# A Study of Cellular Traffic Data Prediction by Kernel ELM with Parameter Optimization
## 2. Accident Description and Prediction Method
### Prediction Methods
#### 2.2.2 kELM Parameter Optimization  
For the kernel ELM algorithm, it is important to select appropriate parameters. Manual selection of the optimal parameters requires a large number of experiments, and the process is tedious. The optimal parameters may not be found. In this study, the metaheuristic optimization algorithm was used for kELM parameter optimization. [PERSON] and [PERSON] (1997) pointed out that none of the optimization algorithms can solve all optimization problems. There are four kernel functions that are commonly used. In order to find the optimal parameters of kELM with different kernel functions, we employed three optimization algorithms to optimize the parameters of kELM: MFO, MVO, and PSO.  
PSO was first proposed by [PERSON] and [PERSON] in 1995, and its basic concept was derived from the study of the foraging behavior of birds, with particles used to simulate individual birds. Each particle can be regarded as a searching individual in the n-dimensional search space. The current position of a particle is a candidate solution of the corresponding optimization problem. The flight process of a particle is the individual search process. The flight speed of a particle can be dynamically adjusted according to the historical optimal position of the particle and the historical optimal position of the population.  
MVO is an optimization algorithm proposed by [PERSON] et al. and inspired by the multiverse theory. In the multiverse theory, there are multiple parallel universes in the world, and these universes exchange matter through white holes, black holes, and wormholes. The MVO algorithm takes expansion rate as fitness function and uses the material exchange capacity of white holes, black holes, and wormholes to improve the expansion rate of the universe so as to search for the best location of the universe.  
MFO is a new group intelligence optimization algorithm proposed by [PERSON] in 2015. It is derived from the navigation method of transverse positioning of the night moth, which maintains its flight by maintaining its own angle of light relative to the moon. The near-parallel light of surface is used to keep its flight straight. The main advantages of the algorithm are simple structure, few parameters, and better optimization ability.  
The three optimization algorithms were used for optimal parameter searching of kELM, as shown in Figure 1. The pseudocode is shown in Table 2.  
\begin{table}
\begin{tabular}{l} \hline
**Input:** Max_Iterations, Boundaries, X, Population \\ Initialization all parameters \\
**while**_Iteration \(<=\) Max Iterations_ \\
**for** each individual indexed by \(j\) in Population \\ Evaluate fitness of each individual: \(\frac{1}{n}\sum\limits_{i}^{n}\left|y_{i}-\hat{y}_{i}\right|/y_{i}\times 100\%\) \\
**end for** \\ Search for the optimal fitness of the current iteration and update \\
**for** each individual indexed by \(j\) in Population \\ Update individual location \\
**end for** \\ _Iteration \(\leftarrow\) Iteration \(+\) 1_ \\
**Output:**\(C,k\) \\ \hline \end{tabular}
\end{table}
Table 2: The pseudocode of multiverse optimizer (MVO), particle swarm optimization (PSO), and moth-flame optimization (MFO) to optimize the parameters of kELM.