## 3 Method
### Overall Framework of ICSO  
The ICSO algorithm develops based on the original CSO, which consists of HC and VC. HC primarily manages information exchange among different individuals, enhancing their exploration capability through such external exchanges, aiding the population in finding better solutions. In contrast, VC focuses on interactions between different dimensions within an individual, leading to escaping local optima, thus achieving a refined and optimized performance. The original CSO faces challenges in search efficiency and achieving global optimality due to the randomness in its search direction. To address these problems, ICSO incorporates concepts of local and global optima from PSO, using information from optimal solutions as perturbation factors to guide the search process. This enhancement enables ICSO to maintain the original CSO's strong global search ability while more effectively exploring the search space by heuristically guiding the population towards known optimal positions. The pseudocode and architecture of ICSO are shown in Algorithm 1 and Figure 1, respectively, which resembles traditional evolutionary algorithms in its process. Initially, the population is initialized with random Gaussian noise (Line 1 in Algorithm 1 and \"Random Gaussian Noise\" in Figure 1). Subsequently, the iterative evolution core revolves around \"Improved HC\", \"VC\", and \"Selection based on _fitness_\". In each iteration, the improved horizontal crossover is employed to compute the new noise for individuals, leveraging crossover operations between distinct individuals within the population to broaden the exploration of the latent space (Line 9 in Algorithm 1 and \"Improved HC\" in Figure 1). Concurrently, the vertical crossover performs a crossover operation across dimensions within the same individual, fostering integration and innovation among diverse features (Line 17 in Algorithm 1 and \"VC\" in Figure 1). Notably, regardless of the crossover operation applied, individuals undergo a renewed fitness evaluation, which subsequently updates both local and global optimal solutions, ensuring the population's continuous progression towards optimality (Line 3, 10, and 18 in Algorithm 1 and \"Selection based on _fitness_\" in Figure 1). Ultimately, the algorithm terminates autonomously upon reaching a predefined iteration limit or satisfying specific convergence criteria, outputting the meticulously selected optimal Gaussian noise (Line 27 in Algorithm 1 and \"Optimal Gaussian Noise\" in Figure 1). ```
0: The number of individuals \(n\)
0:
1: Initialize the position \(\mathbf{X}_{i}\) for each individual (\(i=1,2,...,n\)) using Gaussian noise. 2:for\(i=1\) to \(n\)do
3: Calculate the fitness \(\mathbf{F}_{i}\) which formulates as Equation (13)
4: Set the personal best position \(\mathbf{pbest}_{i}=\mathbf{X}_{i}\)
5:endfor
6: Set the global best position \(\mathbf{gbest}\)
7:for\(t=1\) to \(iter_{max}\)do
8:for\(i=1\) to \(n\)do
9:\(\mathbf{X}_{i+1}\) = Improved Horizontal Crossover(\(\mathbf{X}_{i}\)) which formulates as Equation (14)
10:\(\mathbf{F}_{i+1}\) = Calculate Fitness(\(\mathbf{X}_{i+1}\)) which formulates as Equation (13)
11:if\(\mathbf{F}_{i+1}<Fitness(\mathbf{pbest}_{i})\)then
12: Update personal best position \(\mathbf{pbest}_{i+1}=\mathbf{X}_{i+1}\)
13:endif
14:if\(\mathbf{F}_{i+1}<Fitness(\mathbf{gbest})\)then
15: Update global best position \(\mathbf{gbest}=\mathbf{X}_{i+1}\)
16:endif
17:\(\mathbf{X}_{i+1}\) = Vertical Crossover(\(\mathbf{X}_{i}\)) which formulates as Equation (15)
18:\(\mathbf{F}_{i+1}\) = Calculate Fitness(\(\mathbf{X}_{i+1}\)) which formulates as Equation (13)
19:if\(\mathbf{F}_{i+1}<Fitness(\mathbf{pbest}_{i})\)then
20: Update personal best position \(\mathbf{pbest}_{i+1}=\mathbf{X}_{i+1}\)
21:endif
22:if\(\mathbf{F}_{i+1}<Fitness(\mathbf{gbest})\)then
23: Update global best position \(\mathbf{gbest}=\mathbf{X}_{i+1}\)
24:endif
25:endfor
26:endfor
27: Set the optimal Gaussian noise gbest

Figure 1: Architecture of ICSO.