## 4 Proposed Work
### Unequal Cluster-Tree Topology Construction
\begin{array}{l} \ken_{dec}+ke_{sp}dist^{2},\ (CM\ to\ CH)\\ \ken_{dec}+ke_{ap}dist^{4},\ (CH\ to\ BS)\end{array} \right. \tag{3}\]  
In which, \(T_{x}(en)\) denotes energy required for transmission, \(\epsilon_{sp}\)_and_\(\epsilon_{ap}\) denotes power consumption of amplifier in free space and multi-path fading channel models and \(en_{dec}\) denotes the signal processing energy, IE represents initial energy, \(en_{amp}\) denotes energy required for amplification and k represents length of message bits. \[R_{x}(en)\ =\ R_{x}(en_{dec}) \tag{4}\]  
In order to compute the energy consumption of the CH, both the energy consumption during inter-cluster and intra-cluster routing are to be calculated which are expressed as the following equations. Equation (5) represents the energy required for CH in intra-cluster routing \((CH-intra(en))\) which is equal to the sum of the energy required for reception of signals inside the cluster \((CH-R_{x}-intra(en))\) and the energy required for aggregation of received signals \((CH-df-intra(en))\). In Equation (6), the energy consumption of CH in inter-cluster routing \((CH-inter(en))\) is computed which equals to the sum of energy required for the transmission of signals between the clusters \((CH-T_{x}-intra(en))\) and the energy required for the sensing of signals \((CH-CS-inter(en))\), where \(\gamma\) denotes the compression ratio and \(CS(en)\) denotes the sensing cost. The total energy consumption of the wireless sensor network is found from the remaining energy, which can be calculated from Equations (8)-(10). \[\begin{array}{l}CH-intra(en)=CH-R_{x}-intra(en)+CH-df-intra(en)\\ \  
In which y and z denote the location coordinates of the sensors, respectively. The capacity of the node is referred in terms of buffer size which can be represented as,  
\[C=\frac{Initial_{BS}}{initial_{BS}-current_{BS}} \tag{12}\]  
The MoBWo computes the fitness value for each node based on the objective and selects the optimal cluster head. In the procreation mode two nodes are selected as parents and two nodes are selected as children in which the child nodes are expressed as,  
\[\left\{ \begin{array}{l}q_{1}=\gamma\times p_{1}+(1-\gamma)\times p_{2}\\ q_{2}=\gamma\times p_{2}+(1-\gamma)\times p_{1}\end{array} \right. \tag{13}\]  
Once the procreation mode selects the nodes, the cannibalism mode is carried out in which only the fittest nodes are selected. Based on the population of the procreation mode, the mutation is carried out and finally the optimal CH is selected. The nodes in each cell form clusters with the CH while the CHs form tree with BS. Data transmission takes place through the CHs selected optimally by the MoBWo algorithm. This phase minimizes energy consumption and increases data transmission efficiency. Algorithm 2 explains the process of selection the optimal node as the cluster head. ```
Input: No.of. iterations, PP, CR, PM Output: Optimal cluster head  Population initialization of nodes;  Calculate reproduction number \(``\boldsymbol{r}\"\);  From P1 select best \(\boldsymbol{m}\) results \(\boldsymbol{k}\) = 1 to \(\boldsymbol{m}\)do  From P1 arbitrarily select two nodes as parents:  Using Eq(1)/generate children;  Father is destroyed;  Destroy some children based on CR;  Save no. of. Nodes \(\boldsymbol{p}^{2}\) End  Calculate the no. of mutation nodes \(\boldsymbol{m}\) based on PM;  For k = 1 to \(\boldsymbol{m}\)do  Select a node from P1;  Generate new node by random mutation  Save the new nodes into P3;  End for  Update \(P=\boldsymbol{p}_{2}+\boldsymbol{p}_{3}\);  Get the best node from P;
```  
**Algorithm 2** CH selection