# Multi Swarm Optimization Based Clustering with Tabu Search in Wireless Sensor Network
## 3 Methodology
### Multi Swarm Optimization Based Clustering (MSO)  
This work discusses the multi-PSO swarm, which does not generalize instantly as there is no interaction between the swarm. There might be interaction if it is right to attract another swarm; however, one swarm decreases through a number of information sharing topologies. Two multi-swarm methods are suggested here. Multi-Charged Particle Swarm Optimization (CPSO) is a multi-population variant of CPSO. Multi-Quantum Swarm Optimization (MQSO) exploits quantum swarms based on quantum in place of traditional atom objectives.  
[PERSON] introduced CPSO [31] with the basis of the orbit model of a nucleus atom that is orbited by electrons. In CPSO, the charge is given to a certain proportion of particles that repel other charged particles. Charged particles are those given a charge, whereas the others are termed neutral particles. Vanilla update equation is used to update particle velocities with an additional term based on their proximity to other particles.  
\[\overrightarrow{v_{i}}(t+1)=w\overrightarrow{v_{i}}(t)+c_{1}\overrightarrow{ r_{1}}(t)(\overrightarrow{pbest}-\overrightarrow{x_{i}}(t))+c_{2} \overrightarrow{r_{2}}(t)(\overrightarrow{gbest}-\overrightarrow{x_{i}}(t)) \tag{1}\]  
In Equation (1), \(\overrightarrow{v_{i}}\) is the velocity of particle \(i\), \(\overrightarrow{x_{i}}\) is the position of the particle, \(\overrightarrow{pbest}\) is the personal best position of the particle, and \(\overrightarrow{gbest}\) is the swarm's best-found position, assuming a star neighborhood topology. The constants \(w\in[0,\,1],\ c_{1}\geq 0,\ and\ c_{2}\geq 0\) are the inertia, cognitive, and social weights, respectively, which are user-supplied parameters. Inertia applies a portion of the previous velocity to the current velocity in an attempt to keep the direction of the particle from changing. The cognitive and social components verify the involvement obtained from the personal best and global best positions, respectively. At last, \(\overrightarrow{r_{1}}(t)\) and \(\overrightarrow{r_{2}}(t)\) are vectors sampled from a uniform distribution in the range [0, 1], giving the PSO algorithm its stochastic element.  
The CPSO velocity update equation is given as (2):  
\[\overrightarrow{v_{i}}(t+1)=w\overrightarrow{v_{i}}(t)+c_{1}\overrightarrow{ r_{1}}(t)(\overrightarrow{pbest}-\overrightarrow{x_{i}}(t))\ c_{2}\overrightarrow{r_{2}}(t)(\overrightarrow{gbest}- \overrightarrow{x_{i}}(t))+\sum_{\forall j\
eq i}a_{ij} \tag{2}\]  
TS which could congregate hypothetically symptomically to the global optimum solution; more timespan is needed in achieving the near-global minima. Integrating TS to MSO as a local development method can permit the protocol to maintain the population diversity, avoiding directing towards misguiding local optimum. In TS, average energy utilization is greater than MSO, and the calculation time is less in TS than MSO. Through the merger of both techniques, a compromise between them is avoided. For the hybrid approach, simple MSO and generalized TS are used. The following steps are used and implemented in the proposed algorithm.  
* Step 1: Initialization of location and energy of nodes and BS.
* Step 2: Cluster formation take place through computation of the distance between nodes that correspond to the base station and energy level of the nodes.
* Step 3: Verify the optimal local position through MSO.
* Step 4: Find out the optimal global position--the global optimal is computed by initializing the Tabu list with MSO solution and Tabu memory entries to zero. Routes are swapped and create an entry in Tabu memory. The limitations are confirmed.
* Step 5: Find out the subsequent place lest the fitness value exists in the Tabu list, and that fitness value is noted. The optimal solution from the Tabu list with the least hop routing is considered.