## 3 Proposed Model
### Proposed Mobile-Aware Cluster Head-Election Scored (MACHES) Algorithm
#### 3.3.2 Mobility-Aware Cluster-Head Election Scored (MACHES) Procedure
This can be specified as follows:  
\[S_{(i)M}=\alpha\bigg{(}1-\frac{\Delta d_{i}}{d_{max}}\bigg{)}+\beta\bigg{(}1 -\frac{\Delta\theta_{i}}{\theta_{max}}\bigg{)} \tag{12}\]  
where \(\Delta d_{i}\), \(d_{max}\) are, respectively, the displacement of the node \(i\) and maximum possible displacement. The variables \(\Delta\theta_{i}\), \(\theta_{max}\) are, respectively, the change in direction of the node \(i\)'s movement and maximum possible change in direction (typically \(\pi\) radians). The variables \(\alpha\) and \(\beta\) are control weighting factors for determining the probability of being chosen as the candidate CHs. This score helps to select CHs that maintain their positions within the cluster boundary for extended periods. This mobility score is integrated into other two metrics, distance and residual energy-related ratio in (10) and (11); it can ensure that CH selection accounts for stability as well as network efficiency. The total score of being a CH can be written as follows:  
\[S_{CH}=w_{1}S_{(i)M}+w_{2}S_{(i)BS}+w_{3}S_{(i)CC}. \tag{13}\]  
This comprehensive scoring mechanism allows CHES to prioritize nodes that exhibit a combination of mobility stability, energy efficiency, and proximity to the BS. By electing CHs with these properties, CHES minimizes cluster reconfiguration costs, balances energy consumption across the network, and ensures stable communication, even in dynamic WSN environments. * Total Transmission Distance Metric. If there is a discrepancy between the scores relative to the BS and the CC, the decision is based on a comparative analysis of potential energy consumption. This involves calculating the total transmission distance, which includes both the distances from all nodes within the cluster to the candidate CH and from the CH to the BS, thus ensuring an energy-efficient selection of the CH. The final selection of a CH involves a calculated comparison of total transmission distances \(d_{(i)total}\) for node \(i\):  
\[d_{(i)total}=d_{(i)t0 BS}+\sum_{j=1}^{N}d_{(i)(j).} \tag{14}\]  
Here, the \(d_{(i)t0 BS}\) is the distance between the node \(i\) and BS, while the second term aggregates the distances from the node \(i\) to all other nodes within the same cluster. Subsequently, a candidate node with the shortest total transmission distance is then elected as the cluster head. This total includes the distance from the node to the base station plus the cumulative distances from all member nodes within the cluster to the candidate, ensuring the elected head minimizes overall network energy consumption. The node with the smallest total transmission distance under this criterion secures the CH position, efficiently balancing energy usage with operational demands. * Cluster Head Selection Strategy. If multiple nodes exhibit identical score values for potential CH candidacy, the selection process is refined to prioritize proximity to the base station for \(S_{BS}\) and proximity to the CC for \(S_{CC}\) as the CH candidate. Furthermore, if these candidates have equivalent scores, the node with the shortest distance to the base station is chosen to minimize energy consumption, thereby optimizing the network's operational efficiency. Following the election, the designated CH collects and transmits data to the BS, adhering to protocols similar to those established by LEACH. The detailed procedure of this proposed strategy is shown in algorithm. * Proposed Protocol with MACHES algorithm. When implementing the MACHES algorithm, the initial parameters are configured according to the network deployment scenario as follows: number of nodes (\(N\)), area size (\(M\)), BS location, number of rounds, initial energy of sensor nodes (\(E_{init}\)), energy required for transmitting or receiving the data bit (\(E_{T},\ E_{R}\)), message size (\(l\)), radio amplifier energy coefficient for free space and multipath transmission (\(\epsilon_{fs},\ \epsilon_{mp}\)), threshold distance (\(d_{th}\)), and energy required for data aggregation (\(E_{DA}\)).