## 3 Improved Snake Optimization Algorithm for Melting Point Optimization Solution
### Improved Snake Optimization Algorithm
#### 3.2.2 Elite Reverse Learning Mechanism  
In many cases, the process of solving a problem typically starts from scratch or with a random value and gradually approaches the optimal solution. For instance, this applies to parameters such as weights in neural networks, population parameters in swarm intelligence algorithms, kernel parameters in support vector machines, and so on. If the initial random value happens to be close to the optimal solution, the problem can be quickly resolved. However, there is also the worst-case scenario where the random value is far from the optimal solution, resulting in a significant amount of time spent during the solving process. Without prior knowledge, obtaining a good random value at the beginning is unlikely. Moreover, from a logical perspective, the problem-solving process can explore various directions. By incorporating reverse solutions of the optimal solution as feasible solutions, thereby expanding the search space, the efficiency of optimization can be improved. This constitutes the core theory behind reverse learning.  
To enhance the global optimization capability of the SO algorithm and prevent it from getting stuck in local optima, an elite reverse learning strategy is introduced. During the process of generating offspring for snake individuals, a reverse learning strategy is applied to elite individuals to generate corresponding reverse solutions. These reverse solutions are then compared with the original solutions, and individuals with higher fitness are selected to proceed to the subsequent steps. This accelerates the convergence speed of the algorithm and expands its search range. Let the original solution of the current snake individual in the D-dimensional search space be represented by:  
\[X_{i}=(x_{1},x_{2},\cdots,x_{D}) \tag{17}\]  
The reverse solution of the original solution is represented as follows:  
\[\overline{X_{i}}=(\overline{x_{1}},\overline{x_{2}},\cdots\overline{x_{D}}) \tag{18}\]  
\[\overline{x_{i}}=k\times(x_{\text{imax}}+x_{\text{imin}})-x_{i} \tag{19}\]  
The snake individual with the highest fitness value within the current population is referred to as the elite individual, as shown in Equation (20):  
\[f(X_{i}^{e})=\text{Max}(f(x_{i})) \tag{20}\]  
The construction of reverse solutions for elite individuals can increase the diversity of the population. Selecting the optimal value between the current candidate solution and the reverse solution for further steps enhances the algorithm's convergence ability and broadens its search range. The calculation method for the elite reverse solution is shown in Equations (21) and (22):  
\[\overline{X_{i}^{e}}=(\overline{x_{1}^{e}},\overline{x_{2}^{e}},\cdots, \overline{x_{3}^{e}}) \tag{21}\]  
\[\overline{x_{i}^{e}}=k\times(x_{\text{imax}}+x_{\text{imin}})-x_{i}^{best} \tag{22}\]  
In the equations, \(X_{i}^{e}\) represents the current elite individual, \(\overline{X_{i}^{e}}\) denotes the corresponding reverse solution of the current elite individual, and \(k\) is a uniformly distributed random function over the interval \([0,1]\).