# Research on Transmission Task Static Allocation Based on Intelligence Algorithm
## 3 Methodologies
### Dspo
#### 3.4.2 Particle Position Update Calculation  
According to the definition of particle motion direction and particle motion target, a new update strategy of DPSO is proposed. The particle velocity update operation is to calculate the particle motion direction and the particle motion target. The emission effect evaluation value of each task of the particles is calculated according to the particle position, which is recorded as \(XV_{i}\):  
\[XV_{i}=\big{(}xv_{i1},xv_{i2},\dots,xv_{ij},\dots,xv_{in}\big{)},\ \ i=1,2,\dots,K,\ \ \ xv_{ij}=Va_{j}\,x_{ij} \tag{22}\]  
where \(x_{ij}\) is the currently assigned task code of the \(j\)th equipment represented by the \(i\)th particle in the particle position definition, and \(Va_{j}\,x_{ij}\) represents the transmission effect evaluation value in the effect evaluation matrix when the \(j\)th equipment executes the \(j\)th task. Similarly, the transmission effect evaluation value sequence of particle best and global best is recorded as \(\ \mathit{Pbest}V_{i}\), \(\mathit{Gbest}V\):  
\[\mathit{Pbest}V_{i}=\big{(}pv_{i1},pv_{i2},\dots,pv_{ij},\dots,pv_{in}\big{)},\ i=1,2,\dots,K\ \ \ \ \ pv_{ij}=Va_{jp_{ij}} \tag{23}\]  
\[\mathit{Gbest}V=(gv_{1},gv_{2},\dots,gv_{i},\dots,gv_{n}),\ \ \ gv_{i}=Va_{j}\,g_{i} \tag{24}\]  
where \(p_{ij}\) is the task code of the \(j\)th equipment indicated in the definition of the particle best position of the \(i\)th particle, and \(Va_{jp_{ij}}\) represents the transmission effect evaluation value in the effect evaluation matrix when the \(j\)th equipment performs the \(p_{ij}\) task. Similarly, it is the \(g_{i}\) task code of the \(j\)th equipment indicated in the global best definition, and \(Va_{j}\,g_{i}\) represents the transmission effect evaluation value in the effect evaluation matrix when the \(j\)th equipment executes the \(g_{i}\) task. The DPSO calculates the D-value between the current particle and the particle best according to the D-value between the two data series of Formulas (22) and (23), and calculates the D-value between the current particle and the global best according to the D-value between the two data series of Formulas (22) and (24). The maximum D-value is selected, that is, the maximum D-value between the evaluation values, as the motion direction option of particles. At the same time, the position of the particle best and the global best of the maximum D-value position is recorded, that is, the task code of the corresponding position in Formulas (20) and (21). The selection of particle best and global best selects the iteratively updated particle motion direction according to the probability model, and the task code is the particle motion target. Taking particle best as an example, through the comparison of \(XV_{i}\) and \(\mathit{Pbest}V_{i}\) calculations, the maximum value of \(Va_{jp_{ij}}-Va_{j}\,x_{ij}\) at the time \(j=L\), and then \(L\) is determined as the motion direction calculated according to the particle best, that is, only \(VD_{i}=(0,0,\dots,1,\dots,0)\), the \(L\)th value is 1, and the other value is 0. The motion target is \(VT_{i}=(0,0,\dots,Tr_{L}.TaskNo,\dots,0)\), where \(Tr_{L}.TaskNo\) is the task code with the value in the \(L\)-th position in Formula (18). A summary of the DPSO parameters proposed to solve TTSA are presented in Table 2.