## 4 Survey of Existing Works
### PSO in WSNs
#### 4.1.3 PSO in Energy Aware Clustering
In variant, the inertia weight \(w\) is decreased linearly from 0.9 in first iteration to 0.4 in the last iteration. In PSO with time varying acceleration constants, inertia weight is set constant, and acceleration constants \(c_{1}\) and \(c_{2}\) are varied linearly in every iteration, so the particles move in large steps initially but the step size reduces in every iteration. In hierarchical PSO with time varying acceleration constants method, the particle update is not influenced by the velocity in previous iteration. Thus, re-initialization of velocity is done when the velocity stagnates in the search space. Therefore, a new set of particles is automatically generated according to the behaviour of the particles in the search space, until the convergence criterion is met. Lastly, the PSO with supervisor student variant updates its position according to Equation (8). This method introduces a novel parameter called momentum factor (mc) which updates the positions of particles (refer to Table 1 for other notations). In this strategy the velocity of the particle is updated only if its fitness at the present iteration is not better than that of previous iteration. The velocity acts as a pilot (supervisor) by getting the accurate direction, whereas the position \begin{table}
\begin{tabular}{c c} \hline \(w\) & inertia weight \\ \(v_{u}^{*}\) & old velocity calculated for each particle \\ \(v_{u}^{*1}\) & new velocity calculated for each particle \\ \(c_{1}\) and \(c_{2}\) & self confidence factor and the swarm confidence factor \\ \(r_{1}\) and \(r_{2}\) & random numbers \\ \(p_{u}^{*}\) & particles own past best position \\ \(x_{u}^{*}\) & old position calculated for each particle \\ \(p_{u}^{*}\) & the best position a particle attained in the whole swarm \\ \hline \end{tabular}
\end{table} 
Table 1: Notations used in PSO. (student) obtains a right step size along the direction. A detailed comparative analysis of the algorithms for optimal clustering is presented. This scheme considers only the physical distances between nodes and their assigned cluster-heads, but not the energy available to the nodes:  
\[x_{id}^{n+1}=(1-mc)\times x_{id}^{n}+mc\times v_{id}^{n+1} \tag{8}\]  
[PERSON] _et al._[61] have considered a slightly different case in which a node and its CH are engaged in a multi-hop communication. The proposed algorithm synthesized the intuitionist advantages of graph theory [62] and optimal search capability of PSO [63]. They calculated the distance based on minimum spanning tree of the weighted graph of the WSN. The CHs were elected by maximum residual energy and in turns and by probabilities separately. The best route between a node and its CH is derived from all the optimal trees on the basis of energy consumption. The authors concluded that the network lifetime has almost nothing to do with the BS location or the residual energy of the node. Once the topology of the network is decided, the lifetime is settled. They also mentioned that there are two ways to improve the network lifetime. One way is to reduce the energy consumption for transmitter or receiver start up. Other way is to optimize the network topology. The performance was compared with three mechanisms of CH election: energy-based, auto-rotation-based, and probability-based. The results show that the PSO-based clustering methods ensure prolonged network lifetimes.