## 5 Proposed Methodology
### Particle Swarm Optimization  
The technique used for optimizing non-linear continuous functions is called PSO. PSO is simple to use and can locate optimum or nearly perfect solutions. The most important work for the PSO technique is the information exchange among the swarm of particles. To allow us to discover the best response inside the search area, each particle can be looked after. Both the collective and personal information from the whole swarm of particles contributes to directing the search mechanism. The PSO technique is a special type of iterative algorithm. Each individual particle tries to move nearer to the perfect outcome throughout each successive iteration. Each iteration ends with a comment about the swarm's greatest choice among the past various options. The PSO is an efficient technique for path planning in this experiment to get the shortest path between each coordinate of a predefined surveillance location available inside the surveillance zone. Thus, after obtaining to the shortest path, we can optimize the energy efficiency of MR during navigation. By PSO, each particle combines its individual search track record along with the histories of the remaining particles to find the problem's solution. It might ultimately discover the suboptimal or optimal approach for an issue over multiple iterations [37]. The enhanced PSO, which is considered an intelligent PSO during this experiment, can be abbreviated in Equations (17) and (18) using Equations (1) and (2) [38]. \[v_{i,j}(t+1)= w*v_{i,j}(t)+ c_{1}*r_{1}*(pbest_{i,j}(t)-x_{i,j}(t))+ c_{2}*r_{2}*(gbest_{i,j}(t)-x_{i,j}(t)), \tag{17}\] \[x_{i,j}(t+1), x_{i,j}(t)+ v_{i,j}(t+1), \tag{18}\]  
where the \(i\)th particle is \(i\), \(d\)th dimension for the particle is \(j\) and \(t\)th generation is \(t\). The learning factors denoted by \(c_{1}\) and \(c_{2}\), within the range between 0 and 2. The independent random functions are denoted by \(r_{1}\) and \(r_{2}\). Figure 3 represents the model of intelligent PSO used in this paper. Where, the position and velocity of the particle upon each iteration are represented by the bold arrows, global best position and personal best position are depicted by light arrows, and components of equation 17 are depicted by dotted arrows respectively. The updated velocity in Equation (17) consists of mainly three sections, including inertia weight, cognition section, and social section. The inertia weight section is represented as the influence factor for the velocity of particles by inertia. The cognition section is for the influence factor of the individual optimal value, and the social section provides the influence factor for the global optimum. Because of its simplicity and effective performance, the conventional PSO strategy outlined above is being utilized extensively in a range of optimizing scenarios, and several types of techniques have also been developed to enhance the classical PSO's functionality [39]. [PERSON] and [PERSON] presented a technique in [40; 41; 42] for the inertia weight \(w\) as linearity decrement on the generations of iteration. The current weight for the inertia weight \(w\) can be estimated as Equation (19):  
\[w_{c}=\left(w_{i}-w_{f}\right)*\ \frac{(Max_{iter}-iter)}{Max_{iter}}+w_{f}, \tag{19}\]  
where the initial and final inertia weights are \(w_{i}\) and \(w_{f}\) respectively; the number of maximum iterations is \(Max_{iter}\), and the current iteration number is denoted by \(iter\). In general, an increased inertia weight can lead the PSO to support extensive exploration, whereas a smaller value might result in limited exploration. That is why \(w_{i}\) and \(w_{f}\) frequently default to 0.9 and 0.4, consequently, as their starting and end values. In improved PSO, the ratio between both exploration and extraction is frequently adjusted using dynamic and time  
Figure 3: Model representation of particle swarm optimization. -dependent inertia weights. This can result in faster convergence times and higher-quality solutions.