# A Local Search-Based Generalized Normal Distribution Algorithm for Permutation Flow Shop Scheduling
## 5 Results and Comparisons
### Comparison under Carlier
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline
**Instances** & _Algorithm_ & \(Z^{\prime}\) & _BRE_ & WRE & _ARE_ & _Z\({}_{\text{avg}}\)_ & _Time(MS)_ & _SD_ & \(Z^{\prime}\) & _BRE_ & WRE & _ARE_ & _Z\({}_{\text{avg}}\)_ & _Time(MS)_ & _SD_ \\ \hline \multirow{10}{*}{_Car01_} & HIGNDO & & 0.0000 & 0.0000 & 0.0000 & 7038.0000 & 0.0077 & 0.0000 & & 0.0000 & 0.0000 & **0.0000** & **7720.0000** & **0.0558** & **0.0000** \\ \cline{2-13}  & HIGNDO & & 0.0000 & 0.0000 & 0.0000 & 7038.0000 & 0.0078 & 0.0000 & & 0.0000 & 0.0000 & 0.0131 & 0.0014 & 7731.1667 & 0.0636 & 30.1575 \\ \cline{2-13}  & HIGNDO & & 0.0000 & 0.0000 & 0.0000 & 7038.0000 & 0.0079 & 0.0000 & & 0.0000 & 0.0131 & 0.0028 & 7741.9000 & 0.1949 & 36.3129 \\ \cline{2-13}  & HMPA & & 0.0000 & 0.0000 & 0.0000 & 7038.0000 & 0.0192 & 0.0000 & & 0.0000 & 0.0000 & 0.0000 & 0.0039 & 0.0011 & 7728.4000 & 1.0569 & **10.1114** \\ \cline{2-13}  & HWOA & _7038_ & 0.0000 & 0.0000 & 0.0000 & 7038.0000 & 0.0052 & 0.0000 & & 0.0000 & 0.0000 & 0.0000 & 0.0015 & 7731.4333 & 0.1961 & 11.6152 \\ \cline{2-13}  & HEO & & 0.0000 & 0.0195 & 0.0011 & 7045.9000 & 0.0091 & 29.9426 & & 0.0000 & 0.0135 & 0.0048 & 7756.7000 & 0.2393 & 37.5501 \\ \cline{2-13}  & HSCA & & 0.0000 & 0.0456 & 0.0043 & 7068.2667 & 0.0830 & 76.6159 & & 0.0000 & 0.0486 & 0.0076 & 7778.6667 & 0.4299 & 104.3537 \\ \cline{2-13}  & HSSA & & 0.0000 & 0.0617 & 0.0048 & 7072.1000 & 0.0079 & 107.6947 & & 0.0000 & 0.0486 & 0.0078 & 7780.0000 & 0.0668 & 72.7736 \\ \cline{2-13}  & HTSA & & 0.0000 & 0.0997 & 0.0395 & 7315.6667 & 0.3338 & 286.3707 & & 0.0000 & 0.1124 & 0.0334 & 7977.8333 & 0.6940 & 255.2532 \\ \cline{2-13}  & HGA & & 0.0000 & 0.0169 & 0.0018 & 7050.6000 & 0.0105 & 29.1692 & & 0.0000 & 0.0000 & 0.0153 & 0.0099 & 7796.1000 & 0.6052 & 40.0161 \\ \hline \multirow{10}{*}{_Car02_} & HIGNDO & & 0.0000 & 0.0000 & 0.0000 & 7166.0000 & 0.0200 & **0.0000** & & 0.0000 & **0.0000** & **8505.0000** & **0.0134** & **0.0000** \\ \cline{2-13}  & HIGNDO & & 0.0000 & 0.0000 & 0.0000 & 7166.0000 & **0.0151** & **0.0000** & & 0.0000 & **0.0000** & **8505.0000** & **0.0192** & **0.0000** \\ \cline{1-1} \cline{2-13}  & HGNDO & & 0.0000 & 0.0000 & 0.0000 & 7166.0000 & 0.0152 & **0.0000** & & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 & 0.0000 \\ \cline{1-1} \cline{2-13}  & HMPA & & 0.0000 & 0.0293 & 0.0010 & 7173.0000 & 0.3175 & 37.6962 & & 0.0000 & 0.0540 & 0.0070 & 8564.4333 & 0.5601 & 101.8279 \\ \cline{1-1} \cline{2-13}  & HWOA & & 0.0000 & 0.0000 & 0.0000 & **7166.0000** & 0.0224 & **0.0000** & & **0.0000** & **8507.1667** & 0.0552 & **11.6679** \\ \cline{1-1} \cline{2-13}  & HEO & & 0.0000 & 0.0293 & 0.0078 & 7222.0000 & 0.0980 & 92.8655 & & 0.0000 & 0.0396 & 0.0076 & 8569.7000 & 0.1632 & 78.3812 \\ \cline{1-1} \cline{2-13}  & HSCA & & 0.0000 & 0.1136 & 0.0347 & 7414.6000 & 0.2283 & 344.7938 & & 0.0000 & 0.0770 & 0.0223 & 8694.8667 & 0.5217 & 190.9799 \\ \cline{1-1} \cline{2-13}  & HSSA & & 0.0000 & 0.1231 & 0.0183 & 7297.4333 & 0.0313 & 262.8529 & & 0.0000 & 0.0366 & 0.0109 & 8597.9667 & **0.0492** & 95.4919 \\ \cline{1-1} \cline{2-13}  & HTSA & & 0.0000 & 0.1749 & 0.0788 & 7730.5333 & 0.4812 & 420.7919 & & 0.0000 & 0.1250 & 0.0461 & 8897.4000 & 0.8095 & 345.5301 \\ \cline{1-1} \cline{2-13}  & HGA & & 0.0000 & 0.0293 & 0.0063 & 7211.10000 & 0.1966 & 84.1088 & & 0.0000 & 0.0582 & 0.0084 & 8576.1667 & 0.4249 & 115.9747 \\ \hline \hline \multirow{10}{*}{_Car03_} & HIGNDO & & 0.0000 & **0.0000** & **0.0000** & **7312.0000** & & 0.0953 & **0.0000** & & 0.0000 & **0.0000** & **6590.000** & **0.0067** & **0.0000** \\ \cline{1-1} \cline{2-13}  & HIGNDO & & 0.0000 & **0.0000** & **0.0000** & **7312.0000** & & **0.0455** & **0.000** & & 0.0000 & **0.0000** & **6590.0000** & **0.0051** & **0.0000** \\ \cline{1-1} \cline{2-13}  & HGNDO & & **0.0000 Figure 4: Comparison in terms of BRE, ARE, and WRE on Carlier instances. Figure 5: Comparison in terms of time, SD, and Avg on Carlier instances. Figure 6: Boxplot for Car03 instance.