## 3 Methodology
### PSO Deep-ConvLSTM Network
#### 3.2.1 Dynamic Adjustment  
In the PSO algorithm, for each particle k in the swarm, the velocity and position are updated at each \((i+1)^{th}\) iteration using the following Equation (4):  
\[\left\{ \begin{array}{l}V_{k}=\omega V_{k}(i+1)+c_{1}r_{1}(p_{best,i}^{k}-X_{k }(i))+c_{2}r_{2}(g_{best,i}-X_{k}(i))\\ X_{k}(i+1)=X_{k}(i)+V_{k}(i+1)\end{array} \right. \tag{4}\]  
where \(p_{best,i}^{k}\) is the individual best position of the particle k in the \(i^{th}\) iteration; \(g_{best,i}\) is the global best position of any particle in the \(i^{th}\) iteration; \(\omega\) is the inertia weight, which is a non-negative number and is used to adjust the search range of the solution space; \(c_{1}\) and \(c_{2}\) are the real acceleration coefficients that control how much the global and individual  
Figure 4: PSO Deep-ConvLSTM model architecture. best positions should influence the particle's velocity; \(r_{1}\) and \(r_{2}\) are uniformly distributed random numbers in the range of 0 and 1, used to maintain an adequate level of diversity. Algorithm 1 delineates the particle swarm optimization algorithm in pseudocode format. ```
INPUT: Fitness function, lower bound, upper bound is part of the problem, i.e., it will be given in the problem. N (population size), and T (the maximum number of iterations) are to be chosen by the user. \(c_{1},c_{2}\) and \(\omega\) update by the given equation. 1. Initialize a random population (P) and velocity (\(v\)) within the bounds; 2. Evaluate the objective function value (\(f\)) of P; 3. Assign \(p_{best}\) as \(p\) and \(f_{best}\) as \(f\); 4. Identify the solution with the best fitness and assign that solution as \(g_{best}\) and fitness as \(f_{gbest}\) For iteration: for\(i=1\) to T: for\(k=1\) to N:  Determine the velocity (\(v_{k}\)) of \(k^{th}\) particle;  Determine the new position (\(X_{k}\)) of \(k^{th}\) particle;  Bound \(X_{k}\):  Evaluate the objective function value \(f_{k}\) of \(k^{th}\) particle;  Update the population by including \(X_{k}\) and \(f_{k}\);  Update \(p_{best}^{k}\) and \(f_{gbest}\) if \(f_{k}<f_{p_{best}^{k}}^{\mu}\) then \(\left\{ \begin{array}{l}p_{best}^{k}=X_{k}\\ f_{gbest}=f_{k}\end{array} \right.\) Update \(g_{best}\) and \(f_{gbest}\) if \(f_{p_{best}^{k}}<f_{gbest}\) then \(\left\{ \begin{array}{l}g_{best}=p_{best}^{k}\\ f_{gbest}=f_{p_{best}^{k}}\end{array} \right.\)  end for  end for
```  
**Algorithm 1**The pseudocode of the algorithm is as follows  
The inertia weight denoted as \(\omega\) in the PSO algorithm, plays a crucial role in managing the inertia of particles and endorsing an expansive exploration of the search space. It functions as an integral parameter in striking a balance between the algorithm's global and local search capabilities. An established method of allocating inertia weights involves a linearly decreasing approach, offering ease of implementation. However, with a linear increase in iteration numbers, this strategy may subsequently shrink the inertia weight excessively, dampening the algorithm's global search capability and precipitating a potential entrapment in local optima. Moreover, as the algorithm advances into its late stages, the swarm's diversity is at risk of being diminished, reflecting a decelerated convergence speed [24]. In the PSO algorithm's purview, the learning factors \(c_{1}\) and \(c_{2}\) primarily mediate the step size adjustment for the particle's trajectory toward the individual's and flock's optimal positions. To hasten the search process during the preliminary iterations and enhance the global search capability, a decrease in \(c_{1}\)/\(s\) value coupled with an increase in \(c_{2}\)/\(s\) value is typically advocated, thereby fostering local refinement searches during the algorithm's later iterations. However, while present optimization research seldom espouses the optimization of learning factors, traditional PSO algorithms tend to fixate \(c_{1}=c_{2}\) at constant values, potentially failing to cater to pragmatic application needs.