## 5 Results and Analysis
### Test Performance  
#### 5.1.1 The Performance of Evolved Rules  
Tables 4-6 show the test performance of the FS-IGEP, IGEP, GEP, and other representative benchmark rules in the three considered scenarios. In the tables, the Wilcoxon rank sum test was performed upon the results of the FS-IGEP, IGEP, and GEP algorithms, and the one that was statistically significantly better has been marked in bold.  
For the MS scenario, the FS-IGEP algorithm significantly outperformed both the GEP algorithm and the compared benchmark rules in all simulated cases (a negative value indicates an advantage over the reference rule). In 20 experiments, FS-IGEP demonstrated superior outcomes in comparison to the IGEP algorithm, while in seven experiments, no significant difference was observed. Table 5 displays the significant outcomes, where the superior results have been highlighted in bold. This indicates that the FS-IGEP algorithm had the ability to generate competitive rules in experiments that were more challenging. Regarding the MFT scenario, it can be observed from Table 6 that the FS-IGEP method exhibited the most favorable performance metrics, with values changing from \(-\)11.54 \(\pm\) 0.37 to \(-\)22.46 \(\pm\) 0.69, out of all the methods that were taken into consideration. More specifically, the rule performance of the FS-IGEP was better than the IGEP rules in 22 cases, with no significant difference being found only in five cases. Additionally, compared to situations with low shop utilization, the gaps increased in scenarios with high shop utilization (indicated in bold). It is noteworthy that the modification of the tightness factor exhibited minimal influence on the job flow time, which is consistent with our expertise in the field. In relation to the MWT scenario, it was observed that the FS-IGEP algorithm outperformed other algorithms across all 27 instances. Table 7 shows the test performance value of the FS-IGEP rules varied from \(-\)5.11 \(\pm\) 0.35 (lowest value) to \(-\)13.68 \(\pm\) 1.26 (highest value) in 27 scenarios. The FS-IGEP algorithm yielded superior outcomes in comparison to the IGEP and GEP algorithms, particularly in extreme instances with high shop utilization levels and tight due dates. As evidenced by the results, the solution quality of the rules generated using GEP was inferior to that of the other algorithms across all scenarios.  
The experimental results revealed the following observations: (1) The results obtained using the GEP-based algorithms surpassed those of the benchmark rules, indicating the superiority of the GEP algorithm in the automatic evolution of dispatching rules; (2) In three different dynamic job-shop scenarios, the FS-IGEP algorithm outperformed IGEP, GEP, and other typical benchmark rules by a substantial margin. This result suggested that focusing only on the core GEP characteristics can greatly enhance the test performance of the GEP-evolved rules; (3) The rules designed with the FS-IGEP algorithm achieved lower standard deviations than the other algorithms in most of the test sets, which indicated thehigh robustness of the designed rules and further demonstrated the effectiveness of the FS-IGEP algorithm in different scheduling environments.