# Evolutionary Algorithms for Optimization Sequence of Cut in the Laser Cutting Path Problem
## 4 Overview of Application of ABRKGA to LCPP
### An Eulerian Heuristic to Generate Improved Individuals for LCPP
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Instances**}} & \multicolumn{2}{c}{**GAP**} & \multicolumn{4}{c}{**GAP**} \\  & **Fitness (\%)** & **Time (\%)** & **Time (\%)** & **Fitness (\%)** & **Time (\%)** & **Time (\%)** \\ \hline albano\_[0.997] & \(0.04\%\) & \(-101.95\) & \(32.97\%\) & \(-3.65\%\) & \(-176.00\) & \(58.67\%\) \\ albano\_[0.998] & \(-0.17\%\) & \(-106.44\) & \(34.42\%\) & \(-3.59\%\) & \(-176.76\) & \(58.92\%\) \\ albano\_[0.999] & \(-0.22\%\) & \(-112.68\) & \(36.44\%\) & \(-4.16\%\) & \(-181.65\) & \(60.55\%\) \\ blaz1\_[0.997] & \(1.03\%\) & \(7.36\) & \(-17.10\%\) & \(0.22\%\) & \(-5.13\) & \(12.79\%\) \\ blaz1\_[0.998] & \(1.03\%\) & \(7.08\) & \(-16.45\%\) & \(0.22\%\) & \(-4.46\) & \(11.13\%\) \\ blaz2\_[0.999] & \(1.03\%\) & \(5.00\) & \(-11.62\%\) & \(0.15\%\) & \(-5.30\) & \(13.23\%\) \\ blaz2\_[0.997] & \(0.87\%\) & \(122.07\) & \(-69.98\%\) & \(0.29\%\) & \(67.81\) & \(-76.84\%\) \\ blaz2\_[0.998] & \(0.92\%\) & \(48.69\) & \(-27.91\%\) & \(0.12\%\) & \(26.52\) & \(-30.06\%\) \\ blaz2\_[0.999] & \(0.95\%\) & \(55.79\) & \(-31.98\%\) & \(-0.11\%\) & \(37.00\) & \(-41.93\%\) \\ blaz3\_[0.997] & \(0.20\%\) & \(408.29\) & \(-207.00\%\) & \(0.46\%\) & \(697.74\) & \(-343.92\%\) \\ blaz3\_[0.998] & \(-0.21\%\) & \(213.07\) & \(-108.02\%\) & \(0.24\%\) & \(373.82\) & \(-184.25\%\) \\ blaz3\_[0.999] & \(-0.49\%\) & \(125.50\) & \(-63.63\%\) & \(-0.26\%\) & \(158.83\) & \(-78.29\%\) \\ dispel1\_[0.997] & \(0.23\%\) & \(-33.86\) & \(71.73\%\) & \(-0.26\%\) & \(-22.38\) & \(46.40\%\) \\ dispel1\_[0.998] & \(0.19\%\) & \(-34.16\) & \(72.37\%\) & \(-0.28\%\) & \(-22.80\) & \(47.27\%\) \\ dispel1\_[0.999] & \(0.03\%\) & \(-34.63\) & \(73.36\%\) & \(-0.46\%\) & \(-23.56\) & \(48.85\%\) \\ dispel2\_[0.997] & \(-0.91\%\) & \(-10.77\) & \(45.52\%\) & \(-0.10\%\) & \(-20.31\) & \(52.89\%\) \\ dispel2\_[0.998] & \(-0.92\%\) & \(-11.08\) & \(46.87\%\) & \(-0.20\%\) & \(-20.77\) & \(54.09\%\) \\ dispel2\_[0.999] & \(-1.12\%\) & \(-11.56\) & \(48.87\%\) & \(-0.25\%\) & \(-21.37\) & \(55.64\%\) \\ fu\_[0.997] & \(-2.79\%\) & \(-39.70\) & \(74.60\%\) & \(-1.96\%\) & \(-34.01\) & \(80.34\%\) \\ fu\_[0.998] & \(-2.79\%\) & \(-39.56\) & \(74.34\%\) & \(-2.07\%\) & \(-34.26\) & \(80.94\%\) \\ fu\_[0.999] & \(-2.76\%\) & \(-39.67\) & \(74.55\%\) & \(-2.00\%\) & \(-34.20\) & \(80.79\%\) \\ inst\_10 pol\_[0.997] & \(1.26\%\) & \(-22.98\) & \(54.69\%\) & \(0.09\%\) & \(-1.58\) & \(4.18\%\) \\ inst\_10 pol\_[0.998] & \(1.28\%\) & \(-23.01\) & \(54.76\%\) & \(0.19\%\) & \(-0.27\) & \(0.71\%\) \\ inst\_10 pol\_[0.999] & \(1.30\%\) & \(-23.83\) & \(56.71\%\) & \(0.25\%\) & \(-0.07\) & \(0.20\%\) \\ inst\_16 pol\_[0.997] & \(0.52\%\) & \(-43.89\) & \(72.43\%\) & \(-0.87\%\) & \(-67.10\) & \(34.16\%\) \\ inst\_16 pol\_[0.998] & \(0.34\%\) & \(-44.14\) & \(72.84\%\) & \(-1.00\%\) & \(-64.85\) & \(33.02\%\) \\ inst\_16 pol\_[0.999] & \(0.42\%\) & \(-44.72\) & \(73.82\%\) & \(-0.99\%\) & \(-65.33\) & \(33.26\%\) \\ inst\_2 pol\_[0.997] & \(-1.13\%\) & \(-2.00\) & \(25.39\%\) & \(0.00\%\) & \(-3.74\) & \(56.66\%\) \\ inst\_2 pol\_[0.998] & \(-1.13\%\) & \(-2.27\) & \(28.88\%\) & \(0.00\%\) & \(-3.88\) & \(57.84\%\) \\ inst\_2 pol\_[0.999] & \(-1.13\%\) & \(-2.86\) & \(36.28\%\) & \(0.00\%\) & \(-4.05\) & \(60.40\%\) \\ inst\_3 pol\_[0.997] & \(0.00\%\) & \(-3.42\) & \(41.78\%\) & \(0.00\%\) & \(-5.14\) & \(51.10\%\) \\ inst\_3 pol\_[0.998] & \(0.00\%\) & \(-3.61\) & \(44.15\%\) & \(0.00\%\) & \(-5.24\) & \(52.17\%\) \\ inst\_3 pol\_[0.999] & \(0.00\%\) & \(-3.66\) & \(44.79\%\) & \(0.00\%\) & \(-5.34\) & \(53.10\%\) \\ inst\_4 pol\_[0.997] & \(0.37\%\) & \(-10.26\) & \(63.12\%\) & \(0.05\%\) & \(-5.05\) & \(36.42\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: GAP comparison _e_-BRKGA x _e_-ABRKGA to connected (C) and separated (S) instances. ## References

* [PERSON] (2016) [PERSON]; [PERSON] Approaches to tackle the nesting problems. In _Artificial Intelligence Perspectives in Intelligent Systems_; Springer: Berlin/Heidelberg, Germany, 2016; pp. 285-295.