# Modified Coral Reef Optimization Methods for Job Shop Scheduling Problems
## 4 Experiment Results and Discussion
### Experiment Results
#### 4.3.1 Search Performance on CRO-Based Algorithm with Different Reef Sizes
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Table 3 shows that the local search strategies have made the CRO algorithm more stable, as the amplitude of the mean between the best to the worst and the standard deviation in all cases have improved. CROLS2 demonstrates greater stability with smaller standard deviations than CRO and CROLS1 in most instances. Additionally, local search methods assist in reducing the worst-case of CROLS1 and CROLS2 compared to CRO. Similar to the best value acquired by each hybrid algorithm, the local search technique helps CROLS1 and CROLS2 reach the best-known optimal values for the situations examined. In most instances, CROLS1 and CROLS2 can get the best-known outcomes with reef sizes of 10 \(\times\) 10 and 20 \(\times\) 20. However, for instances of high complexity, such as LA39 and LA40, the best results can only be reached with reef sizes of 30 \(\times\) 30. CROLS1 and CROLS2 significantly reduce the search duration compared to the original method. This is more noticeable when the complexity of the instance is greater; the computational time can be reduced by up to 30% for LA40. In addition, for complex cases such as LA39 and LA40, the CROLS2 algorithm surpasses CROLS1 when outcomes are similar, but the execution time is reduced by more than 10%. Technically, CROLS1 and CROLS2 have 20% and 100% more fitness function calls than the original algorithm since they employ local search techniques. Even though this increases the amount of computational work, it helps the algorithm converge quickly and experimentally shows that CROLS1 and CROLS2 are still more rapid at searching than the original CRO. To evaluate the improvement of the two hybrid algorithms compared to CRO statistically, we performed [PERSON]'s test on the data in Table 3. [PERSON]'s test, based on the ranking, will be utilized to determine the difference between three CRO-based algorithms using experimental findings collected from 16 LA instances and categorized by three reef sizes 10 \(\times\) 10, 20 \(\times\) 20, and 30 \(\times\) 30. The \"mean rank\" and [PERSON]'s test statistic results of three algorithms participating in the evaluation will be described in Tables 4 and 5, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{3}{c}{**Mean Rank**} \\ \cline{2-4}  & **Reef Size 10 \(\times\) 10** & **Reef Size 20 \(\times\) 20** & **Reef Size 30 \(\times\) 30** \\ \hline CRO & 3.00 & 2.69 & 2.94 \\ \hline CROLS1 & 1.56 & 2.06 & 1.47 \\ \hline CROLS2 & 1.44 & 1.25 & 1.59 \\ \hline \hline \end{tabular}
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Table 4: Mean rank of three CRO-based algorithms. \begin{table}
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**Instance** & **Size** & **Reef Size** & **Method** & **Opt** & **Best** & **Worst** & **Mean** & **SD** & **Time (s)** \\ \hline \multirow{8}{*}{LA40} & \multirow{4}{*}{\(15\times 15\)} & CRO & 1222 & 1396 & 1506 & 1451.25 & 49.25 & 875 \\  & & CROLS1 & 1222 & 1240 & 1336 & 1313.27 & 11.24 & 728.45 \\  & & CROLS2 & 1222 & 1269 & 1305 & 1288.45 & 35.41 & 625.36 \\ \cline{2-8}  & & CRO & 1222 & 1364 & 1455 & 1390.35 & 58.7 & 826.82 \\  & & CROLS1 & 1222 & 1240 & 1299 & 1270.27 & 35.09 & 674.73 \\  & & CROLS2 & 1222 & 1239 & 1299 & 1273.09 & 30.93 & 568.82 \\ \cline{2-8}  & & CRO & 1222 & 1342 & 1424 & 1374.33 & 24.88 & 739.82 \\  & & CROLS1 & 1222 & 1228 & 1264 & 1238.25 & 15.89 & 585.45 \\  & & CROLS2 & 1222 & 1232 & 1279 & 1248.45 & 23.22 & 495.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._According to Table 4, there is little difference in the mean rank of the CRO algorithm between reef sizes. The mean rank of CROLS1 and CROLS2 are significantly different from CRO, indicating that local search techniques substantially impact these two algorithms. Table 5 provides the test statistics for [PERSON]'s test with a significance level of \(\alpha=0.05\).