## 3 Theoretical Analysis and Model Construction
### Reconstruction Model of Hybrid Intelligent Optimization Algorithm
#### 3.2.3 The Program of MPGA-SIRT Hybrid Intelligent Algorithm  
In this study, the hybrid intelligence algorithm of MPGA-SIRT has been adopted to reconstruct the geological environment within a working face, which can fully combine the advantages of the global search provided by an intelligent algorithm and the local search provided by a traditional linear algorithm. The flow chart of the proposed MPGA-SIRT program is shown in Figure 3.  
1. Initialize populations  
There were a total of 10 populations in the calculation process during each iteration. Each population contained 20 individuals, and each individual represented a feasible solution for the electromagnetic wave absorption coefficient required for optimization. Binary encoding was applied in this program with an encoded bit number of 20, and the initialized populations were generated. The initial iterative algebra _Iter_ is set to 1.  
The fitness value of each individual for each population was calculated, and then the genetic operations were performed according to the fitness value to generate a better solution of the absorption coefficient distribution. The selection probability is the ratio between the number of parent individuals selected for genetic manipulation and the total number of individuals, which is randomly selected between 0.9 and 0.95. Different populations perform different crossover and mutation probabilities; the crossover probability is randomly selected between 0.7 and 0.9, and the mutation probability is randomly selected between 0.001 and 0.05 [42,43].
2. Immigration operation  
For each population that had undergone genetic operations, migration operations were performed to enable the exchange of high-quality information between multiple populations. Specifically, the individual with the worst quality (i.e., the lowest fitness value) in the target population was replaced with the one with the highest quality (i.e., the highest fitness value) in the source population. Through the coevolutionary search by multiple populations with different genetic parameters, the performance of the global search for the objective function's optimal solution could be improved.
3. Manual selection operation  
After evolution, the optimal individual in each population was selected, and then the optimal individuals of all populations (i.e., elite individuals) were chosen and stored separately in the _Iter_ generation after comparison. _Iter_ = _Iter_ + 1. To ensure that elite individuals produced by different populations during evolution were not destroyed or omitted, they did not undergo genetic operations.  
If _Iter_ > 500, the process of genetic evolution would stop, and the result of electromagnetic wave absorption coefficient distribution \(X_{0}\) was acquired. Otherwise, go to (2).  
4. SIRT algorithm  
The result \(X_{0}\) obtained by the global search of MPGA was used as the initial model for the local inversion of the SIRT, and the repeated iteration was conducted according to the following formula:  
\[X_{g+1}=X_{g}+\sum_{i=1}^{A}\frac{Y_{i}-D_{i}X_{g}}{D_{i}\cdot D_{i}^{T}}D_{i} ^{T} \tag{7}\]  
where \(D_{i}\) was the \(i\)th row vector of \(D\), \(D_{i}^{T}\) was the transpose of \(D_{i}\), \(g\) was the current iteration steps of SIRT, and the initial value of \(g\) was 1. \(X_{g}\) represents the electromagnetic wave absorption coefficient distribution results after the iteration steps of \(g\). The distribution result with a global optimum was finally obtained when the current iteration steps \(g\) reached the maximum 500 iterations.  
Figure 3: Flow chart of the proposed MPGA-SIRT program.