solution quality. By comparing the Pareto fronts and their hypervolume values, we provide insights into the relative effectiveness of the algorithms in producing diverse and high-quality trade-off solutions. Table 5 presents the case studies employed in our experimental evaluation. These studies are derived from actual patient and device scenarios, with sensitive details obscured through data normalization to comply with non-disclosure agreements. These confidentiality measures mandated by data protection requirements do not affect the significance of  
Figure 4: Example Solution 3 Gantt. Figure 5: Example Solution 4 Gantt. the findings. Key parameters, such as patient and device counts, define these scenarios. To maintain consistent evaluation conditions across experiments, a maximum execution time (time limit) was implemented, as shown in the final column of Table 5.  
The findings from these case studies are systematically presented in Table 6, facilitating comparative analysis and insightful deductions. Our analysis focuses on three key aspects: the distribution of solutions, the Pareto front's spread, and the most significant solutions within the convex hull (detailed in Appendix C). Both algorithms generate their respective Pareto-optimal solution sets. To determine the overall Pareto-optimal front, these sets are combined, as solutions from one algorithm may be dominated by those from the other. Performance is evaluated using several metrics. First, we count the number of solutions from each algorithm that are included in the final Pareto front (see column 'No. Pareto-Optimal Solutions' in Table 6). Second, we determine the number of solutions from each algorithm that are excluded from the final Pareto front due to the dominance of solutions from the other (refer to column 'No. Dominated Solutions' in Table 6). Next, the final convex hull is computed, and the number of solutions from each algorithm within it is tallied ('No. Solutions in the Convex Hull' column). Finally, we calculate the hypervolume associated with each algorithm's Pareto front. For comprehensive details, please refer to the provided complete dataset. In the first experiment (Table 5), we visually compare the Pareto fronts produced by NSGA-II (blue circles) and SCIP 2-OBJ (red squares) in Figure 6. This comparison helps evaluate solution performance. NSGA-II generated a front with 10 solutions, while SCIP 2-OBJ produced 15. The dominated regions (hypervolumes) for each front are shaded in blue and red, respectively. Solutions dominated by those from the other front are marked with crosses and were excluded from further analysis for clarity. For example, at a cost of 350, the NSGA-II solution dominates its SCIP counterpart due to higher quality of care. The final combined Pareto front includes only non-dominated solutions: 9 from NSGA-II and 12 from SCIP 2-OBJ. The convex hull, representing the most promising subset, is indicated by green-filled markers and a dashed line (see Appendix C).