# GASP: Genetic Algorithms for Service Placement in Fog Computing Systems
## 4 Experimental Results
### Comparison of Evolutionary Strategies and Operators
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Strategy or** & \(\mathbf{\rho=0.5}\), \(\delta\mu=0.01\) & \(\mathbf{\rho=0.5}\), \(\delta\mu=0.1\) & \(\mathbf{\rho=0.5}\), \(\delta\mu=1.0\) \\
**Operator** & \(\mathbf{\epsilon\) [\%]} & \# Gen. & \(\mathbf{\epsilon\) [\%]} & \# Gen. & \(\mathbf{\epsilon\) [\%]} & \# Gen. \\ \hline \hline \multicolumn{6}{c}{**Evolutionary Strategies**} \\ \hline _Simple_ & \(-0.20\pm 0.01\) & \(0.00\pm 0.00\) & \(0.53\pm 0.07\) & \(0.00\pm 0.00\) & \(0.54\pm 0.15\) & \(23.43\pm 3.82\) \\ \(\mu+\lambda\) & \(-0.27\pm 0.01\) & \(0.00\pm 0.00\) & \(0.02\pm 0.05\) & \(0.00\pm 0.00\) & \(0.65\pm 0.17\) & \(21.36\pm 3.68\) \\ \hline \multicolumn{6}{c}{**Selection Operators**} \\ \hline _Tournament_ & \(-0.21\pm 0.01\) & \(0.00\pm 0.00\) & \(0.52\pm 0.08\) & \(0.00\pm 0.00\) & \(0.54\pm 0.13\) & \(23.85\pm 3.69\) \\ _Roulette_ & \(0.23\pm 0.27\) & \(0.00\pm 0.00\) & \(1.54\pm 0.26\) & \(0.00\pm 0.00\) & \(11.25\pm 0.56\) & \(300.00\pm 0.00\) \\ \hline \multicolumn{6}{c}{**Mutation Operators**} \\ \hline _Shuffle_ & \(-0.23\pm 0.01\) & \(0.00\pm 0.00\) & \(0.48\pm 0.04\) & \(0.00\pm 0.00\) & \(1.92\pm 0.29\) & \(30.29\pm 5.79\) \\ _Uniform Int_ & \(-0.21\pm 0.01\) & \(0.00\pm 0.00\) & \(0.53\pm 0.08\) & \(0.00\pm 0.00\) & \(0.54\pm 0.15\) & \(22.82\pm 3.66\) \\ \hline \multicolumn{6}{c}{**Crossover Operators**} \\ \hline _Uniform_ & \(-0.20\pm 0.01\) & \(0.00\pm 0.00\) & \(0.52\pm 0.07\) & \(0.00\pm 0.00\) & \(0.53\pm 0.13\) & \(24.21\pm 3.48\) \\ _One Point_ & \(-0.24\pm 0.01\) & \(0.00\pm 0.00\) & \(0.28\pm 0.08\) & \(0.00\pm 0.00\) & \(0.81\pm 0.19\) & \(27.50\pm 4.26\) \\ _Two Points_ & \(-0.23\pm 0.01\) & \(0.00\pm 0.00\) & \(0.34\pm 0.07\) & \(0.00\pm 0.00\) & \(0.78\pm 0.17\) & \(26.27\pm 4.10\) \\ _UPMX_ & \(-0.27\pm 0.01\) & \(0.00\pm 0.00\) & \(0.11\pm 0.07\) & \(0.00\pm 0.00\) & \(1.07\pm 0.22\) & \(27.38\pm 4.28\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Evolutionary strategies. preserves the most important characteristics that is the load balancing. However, this behavior has a negative impact in the \(\delta\mu=1\) scenario as it hinders a more free exploration of the solution space. On the other hand, a uniform mutation operator provides better performance for the \(\delta\mu=1\) scenario, but at the expense of a less effective search for the optimum when \(\delta\mu=0.01\) or \(\delta\mu=0.1\). Finally, we compare the four crossover operators. The basic performance of these operators are quite similar, with a limited difference in both \(\epsilon\) and in the number of generations to reach convergence. We also observe the opposite behavior between the scenarios where the load balancing is more important than the search for the closest fog nodes (\(\delta\mu=0.01\) and \(\delta\mu=0.1\)) compared to the opposite case, where distance reduction through optimized topology plays an important role in performance (\(\delta\mu=1\)). However, due to the reduced impact of this parameter, we consider as the best option the uniform crossover, due to its fast and simple implementation and due to its stable performance over the different scenarios.