## 3 The Proposed Model
### Parameter Tuning Process  
For the optimal adjustment of the WELM parameters, the KSA is utilized in this study. The krill swarm algorithm (KSA) [29] is a commonly used intelligent optimization technique, due to its benefits of strong search diversity, few adjusted parameters, and simple operation. The KSA approach originated from mutual communication and krill foraging. In the presented approach, the location of every individual krill represents a potential solution. The location of each krill is commonly specified in the following:  
1. Individual swimming due to population migration: \[N_{i}^{new}=N^{\max}\alpha_{i}+\omega_{n}N_{i}^{old}\] (10) \[\alpha_{i}=\alpha_{i}^{local}+\alpha_{i}^{target}\] (11)  
From the equation, the maximum induction speed can be represented as \(N^{\max}\), and taken as 0.01 \((\text{ms}^{-1})\), and \(\omega_{n}\) refers to the inertia weight of motion-induced range from \([0,1]\). \(N_{i}^{old}\) represents prior movement, whereas \(\alpha_{i}^{target}\) and \(\alpha_{i}^{local}\) indicate the target and the existing positions, respectively.
2. Foraging behaviour: \[F_{i}=V_{f}\beta_{i}+\omega_{f}F_{i}^{old}\] (12) \[\beta_{i}=\beta_{i}^{food}+\beta_{i}^{best}\] (13)  
Figure 3: Structure of Weighted ELM.  
Now, the individual direction of foraging for krill was denoted as \(\beta_{i}\). \(\beta_{i}\) indicates the attractive direction of food, and \(\beta_{i}^{best}\) indicates the direction of individual krill with the optimal fitness value. \(V_{f}\) represents the foraging speed that takes as 0.02 (ms\({}^{-1}\)), and \(\omega_{f}\) represents the inertia weight that ranges from [0, 1]. \(F_{i}^{old}\) signifies the location change due to the preceding foraging motion of the \(i\)-\(th\) individual krill; \(F_{i}\) denotes the location change due to the existing foraging motion of the individual \(i\)-\(th\) krill.
3. Random diffusion of individual krill: \[D_{i}=D^{\max}\delta\] (14)  
In Equation (14), \(D^{\max}\) indicates the maximal disturbance (diffusion) velocity, and \(\delta\) denotes an arbitrary direction vector that ranges from \([-1,\ 1];D_{i}\) signifies the location change due to arbitrary diffusion of \(i\)-th individual krill.  
The swimming direction of each krill can be defined by the fusion of abovementioned factors that change in the direction with minimum fitness value. The foraging and induced motions have local and global searching functions. After the process is iteratively updated, two measures are simultaneously implemented, which make stable and powerful optimization algorithms.  
The location vector from \(t\) to \(t+\Delta t\) is formulated by:  
\[X_{i}(t+\Delta t)=X_{t}(t)+\Delta t\frac{dX_{i}}{dt} \tag{15}\]  
Here, \(\Delta t\) indicates the factor for the step size.  
\[\Delta t=C_{t}\sum_{j=1}^{NV}(UB_{j}-LB_{j}) \tag{16}\]  
Now, \(NV\) indicates the overall amount of parameters, whereas \(LB_{j}\) and \(UB_{j}\) denote the upper as well as lower bounds of the \(j\)-th parameter.  
The KSA system grows a fitness function (FF) for attaining higher classifier performance. It resolves the positive integer for denoting the best efficiency of candidate results. In this work, the minimization of the classification error rate is measured FF, as shown in Equation (17).  
\[\begin{split}& fitness(x_{i})=ClassifierErrorRate(x_{i})\\ &=\frac{number\ of\ misclassified\ lead\ samples}{Total\ number\ of\ samples}*100\end{split} \tag{17}\]