# Comparison of Heuristic Algorithms in Discrete Search and Surveillance Tasks Using Aerial Swarms
## 5 Comparison of the Algorithms
### Quantitative Comparison  
#### 5.1.1 Plain Scenarios  
In Table 4, the results of the simulations have been presented for the plain scenario. For each of the three models, the mean efficiency among 200 scenarios and the mean fitness value are shown. Notice that in turn for each of the scenarios, the efficiency and the fitness is the result of the mean of 100 trials. For Model 1, the best algorithms turn out to be A4, A3, A7 and A1, with an efficiency between 70 and 78%. In any case, the efficiencies of all algorithms lie above 78% of the maximum efficiency (0.61/0.78 = 0.78), which may indicate a bad representation of the real performance of the algorithm. Note that even a random movement, which a priori is considered as very inefficient, achieves mean absolute efficiency values of 61%. The fitness values based on this model indicate that the algorithms A3, A7, A4 and A1 combine good efficiencies with low noises due to the initial conditions. We should underline the important drop in the fitness values compared with the efficiency for algorithms A2, A5 and A6, which indicates a high variance in the efficiency depending on the initial conditions. The case of Model 2 is similar, although the values are in general lower. The best algorithms based on it are A3 and A7. However, in this case, the differences between the algorithms are lower, all the efficiencies lying between 0.57 and 0.61. Again, there are remarkable drops in the fitness for algorithms A2, A5 and A6. In Figure 14, the efficiencies distributions as per Models 1 and 2 for the 200 scenarios have been represented, in descending order of mean efficiency. Note the high variance in the efficiency of A5 for both models, which indicates that the algorithm is very sensitive to the scenario. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Model 1**} & \multicolumn{2}{c}{**Model 2**} & \multicolumn{2}{c}{**Model 3**} \\ \hline  & **Eff** & **Fit** & **Eff** & **Fit** & **Eff** & **Fit** \\ \hline A1: Behaviors set & 0.70 & 0.58 & 0.57 & 0.49 & 0.39 & 0.29 \\ A2: Random & 0.61 & 0.21 & 0.57 & 0.20 & 0.09 & 0.03 \\ A3: Closest & 0.75 & 0.68 & 0.62 & 0.57 & 0.36 & 0.27 \\ A4: Boundary & 0.78 & 0.67 & 0.59 & 0.53 & 0.31 & 0.22 \\ A5: Energy & 0.66 & 0.21 & 0.59 & 0.19 & 0.16 & 0.04 \\ A6: Billiard & 0.61 & 0.23 & 0.55 & 0.22 & 0.16 & 0.05 \\ A7: Lanes & 0.73 & 0.68 & 0.61 & 0.57 & 0.35 & 0.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Efficiencies and fitness values for each algorithm, based on the three models depicted in Section 2.4. In the case of Model 3, the results are different. First, the efficiencies are in general lower, with their average between 9 and 39%. We can distinguish two groups of algorithms: the first group, composed by A1, A3, A7 and A4, achieves high efficiencies, higher than 0.31. The second group, made up of A6, A5 and A2, reaches efficiencies between 0.09 and 0.16. Note that with this model, the worst algorithm (A2, random movement) is four-times less efficient than any of the first group, which may be a sensible result. Regarding the fitness, the same drop from the efficiency values shows up again in A2, A5 and A6. A1 reaches the highest fitness value, indicating robustness against the initial conditions. In Figure 15, the efficiencies based on Model 3 and the associated fitness values have been represented for each algorithm, for all the scenarios. Note that A3 and A7, although reaching high efficiencies, present a high variance depending on the scenario. In 75% of the scenarios, both algorithms reach an efficiency that lies between 0.17 and 0.55, which is a wide interval compared with A1, with the interval from 0.35 to 0.40 comparatively narrow. A similar situation takes place regarding the fitness, in Figure 15b. Although A7 may reach up to 0.50 of fitness in some scenarios, it is also possible that it drops to 0.10 in some other. A similar behavior is present in A3. On the other hand, A1 only reaches maximum fitness values of 0.4; however, the values among the scenarios are more stable.