## 3 Coverage Control Using Memetic Algorithm
### Wake-up Scheme  
Considering the energy-efficient coverage, we propose a wake-up scheme to awaken some sleeping nodes to recover the uncovered POIs due to energy exhaustions on some sensing nodes. When applying the proposed CoCMA to a CWSN [26], we assumed that the power for the sink of the network is sufficient to carry out the CoCMA operation and the wake-up scheme. In the CWSN [26], each sensor node is capable of communicating with the sink directly. In the following paragraphs, the proposed CWSN-based wake-up scheme will be described in detail. For the CWSN [26], sensor nodes self-organize themselves into several clusters. In each cluster, only one node can serve as a cluster head. The CWSN uses a TDMA (Time Division Multiple Access) approach to achieve communication between the nodes and their cluster head. Moreover, the cluster head is able to communicate with the remote base station directly and in charge of forwarding the messages received from its cluster nodes to the base station. The head node will set up a TDMA schedule and transmit it to its cluster nodes. The cluster nodes can use the TDMA schedule to arrange the time slots for each node. After the setup phase, the nodes will be in a steady-state phase to forward the data packets to their cluster head. An example of a time slot arrangement in a round is illustrated in Figure 7. In the CWSN [26], the clusters can be re-established in each \"round\". A new cluster head is also elected in every round. Figure 7: An illustration of time slot arrangement in one round in CWSN. When the sink receives the signal transmitted from a dying node, it will determine which nodes should be active and then activates them, when another new round comes. According to the MA-based schedule for sensor nodes, some sensor nodes are switched to sleeping mode, and the remaining sensor nodes are responsible for the sensing task. The MA-based schedule of sensor nodes is conducted in the first round, and the proposed wake-up scheme awakens some sensor nodes in the next round if there is one sensor node about to run out its energy. According to the coverage vector, which is defined in Section 3.2.2, the sensing coverage can be evaluated by using bitwise Boolean operations. If one node \(n_{i}\) exhausts its energy, the sink will re-evaluate the coverage of the CWSN and find the uncovered POIs by:  
\[\pi_{\text{uncovered}}^{n_{i}}=\pi_{n_{i}}^{\lambda}\oplus\pi_{n_{i}}^{\
u}, \tag{12}\]  
where \(\oplus\) denotes the Boolean exclusive disjunction (also called exclusive or), \(\pi_{n_{i}}^{\lambda}\) denotes the original synthetic coverage vector of all sensor nodes including sensor node \(n_{i}\), \(\pi_{n_{i}}^{\lambda}\) denotes the synthetic coverage vector without sensor node \(n_{i}\), and \(\pi_{\text{uncovered}}^{n_{i}}\) denotes the vector that indicates which points are not uncovered. Some definitions should be given before proposing the wake-up scheme. **Definition 1**. Let node \(n_{i}\in C\), where \(C\) is the set of all sensor nodes, and \(i\in\llbracket 1,\ N\rrbracket\). **Definition 2**. The \(u_{i}\) denotes the set of all neighboring nodes of \(n_{i}\), where \(i\in\llbracket 1,\ N\rrbracket\). Here \(u_{i}\) is defined as \(u_{i}=\{n_{j}\in C\big{|}\text{distance}(n_{i},\ n_{j})<\lambda\cdot r_{s},\ i \
eq j,\ j\in\llbracket 1,\ N\rrbracket\}\), where \(\lambda\) is a constant. We suppose that two nodes are neighbors if the Euclidean distance between them is smaller than \(\lambda r_{s}\). **Definition 3**. Let \(\psi_{i}\) be defined as \(\psi_{i}=\{n_{i}\in u_{i}\big{|}\sum\limits_{\forall k}\pi_{\text{*}}\cap\pi_{ \text{uncovered}}^{n_{i}}\geq\mathbb{I}\}\), which represents the set of the nodes that have the overlapped POIs between their synthetic coverage vectors and \(\pi_{\text{uncovered}}^{n_{i}}\), where \(\pi_{\text{*}}\) denotes the synthetic coverage vector of \(n_{\text{*}}\), and \(h\) denotes each vector element in \(\pi_{\text{*}}\cap\pi_{\text{uncovered}}^{n_{i}}\).