# The Porcupine Measure for Comparing the Performance of Multi-Objective Optimization Algorithms
## 4 Regarding 2-Dimensional Attainment Surfaces
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{**Geometry**} & \multirow{2}{*}{**True**} & \multicolumn{4}{c}{**Intersection Line Generation Approach**} \\  & & & **Rotation-Based** & **Random** & **ASSIL** \\ \hline \multirow{4}{*}{Case 1} & Concave & (73.27, 26.73) & (71.00, 29.00) & (76.80, 23.20) & (73.20, 26.80) \\  & Convex & (70.37, 29.63) & (85.10, 14.90) & (85.60, 14.40) & (70.30, 29.70) \\  & Line & (70.00, 30.00) & (74.60, 25.40) & (79.30, 20.70) & (70.00, 30.00) \\  & Mixed & (69.67, 30.33) & (73.20, 26.80) & (82.10, 17.90) & (69.80, 30.20) \\  & Disconnected & (77.50, 22.50) & (82.70, 17.30) & (86.90, 13.10) & (77.50, 22.50) \\ \hline \multirow{4}{*}{Case 2} & Concave & (50.00, 50.00) & (41.00, 59.00) & (67.60, 32.40) & (50.00, 50.00) \\  & Convex & (86.60, 13.40) & (83.00, 17.00) & (96.40, 3.60) & (86.60, 13.40) \\  & Line & (66.67, 33.33) & (59.00, 41.00) & (81.30, 18.70) & (66.60, 33.40) \\  & Mixed & (66.99, 33.01) & (59.60, 40.40) & (81.60, 18.40) & (66.90, 33.10) \\  & Disconnected & (60.00, 40.00) & (51.60, 48.40) & (75.80, 24.20) & (60.00, 40.00) \\ \hline \multirow{4}{*}{Case 3} & Concave & (79.21, 20.79) & (73.80, 26.20) & (92.60, 7.40) & (79.20, 20.80) \\  & Convex & (97.81, 2.19) & (97.20, 2.80) & ( 99.90, 0.10) & (97.80, 2.20) \\  & Line & (86.67, 13.33) & (83.00, 17.00) & (96.50, 3.50) & (86.60, 13.40) \\  & Mixed & (88.01, 11.99) & (84.80, 15.20) & (95.60, 4.40) & (87.90, 12.10) \\  & Disconnected & (90.00, 10.00) & (87.30, 12.70) & (97.60, 2.40) & (90.00, 10.00) \\ \hline \multirow{4}{*}{Case 4} & Concave & (50.00, 50.00) & (50.00, 50.00) & (49.00, 51.00) & (50.00, 50.00) \\  & Convex & (50.00, 50.00) & (50.00, 50.00) & (50.60, 49.40) & (50.00, 50.00) \\  & Line & (50.00, 50.00) & (50.00, 50.00) & (54.00, 46.00) & (50.00, 49.90) \\  & Mixed & (55.71, 44.29) & (54.30, 45.70) & (**50.70, 49.30**) & (55.70, 44.30) \\  & Disconnected & (69.14, 30.86) & (73.00, 27.00) & (**77.80, 22.20**) & (69.10, 30.90) \\ \hline \multirow{4}{*}{Case 5} & Concave & (50.00, 50.00) & (50.00, 50.00) & (49.50, 50.50) & (50.00, 50.00) \\  & Convex & (50.00, 50.00) & (50.00, 50.00) & (50.40, 49.60) & (50.00, 50.00) \\ \cline{1-1}  & Line & (50.00, 50.00) & (50.00, 50.00) & (49.20, 50.80) & (50.00, 50.00) \\ \cline{1-1}  & Mixed & (45.56, 54.44) & (45.30, 54.70) & (43.40, 56.60) & (45.60, 54.40) \\ \cline{1-1}  & Disconnected & (45.43, 54.57) & (45.00, 55.00) & (45.40, 54.60) & (45.40, 54.60) \\ \hline \multirow{4}{*}{Case 6} & Concave & (50.00, 50.00) & (50.00, 50.00) & (48.00, 52.00) & (50.00, 50.00) \\ \cline{1-1}  & Convex & (50.00, 50.00) & (50.00, 50.00) & (49.50, 50.50) & (50.00, 50.00) \\ \cline{1-1}  & Line & (50.00, 50.00) & (50.00, 50.00) & (49.30, 50.70) & (50.00, 50.00) \\ \cline{1-1}  & Mixed & (42.47, 57.53) & (42.90, 57.10) & (37.70, 62.30) & (42.50, 57.50) \\ \cline{1-1}  & Disconnected & (45.00, 55.00) & (44.70, 55.30) & (44.10, 55.90) & (45.00, 55.00) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the results of KC measure with ASSIL; blue indicates performance of 5% worse than the competing algorithm, and red indicates performance of 5% better than the competing algorithm.