# 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 c c c c} \hline \hline \multirow{2}{*}{**Instances**} & \multicolumn{2}{c}{**Best**} & \multicolumn{2}{c}{**Worst**} & \multicolumn{2}{c}{**Average**} & \multicolumn{2}{c}{**Std. Deviation**} & \multicolumn{2}{c}{**Variation**} \\  & **Fitness** & **Exec.** & **Fitness** & **Exec.** & **Fitness** & **Exec.** & **Fitness** & **Exec.** & **Fitness** & **Exec.** & **Fitness** & **Exec.** \\ \hline \hline  & 53.90 & 88.38 & 54.05 & 89.77 & 53.96 & 99.07 & 0.05 & 10.07 & 0.09 & 10.17 \\ fu & 23.82 & 185.16 & 23.95 & 167.60 & 23.89 & 184.48 & 0.04 & 8.75 & 0.15 & 4.75 \\ inst\_10 pol & 127.00 & 106.61 & 127.38 & 83.24 & 127.15 & 90.21 & 0.14 & 8.70 & 0.11 & 9.64 \\ inst\_16 pol & 76.75 & 127.63 & 76.90 & 155.89 & 76.83 & 132.18 & 0.07 & 9.35 & 0.09 & 7.07 \\ inst\_2 pol & 33.13 & 22.73 & 33.13 & 22.73 & 33.13 & 24.08 & 0.00 & 1.36 & 0.00 & 5.63 \\ inst\_3 pol & 39.25 & 28.00 & 39.25 & 28.00 & 39.25 & 27.29 & 0.00 & 0.81 & 0.00 & 2.96 \\ inst\_4 pol & 57.38 & 33.77 & 57.38 & 33.77 & 57.38 & 34.24 & 0.00 & 0.84 & 0.00 & 2.47 \\ inst\_5 pol & 69.63 & 44.46 & 69.63 & 44.46 & 69.63 & 42.25 & 0.00 & 1.51 & 0.00 & 3.58 \\ inst\_6 pol & 81.75 & 52.45 & 81.75 & 52.45 & 81.75 & 51.25 & 0.00 & 2.27 & 0.00 & 4.44 \\ inst\_7 pol & 96.88 & 65.46 & 97.00 & 60.37 & 96.98 & 63.25 & 0.04 & 4.48 & 0.04 & 7.08 \\ inst\_spol & 105.75 & 72.59 & 106.00 & 68.80 & 105.82 & 67.04 & 0.09 & 3.05 & 0.08 & 4.55 \\ inst\_9 pol & 124.00 & 103.57 & 124.25 & 73.90 & 124.06 & 82.43 & 0.09 & 8.76 & 0.07 & 10.63 \\ inst\_26 pol & 160.50 & 306.98 & 166.74 & 306.34 & 164.00 & 305.81 & 1.91 & 1.27 & 1.16 & 0.42 \\ rco1 & 140.28 & 116.84 & 141.14 & 132.15 & 140.77 & 122.01 & 0.30 & 10.78 & 0.21 & 8.83 \\ rco2 & 270.71 & 301.86 & 271.90 & 301.45 & 271.41 & 301.52 & 0.35 & 0.32 & 0.13 & 0.10 \\ rco3 & 394.67 & 302.78 & 398.84 & 302.69 & 396.89 & 302.42 & 1.22 & 0.40 & 0.31 & 0.13 \\ shapes2 & 215.26 & 293.88 & 217.22 & 301.44 & 216.07 & 297.58 & 0.62 & 4.67 & 0.28 & 1.57 \\ shapes4 & 427.55 & 302.73 & 436.58 & 303.90 & 430.10 & 303.17 & 3.14 & 0.53 & 0.73 & 0.17 \\ spfc & 144.11 & 236.94 & 144.92 & 212.40 & 144.38 & 227.10 & 0.27 & 13.54 & 0.19 & 5.96 \\ trousers & 305.90 & 312.92 & 308.70 & 309.30 & 307.52 & 311.11 & 0.80 & 2.24 & 0.26 & 0.72 \\ \hline Exec. time (avg) & & 172.82 & & 169.93 & & 170.70 & & & & \\ \hline \hline  & & & & & & & & & & & \\ \end{tabular}
\end{table} 
Table 7: \(e\)-BRKGA applied to the connected set of instances (C). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instances**} & \multicolumn{2}{c}{**Best**} & \multicolumn{2}{c}{**Worst**} & \multicolumn{2}{c}{**Average**} & \multicolumn{2}{c}{**Std. Deviation**} & \multicolumn{2}{c}{**Variation**} \\  & **Fitness** & **Exec. ** & **Fitness** & **Exec. ** & **Fitness** & **Exec. ** & **Fitness** & **Exec. ** & **Fitness** & **Exec. ** \\ \hline \hline  & 101.38 & 309.54 & 106.48 & 310.74 & 102.45 & 309.21 & 1.99 & 0.95 & 1.94 & 0.31 \\  & blaz1 & 156.25 & 44.97 & 157.86 & 38.89 & 156.71 & 43.02 & 0.51 & 2.31 & 0.32 & 5.37 \\  & blaz2 & 271.97 & 169.48 & 278.18 & 181.48 & 275.21 & 174.44 & 2.24 & 9.97 & 0.81 & 5.71 \\  & blaz3 & 423.04 & 192.78 & 426.93 & 190.56 & 424.83 & 197.24 & 1.25 & 13.47 & 0.29 & 6.83 \\  & dighe1 & 71.05 & 40.65 & 71.53 & 55.55 & 71.22 & 47.21 & 0.18 & 5.42 & 0.26 & 11.48 \\  & dighe2 & 53.94 & 23.29 & 54.26 & 22.96 & 54.06 & 23.65 & 0.08 & 1.52 & 0.15 & 6.41 \\  & fu & 23.89 & 56.28 & 24.13 & 47.34 & 24.00 & 53.21 & 0.06 & 2.70 & 0.24 & 5.07 \\ inst\_10 pol & 128.69 & 40.99 & 129.50 & 41.32 & 129.01 & 42.02 & 0.23 & 3.33 & 0.18 & 7.94 \\ inst\_16 pol & 77.73 & 58.66 & 78.25 & 62.17 & 77.95 & 60.59 & 0.18 & 3.84 & 0.24 & 6.34 \\ inst\_2 pol & 33.13 & 6.12 & 33.13 & 6.12 & 33.13 & 7.87 & 0.