## 3 Materials and Methods
### Methods
#### 3.2.2 Evolutionary Algorithm-Based Iterated Local Search
\begin{table}
\begin{tabular}{l l} \hline \hline
**Operation** & **Description** \\ \hline \(X\).add(\(x\), L) & Add a new member \(x\) to a bounded list \(X\) with bound size L such that when a new entry updates the size of \(X\) to L + 1, the item at the top of the list is removed. \\ \(X\).add(\(x\), L, t) & The addition of \(x\) from the previous operation is repeated \(t\) times. \\ H & An operation sequence or simply a sequence. \\ A & The bounded list for storing the most recent sequences that improved the best global solution. \\ Rnd.Real(\(x\), \(y\)) & This such that \(x<\delta<y\). \\ Rnd.Int(\(x\), \(y\)) & This such that \(x\leq\delta<y\). \\ Rnd.Bool() & Randomly generate a Boolean variable. \\ better(\(x\), \(y\)) & Denotes based on their objective function values. \\ \(P_{w}^{1}\), \(P_{w}^{2}\) & Bounded lists for recently rewarding parameter values for the LLHs. The former is kept for perturbative LLHs \\ \(p_{l}^{1}\), \(p_{l}^{2}\) & while the latter is kept for local search LLHs. \\ \(p_{l}^{1}\), \(p_{l}^{2}\) & The fixed lists of all possible parameter values available for the perturbative and local search LLHs, respectively. \\ \(L_{p}\) & The bound size for the \(P_{w}^{1}\) and \(P_{w}^{2}\) lists. \\ \(A_{t}\) & value = 15. \\ \(H_{t}\) & Similar to \(A_{t}\), but applied to the operation sequences. Experimental value = 1. \\ nA & The number of non-improving iterations completed so far for an acceptance strategy. \\ nH & Similar to nA, but applied to the operation sequences. \\ \(imp_{A}\) & The number of improving iterations completed so far for an acceptance strategy. \\ \(imp_{H}\) & Similar to \(imp_{A}\), but for LLHs \\ \(L_{add}\) & A pre-determined list of possible values that could be added to the value of the current acceptance strategy during its mutation. \\ \(P_{A}\) & A bounded list of rewarding acceptance strategies based on the improvement of the global best solution. \\ \(H_{pert}\) & A list of combinations of mutation and ruin-recreate LLHs perturbative heuristics for a problem domain. \\ rndSel() & A function that returns a random member of a list. \\ A & The current value of the temperature parameter being used by the acceptance mechanism. \\ cur\_a & The currently engaged acceptance strategy. \\ \(S_{b}\) & The best solution found so far. \\ \(S^{\
u}\) & The proposed solution after a perturbation–intensification cycle. \\ \(S_{0}\) & The incumbent solution during the search process. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Description of Operations of the EA-ILS hyper-heuristic. Figure 1: Sample operation sequence in the EA-ILS hyper-heuristic. ```
1 Variable: runtime
2. \(S_{0}\leftarrow\) generateInitialSolution()
3. \(S_{b}\gets S_{0}\)
4. init()
5. while getElapsedTime() < runTime
6. \(H\leftarrow\) mdSel(\(A\))
7. for i \(\gets\) 1 to p + 1 \(\rhd p\) is the number of offspring
8. if i > 1
9. \(H\leftarrow\) mutate(H)
10. endif
11. setParam()
12. while nH < \(H_{l}\)



total elapsed time since the beginning of the EA-ILS hyper-heuristic run on an instance of a problem. In Line 5, a sequence \(H\) is randomly picked from the bounded list of sequences (\(A\)) initialized in Line 3. This bounded list is set up to keep the sequences that generated the best new solutions when they were applied. Line 6 is the loop that controls the mechanism of applying sequences and their mutations. There are only two iterations completed by the loop because the value of \(p\) is set to 1 so that every selected sequence spawns an offspring that is tried before the selection of another sequence from archive \(A\). The mutation evolutionary operator designed for the EA-ILS hyper-heuristic is applied to \(H\) in Line 8 during the second iteration of the inner loop in Line 6 to likely produce another sequence. The parameters for the perturbative LLHs in the sequence are set in Line 10. This only happens to the perturbative LLHs that use the _intensity of mutation_ parameter.