# Integrated Simulation-Based Optimization of Operational Decisions at Container Terminals
## 3 Results and Discussion
### Approximated Optima  
Both the preparatory study and the first screening of all executed experiments created first impressions of the underlying processes. Within the parameter configuration tree, there are exceptionally low-performing solutions. This raises the following question: Which of the meta-heuristics identified the best parameter configuration? To determine this, for each optimization run, the experiment with the highest fitness is extracted. During optimization, both TPE and BO select the next experiment with the greatest expected improvement. Hence, in contrast to SA, after a phase of exploitation (i.e., minor adjustments), a phase of exploration (i.e., larger changes) can follow. RS is the most extreme example since exploitation is never sought. This, in turn, means that the best result of an optimization run can appear at any position of the sequence of recorded experiments. In Figure 8, the four meta-heuristics TPE, BO, SA, and RS are compared for each scenario with 3, 4, 5, and 6 QCs. Consistent with the preparatory study, the results for 5 QCs are far worse than those of all other scenarios. Each of the meta-heuristics shows outliers in at least three of the boxplots, which indicates the importance of stochastic influences during the search process. There is no clear ranking among the meta-heuristics. For 3 QCs, BO performs considerably worse than the other three meta-heuristics. These results are similar for 4 and 5 QCs, although with less severity. This is especially interesting since, for 6 QCs, BO produces the highest median. Over the first three scenarios, RS and SA have very similar performances, and for 6 QCs, SA has the worst median, with outliers in both directions. TPE performs very well in the first three scenarios, providing many of the best solutions with few outliers that are substantially worse. For 6 QCs, the median of TPE is much lower than that of BO. However, in two instances, BO arrived at substantially lower-performing solutions. The differences between meta-heuristics were examined statistically. A significance level of \(\alpha=0.01\) was chosen for the whole study and corrected for each test using Bonferroni correction. To make general statements regarding the meta-heuristics, all scenarios (different numbers of QCs) are agglomerated. The large number of outliers for some of the meta-heuristics precludes the assumption of a normal distribution and requires a nonparametric approach. Hence, a Kruskal-Wallis H test was employed. The test statistic of \(H=31.303\) leads to \(p\ll 0.005\). Hence, the null hypothesis that the four groups stem from a single population is rejected. In a posthoc [PERSON]'s test for pairwise comparison, only TPE was significantly different from the other meta-heuristics. In other words, BO and SA are not significantly different from RS. The comparison of descriptive statistics (as the reader can approximate from Figure 8) shows the superiority of TPE in this study. The wide range of approximated optima and the large difference between meta-heuristics are indicators of the complexity of the simulation model. The parameter configurations of all optima are more closely examined in the following. The meta-heuristics always determine that the fixed assignment of YTs to QCs leads to an inferior performance compared with pooling. Furthermore, in all instances, the pairing of each QC with its clos  
Figure 7: Time difference between maximum and minimum working times of YTs. est YBs performs better than delivering each container to a randomly chosen YB. In contrast to these parameters, the parameter _Dispatching Weight_ shows no clear interpretable results. In Figure 9, the frequencies of specific numbers of YBs for 3, 4, 5, and 6 QCs are depicted. A small number of YBs creates a bottleneck in the yard, while having too many YBs leads to a low utilization of each YB as well as longer travel paths of the YTs. The fewer YBs are used, the shorter the traveled paths, the higher the probability that an unloading job and a loading job can be combined.