## 3 Methodology
### The Well Sequence
Compare the current particle's fitness score \(x_{z}\) in the swarm and its old global best location \(g_{z}^{best}\) If the current fitness score \(x_{z}\) is greater than \(\delta_{z}^{best}\), then substitute \(g_{z}^{best}\), with \(x_{z}\); else retain the \(x_{z}\) unchanged
11. Compute \(\gamma_{z+1}\rightarrow\) updated velocity vector
12. Compute \(\gamma_{z+1}\rightarrow\) updated position vector
13. Go to step 2; If the stopping criteria does not met; else terminate. ```

**Algorithm 4** Proposed Pseudo Code of DE Using Novel Method of Initialization

In our other contribution in the paper, we proposed by introducing three new methods of initialization of population DE-KE, DE-WE, and DE-TO. Algorithm 4 shows the proposed distribution-based DE initialization. Algorithm 4 proposes Pseudo Code of DE Using Novel Method of Initialization

```
1. Input: \(xi\) = (\(xi\)1, \(xi\)2, \(xi\)3, \(\ldots\), \(xi\)\(D\)), Population size 'N-P', Problem Size 'D', Mutation Rate 'F', Crossover Rate 'C-R'; Stopping Criteria [Number of Generation, Target], Upper Bound 'U', Lower Bound 'L'  Output: \(xi\), = Global fitness vector with minimal fitness value  Pop = Initialize of Parameters (N-P, D, U, L); Generate initial population Using WELL,Knuth,Torus  While (Stopping Criteria \(\
eq\) True) do  Best Vector = Evaluate Pop (Pop);  vx = Select Rand Vector (Pop);  I = Find Index Vector (vx);  Select Rand Vector (Pop,v1,v2,v3) where v1 \(\
eq\) v2 \(\
eq\) v3 \(\
eq\) vx  yy = v1, + F(v2 \(-\)v3) For (i = 0; i++; i < D\(-\)1) If (randj [0, 1) < C-R) Then  U[i] = vx [i]. else  U[i] = vy [i] End For loop If (Cost Fun Vector(U) \(\leq\) Cost Fun Vector (vx)) Then  Update Pop (U, I, Pop); End IF End While  Retune Best Vector
```

**Algorithm 5** Proposed Pseudo Code of PSO Using Novel Method of Initialization

## 4 Experimental Setup

The parameter for the fair performance comparison is presented in Table 1. The algorithm settings are shown in \[b(\theta,\delta)=(D+r\cos\theta)\sin\delta \tag{7}\]0 For the impartial progress, the correlation condition of the performance evaluation alongside the proposed strategy, all of the parameter was set to the uniform. The simulation has been simulated in C++ and applied on a computer using the C++ language on the computer with the Windows 10 operating system with the specifications of 8 gigabytes of ram and 2.3 GHz Core (M) 2 Duo CPU processor. Hence in our study, we used it to examine the optimization outcomes of the quasirandom-based approaches. A list of those functions is available in \[b(\theta,\delta)=(D+r\cos\theta)\sin\delta \tag{7}\]1 In Table 3, D shows the dimensionality of the problem, S represents the interval of the variables, and fmin denotes the standard global optimum minimum value. In the parameters for the simulation used as c1 = c2 = 1.45, inertia weight w is used in the interval [0.9, 0.4], and swarm size is 50. For simulation, the function dimensions are D = 10, 20, and 30, and the maximum number of epochs is 3000. All techniques have been applied to similar parameters for comparatively effective results. In order to check the performance of each quasirandom sequence bases approach, all of them were tested for 10 runs. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** \\ \hline Search Space & \([-100,100]\) & \\ Dimensions & 10 & 20 & 30 \\ Iterations & 1000 & 2000 & 3000 \\ Population size & 50 & \\ Number of Runs & 10 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental setting of parameters. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Parameters** \\ \hline PSO & c1 = c2 = 1.49, w = linearly decreasing \\ DE & F \(\in[0.4,1]\), \(CR\in 0.6\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters setting of algorithms.