# A Two-Phase Approach for Single Container Loading with Weakly Heterogeneous Boxes
## 3 Computational Experiments
### Numerical Results
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multirow{2}{*}{**CLTRS [4]**} & \multirow{2}{*}{**ID-GLTS [7]**} & \multirow{2}{*}{**BSG-VCS [36]**} & \multicolumn{2}{c}{**BLHM**} \\ \cline{5-6}  & & & & **Avg** & **Best\({}^{*}\)** \\ \hline BR1-001 & 93.83 & 93.80 & 93.53 & **95.12** & 95.83 \({}^{*}\) \\ BR1-002 & 95.45 & 94.94 & **96.01** & 95.24 & 97.67 \({}^{*}\) \\ BR1-003 & 91.03 & 91.03 & 91.03 & **92.11** & 92.67 \({}^{*}\) \\ BR1-004 & 91.84 & 91.84 & 91.84 & **94.55** & 95.26 \({}^{*}\) \\ BR1-005 & **95.14** & **95.14** & **95.14** & 93.85 & 94.63 \\ BR1-006 & 95.72 & 94.63 & **96.02** & 93.20 & 93.49 \\ BR1-007 & **94.14** & 93.57 & 94.03 & 93.74 & 94.60 \({}^{*}\) \\ BR1-008 & 97.05 & 97.05 & **97.18** & 93.88 & 94.53 \\ BR1-009 & 91.57 & 90.62 & **91.87** & 87.61 & 87.61 \\ BR1-010 & **94.81** & 94.67 & **94.81** & 93.10 & 93.20 \\ BR1-011 & 91.49 & 91.84 & **92.54** & 90.37 & 91.11 \\ BR1-012 & **94.08** & 93.67 & 93.67 & 91.45 & 91.95 \\ BR1-013 & 97.14 & 97.43 & **97.60** & 95.34 & 95.58 \\ BR1-014 & 94.37 & 94.63 & **94.70** & 91.30 & 91.68 \\ BR1-015 & 95.38 & 96.74 & **96.96** & 92.84 & 93.29 \\ BR1-016 & 95.75 & 95.55 & **96.20** & 93.14 & 94.21 \\ BR1-017 & 97.80 & 97.29 & **97.97** & 96.21 & 96.40 \\ BR1-018 & 88.49 & 88.49 & 88.49 & **88.95** & 89.57 \({}^{*}\) \\ BR1-019 & 94.73 & 94.73 & **95.13** & 94.40 & 94.81 \\ BR1-020 & 94.20 & **95.23** & 94.30 & 91.53 & 92.46 \\ BR1-021 & **94.69** & 93.77 & **94.69** & 93.47 & 93.48 \\ BR1-022 & **95.34** & 94.46 & 94.73 & 92.58 & 93.89 \\ BR1-023 & 94.15 & 94.67 & 94.69 & **96.53** & 96.54 \({}^{*}\) \\ BR1-024 & 90.75 & 91.18 & 91.42 & **91.51** & 91.63 \({}^{*}\) \\ BR1-025 & 94.83 & **95.25** & 95.17 & 93.27 & 94.26 \\ BR1-026 & **93.81** & **93.81** & **93.81** & 93.17 & 93.67 \\ BR1-027 & 91.67 & 91.95 & 92.54 & **93.60** & 93.60 \({}^{*}\) \\ BR1-028 & 93.84 & 93.46 & **94.73** & 91.46 & 92.53 \\ BR1-029 & 93.95 & 93.92 & **94.45** & 93.52 & 94.45 \({}^{*}\) \\ BR1-030 & 97.54 & 97.13 & **98.09** & 94.43 & 95.08 \\ BR1-031 & 95.54 & 94.65 & **95.67** & 92.84 & 93.32 \\ BR1-032 & **97.01** & **97.01** & **97.01** & 94.84 & 95.07 \\ BR1-033 & 97.63 & 97.55 & **97.75** & 94.17 & 94.88 \\ BR1-034 & 94.62 & 94.62 & **95.47** & 92.66 & 92.87 \\ BR1-035 & 93.60 & 94.05 & **94.14** & 91.74 & 92.30 \\ BR1-036 & **95.47** & 95.36 & 94.68 & 94.05 & 94.51 \\ BR1-037 & 95.16 & 94.97 & **95.42** & 92.65 & 93.16 \\ BR1-038 & 90.64 & 90.11 & 90.71 & **90.92** & 91.30 \({}^{*}\) \\ BR1-039 & 96.40 & 96.48 & 96.48 & 94.07 & 94.19 \\ BR1-040 & **94.52** & 93.96 & 93.98 & 92.96 & 93.53 \\ BR1-041 & 94.55 & 94.97 & **95.39** & 93.89 & 94.55 \\ BR1-042 & 94.24 & 94.86 & **95.29** & 93.47 & 94.37 \\ BR1-043 & 95.61 & 95.75 & **96.18** & 83.98 & 86.02 \\ BR1-044 & 87.97 & **88.21** & **88.21** & 83.97 & 84.03 \\ BR1-045 & **96.38** & 96.23 & **96.38** & 93.76 & 94.12 \\ BR1-046 & **94.13** & **94.13** & **94.13** & 90.80 & 91.27 \\ BR1-047 & 95.39 & 96.16 & **96.29** & 92.83 & 93.56 \\ BR1-048 & **95.95** & 95.45 & 95.49 & 93.95 & 95.65 \\ BR1-049 & **95.03** & 94.29 & 94.77 & 92.61 & 94.10 \\ BR1-050 & 97.55 & 97.76 & **98.16** & 94.45 & 95.56 \\ \hline \hline \end{tabular} \({}^{*}\) The best solution of BLHM over 10 runs is better than the solutions found by the other algorithms.  
\end{table} 
Table 1: Results for group BR1. Concerning group BR2, BLHM obtained the best solutions for seven (out of 100) instances. The average solution of CLTRS, ID-GLTS, BSG-VCS, and BLHM was 94.73, 94.85, 95.38, and 92.52