## 4 Solution Algorithm  
For the problem described in this paper, assuming that the number of OD pairs is \(e\), the product category type is \(p\), the shipping time is \(t\), each OD point pair has \(r\) actual alternative paths, and each alternative path has \(m\) cargo service arcs, and the size of the decision variables in the model is \(e\times p\times t\times(r+1)\times(m+1)\). Therefore, the problem will be solved on an exponentially larger scale as the size of the network and the type of cargo flow increase. According to the characteristics of the proposed model, an improved adaptive genetic algorithm framework-based algorithm is designed for solving the optimization model of the express transport scheme of the high-speed railway. The basic flow of the algorithm is shown in Figure 4.  
Step 1: Parameter initialization. Input the required parameters, as shown in Table 2.  
Step 2: Chromosome encoding. A binary encoding form is used with chromosomes encoded as \(e\times p\times t\) gene fragments \(X\), where each gene fragment includes \(r+1\) gene loci on each gene fragment, representing the choice of \(r+1\) alternative paths for the cargo stream represented by that gene fragment \(X\), with a separate artificial virtual path that is used for the loading of infeasible flow. Step 3: Initial population generation. The initial population generation rules are set: (i) mixed sorting by cargo class level and transport demand size; (ii) mixed sorting by cargo class level and transport distance size; (iii) random sorting by cargo class level; and (iv) random sorting by transport distance size. When generating the initial population of individuals, the above initial population rules are chosen randomly so that the quality of the solution is preserved while meeting the requirements of diversity. After determining the priority of each branch cargo flow, it is also necessary to assign paths to cargo flows so that they satisfy the relevant constraints of the model, thus ensuring the feasibility of the network. So simply ensuring that the paths depart later than the dispatch time so that the cargo flows make random choices of paths may not satisfy the model constraints. Therefore, alternative transport options can be traversed in chronological order. In the same way, crossover and mutation of the parentsmay also result in the requirements for the feasibility of the space-time state network not being satisfied, and again, the paths need to be adjusted so that a feasible solution can be derived. Figure 4: Basic flow of the improved adaptive genetic algorithm. Step 4: Fitness value calculation. Choose the objective function as the fitness function, that is, the fitness value is the maximal operation revenue. Step 5: Roulette wheel selection. Use roulette wheel selection to select the better population. Step 6: Improved crossover. The crossover probability is adjusted between the average and maximum fitness of the population based on the fitness of the individuals to improve the quality of the child solutions and the speed of convergence of the genetic algorithm, and the crossover operator is designed as shown in Equation (16). \[P_{c}= \begin{cases}k1\cdot\frac{F_{max}-F}{F_{max}-F_{avg}}&\text{if }F\geq F_{avg}\\ k3&\text{if }F<F_{avg}\end{cases}  \tag{16}\]  
\(P_{c}\) is the crossover probability, \(k1\) and \(k3\) are crossover probability parameters, \(F_{max}\) is the maximum adaptation of the population, \(F_{avg}\) is the average adaptation of the population, and \(F\) is the larger adaptation value of the two individuals participating in the crossover. Step 7: Improved mutation. The mutation probability is likewise adjusted between the average and maximum fitness of the population based on the fitness of the individuals. The mutation operator is designed as shown in Equation (17). \[P_{m}= \begin{cases}k2\cdot\frac{F_{max}-F}{F_{max}-F_{avg}}&\text{if }F\geq F_{avg}\\ k4&\text{if }F<F_{avg}\end{cases}