## 4 Robust Learning-Based GWO Algorithm (RLGWO)
### Opposition-Based Learning for Candidate Generation Strategy  
Opposition-based learning (OBL) [25] has recently been utilized to accelerate the convergence rate of several optimization algorithms. The OBL technique can be used to generate potential candidate solutions by considering both the current population and its opposite population. It has been proved in many studies worldwide that opposition candidate solutions are more likely to get closer to the global optimum solution than a randomly generated candidate solution. There have been many advanced applications of this learning mechanism in several soft computing techniques, as reported in [35; 36; 37; 38].  
Figure 2: Adjustment probability at different iteration periods.  
The two definitions below show the important aspects of OBL, the opposite number and opposite point [25]:  
_Definition--_ Let \(x\in\mathbb{R}\) be a real number defined in a certain interval: \(x\in[a,b]\). The opposite number \(x^{opp}\) is defined as follows:  
\[x^{opp}=a+b-x \tag{18}\]  
_Definition--_ Let \(P(x_{1},x_{2},\ldots,x_{n})\) be a point in an n-dimensional coordinate system with \(x_{1},x_{2},\ldots,x_{n}\in\mathbb{R}\) and \(x\in[a_{i},b_{i}]\). The opposition point \(P^{opp}\) is completely defined by its coordinates \(x_{1}^{opp},x_{2}^{opp},\ldots,\ x_{n}^{opp}\) where  
\[x_{1}^{opp}=a_{i}+b_{i}-x_{i}\ i=1,\ 2,\ldots,n \tag{19}\]  
In the proposed RLGWO, after defining the replacement of the leader with a candidate solution in Section 4.1, a random candidate solution can easily be created in the search space to guide the hunting group to get rid of the current local optimum solution. However, the random candidate may not be guaranteed to improve the solution; in particular, when dealing with large and complex spaces, it is probable that it will lead the hunting group into another local optimum. Using the OBL can ensure the generation of a candidate more effectively.  
In Figure 3, it is clear to see that the difference between the current and the previous solution in the first half of the iteration changes violently. This circumstance can be explained by the fact that the hunting group is carrying out the exploration phase. This means that the grey wolves are attempting to search the hold space to figure out promising areas for the global optimum. The alpha will have a significant influence on the hunting group, since it is the best solution. Therefore, in this certain period, replacing the alpha with its opposite position is a wise course of action to escape the local optimum.  
The remaining half of the total course of iteration is the exploitation phase, when the grey wolf scales down the search space and concentrates on a certain area to find the optimum solution. To prevent the omega from moving away from the global optimum and  
Figure 3: The convergence rate of the search mechanism.  
to ensure the efficiency of the algorithm, the alpha acts as the main leader and the beta (or gamma) may be replaced by its opposite position. Since the beta and gamma have almost the same potential ability, the beta will be removed if the random number is greater than 0.5, and conversely, gamma will be substituted if it is less than this value.  
The details of the generating candidate are described in Algorithm 2.  
```
1:At iteration \(k\)th;
2:Generate a random number \(rand()\) between [0,1];
3:if \(P_{adjust}<rand()\)
4:Keep alpha, beta, and gamma as the leader;
5:else
6:if \(k\)th \(<\frac{Maxlt}{2}\)then
7:\(X_{a}\leftarrow\min(alpha)+max(alpha)-X_{a}\);
8:else
9:Generate a random number \(rand()\) between [0,1];
10:if \(rand()>0.5\)
11:\(X_{\beta}\leftarrow\min(beta)+max(beta)-X_{\beta}\);
12:else
13:\(X_{\delta}\leftarrow\min(gamma)+max(gamma)-X_{\delta}\);
```  
**Algorithm 2**. Opposition-based learning for candidate generation strategy