# Automated Generation of Hybrid Metaheuristics Using Learning-to-Rank
## 5 Experiment Evaluation
### Experimental Results and Discussion
As shown in Table 9, the LTR-MHA predominantly achieves the '+' symbol across most cases, indicating that its performance on the CEC2017 benchmark optimization tasks is significantly superior to that of the other algorithms. In summary, the LTR-MHA shows significant advantages in solution precision, convergence speed, and statistical significance. Across tests on unimodal, simple multimodal, hybrid, and composite functions, the LTR-MHA consistently yields the lowest average fitness values in most scenarios while maintaining the lowest or second-lowest standard deviations. Moreover, the LTR-MHA is able to rapidly approach the optimal regions, particularly in simple multimodal and composite functions. Although the model prediction process leads to longer runtimes, this additional computational cost is offset in the long term by the algorithm's ability to efficiently solve a wide range of problem instances. In contrast, traditional metaheuristic algorithms exhibit acceptable performance in specific functions \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Funcs** & **WOA** & **HHO** & **GA** & **ISGA** & **RLWOA** & **Rand-MHA** & **LTR-MHA** \\ \hline F1 & 0.4819 & 1.4700 & 0.7766 & 4.8352 & 57.3926 & 3.5126 & 70.4798 \\ F3 & 0.4377 & 1.4866 & 0.7803 & 4.9267 & 58.1473 & 3.5139 & 58.2547 \\ F4 & 0.4392 & 1.4842 & 0.7704 & 4.8159 & 57.9638 & 3.4413 & 57.8522 \\ F5 & 0.4321 & 1.5854 & 0.8290 & 5.2847 & 58.7264 & 3.4510 & 64.2786 \\ F6 & 0.4910 & 1.7595 & 0.7793 & 4.9261 & 56.8355 & 5.3804 & 56.2355 \\ F7 & 0.4663 & 2.0480 & 0.8303 & 5.1738 & 57.4909 & 3.5970 & 55.0909 \\ F8 & 0.4799 & 1.7791 & 0.7745 & 4.8632 & 58.6083 & 4.3683 & 61.1083 \\ P9 & 0.4447 & 1.7802 & 0.7644 & 4.7953 & 57.2079 & 3.4204 & 58.7079 \\ F10 & 0.9688 & 3.0292 & 0.8834 & 5.4267 & 58.4041 & 4.3267 & 63.9041 \\ F11 & 0.4923 & 2.6668 & 0.8092 & 5.1252 & 57.1205 & 3.8252 & 54.6205 \\ F12 & 0.5161 & 2.7848 & 0.8552 & 5.3034 & 57.4699 & 3.0934 & 54.9699 \\ F13 & 0.5058 & 2.9435 & 0.8101 & 5.2558 & 57.4127 & 3.9558 & 54.9127 \\ F14 & 0.5039 & 2.8387 & 0.8249 & 5.2831 & 59.4465 & 4.0831 & 64.9465 \\ F15 & 0.4861 & 2.6731 & 0.7965 & 5.1307 & 57.1656 & 3.8307 & 54.6656 \\ F18 & 0.5051 & 3.0541 & 0.8101 & 5.1766 & 57.9965 & 3.8766 & 56.4965 \\ F19 & 0.5852 & 3.6280 & 0.9318 & 5.5323 & 58.0511 & 4.1323 & 55.5511 \\ F21 & 0.5713 & 3.8656 & 0.8651 & 5.6503 & 56.2671 & 4.2503 & 53.7671 \\ F22 & 0.6556 & 4.6999 & 0.9891 & 5.9955 & 57.9133 & 4.5955 & 54.4133 \\ F23 & 0.6968 & 5.0680 & 1.0333 & 6.2073 & 56.4508 & 4.8073 & 53.9508 \\ F24 & 0.6312 & 4.7852 & 0.9419 & 6.0494 & 56.4387 & 4.5494 & 53.9387 \\ F25 & 0.6443 & 4.8955 & 0.9769 & 6.0807 & 55.7819 & 4.6807 & 53.2819 \\ F26 & 0.7358 & 5.8243 & 1.0733 & 6.5357 & 57.1906 & 5.1357 & 54.6906 \\ F27 & 0.8057 & 6.3997 & 1.1641 & 6.7742 & 58.4299 & 5.3742 & 55.9299 \\ F28 & 0.7657 & 5.9329 & 1.3762 & 6.5956 & 55.0276 & 5.1956 & 53.5276 \\ F30 & 0.8444 & 8.8503 & 1.1513 & 7.0268 & 57.3208 & 6.5268 & 54.8208 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Average runtime comparison of LTR-MHA and baseline algorithms (in seconds). or lower-dimensional problems but suffer significant degradation in high-dimensional, complex environments. Therefore, by leveraging a multi-strategy fusion mechanism, the LTR-MHA effectively addresses complex optimization problems, though the trade-off between computational cost and performance should be carefully considered in practical applications based on specific problem requirements.