## 5 Evaluation and Discussion  
For this evaluation, we used a 64-bit Windows 11 operating system with an 11 th generation Intel(r) Core(tm) i7-11700 CPU 2.50 GHz processor and 16 GB RAM. The hybrid metaheuristic algorithm described in the previous section, along with the individual metaheuristic algorithms GA and ABO, was implemented in Java using the NetBeans 15 integrated development environment (IDE). No Java library was used for the implementation of all algorithms that are part of the evaluation (GA, ABO, novel hybrid algorithm). Instead, all implementations were created manually from scratch, so the program code for GA and ABO is practically identical to the program code of the hybrid algorithm that uses GA and ABO. Of course, with the necessary changes to the individual algorithms within the hybrid algorithm to make this hybrid solution work. In this evaluation, we test our new hybrid algorithm on the NP-hard Container Relocation Problem (CRP) using the test set from [36]. As mentioned in the introduction, the main focus of the CRP is to determine an optimal relocation sequence that allows all containers to be retrieved within the designated bay in the container terminal at the port, given their respective priorities and to achieve this goal with as few reshuffles (additional relocations) as possible. The test set consists of restricted CRP, where only the containers blocking the next container to be shipped, may be relocated, which is a much more difficult problem than if other containers may also be relocated (unrestricted CRP) with the goal of minimizing the number of additional relocations. Also, the test set from [36] contains two-dimensional CRPs consisting of one bay with a certain number of columns (stacks) and rows (tiers). The example of a two-dimensional CRP can be seen in Figure 2.  
This test set was selected for testing because it contains CRPs with a maximum occupancy of one bay. Thus, in each CRP problem, the maximum possible number of containers is found with respect to the size of the bay. This further complicates the problem and adds weight to the evaluation of our new hybrid algorithm combining GA and ABO together with SFMT-64 and SFMT-32. Considering the number of rows (tiers) \(R\) and the number of columns (stacks) \(C\) in the bay, the total number of containers that can be placed in the bay is obtained from the formula in [36]:  
\[N=C\times R-\ (R-1), \tag{2}\]  
where \(N\) represents the total number of containers in the bay. This ensures that there is a sufficient number of free container positions within the bay to which blocking containers can be shifted. The evaluation was done for CRPs of different size of the bay. The size of the bay for the first \"group\" of CRPs has the number of columns (stacks) 3, while the size of the rows (tiers) is 3, 4, 5 and 6, respectively. There are four other \"groups\" of CRPs with the same row sizes of 3, 4, 5, and 6, and the column sizes are 4, 5, 6, and 7, respectively. Thus, the number of CRPs with different column and row sizes is 20. Each CRP for each bay size (e.g., 3 \(\times\) 4) consists of 40 different test instances with different layout containers within the bay. The maximum tested bay size (6 \(\times\) 7) meets the specifications of the latest technological RTG cranes in terms of actual bay sizes in port container terminal. Figure 2: Yard bay with 4 rows (tiers) and 5 columns (stacks). The results of our new hybrid algorithm, which combines the GA and ABO algorithms with SFMT PRNGs for the randomization phase, are compared with the results of the individual algorithms GA and ABO, and with the results of the Beam Search Algorithm (BSA) [36], which, to our knowledge, represents the best results for this large and relevant test set of CRPs. For these tests comparing the best possible results of our new hybrid GA + ABO, GA and ABO, certain parameters were established throughout the evaluation process. Table 1 shows all the parameters and their corresponding values.