## Abbreviations
\begin{tabular}{l l} \(P_{a}^{g}\) & population of size \(ps_{a}\) in the MO-ABC algorithm. \\ \(P_{f}^{g}\) & population of size \(ps_{f}\) saving the the fireflies at the beginning of the iteration \(g\) in MO-FA. \\ \(P_{ga}^{g}\) & population of size \(ps_{g}\) saving the the objects at the beginning of \(g\), before acting gravitational \\  & forces in the MO-GSA algorithm. \\ \(P_{m}^{g}\) & regular population in MOEA/D, where each individual is associated to a reference point. \\ \(P_{n}^{g}\) & population of size \(ps_{n}\) saving the parents of the iteration \(g\) in the NSGA-II algorithm. \\ \(P_{s}^{g}\) & regular population of size \(ps_{s}\) in the SPEA2 algorithm. \\ \(\overline{P}_{s}^{g}\) & auxiliary population of size \(\overline{ps}_{s}\) in the SPEA2 algorithm. \\ \(P_{v}^{g}\) & population of unlimited size, saving only non-dominated solutions during the iteration \(g\) in the MO-VNS algorithm. \\ \(ps_{a}\) & population size in the MO-ABC algorithm. It is the cardinal of \(P_{a}^{g}\). \\ \(ps_{m}\) & number of points evenly distributed in the plane I. It is the cardinal of \(Y\). \\ \(ps_{f}\) & population size in the MO-FA algorithm. It is the cardinal of \(P_{f}^{g}\) and \(Q_{f}^{g}\). \\ \(ps_{ga}\) & population size in the MO-GSA algorithm. It is the cardinal of \(P_{ga}^{g}\) and \(Q_{ga}^{g}\). \\ \(ps_{n}\) & population size in the NSGA-II algorithm. It is the cardinal of \(P_{n}^{g}\) and \(Q_{n}^{g}\). \\ \(ps_{s}\) & regular population size in the SPEA2 algorithm. It is the cardinal of \(P_{s}^{g}\). \\ \(\overline{ps}_{s}\) & auxiliary population size in the SPEA2 algorithm. It is the cardinal of \(\overline{P}_{s}^{g}\). \\ \(Q_{f}^{g}\) & population of size \(ps_{f}\) saving the resulting fireflies after applying the attractiveness mechanism \\  & in \(P_{f}^{g}\) in the MO-FA algorithm. \\ \(Q_{ga}^{g}\) & population of size \(ps_{g}\) saving the resulting objects after applying the forces in \(P_{ga}^{g}\) in the MO-GSA algorithm. \\ \(Q_{n}^{g}\) & population of size \(ps_{n}\) saving the offspring generated based on \(P_{n}^{g}\) in the NSGA-II algorithm. \\ \(re_{i}\) & reliability of the sensor \(i\in S_{s}\). \\ \(r_{c}\) & communication radius, \(r_{c}>0\). \\ \(Rpi_{i}(t)\) & number of relayed packets sent by the sensor \(i\in S_{s}(t)\) at time \(t>0\). \\ \(r_{f}\) & parameter determining the performance of the movement operator based on attractiveness in MO-FA, \(r\in[0,1]\). \\ \(r^{m}\) & \(m\)-th point of \(Y\). \\ \(r^{m}_{1}\), \(r^{m}_{2}\) & coordinates of the vector \(r^{m}\). \\ \(r_{s}\) & sensitivity radius, \(r_{s}>0\). \\ \(se_{a}\) & percentage of solutions in \(P_{a}^{g}\) managed by employed forager bees in MO-ABC. \\ \(\bar{S}_{r}\) & set of RN coordinates, \(\forall r\in\bar{S}_{r}\), \(r=(x,y)\) where \(x\in[0,d_{x}]\) and \(y\in[0,d_{y}]\). \\ \(\bar{s}_{r}\) & number of RNs. It is the cardinal of \(\bar{S}_{r}\). \\ \(\bar{S}_{s}\) & set of initial sensor coordinates, \(\forall i\in\bar{S}_{s}\), \(i=(x,y)\), where \(x\in[0,d_{x}]\) and \(y\in[0,d_{y}]\). \\ \(s_{s}\) & number of initial sensors. It is the cardinal of \(\bar{S}_{s}\). \\ \(S_{s}(t)\) & set of sensor coordinates, holding that the energy charge is greater than \(0\) and that there is any path to the sink node, both at time \(t>0\), \(S_{s}(t)\subseteq\bar{S}_{s}\), \(\forall i\in S_{s}\), \(i=(x,y)\), where \(x\in[0,d_{x}]\) and \(y\in[0,d_{y}]\). \\ \(s_{s}(t)\) & number of sensors, holding that the energy charge is greater than \(0\) and that there is any path to the sink node, both at time \(t>0\). It is the cardinal of \(S_{s}(t)\), \(s_{s}(t)\leq\bar{s}_{s}\). \\ \(S_{v}^{g}\) & population of unlimited size saving the solutions from \(P_{v}^{g}\) considered to explore the search space during the iteration \(g\) in the MO-VNS algorithm. \\ \(\tau\) & set of time periods, \(\tau=\{0,1,2,\ldots\}\). \\ \(t\) & time instant, \(t>0\). \\ \(t_{n}\) & network lifetime of the WSN based on the coverage threshold \(co_{th}\). \\ \(\overline{v}_{n}\) & normal vector \((n_{1},n_{2})\) to the plane I. \\ \(when\_{c}f\) & threshold defining when the anti-stagnation mechanism is performed in MO-FA, \(when\_{c}f\in[0,1]\). \\ \(when\_{c}\bar{s}_{ga}\) & threshold defining when the anti-stagnation mechanism is performed in MO-GSA, \(when\_{c}\bar{s}_{ga}\in[0,1]\). \\ \(w_{i}^{c}(t)\) & variable which provides the next device in the minimum path between \(i\in S_{s}(t)\) and the sink \\  & node at \(t>0\), \(w_{i}^{c}(t)\in\{S_{s}(t)\cup S_{r}\}+c-i\). \\ \(Y\) & number of points evenly distributed in the plane I, \(Y=\{r^{1},\ldots,r^{ps_{m}}\}\). \\ \(z_{j,i}^{c}(t)\) & variable assuming \(1\) if \(i\in S_{s}(t)\) is in the minimum path between \(j\in S_{s}(t)\) and the \\  & sink node \(c\) at \(t>0\), and \(0\) otherwise. \\ \end{tabular}