## Abbreviations
\begin{tabular}{l l} \(\alpha\) & path loss exponent, \(\alpha\in[2,4]\). \\ \(A(t)\) & sensitivity area provided by the WSN at time \(t>0\in\tau\). \\ \(a_{p}(t)\) & variable assuming \(1\) if there is at least one sensor \(i\in S_{s}(t)\) at a distance to the demand point \\ \(amp\) & energy cost per bit of the power amplifier, \(amp>0\). \\ \(\beta\) & transmission quality parameter, \(\beta>0\). \\ \(\beta_{0_{f}}\) & parameter determining the performance of the movement operator based on attractiveness in MO-FA, \(\beta\in[0,1]\). \\ \(c\) & sink coordinates, \(c=(x,y)\) where \(x\in[0,d_{x}]\) and \(y\in[0,d_{y}]\). \\ \(CHIMinc_{m}\) & parameter defining how the extreme points of the CHIM are reassigned to increase the search area in MOEA/D, \(CHIMinc_{m}\in[1,\infty)\). \\ \(co_{th}\) & coverage threshold, \(co_{th}\in[0,1]\). \\ \(cro_{m}\) & crossover probability in the MOEA/D algorithm. \\ \(cro_{n}\) & crossover probability in the NSGA-II algorithm. \\ \(cro_{s}\) & crossover probability in the SPEA2 algorithm. \\ \(crow_{m}\) & distance between two consecutive reference points in MOEA/D, \(crow_{m}\in(0,\infty)\). \\ \(\tilde{D}_{p}(t)\) & set of demand points at time \(t>0\), \(\forall p\in\tilde{D}_{p},\ p=(x,y)\) where \(x\in[0,d_{x}]\) and \(y\in[0,d_{y}]\). \\ \(d_{p}(t)\) & number of demand points. It is the cardinal of \(\tilde{D}_{p}(t)\). \\ \(d_{pn}\) & distance between two neighbouring demand points. \\ \(djp_{i}^{c}\) & number of disjoint paths between the sensor \(i\in S_{s}\) and the sink node. \\ \(d_{x}\) & width of the surface, \(d_{x}>0\). \\ \(d_{y}\) & height of the surface, \(d_{y}>0\). \\ \(E_{1},E_{2}\) & extreme points depending on \(F_{1}\) and \(F_{2}\); \(E_{1},E_{2}\in Y\). \\ \(Ec_{i}(t)\) & energy charge of a sensor \(i\in S_{s}(t)\) at time \(t\). \\ \(Ee_{i}(t)\) & energy expenditure of a sensor \(i\in S_{s}(t)\) at time \(t>0\). \\ \(err\) & local channel error, \(err\in[0,1]\). \\ \(F_{1}\) & extreme point \((maxF(f_{1}),minF(f_{2})\) delimiting the objective space, \(F_{1}\in Y\). \\ \(f_{1}\) & AEC of the sensors over the network lifetime. \\ \(F_{2}\) & extreme point \((minF(f_{1}),maxF(f_{2})\) delimiting the objective space, \(F_{2}\in Y\). \\ \(f_{2}\) & ASA provided by the WSN over the network lifetime. \\ \(f_{3}\) & NR provided by the WSN at the beginning of the network lifetime. \\ \(F_{m}^{g}\) & auxiliary population of undefined size in MOEA/D, saving the non-dominated solutions found until the \(g\)-iteration. \\ \(g(x:r^{m},\overrightarrow{v_{n}})\) & function of the \(m\)-th single -objective minimization problem in MOEA/D. \\ \(h_{L}^{i,c}\) & number of hops in the \(l\)-th disjoint path between \(i\in S_{s}\) and the sink node. \\ \(iec\) & initial energy charge of the sensors, \(iec>0\). \\ \(k\) & information packet size in bits, \(k>0\). \\ \(k_{a}\) & random value representing the number of nearest solution used to obtain a new solution by an scout bee in the MO-ABC algorithm, \(k_{a}=2,\ldots,11\). \\ \(\lambda_{f}\) & parameter determining the performance of the movement operator based on attractiveness in MO-FA, \(\lambda\in(0,\infty)\). \\ \(limit_{a}\) & threshold determining when a solution managed by an employed bee should be managed by an scout bee in MO-ABC. \\ \(maxF(\cdot)\) & lower bounds of a fitness function. \\ \(minF(\cdot)\) & upper bounds of a fitness function. \\ \(mut_{f}\) & mutation probability in the MO-FA algorithm. \\ \(mut_{ga}\) & mutation probability in the MO-GSA algorithm. \\ \(mut_{m}\) & mutation probability in the MOEA/D algorithm. \\ \(mut_{n}\) & mutation probability in the NSGA-II algorithm. \\ \(mut_{s}\) & mutation probability in the SPEA2 algorithm. \\ \(mut_{v}\) & mutation probability in the MO-VSN* algorithm. \\ \(n_{1}\), \(n_{2}\) & coordinates of the normal vector \(\overrightarrow{v_{n}}\) to the plane I. \\ \(n_{E_{1},E_{2}}\) & number of divisions on the segment \(E_{1}E_{2}\). \\ \(neigh_{m}\) & number of neighbouring reference points associated to a reference point in MOEA/D. \\ \(neigh_{v}\) & number of neighbourhood structures in the MO-VSN algorithm. \\ \(n_{v}\) & parameter limiting how different could be a solution according to the neighbourhood structure selected in MO-VNS, \(n_{v}\in[1,\infty)\). \\ \(P_{i}(t)\) & number of packets sent by the sensor \(i\in S_{s}(t)\) at time \(t>0\). \\ \end{tabular}