# Chemotherapy Regimen Optimization Using a Two-Archive Multi-Objective Squirrel Search Algorithm
## 4 Experimental Setup and Results Analysis
### Results and Analysis
#### 4.4.5 Robustness Analysis  
In this subsection, a robustness analysis is reported. We simulated various patients by adjusting the parameters of tumor dynamics model listed in Table 9. Subsequently, we applied the TA-MOSSA to generate the chemotherapy regimens of each condition. Figure 11 visualized the Pareto front curves obtained for the original parameters, as well as those increased by 10% and decreased by 10%. Furthermore, Table 9 offers comprehensive performance metrics, including the Hypervolume (HV) and Spacing Metric (SP), for each of the three parameter conditions. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Performance Metrics** & **Proposed Model** & **Literature [20]** & **Literature [22]** & **Literature [42]** \\ \hline Reduction proportion in proliferating tumor cells & 95.87\% & 72.2\% & 92.95\% & 72.40\% \\ Reduction proportion in quiescent tumor cells & 95.65\% & 60.4\% & 89.44\% & 60.50\% \\ Remained bone marrow cells (\(\times 10^{8}\)) & \(1.973\times 10^{8}\) & \(1.002\times 10^{8}\) & \(1.352\times 10^{8}\) & \(1.0092\times 10^{8}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of proposed model with models from the literature. Drawing from Figure 11 and Table 9, the Pareto front curves derived from altered parameters exhibit consistent trends and distribution of solutions. Notably, the curve corresponding to a \(-10\%\) parameter adjustment maintains a similar overall value range to the original parameter curve in the objective space, while the curve with a \(+10\%\) parameter adjustment shows a slightly reduced range. In the area where the number of remained tumor cells is minimal, all three Pareto front curves closely align, suggesting the proposed algorithm consistently excels in devising chemotherapy regimens that notably reduce tumor cells regardless of parameter variations. Furthermore, the fluctuations in HV and SP values of the Pareto fronts before and after parameter adjustments remain within \(1\%\). This stability underscores the algorithm's ability to sustain optimal coverage and even distribution of the Pareto frontiers despite parameter fluctuations. Figures 12 and 13 depict the trends in tumor cell and bone marrow cell populations during aggressive and mild chemotherapy under different parameter conditions, respectively. The efficacy indicators of each chemotherapy regimen are reported in Tables 10 and 11. Figures 14 and 15 depict the long-term dynamics of both scenarios for up to 300 days, while the last doses are given at day 105 and day 106. Figure 12: Tumor cell and bone marrow cell population dynamics during aggressive chemotherapy treatment. Figure 13: Tumor cell and bone marrow cell population dynamics during mild chemotherapy treatment. \begin{table}
\begin{tabular}{c c c c} \hline
**Performance Metrics** & **Original Parameters** & **+10\% Parameters** & **\(-\)10\% Parameters** \\ \hline Remained tumor cells \(\left(\times 10^{10}\right)\) & 2.863 & 3.154 & 2.593 \\ Proportion of remained tumor cells & 28.64\% & 31.54\% & 25.93\% \\ Cumulative damaged bone marrow cells \(\left(\times 10^{10}\right)\) & 2.897 & 2.737 & 3.001 \\ Minimum counts of bone marrow cells \(\left(\times 10^{8}\right)\) & 6.116 & 6.235 & 6.043 \\ Average counts of bone marrow cells \(\left(\times 10^{8}\right)\) & 7.277 & 7.596 & 7.055 \\ Average dose concentration of cisplatin (mg/mL) & 1.908 & 1.929 & 1.904 \\ Average dose concentration of docetaxel (mg/mL) & 1.973 & 1.941 & 1.954 \\ \hline \end{tabular}
\end{table} 
Table 11: Performance metrics of mild chemotherapy treatment under different parameter conditions.