# Parallelization of the Honeybee Search Algorithm for Object Tracking
## 3 Results
### Adjusting the Honeybee Search Algorithm  
This experiment was designed to determine if the time per frame is reduced when the number of generations (explained in Section 2.2) is lower, and what is the optimal number of generations. This experiment considers all the 314 videos of the ALOV dataset. All the tests use NCC, GPU, and HSA. The variation is made in the number of generations. The other configuration parameters of HSA reuse optimal values proposed by [PERSON] and [PERSON] [14; 15; 16] after numerous experiments.  
Figure 9a shows that the average F-score is stable between generations 2 to 10. The difference in score between 2 and 3 generations is 3.50% of the overall standard deviation, and 1.95% between 3 and 4 generations. The leap between 4 and 10 generations is only of 4.02%. On the other hand, there is a notable difference between 1 and 2 generations, measured as 66.79% of the overall standard deviation.  
Figure 9b shows that as the number of generations increases, the average time per frame increases. From 1 to 2 generations, the average time per frame increases by 8.65% of the overall standard deviation. From 2 to 3 generations, the increment is 4.50%. When changing from 3 to 4 generations, time per frame increases by 8.48%. The pattern is caused by the increment in the number of generations for the harvest phase, which is the half of the generations used for the exploration phase. Finally, an increment from 4 to 10 generations causes the average time per frame to increase by 38.82% of the overall standard deviation, showing that the trend continues.  
Figure 10a shows a three-dimensional plot, the axes show the average F-score, the average time per frame and the number of generations; the color of the bars indicates a difference in the average  
Figure 8: Comparison of F-score survival curves between using this work’s NCC (OURS) and the NCC implementation reproduced from [3; 44] (CTRL). Other video trackers are shown for reference.  
Figure 9: The effects of increasing the number of generations of HSA. (**a**) Comparison of F-score. (**b**) Comparison of average time per frame.  
F-score; this helps to visualize the trend observed when the number of generations of HSA varies. After two generations, the average F-score stabilizes. In contrast, the average time per frame keeps increasing. We inferred from that information that two generations provide the right balance between time and score. Nevertheless, the Score-Time Efficiency shows without a doubt that two generations is the best option (Figure 10b).  
As expected, the average time increases with each new generation. This aspect supports the time complexity analysis of parallel HSA with NCC as fitness function: \(O(\frac{gmn}{q})\), where the number of generations is of significant influence. This result shows the practical utility of the Score-Time Efficiency, using it to determine that the optimal number of generations. Also, the observation that the F-score has asymptotic behaviour starting on two generations ensures that selecting that number does not mean a negative effect on accuracy. Figure 11 shows an example of the results that were obtained using two generations, the location of the object (a ball) is obtained with a certain degree of accuracy even when the size and illumination of the object changes.  
Figure 11: Visual example of the results that were obtained using NCC and HSA with two generations. The frames that are shown correspond to the 23 th video of the Light category of the ALOV dataset. Every 14 th frame is shown.  
Figure 10: Selecting the optimal number of generations in terms of average time per frame and F-score using the Score-Time Efficiency. (**a**) Average time per frame vs. F-score vs. generations. (**b**) Comparison of Score-Time Efficiency.