## 4 Simulation Tests and Results
The coefficients of the social and cognitive part (\(c_{1}\) and \(c_{2}\)) were chosen to have the same value, since the particles function in the most efficient way when these two constants co-exist harmonically; on the other hand the inertia weight was altered linearly so that its initial high value boosted global search capability (exploration of the area), whereas this value decreased during the execution of the algorithm so as to boost the partial search capability of the algorithm (exploitation). The size of the swarm differed in respect to the complexity of the problem. Therefore as far as the first two simpler problems were concerned, the size of the swarm was chosen to be equal to 200; while in the last two and most difficult cases the swarm size was chosen equal to 600 particles. In case studies 1 and 3 all sensor nodes were considered to have the equal sensing ranges, while in case studies 2 and 4 the sensor nodes were considered to have different sensing ranges. In each case study the simulation test was executed 30 times and the mean value, the standard deviation of the area coverage, as well as the average time were calculated and are presented in corresponding tables along with the highest value of the area coverage which resulted from the execution of each case. The information concerning the number of evaluations of the fitness function, as well as the standard deviation of this value are also presented in the same table. Additionally, the final positions of the sensor nodes in the area, which were the optimal positions in terms of coverage maximization among these 30 results, are both found and depicted. Moreover, a graphical representation of the best value of the fitness function is provided in accordance with the iterations for one of the 30 executions of the algorithm. Referring to the first four case studies, it must be noted that the order of appearance in their presentation corresponds to a graded degree of difficulty starting from the easiest one to calculate. Also, referring to the last three case studies, the order of appearance in their presentation corresponds to that adopted in [31]. Finally, in all cases studies examined, the term ideal area coverage in the results presented refers to the sum of the area coverage of the available sensor nodes, without taking into consideration the overlaps that may occur among them. In all of the case studies examined, a comparison among the algorithms investigated is performed. Specifically, in the first four case studies, the competing methodologies are the GA and PSO algorithms proposed, whereas in the last three case studies the comparison that takes place is among each one of the proposed algorithms and the algorithms presented in [30] and [31]. This comparison was carried out using t-test methodology, which allows statistical testing of a hypothesis applicable to a population. This methodology is based on the calculation of the p-value, which indicates how compatible the \begin{table}
\begin{tabular}{c c} \hline \hline
**Control Parameters** & **Functions/Values** \\ \hline Inertia Range (w) & [0.1, 1.1] \\ Self-Adjustment Weight \(c_{1}\) & 1.49 \\ Social Adjustment Weight \(c_{2}\) & 1.49 \\ Swarm Size & [200, 600] \\ Function Tolerance & 0.01 (for 20 iterations) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Particle swarm optimization control parameters. data are, with a hypothesis known as the null hypothesis. As null hypothesis it is assumed that the two competing algorithms produce results with the same mean.