# Automated Generation of Hybrid Metaheuristics Using Learning-to-Rank
## 5 Experiment Evaluation  
### Experimental Setup  
In this study, the performance of the LTR-MHA algorithm is evaluated using the CEC2017 benchmark function set [25]. These functions fall into four categories: unimodal functions (F1-F3), simple multimodal functions (F4-F10), hybrid functions (F11-F20), and composition functions (F21-F30). However, during the actual experiments, errors occurred when invoking functions F2, F16, F17, F20, and F29. Upon investigation, it was found that these issues were primarily caused by numerical instabilities or boundary calculation anomalies in the implementation of these functions on specific platforms. Such issues include overflows, division by zero, or undefined logarithmic operations resulting from extreme inputs. Additionally, certain functions exhibited compatibility issues during the porting process. To ensure the stability and fairness of the experimental results, these functions were reasonably excluded to prevent technical problems from interfering with the overall evaluation. The range of all functions is \([-100,100]\), with problem dimensions set to \(D=10\), \(30\), \(50\), and \(100\). Table 3 includes information about the CEC2017. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Type** & **No.** & **Function** & **Dim** & **Range** & **Optimum** \\ \hline Unimodal Function & F1 & Shifted and Rotated Bent Cigar Function & \(10,30,50,100\) & \([-100,100]\) & \(100\) \\  & F3 & Shifted and Rotated Zakharov Function & \(10,30,50,100\) & \([-100,100]\) & \(300\) \\ Simple Multimodal Function & F4 & Shifted and Rotated Rosenbrock’s Function & \(10,30,50,100\) & \([-100,100]\) & \(400\) \\  & F5 & Shifted and Rotated Rastrigin’s Function & \(10,30,50,100\) & \([-100,100]\) & \(500\) \\  & F6 & Shifted and Rotated Expanded Schafer’s F Function & \(10,30,50,100\) & \([-100,100]\) & \(600\) \\  & F7 & Shifted and Rotated Lunacek Bi\_, Rastrigin Function & \(10,30,50,100\) & \([-100,100]\) & \(700\) \\  & F8 & Shifted and Rotated Non-Continuous Rastrigin’s Function & \(10,30,50,100\) & \([-100,100]\) & \(800\) \\  & F9 & Shifted and Rotated Levy Function & \(10,30,50,100\) & \([-100,100]\) & \(900\) \\  & F10 & Shifted and Rotated Schweef’s Function & \(10,30,50,100\) & \([-100,100]\) & \(1000\) \\ Hybrid Function & F11 & Hybrid Function 1 (N = 3) & \(10,30,50,100\) & \([-100,100]\) & \(1100\) \\  & F12 & Hybrid Function 2 (N = 3) & \(10,30,50,100\) & \([-100,100]\) & \(1200\) \\  & F13 & Hybrid Function 3 (N = 3) & \(10,30,50,100\) & \([-100,100]\) & \(1300\) \\  & F14 & Hybrid Function 4 (N = 4) & \(10,30,50,100\) & \([-100,100]\) & \(1400\) \\  & F15 & Hybrid Function 5 (N = 4) & \(10,30,50,100\) & \([-100,100]\) & \(1500\) \\  & F18 & Hybrid Function 8 (N = 5) & \(10,30,50,100\) & \([-100,100]\) & \(1800\) \\  & F19 & Hybrid Function 9 (N = 5) & \(10,30,50,100\) & \([-100,100]\) & \(1900\) \\ Composition Function & F21 & Composition Function 1 (N = 3) & \(10,30,50,100\) & \([-100,100]\) & \(2100\) \\  & F22 & Composition Function 2 (N = 3) & \(10,30,50,100\) & \([-100,100]\) & \(2200\) \\  & F23 & Composition Function 3 (N = 4) & \(10,30,50,100\) & \([-100,100]\) & \(2300\) \\  & F24 & Composition Function 4 (N = 4) & \(10,30,50,100\) & \([-100,100]\) & \(2400\) \\  & F25 & Composition Function 5 (N = 5) & \(10,30,50,100\) & \([-100,100]\) & \(2500\) \\  & F26 & Composition Function 6 (N = 5) & \(10,30,50,100\) & \([-100,100]\) & \(2600\) \\  & F27 & Composition Function 7 (N = 6) & \(10,30,50,100\) & \([-100,100]\) & \(2700\) \\  & F28 & Composition Function 8 (N = 6) & \(10,30,50,100\) & \([-100,100]\) & \(2800\) \\  & F30 & Composition Function 10 (N = 3) & \(10,30,50,100\) & \([-100,100]\) & \(3000\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: CEC2017 test suite. The objective of the experiments is to confirm the effectiveness of the LTR-MHA method, focusing on three aspects: convergence speed, solution precise, and computing efficiency. The LTR-MHA is compared against individual metaheuristic algorithms, namely the WOA, HHO, and the GA.