# Modified Coral Reef Optimization Methods for Job Shop Scheduling Problems
## 4 Experiment Results and Discussion
### Experiment Results
#### 4.3.5 Convergence Ability  
The algorithm's ability to converge to the optimal solution is a second criterion for comparison. The collection of data is dependent on the experimental outcomes of the LA01 instance. Table 10 displays the average number of generations required to discover the optimal solution for three CRO algorithms with three different reef sizes.  
First, as the reef size parameter increases, the number of generations conducted to explore the optimal solution for the three algorithms decreases most noticeably for the original CRO. Second, the two hybrid algorithms have significantly fewer generations than the original. In this scenario, the CROLS2 algorithm exhibits the quickest convergence capability. Experimental results proved that local search strategies significantly enhanced the search process and expedited finding optimal answers. For optimal performance, it is preferable to utilize local search approaches later in the algorithm because they have little impact in the early stages and waste time. Figures 4-6 depict the convergence graph  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reef Size** & **10 \(\times\) 10** & **20 \(\times\) 20** & **30 \(\times\) 30** \\ \hline
**CRO** & **150.5** & **42.2** & **30.4** \\
**CROLS1** & **13.4** & **10.6** & **10.4** \\
**CROLS2** & **12.2** & **8** & **6.4** \\ \hline \hline \end{tabular}
\end{table}
Table 10: Average objective function evaluations test needed to find the optimal solution.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multirow{2}{*}{**Size**} & \multicolumn{5}{c}{**CROLS1**} & \multicolumn{5}{c}{**CROLS2**} \\ \cline{3-8}  & & **10 \(\times\) 10** & **20 \(\times\) 20** & **30 \(\times\) 30** & **10 \(\times\) 10** & **20 \(\times\) 20** & **30 \(\times\) 30** \\ \hline LA01 & \(10\times 5\) & 0 & 0 & 0 & 0 & 0 & 0 \\ LA02 & \(10\times 5\) & \(1.68\) & 0.46 & 0.15 & 1.68 & 0.46 & 0.15 \\ LA06 & \(15\times 5\) & 0 & 0 & 0 & 0 & 0 & 0 \\ LA07 & \(15\times 5\) & 1.01 & 0.56 & 0 & 1.01 & 0.56 & 0 \\ LA11 & \(20\times 5\) & 0.49 & 0 & 0 & 0.49 & 0 & 0 \\ LA12 & \(20\times 5\) & 0.29 & 0 & 0 & 0.29 & 0 & 0 \\ LA16 & \(10\times 10\) & 2.43 & 0.32 & 0.32 & 2.75 & 0.32 & 0.32 \\ LA17 & \(10\times 10\) & 1.53 & 0.51 & 0.51 & 1.4 & 0.51 & 0.51 \\ LA21 & \(15\times 10\) & 2.2 & 2.28 & 0.96 & 1.34 & 2.28 & 0.96 \\ LA22 & \(15\times 10\) & 5.18 & 1.83 & 0.86 & 4.75 & 1.73 & 0.86 \\ LA26 & \(20\times 10\) & 7.14 & 3.12 & 0.66 & 7.47 & 3.12 & 0.66 \\ LA27 & \(20\times 10\) & 5.51 & 5.67 & 1.62 & 5.43 & 4.78 & 0.73 \\ LA32 & \(30\times 10\) & 4.43 & 4.43 & 3.35 & 4.54 & 4.43 & 3.35 \\ LA33 & \(30\times 10\) & 8.44 & 5.76 & 5 & 8.32 & 5.76 & 5 \\ LA39 & \(15\times 15\) & 12.17 & 10.54 & 8.03 & 9.25 & 10.46 & 8.03 \\ LA40 & \(15\times 15\) & 12.77 & 10.15 & 9.33 & 10.39 & 10.23 & 9 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Improve performance of two hybrid algorithms.  
of three CRO, CROLS1, and CROLS2 methods for three reef sizes (10 \(\times\) 10, 20 \(\times\) 20, and 30 \(\times\) 30) in five instances LA01, LA16, LA26, LA32, and LA40.  
Figure 4: Convergence graph of CRO-based with reef size 10 \(\times\) 10: (a) LA01, (b) LA16, (c) LA26, (d) LA32, (e) LA40.  
Figure 5: Convergence graph of CRO-based with reef size 20 \(\times\) 20: (**a**) LA01, (**b**) LA16, (**c**) LA26, (**d**) LA32, (**e**) LA40.  
The optimal solution (corresponding to the makespan value 666) of the LA01 instance is shown in Figure 7 through Gantt-chart, including ten jobs (J1-J10) and five machines (M0-M4), with each color representing a job.  
Figure 6: Convergence graph of CRO-based with reef size 30 \(\times\) 30: (**a**) LA01, (**b**) LA16, (**c**) LA26, (**d**) LA32, (**e**) LA40.