# Automated Generation of Hybrid Metaheuristics Using Learning-to-Rank
## 5 Experiment Evaluation
### Experimental Setup
Under the same algorithmic framework, a comparison is conducted with the Rand-MHA method, which adopts a random update strategy. In the Rand-MHA, the update operation is randomly selected at each position update step, without relying on any learning process, meaning that each update operation has an equal probability of being chosen. Additionally, our approach is compared to two recent improved algorithms, namely the ISGA [8] and RLWOA [13]. In all comparative experiments, the algorithm parameters are uniformly configured to ensure the fairness and reproducibility of the experiments. Specifically, during the training phase, one function from each of the four categories in the CEC2017 benchmark suite is selected to form the training function set. In this study, functions F1, F4, F11, and F21 are chosen as the training set. Therefore, these four functions are excluded from the testing phase to avoid evaluation bias, as they have been used to train the Learning-to-Rank model. This ensures a fair performance comparison on unseen benchmark functions. For each function in the benchmark set, algorithms are each run 15 times, with the population size and iterations set to 30 and 500, respectively. Other settings are summarized in Table 4 for reproducibility. To further eliminate the influence of initial randomness, all algorithms use the same initial population configuration, ensuring that performance differences arise primarily from the algorithmic mechanisms rather than stochastic factors. Subsequently, the historical information of the optimal solutions is used as training data to train the predictive model based on a Random Forest ranking algorithm. During the testing phase, the trained predictive model is applied to test functions other than F1, F4, F11, and F21. To reduce the effect of randomness on the experimental outcomes, each algorithm is executed independently 15 times. \begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Algorithm** & **Parameter** & **Value** \\ \hline WOA & \(a\) & Linearly decreased from 2 to 0 \\  & \(b\) & 1 \\ \hline HHO & Lévy flight \(\beta\) & 1.5 \\ \hline GA & Crossover rate \(croRate\) & 0.3 \\  & Mutation rate \(mutRate\) & 0.08 \\  & Selection operation & Tournament (size = 3) \\  & Crossover operation & Single-point crossover \\  & Mutation operation & Randomly replace selected genes within feasible range \\ \hline ISGA & Weighting parameter \(w\) & Linearly decreasing from 0.9 to 0.4 \\  & Perturbation factor & The perturbation is computed as a random number \(\text{rand}\in[-1,1]\) multiplied by a linearly decreasing factor \((1-t/max\_iter)\) \\ \hline RLWOA & \(a\) & Linearly decreased from 2 to 0 \\  & \(b\) & 1 \\  & Weighting parameter \(\sigma\) & 0.6 \\  & Learning rate & Linearly decreased from 0.9 to 0.1 \\  & Discount factor & 0.8 \\ \hline LTR-MHA & Model & Random Forest (scikit-learn) \\  & RF parameters & n\_estimators=50, max\_depth=10, min\_samples\_split=10, min\_samples\_leaf=5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameter configurations for all algorithms used in the experiments.