# Automated Generation of Hybrid Metaheuristics Using Learning-to-Rank
## 5 Experiment Evaluation
### Experimental Results and Discussion  
Tables 5-7 present a comparison of the results between the LTR-MHA and the baseline algorithms, focusing on the mean, standard deviation, and best solution values. The best average value is highlighted in bold. The statistics demonstrate that our proposed method significantly outperforms the others in solving various test functions across different dimensions. Specifically, in solving unimodal and simple multimodal functions (as shown in Table 5), the LTR-MHA consistently achieves the lowest average values across most functions, demonstrating a remarkable advantage. Additionally, the LTR-MHA maintains the lowest or second-lowest standard deviation in nearly all functions and dimensions, indicating a more stable convergence process. In certain cases, such as functions F3, F7, and F9, the GA occasionally attains the lowest average value, suggesting that traditional heuristic algorithms still remain competitive when dealing with relatively simple problem structures. Furthermore, the RLWOA occasionally obtains the best average value among all compared methods, highlighting the effectiveness of parameter adaptation based on reinforcement learning. Overall, the RLWOA ranks directly after the LTR-MHA and Rand-MHA in solution precision. Moreover, although the Rand-MHA performs reasonably well in terms of solution accuracy, its generally higher standard deviations reveal a lack of stability in the algorithm's performance. Table 6 shows that the performance gap between algorithms increases when evaluated on hybrid functions. The LTR-MHA achieves the lowest average values on F14 and F18 and secures the best solutions across nearly all dimensions while also maintaining the lowest standard deviations. This demonstrates its ability to obtain high-precision solutions and maintain excellent convergence consistency in high-dimensional search spaces. The GA and Rand-MHA, on the other hand, approach the LTR-MHA's performance on certain functions. In particular, the Rand-MHA and the GA outperform the LTR-MHA in terms of average performance on F13 and F15. This indicates that the LTR-MHA's learning model still has room for improvement in terms of stability and accuracy when handling certain complex hybrid structures. By contrast, the performance of the WOA and HHO degrades significantly in high-dimensional environments, with their convergence curves exhibiting considerable fluctuations. The ISGA and RLWOA exhibit comparable results to the baseline methods but do not surpass the LTR-MHA on the tested hybrid functions, indicating limitations when addressing complex hybrid functions. When tackling the composition functions in the CEC2017 benchmark (Table 7), the LTR-MHA demonstrates a significant advantage across most functions: it consistently achieves the lowest average values (e.g., F22, F23, F24, and F30), as well as the best solutions, while maintaining relatively low standard deviations. The GA performs notably well on certain high-dimensional problems (e.g., F25). The RLWOA obtains the best average value on F28, ranking after the LTR-MHA in overall composition function performance. Although the Rand-MHA approaches the performance of the LTR-MHA in some lower-dimensional scenarios, its results exhibit considerable fluctuations in high-dimensional settings. Overall, the WOA and HHO show relatively poor performance, indicating limited adaptability to complex problems. In summary, the LTR-MHA delivers the best overall performance in composition function optimization, particularly excelling in high-dimensional problems by balancing both accuracy and robustness, while traditional algorithms remain competitive only in specific, simpler cases. To balance problem complexity with an effective evaluation of algorithmic performance, the convergence speed and runtime analyses are conducted using the 30-dimensional test functions. On one hand, 10-dimensional problems are relatively simple and may not adequately demonstrate the advantages of the algorithm in complex search spaces.