## 3 Proposed Method
1 Initialize the parameters popsize(\(N\)), \(Max\),\(teraition\);
2 Initialize the positions of slime mold \(X_{i}(i=1,2,3\dots,N)\) ;
3 while\(t<MaxIt\)do
4 Calculate the fitness of all slime mold;
5 Update \(bF\), \(X_{b}\);
6 Calculate the \(W\) by Equation (3);
7 foreach slime molddo
8 if\(r_{1}<0.8\)then
9 if\(r_{2}<\)then
10 update the position using Equation (6);
11 else
12 Update \(p\), \(vb\), and \(vc\);
13 Update position by Equation (1);
14
15 end if
16
17 else
18 if\(r_{3}<0.5\)then
19 Operate Dynamic quantum rotation gate by Algorithm 2;
20 else
21 Calculate opposition solution \(X_{OBL}\) of individual \(X\) by Equation (16);
22
24 end if
25
26 end if
27
28 end if
29
30 end if
310
32 end if
32 Return bestFitness,\(X_{b}\)
```  
**Algorithm 7**Pseudo-code of the DQOBLSMA  
### Improved SMA  
To explore the solution space of complex optimization problems more efficiently, we propose two strategies based on the original SMA algorithm: the DQRG and OBL strategies. In the proposed method, two main conditions are considered to execute the proposed policy procedures. The first condition is the execution of SMA or two other strategies. If \(r_{2}<0.8\), then SMA is executed to update the position. Otherwise, the second condition is checked to determine the strategy to adopt. If \(r_{3}<0.5\) in the second condition, the solution will be updated using the DQRG; otherwise, OBL will be executed for the searched individual. The pseudo-code of the DQOBLSMA is shown as Algorithm 3:  
``` Input: Population size \(N\), Maximum number of iteration \(MaxIt\). Output: The best location \(X_{b}\), the best fitness value \(bF\). 1 Initialize the parameters popsize(\(N\)), \(Max\),\(teraition\);
2

### Computational Complexity Analysis

The computational complexity of the DQOBLSMA depends on the population size (\(N\)), dimension size (\(D\)), and maximum iterations (\(T\)). First, the DQOBLSMA produces the search agents randomly in the search space, so the computational complexity is O(\(N\times D\)). Second, the computational complexity of calculating the fitness of all agents is O(\(N\)). The quick-sort of all search agents is O(\(N\times\log N\)). Moreover, updating the positions of agents in the original SMA is (\(N\times D\)). Therefore, the total computational complexity of original SMA is O(\(N\times D+N\times T\times(1+D+\log N)\)). Updating the positions through the DQRG is O(\(N\times D\)) (maximum), and the OBL is O(\(N\)) (maximum). Updating the position using DQRG and the original SMA will not be done simultaneously. In summary, the final time complexity is O(DQOBLSMA) = O(\(N\times D+N\times T\times(1+D+\log N)\))(maximum). In summary, the improved strategy proposed in this paper does not increase the computational complexity when compared with the original SMA. ## 4 Experiments and Discussion

We conducted a series of experiments to verify the performance of the DQOBLSMA. The classical benchmark functions are introduced in Section 4.1. In the experiments of test functions, the impacts of two mechanisms were analyzed; see Section 4.2. In Section 4.3, the DQOBLSMA is compared with several advanced algorithms. In Section 4.4, the convergence of the algorithms is analyzed. The performance of the DQOBLSMA was investigated using the mean result (Mean) and standard deviation (Std). In order to accurately make statistically reasonable conclusions, the results of the benchmark test functions were ranked using the Friedman test. In addition, the [PERSON]'s rank-sum test was used to assess the average performances of the algorithms in a statistical sense. In this study, it was used to test whether there was a difference in the effect of the DQOBLSMA compared with those of other algorithms in pairwise comparisons. When the p-value is less than 0.05, the result is significantly different from the other methods. The symbols \"\(+\)\", \"\(-\)\", and \"\(=\)\" indicate if the DQOBLSMA is better than, inferior to, or equal to the other algorithms, respectively.