# Developing a Generalized Regression Forecasting Network for the Prediction of Human Body Dimensions
## 3 Methodology of the GRFN
### Construction of MMPSO Algorithm for Body Dimension Prediction  
#### 3.3.1 Sine Chaotic Opposite-Based Learning Population Initializations  
Initial population diversity is crucial to improving the search zone, optimization precision, and convergence speed. The chaotic parameters are characterized by their randomness, ergodicity, and regularity. Currently, the most common chaotic mappings [36] include tent, logistic, and sine types. Sine chaos is a self-mapping mode characterized by infinite folding. During optimization, opposite-based learning (OBL) can quickly find an approximate reverse solution. Accordingly, an elitist greedy strategy is adopted to select the optimal population, effectively improving the quality of solutions in the search zone. Therefore, sine chaos is employed to generate an initial population with the greatest diversity. The one-dimensional mapping of the sine chaos is expressed as follows:  
\[\left\{\begin{array}{l}Z_{i+1}=\sin(2/Z_{i}),i=0,1,\ldots,N\\ -1\leq Z_{i}\leq 1,Z_{i}\
eq 0\end{array}\right.. \tag{16}\]  
To avoid the generation of fixed and zero points in the closed interval \([-1,1]\), the initial value should not be set to zero. The sine chaos sequence is converted into a set of \(D\) pseudo-random numbers, \(Z_{i,j}\), and is inversely mapped into variables \(x_{i,j}\):  
\[x_{i,j}=lb_{j}+(ub_{j}-lb_{j})\cdot abs(z_{i,j}), \tag{17}\]  
where \([lb_{j},ub_{j}]\) is the dynamic search zone boundary along dimension \(j\), and \(z_{i,j}\) represents the \(j\)-th dimensional component of the \(i\)-th pseudo-random number. Next, the OBL strategy [27] is utilized to generate an opposite-based population, \(\text{X}^{\prime}=\{\text{X}^{\prime}_{i},i=1,2,\ldots,N\}\), and the individual term, \(x^{\prime}_{i,j}\), can be defined as  
\[x^{\prime}_{i,j}=k\cdot(lb_{j}+ub_{j})-x_{i,j}, \tag{18}\]  
where the generalized coefficient, denoted as \(k\in\text{U}(0,1)\), is sampled from a uniform distribution. Finally, employing the elitist greedy strategy, the reversed population, \(\text{X}^{\prime}\), and initial population after sine-mapping, \(\text{X}\), are merged into a new population, \(\text{X}_{new}=\{\text{X}^{\prime}\cup\text{X}\}\). From this, the initial \(N\) particles with the most suitable fitness score are chosen as \(\text{X}\). In an initialization learning environment, the heterogeneous search behavior of multi-subpopulation diversities is utilized. According to a fitness value difference, \(D_{f}\), ascending sort, the population particles are grouped into elite (i.e., teacher subgroup \(\text{X}_{ST}\)), ordinary (i.e., independent learner subgroup \(\text{X}_{SI}\)), and poor (i.e., student subgroup \(\text{X}_{SS}\)) categories. The classification method is as follows:  
\[\text{X}_{i}\in\left\{\begin{array}{l}\text{X}_{ST},\text{ }if\text{ }D_{f}\leq\lambda_{r}\\ \text{X}_{SI},\text{ }if\text{ }\lambda_{r}\leq D_{f}\leq(1-\lambda_{r})\\ \text{X}_{SS},\text{ }if\text{ }D_{f}\geq(1-\lambda_{r})\end{array}\right. \tag{19}\]where swarm ratio \(\lambda_{r}=30\%\), and \(1-\lambda_{r}=70\%\).