## 4 Proposed 3D-UWSN Design
### Clustering  
In this proposed research DEDG 3D-UWSN, the sensor nodes are clustered into several clusters, and an optimal CH is selected in each cluster using an MO-SHO algorithm according to some key parameters. Initially, the CHs are selected, and the sensors within their coverage are added as cluster members (CMs). These sensors are affiliated to that CH and form a cluster. The selection of the CHs is made in relay; a CH is selected for a period of time until another sensor is selected as the next CH in turn. The selection of CHs is therefore made alternately. The cluster heads are responsible for managing the nodes within the cluster; therefore, the clustering with optimal head selection reduces the energy consumption in data gathering. Multi-Objective Spotted Hyena Optimization (MO-SHO) Algorithm  
Spotted hyenas are wild animals that usually live and hunt in groups and rely on a network of trusted friends with the ability to recognize the location of the prey. MO-SHO is a meta-heuristic algorithm modeled by analyzing the social hunting behavior of spotted hyenas. MO-SHO imitates the cohesive clusters between trusted spotted hyenas which are helpful for efficient co-operation and maximize the fitness. In this research, the hunting technique and the social relations of spotted hyenas are mathematically modeled to design the MO-SHO and perform optimization. To define the behavior of spotted hyenas mathematically, we suppose that the best search agents (the best hyenas hunters) are whichever have optimum knowledge of the location of the prey. The other search agents (other hyena followers) make a cluster towards the best search agent and save the best solutions obtained to update their positions. The MO-SHO algorithm (Algorithm 1) is used for clustering with optimal head selection that reduces the energy consumption in data gathering. The mathematical model of the MO-SHO behavior is formulated as [47]:  
\[\overset{\rightarrow}{d_{H}}=\left|\overset{\rightarrow}{C_{1}}\times\overset {\rightarrow}{P_{b}}(t)-\overset{\rightarrow}{P_{H}}(t)\right| \tag{1}\]  
\[\overset{\rightarrow}{P_{H}}(t+1)=\overset{\rightarrow}{P_{T}}(t)-\overset {\rightarrow}{C_{2}}\times\overset{\rightarrow}{d_{H}} \tag{2}\]  
The distance between the hyena is \(\overset{\rightarrow}{d_{H}}\) at \(t\) iteration. The terms \(\overset{\rightarrow}{C_{1}}\) and \(\overset{\rightarrow}{C_{2}}\) are the vector coefficients, \(\overset{\rightarrow}{P_{H}}\) represents the current position of the hyena and the \(\overset{\rightarrow}{P_{b}}\) vector defines the best position. The best positions of the hyenas are given as:  
\[N_{H}=Sol\ \left(\overset{\rightarrow}{P_{h_{1}}},\ \overset{\rightarrow}{P_{h_{1}+1}},\ \overset{ \rightarrow}{P_{h_{1}+2}},\ldots,\left(\overset{\rightarrow}{P_{h_{1}}}+ \overset{\rightarrow}{r}\right)\right) \tag{3}\]  
\(N_{H}\) is the total number of hyenas, \(\overset{\rightarrow}{r}\) indicates the random vector whose values are \([0.5,\ 1]\) and their solutions are represented as sol, which is the best positions of the hyenas. Hyenas are the search agents that are the sensors from which the best is chosen. The last-stored, best solution is given as:  
\[\vec{P_{H}}(t+1)=\frac{\vec{G_{H}}}{N_{H}} \tag{4}\]  
Here, \(\vec{G_{H}}\) represents the group of optimal solutions that is obtained based on the position of the best hyenas. In fitness, the node degree is defined as the total number of neighbors connected with the particular node. The node degree \(N_{d}\) for the sensor in \(L_{1}\) is mathematically formulated by:  
\[N_{d}=\frac{\sum_{1}^{l}\left(s_{l},s_{j}\right)}{\left(s_{l}-1\right)} \tag{5}\]  
\(s_{l}\) is the total number of sensors that exists in \(L_{1}\), and \(I\) and \(j\) are the two sensor nodes which are 1 if the sensors are linked; otherwise they are 0. Then, the node lifetime is expressed as:  
\[N_{L}=\frac{RE}{ED} \tag{6}\]  
The node lifetime \(NL\) is computed from the residual energy of the sensor nodes \(RE\) to that of the energy drain rate \(ED\).