# An Intelligent Optimization Algorithm for Constructing a DNA Storage Code: NOL-HHO
## 4 Test of the Proposed Algorithm NOL-HHO
### Comparison of Test Results with Other Algorithms  
We compared the NOL-HHO algorithm with the HHO [34], GA [34], PSO [45], BBO [45], FPA [46], GWO [47], BAT [48], FA [49], MFO [50], and DE [45] optimization algorithms for the mean (AVG) and standard deviation (STD) results of 23 test functions to demonstrate the effectiveness of our improvement. In addition, in order to conduct experiments fairly, all tests were performed under the same conditions, using 30 search agents uniformly in 500 iterations. At the same time, each benchmark function was executed independently 30 times to reduce the randomness of the results, and the specific results are shown in Tables 1 and 2. To further compare the performance between these algorithms, we studied the effect of dimensions on the quality of the solution and the efficiency of the optimization when the dimension changed. In addition to a 30-dimensional test, the NOL-HHO algorithm and the HHO original algorithm were compared at the 100-, 500-, and 1000-dimensional means and standard deviations, as shown in Table 3. The evaluation criterion was that the closer the mean was to the global optimal value the better and the closer the standard deviation was to 0 the better. The results of all comparison algorithms were taken from the original paper of the HHO algorithm and the best results from all of the above tests are marked in bold.  
As can be seen from Table 1, for the unimodal benchmark functions (\(F_{1}\)-\(F_{7}\)), the mean or standard deviation test results of the NOL-HHO algorithm were significantly better than for other algorithms, and functions \(F_{1}\)-\(F_{4}\) reached a global optimal value in Table S1, indicating that the improved algorithm had a stronger benchmark exploitation capability. In terms of multi-dimensional function testing (\(F_{8}\)-\(F_{13}\)), NOL-HHO also showed superior performance as compared with HHO and other algorithms. The mean and standard deviation of \(F_{9}\)-\(F_{11}\) reached global optimal values, as shown in Table S2. The mean of the remaining functions of NOL-HHO were closer to the optimal value, and the standard deviation was more stable as compared with the other algorithms. This shows that it had a strong exploration capability. For fix-dimension multimodal benchmark functions (\(F_{14}\)-\(F_{23}\)), it can be seen from Table 2 that the mean was better, except for the function \(F_{20}\) and the global optimality reached 90%. Functional tests of this different type of problem illustrate the superiority of the overall performance of the NOL-HHO algorithm.  
In order to compare the effects before and after the improved HHO algorithm, we drew a fitness curve diagram of the unimodal functions and the multimodal functions, as shown in Figures 5 and 6, using test functions \(F_{8}\) and \(F_{21}\). In the unimodal function \(F_{8}\), although the original algorithm also achieved a global optimal solution, it fell into a local optimum during the search process, while NOL-HHO did not, and the convergence speed was faster for NOL-HHO. The HHO algorithm in the multimodal function \(F_{21}\) converged on the local area and easily reached a global optimal value after our refinements. This shows that NOL-HHO can maintain a good balance between the exploratory and exploitative nature of dealing with different dimensional problems, and it was better at jumping out of local optima by enriching the population.  
In the following, we also tested the mean and standard deviation of different dimensions for the NOL-HHO and HHO algorithms, and the results are shown in Table 3. In the 100-, 500-, and 1000-dimensional tests, NOL-HHO performed 100% better than the original algorithm. This shows that even in high-dimensional situations, NOL-HHO is quite competitive in finding the best solution, and its performance remains consistently superior when realizing cases with many variables.