## 2 Methodology
### Cluster Head Selection  
A cluster head with more than one node eligible to act as nodes are named \"cluster congregation (CGA)\". The CGAs are in charge of acquiring and consolidating data from the members of the clusters before sending them on to the cluster heads using a hybrid MAC protocol. To transfer sensed data to its CGA (low-level MAC), the members of cluster nodes use a CSMA/CA protocol to acquire the channel. Every CGA, on the other hand, sends the gathered information to its CH during its given TDMA session (high-level MAC).  
Each member of the cluster turns on its radio communication modules in the steady-state period to transmit the perceived data to the appropriate CGA. As a result, the nodes  
Figure 4: Model for dissipation of energy.  
would only be activated throughout their operating hours, and they will otherwise hibernate. The data are aggregated, compressed and forwarded to the cluster heads by the CGAs. As a result, the intra-cluster transmission mechanism is multi-hopping [28]. Moreover, every CH sends the data it receives to the base stations. The cluster heads transmit END round notifications to the participants after the base station receives all the data. For each round, the total energy used by the cluster head is illustrated in Equation (5). The \(W_{R}\) denotes the total energy drawn by a CH in each round; \(W_{SCH}\) shows the energy utilized at the CH selection step; \(W_{ACH}\) represents the energy utilized to broadcast the CH advertisement; \(W_{RCJ}\) shows the energy utilized to acquire the joint request from non-CH nodes; \(W_{RC}\) represents the energy utilized to acquire the sensed data from member of the cluster; \(W_{SC}\) is energy utilized to send the aggregated data from the CH to the base station.  
\[W_{R}=W_{SCH}+W_{ACH}+W_{RCJ}+W_{RC}+W_{SC} \tag{5}\]  
I \(W_{R}\) depicts the \(W_{SCH}(o,t)=\left((o_{c}/\alpha)*(W_{EC}+\epsilon_{frs}distance^{2}tobasestation)\right)\)  
where \(o_{c}\) represents the size of the control packet  
\(W_{ACH}(o,t)=o_{c}*W_{elect}\);  
\(W_{RCJ}(o)=N_{cm}*o_{c}*W_{ele}\);  
\(W_{RC}(o)=g*(N_{crao}*o_{distance}*W_{ele})\);  
\(W_{SC}(o,t)=(o_{distance}/\alpha)*(\epsilon_{frs}distance^{2}tobasestation)\).  
On either side, the overall energy utilized by the members of the clusters and congregations of each cluster node in every round \((W_{MR})\)\((W_{GRA})\) can be computed as described in Equation (6). \(W_{MR}\) denotes the total energy utilized by a cluster member in each round; \(W_{MoJ}\) shows the energy utilized to transmit a joint message to the CH; \(W_{MO}\) denotes the energy utilized to send the sensed data from a member of the cluster to the cluster head.  
\[W_{MR}=W_{MTA}+W_{MoJ}+W_{MO} \tag{6}\]  
and  
\[W_{GT}=W_{Gsp}+W_{GR}+W_{Gap}+W_{GS} \tag{7}\]  
\(W_{GT}\) signifies the energy the cluster congregation uses; \(W_{Gsp}\) shows the energy utilized to broadcast the cluster congregation advertisement; \(W_{Gap}\) denotes the energy utilized by the process of data aggregation. Based on the utilization of energy, the behavior of the node can be depicted in the proposed protocol which assumes that for every round the node \(n_{a}\) should take one of the three roles: cluster head, member of the cluster or congregation of clusters. Therefore, the evaluation of the utilization of energy W for node \(n_{a}\) is based on the role over every round r1.  
The fitness function for all the clusters for every round in the SFO is described with the objective function: CH fitness value = F1(CH). There are different objectives in preventing failure of the sink node among which is evaluating the bandwidth of the CH which includes the maximal number of data sent to the base station from CH.