## 4 Optimization of Microseismic Monitoring Network Design Based on Particle Swarm Optimization  
### Improved Particle Swarm Algorithm  
Particle swarm optimization (PSO) is an evolutionary computing technique, which originated from the study of predation behavior of birds and was first proposed by [PERSON] and [PERSON] [26]. In PSO, the solution to each optimization problem is considered as a particle in the search space [27]. All particles have an adaptive value determined by the optimized function, and each particle also has a velocity to determine its flying direction and distance. Then, the particles search the solution space following the current optimal particle. PSO initializes to produce a group of random particles and then finds the optimal solution through iteration. In each iteration, the particle updates itself by tracking two extremes. One is the optimal solution reached by each particle in the search through the ages, which is called individual extremum \(P_{best}\). The other is the optimal solution reached by all particles in the whole particle swarm in the search of previous generations, which is called the global extreme value \(g_{best}\). The position of the \(i^{\text{th}}\) particle in the population in n-dimensional space is expressed as \(x_{i}\) = (\(x_{i1}\), \(x_{i2}\), \(\cdots\), \(x_{in}\)), and its velocity is \(v_{i}\) = (\(v_{i1}\), \(v_{i2}\), \(\cdots\), \(v_{in}\)). When finding these two extremes, update the speed and position with the following equation:  
\[v_{i}(\text{k}+1)=wv_{i}(\text{k})+c_{1}rand_{1}(P_{best}-x_{i}(\text{k}))+c_{ 2}rand_{2}(g_{best}-x_{i}(\text{k}))\]  
\[x_{i}(\text{k}+1)=x_{i}(\text{k})+v_{i}(\text{k}+1) \tag{6}\]  
where \(k\) is the iteration number; \(c_{1}\) and \(c_{2}\) are learning factors, which are usually taken between (0, 2); \(rand_{1}\) and \(rand_{2}\) are random Numbers between (0, 1); and \(w\) is the momentum coefficient, whose value can change with algorithm iteration [28]. The traditional particle swarm optimization (PSO) algorithm has defects such as a slow iterative speed and easily falling into local extremums. Bacterial foraging optimization (BFO) is a swarm intelligence algorithm inspired from the foraging behavior of the _E. coli_ bacteria. The BFO is based on three basic processes: chemotaxis, reproduction, and elimination-dispersal [29]. The bacterial foraging algorithm was introduced to the particle swarm optimization (PSO) algorithm, which will be added to the chemotaxis behavior and the elimination-dispersal behavior, such as in Equations (7) and (8), to increase the randomness of particle movement and modify the particle fitness value [30]. When calculating fitness value, the chemotaxis behavior should be increased to improve the searching speed of particles. When the particle is trapped in the local optimum, the elimination-dispersal behavior is increased to rapidly change the direction and carry out the random walk:  
\[Fv_{i}^{cc}(k)=\sum_{i=1}^{l}[-d_{attr}\exp\left(-w_{attr}\sum_{m=1}^{p}{(x_ {m}(k)-x_{i}^{m}(k)}\right)^{2}+\sum_{i=1}^{l}[-h_{rep}\exp\left(-w_{rep}\sum _{m=1}^{p}{(x_{m}(k)-x_{i}^{m}(k)}\right)^{2}]\right.\]  
\[\left.Fv_{i}(k)=Fv_{i}(k)+Fv_{i}^{cc}(k)\right.\]  
\[x_{i}(k)=x_{i}(k)+c_{i}(k)\frac{\Delta(k)}{\sqrt{\Delta^{T}(k)\Delta(k)}}\ ( \text{trapped in the local optimum}) \tag{8}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Monitoring Area** & **Key Areas** & **Sub-Key Areas** & **Normal Areas** \\ \hline the effective range & & & \\ factor \(F_{Q}\) & 1.5 & 1.2 & 1.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The effective range factor of different monitoring areas. where \(C_{i}(k)\) is the forward moving step of particle \(i\) in \(k^{\text{th}}\) iteration, and \(\Delta(k)\) is a unit vector in the random direction at \(k^{\text{th}}\) iteration and takes the value \([-1,1]\).