# Fast, Lightweight, and Efficient Cybersecurity Optimization for Tactical-Operational Management
## 3 Experiments Design and Result
### Execution and Experiment Results  
The time required by FLECO to generate solutions after executing the test suite is shown in Table 4. Every row represents a combination where 225 FLECO executions are summarized. The table shows, hence, the whole 2700 FLECO executions. The time mean, standard deviation, and median of every test case are presented in columns \(t\), \(\sigma(t)\), and \(t\), respectively. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Strategic Constraints** & **IG1** & **IG2** & **IG3** & \begin{tabular}{c} **Cumulated** \\ **IG1** \\ \end{tabular} & \
\begin{tabular}{c} **Cumulated** \\ **IG2** \\ \end{tabular} &
\begin{tabular}{c} **Cumulated** \\ **IG3** \\ \end{tabular} \\ \hline Asset constraints & 1 & 1 & 1 & 1 & 1 & 1 \\ Function constraints & 1 & 1 & 1 & 2 & 2 & 2 \\ Category constraints & 2 & 2 & 3 & 4 & 4 & 5 \\ Expected outcomes constraints & 5 & 11 & 17 & 9 & 15 & 22 \\ Total constraints & 9 & 15 & 22 & 9 & 15 & 22 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Coverage provided by the synthetic set of strategic constraints depending on each IG. It is noteworthy that the FLECO algorithm demonstrated a 100% convergence rate in all 2700 executions (225 per case of analysis) conducted. This is of significant importance for the practical application of the algorithm to the real-world problem it is designed to address. Notably, despite being permitted a convergence time up to five minutes, the average time required by FLECO was \(\approx\) 1.39 \(\pm\) 0.31 s in the worst-case scenario. However, in the majority of the analysis cases, the minimum time to obtain a feasible solution was less, reaching \(\approx\) 0.21 \(\pm\) 0.07 s in the most favorable case. The convergence time tends to increase with an escalation in the number of constraints in the implementation group, i.e., when the chromosomes are larger, but even in these cases it is maintained below (and far from) the defined limit. Thus, the requirement of achieving a solution in less than five minutes is greatly accomplished by FLECO, which has been demonstrated to be fast. Moreover, all the experiments have been executed in hardware below the specified requirements, achieving the mentioned values, which reveals also that FLECO is efficient in the use of resources. Regarding the quality of the generated solutions, in Tables 5 and 6, the fitness means, \(fi(\overrightarrow{x})\), for each optimization function and for the weighted function are shown, together \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**IG** & **Strategic Constraints Levels** & \(\mathbf{-}\) & \(\mathbf{\sigma(t)}\) & \(\mathbf{\hat{t}}\) \\ \hline
1 & A & 0.211166 & 0.071250 & 0.200270 \\
1 & A-F & 0.219383 & 0.108698 & 0.223835 \\
1 & A-F-C & 0.236180 & 0.099249 & 0.246635 \\
1 & A-F-C-EO & 0.245545 & 0.192466 & 0.191478 \\
2 & A & 0.667603 & 0.152436 & 0.677265 \\
2 & A-F & 0.634475 & 0.173134 & 0.661716 \\
2 & A-F-C & 0.712537 & 0.253927 & 0.760814 \\
2 & A-F-C-EO & 0.388333 & 0.214490 & 0.294797 \\
3 & A & 1.241601 & 0.322026 & 1.300380 \\
3 & A-F & 1.291096 & 0.309675 & 1.315561 \\
3 & A-F-C & 1.387193 & 0.308389 & 1.449513 \\
3 & A-F-C-EO & 0.574846 & 0.261707 & 0.519179 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Time required for each analysis case.