# Hyper-Heuristic Based on ACO and Local Search for Dynamic Optimization Problems +
## 4 Computational Tests
### Experimental Results and Discussion  
We first present Table 1, containing the results of 24 instances from the KROA family, without arc blocking. The experiments show that HULK outperforms the other methods in all symmetric and asymmetric instances and \(\mathcal{MMAS}\) + US have better performance than \(\mathcal{MMAS}\) + LK. From this first set of instances, we can already observe HULK efficiency. In the literature, we have not found results for asymmetric instances from the KROA family. Therefore, we choose four algorithms to compare HULK with a magnitude of change \(m=0.1\). They use immigrant schemes (that arise as the most promising mechanisms due to their structural simplicity even superior in computational performance) [35], RIACO (random ACO), EIACO (elitism-based immigrants ACO) and MIACO (memory-based immigrants ACO) are detailed in [36]. The last one is the best result among the four strategies presented in [27] of the procedure named ALNS (adaptive-large-neighborhood Search-based immigrant schemes). Obeserve that ALNS outperforms the other three immigrant schemes, but HULK is better than the best ALNS for at least 6.8% (KROA100.tsp) and at most 14.6% (KROA200.tsp). Since LSO has an asymptotic behavior considering its initial solution, i.e., it will have at least the same value as its initial solution, the comparisons presented in Table 2 show that HULK is much better than any other immigrant scheme approach. Thus, the remaining tests will compare HULK to the best procedures presented in [8] in instances with higher dimensions, barely explored previously in the literature, and we will show another variant of DTSPs considering arc blocking when generating the dynamic changes, as one extension of the results in [8]. The problems considering arc blocking seem to be more difficult to solve--see Tables 1 and 2 (KROA100 family), where HULK has outperformed the compared methods in all cases. However, when we include arc blocking, the superiority of HULK is still evident, but we observe in Tables 3 and  
metric and asymmetric problems, respectively. Table 5 presents the statistical analysis of the results, performing pairwise _Wilcoxon_ rank-sum statistical tests with a significance level of 0.05 (see Julia library: HypothesisTests.jl, at [[https://juliastats.org/HypothesisTests.jl/stable/nonparametric/](https://juliastats.org/HypothesisTests.jl/stable/nonparametric/)]([https://juliastats.org/HypothesisTests.jl/stable/nonparametric/](https://juliastats.org/HypothesisTests.jl/stable/nonparametric/)), accessed on 22 October 2021). To better visualize the results, we apply the following symbols: \"\(+\)\" (if the first algorithm is better than the second one)\"\(++\)\" (if the first algorithm is significantly better than the second one), \"\(-\)\" (if the second algorithm is better than the first one), \"\(-\)\(-\)\" (if the second algorithm is significantly better than the first one) and \"\(\sim\)\" (if there is no significant difference between them). It is significantly better when the statistics show difference between the algorithms and the percentage difference between the average offline performance is greater than 2.0%, and when they have no significant difference when the statistics show it or the percentage difference between the average offline performance is less or equal to 0.1%.