# An Energy-Efficient Evolutionary Clustering Technique for Disaster Management in IoT Networks
## 3 Proposed Method
### Cluster Head Selection Phase
#### 3.3.4 Clustering Steps
The \(g\_b\), as the global best location, is determined by selecting the best solution of \(p\_bs\). In this paper, the nodes that harmonize with \(g\_bs\) are taken, and the closest nodes to these harmonies form CHs. The velocity (V) and location (X) of the particles can be updated as follows [23; 29]: \[\mathrm{V_{xy}\left(r+1\right)}=\omega V_{xy}\left(r\right)+r_{a}c_{a} \left(p\_bxy-X_{xy}\left(r\right)\right)+r_{b}c_{b}\left(g\_bxy-X_{xy}\left(r \right)\right)\] (20) \[\mathrm{X_{xy}\left(r+1\right)}=X_{xy}\left(r\right)+V_{xy}\left(r+1\right)\] (21) where the index \(xy\) denotes the \(x\)th particles and dimension, \(c_{a}\) and \(c_{b}\) are acceleration constants, \(r_{a}\) and \(r_{b}\) are the random uniform amount in \([0,1]\), and factor \(\omega\) is the inertia weight factor. Selecting a suitable value of \(\omega\) creates a balance between exploration and exploitation [46]. In [29], the linear reduction of factor \(\omega\) has a positive effect on the efficiency of the application of WSNs, while in [46], the authors proposed a nonlinear time-varying inertia weight formula that led to a faster convergence than the linear inertia factor used in [29; 45]. Therefore, to enhance efficacy, we use the following high-order (\(\propto\)) nonlinear formula: \[\omega=\omega_{\max}-(\omega_{\max}-\omega_{\min})\left(\frac{\text{iter}}{\text {r}_{\max}}\right)^{\infty}\] (22) where iter is the current of iteration and \(\text{r}_{\max}\) is the total number of iterations. Equation (22) [46] decreases nonlinearly from \(\omega_{\max}=0.9\) to \(\omega_{\min}=0.4\) and finds a suitable value at each round. The obtained results of [46] show that excellent performance is achieved when \(\propto\leavevmode\
obreak\ =1/\,\pi^{2}\) and the two constants \(c_{a}\) and \(c_{b}\)--as cognitive and social parameters--have the value 2. The location and velocity of the particles are calculated and updated at each round of the proposed method and for each row in PHM. As mentioned above, the closest nodes to \(g\_b\) will be the optimal CHs. * Going Back to the First Step or Stopping the Algorithm When all the rounds of the clustering phase come to an end, the algorithm stops and a total number of \(k\) optimal CHs are determined for the routing phase. Otherwise, the algorithm goes back to the second step and repeats until it finds optimal or near-optimal solutions. However, before the next round starts, the values of HMCR and PAR in Algorithm 1 are required to be updated as follows [31]: \[Update1:\text{HMCR}\left(\text{Iter}+1\right)=\text{HMCR}.\min+\left(\frac{ \text{Iter}}{\text{r}_{\max}}\right)\times\left(\text{HMCR}.\max-\text{HMCR}. \min\right)\] (23) \[Update2:\text{PAR}\left(\text{Iter}+1\right)=\text{PAR}.\max-\left(\frac{ \text{Iter}}{\text{r}_{\max}}\right)\times\left(\text{PAR}.\max-\text{PAR}. \min\right)\] (24) These dynamic updates in the search process enhance the exploration capacity of the first stages and lead to the improvement of the local search in the last stages [31] because the variation of the HMCR value affects the diversity and convergence of PHM, with similar results for the PAR value in terms of the local and global optimum [34; 41; 42]. Hence, the initial values of Equations (23) and (24) are adjusted according to [31].