## 3 Materials and Methods
### Methods
#### 3.2.2 Evolutionary Algorithm-Based Iterated Local Search
Line 11 marks a cycle of repeated application of an operation sequence until it no longer improves the global best solution \(S_{b}\). In Line 12, the current operation sequence is applied to a solution by successively applying the perturbative LLHs in the sequence before the execution of the local search module for intensification. The acceptance strategy may be changed after applying a sequence. This will depend on whether the number of consecutive non-improving iterations allowed for the current acceptance strategy has elapsed or not, as in Line 13 of Algorithm 2. The value of the parameter to be applied for a perturbative or local search LLH is selected based on a random value through the function set-Param()described by Algorithm 3. This random value is checked against the value of \(\varphi=0.5\). Consequently, the parameter is selected at 50% probability from a recency list of parameters with accepted solutions; otherwise, it is selected from the general list of a parameter value \(P_{f}\). There are two versions of \(P_{f}\): one is maintained for the perturbative LLHs while the other is maintained for the local search LLHs. The value of \(P_{f}^{1}=\{0.0,\ 0.1,\ \ldots,\ 0.6\}\) and that of \(P_{f}^{2}=\{0.5,\ 0.6,\ 0.7\}\). ``` \(\delta\gets\)\(\text{{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{ \rm{\rm{\rm{\rm{ \rm{ \rm{  }}}}}}{{} {{}}{{}}{{}}{{{}}{{}}{{}{{}{}{{}}{{}{}{}{}{{}{}{}{}{{}{}{}{}{}{}{}{{}{}{}{}{}{}{{}{}{}{}{}{}{{}{}{}{}{}{{}{}{}{{}{}{}{}{{}{}{}{}{{}{}{}{{}{}{}{{}{}{}{{}{}{}{{}{}{{}{}{{}{}{{}{}{{}}{{}{{}{}{{}{}{{}}{{}{}{{}{}{{}{}{{}{}{{}{}{}{{}{}{{}{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{}{{}{}{}{{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{}{{}{}{}{{}{}{{}{}{{}{}{}{{}{}{{}{}{}{{}{}{{}{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{{}{}{}{{}{}{{}{}{}{{}{}{{}{}{}{{}{phase is carried out through the LS-Seq local search procedure, and the resulting solution gets screened by the acceptance mechanism in Line 14 of Algorithm 2. A different strategy is taken in the local search module of the EA-ILS hyper-heuristic for applying local search heuristics during the intensification phase. Instead of applying the heuristics in a variable neighborhood style as in [21; 49], HMM is employed to automatically learn promising sequences of local search LLHs. A vector iScore of size n and an n \(\times\) n matrix called pScore are maintained for the n local search LLHs. A roulette wheel procedure is employed to select the first local search LLH in an iteration of the local search phase based on the values of the iScore vector. Subsequent selections through a roulette wheel procedure are performed with the pScore matrix that captures the transition probability of selecting a given j local search LLH after applying a previous one \(i\). Line 28 of Algorithm 2 updates the bounded list of high-quality sequences discovered during the search process. This update is achieved by adding the recently applied sequence to the bounded list if it has updated the global best solution at least once during its usage. In Line 29 of Algorithm 2, \(imp_{H}\) copies of a sequence are added to the bounded list. The major features of the EA-ILS hyper-heuristic are explicated as follows:  
* The sequence of perturbative LLHs is discovered by an evolutionary algorithm, which means that the EA-ILS hyper-heuristic does not use a mainstream selection mechanism;
* The _temperature_ parameter of the acceptance mechanism, that is, the APW of the present study, oscillated during the search process;
* The intensification phase in most ILS-based hyper-heuristics such as the FS-ILS algorithm was achieved through a local search procedure based on the VND. The EA-ILS hyper-heuristic carries out intensification through a procedure based on the HMM.