## 5 Validation Demonstration
### Numerical Results  
Table 9 depicts the parameters used in this study associated with DE. Herein, two other algorithms, Genetic Algorithm (GA) [43] and Particle Swarm Optimization (PSO) [44], were also applied independently under the same conditions. We ran the above three algorithms 10 times independently. Figure 8 shows the best evolutionary curves corresponding to the three algorithms, obtained with the evolutionary generations of the algorithm as abscissa and the optimization objective function \(D_{B}\) in Equation (26) as the ordinate. The smaller is the threat gap, the better is the corresponding planning. In particular, the final objective function values obtained by DE and PSO are considerably better than that of GA. Comparing DE with PSO, although the two final objective function values are basically the same, DE converges to a satisfactory solution at a faster rate, in about 60 generations, whereas PSO required about 280 generations. The minimum DE threat gap is 20.6594 with the best individual as [4; 1, 1, 2, 3, 1, 1, 5, 1, 1, 21, 8, 14, 7, 27, 6, 28, 38, 33, 40]. \begin{table}
\begin{tabular}{c c} \hline
**Node Number** & **Loop Number** \\ \hline
4 & 17 \\
5 & 65 \\
6 & 33 \\ \hline \end{tabular}
\end{table} 
Table 7: Loops distribution. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Parameter** & **\(F\)** & **CR** & **NP** & **G** \\ \hline Value & 0.5 & 0.2 & 200 & 500 \\ \hline \end{tabular}
\end{table} 
Table 9: DE parameters. We statistically analyzed the results, as shown in Table 10. The optimal value, the worst value, the mean value, the middle value, and the variance of the function in the 10 running results were tabulated. The optimal and worst value illustrate the merits of the scheme. The average value reflects the overall quality of the algorithm. The mid-value explains the convergence speed of the algorithm, to a certain extent. The variance is the overall stability of the algorithm. All DE indexes are better than those of GA and PSO. Although the optimal solution found by PSO is close to the optimal solution calculated by DE, the mid-value and variance corresponding to the PSO result are inferior to those of DE. In summary, DE has better efficiency and stability for this model. As for multi-objective optimization, NSDE and NSGA-II were used to optimize the weapons development scheme to obtain the Pareto optimal set, and then the TOPSIS method was used to find the compromise solution. Similarly, we ran the two algorithms 10 times independently. Each algorithm obtained 10 Pareto sets. Then, these solutions were sorted. The best solutions were selected to form the Pareto solution set of the two algorithms, as shown in Figure 9, which is plotted with the optimization objective function \(R_{B}\) in Equation (26) as the ordinate, against the optimization objective function \(D_{B}\) in Equation (26) as the abscissa. The coordinate axis is the same in Figure 10. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **DE** & **GA** & **PSO** \\ \hline Optimal & 20.6594 & 25.4480 & 21.1367 \\ Worst & 21.3432 & 26.7483 & 24.4506 \\ Mean & 21.0385 & 26.0738 & 22.0119 \\ Mid & 21.0617 & 26.1466 & 21.7246 \\ Variance & 0.0442 & 0.1945 & 1.0718 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparison of algorithm results. Figure 8: Results of the three algorithms. NSDE has a longer evolutionary curve than the traditional NSGA-II. Comparing the results of the two algorithms, the NSDE Pareto solutions are superior to those of NSGA-II in terms of diversity and convergence. We set the weighted values of the threat gap and the risk objectives as 0.6 and 0.4, respectively. The compromise solution calculated by the TOPSIS method is shown in Figure 10, which is [1, 1, 1, 1, 1, 1, 1, 5, 5, 1, 8, 7, 12, 6, 23, 5, 26, 30, 21, 40]. Uncertainty exists in the weapons R&D process and in all model relationships. A sensitivity analysis was performed for certain variables to examine the uncertainties of the model. Herein, the total budget was set as 200 and 230.