## 5 Experimental Results and Discussions
The comparison of the convergence behavior of SMOBHC with other algorithms, the boxplot illustrations, and the path planning results optimized by SMOBHC and seven other competitive algorithms (selected as examples) are presented for Battlefield 1, Battlefield 2, and Battlefield 3. The boxplot illustrations consist of 20 run results in each box, where the central line (drawn in red) represents the median, the edges of the box represent the 25 th and 75 th percentiles, and the whiskers extend to the most extreme data points that are not considered outliers. Outliers are plotted individually. Figures 8-12 show the convergence behavior of SMOBHC compared to other algorithms, the boxplot illustrations, and the path planning results optimized by SMOBHC and seven other competitive algorithms for Battlefield 1. Figures 13-17 display the same information for Battlefield 2, while Figures 18-22 show the results for Battlefield 3 in the same order of illustration as in Battlefield 1. The SMOBHC also provides very competitive results and outperforms the SMO in most comparison indices (best, worst, mean, and standard deviation values). This result confirms that the integration of the BHC optimizer into the SMO algorithmic structure is useful. Specifically, the addition of the BHC optimizer to the SMO LLP, GLP, and LLD phases can significantly improve its global exploration and exploitation characteristics through the use of both \(\mathcal{B}\)-operator and \(\mathcal{N}\)-operator. Figures 8-10 shows that the SMOBHC has an acceptable convergence speed (specifically for the \(D=30\) and \(D=60\) cases) compared to its competitors. The superiority of SMOBHC can also be seen from the boxplot graphs (Figure 11), which illustrate that SMOBHC has the smallest average value among other algorithms. The non-parametric statistical results, based on [PERSON]'s rank-sum test, indicated in Table 3 prove that SMOBHC performs better than all other algorithms in the three problem dimensions, except for the SMO in the third-dimension case. Figure 12 shows the UCAV flight paths obtained by SMOBHC, SMO, and six other algorithms (selected as examples) for the first-dimension problem. The optimized paths generated by SMOBHC are smooth and can significantly avoid threat areas with the lowest threat cost. It is clear from Figure 12, especially the paths relative to BA, GCMBO, and HS, that their calculated paths have poor quality in terms of stability and avoiding local optima. Other algorithms, such as DE, AOA, and DA, were able to find an acceptable optimal flight path, but with a lower quality compared to SMOBHC and SMO. \[Y^{1}_{\text{threat }center}=[200,-25,-150,\ 95,\ 55,\ 60,\ 0,\ 110,\ 100,-50 ],\]1 Comparative convergence curves of algorithms for battlefield \(1\) with \(D=30\). \[Y^{1}_{\text{threat }center}=[200,-25,-150,\ 95,\ 55,\ 60,\ 0,\ 110,\ 100,-50 ],\]2 Comparative convergence curves of algorithms for battlefield 1 with \(D=90\). \[Y^{1}_{\text{threat }center}=[200,-25,-150,\ 95,\ 55,\ 60,\ 0,\ 110,\ 100,-50 ],\]3 Comparative convergence curves of algorithms for battlefield 1 with \(D=60\). \[Y^{1}_{\text{threat }center}=[200,-25,-150,\ 95,\ 55,\ 60,\ 0,\ 110,\ 100,-50 ],\]4 Boxplot graphs of mean values relative to all algorithms for battlefield 1 with \(D=30\), 60, and 90. \[Y^{1}_{\text{threat }center}=[200,-25,-150,\ 95,\ 55,\ 60,\ 0,\ 110,\ 100,-50 ],\]5 Comparison between SMOBHC and other seven algorithms for battlefield 1 with \(D=30\).