# A Two-Phase Approach for Single Container Loading with Weakly Heterogeneous Boxes
## 4 Conclusions  
In this work, we presented a two-phase approach to tackle the _container loading problem_. The idea behind our algorithm is to decompose the CLP into two subproblems, namely a three-dimensional \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{3-5}  & & & & **Avg** & **Best\({}^{\star}\)** \\ \hline BR2-051 & 96.47 & 96.17 & **96.56** & 94.37 & 95.11 \\ BR2-052 & 95.30 & **95.76** & 95.31 & 93.89 & 94.31 \\ BR2-053 & 92.27 & 93.18 & **94.06** & 93.71 & 94.06 \({}^{\star}\) \\ BR2-054 & 94.38 & 94.90 & **95.31** & 90.77 & 91.81 \\ BR2-055 & 93.03 & 93.60 & **94.33** & 90.92 & 91.55 \\ BR2-056 & 96.26 & 96.26 & **96.84** & 93.05 & 93.87 \\ BR2-057 & 96.46 & 96.41 & **97.14** & 92.09 & 93.28 \\ BR2-058 & **94.97** & 94.11 & **94.97** & 93.86 & 94.58 \\ BR2-059 & 96.63 & 97.13 & 96.72 & 94.60 & 95.86 \\ BR2-060 & **95.64** & 94.62 & **95.64** & 92.03 & 92.35 \\ BR2-061 & 93.03 & **94.80** & **94.80** & 90.51 & 91.77 \\ BR2-062 & 95.81 & 95.77 & **96.15** & 90.74 & 91.31 \\ BR2-063 & **93.80** & 92.84 & 93.54 & 91.43 & 92.99 \\ BR2-064 & **94.74** & 93.11 & 93.60 & 91.71 & 92.17 \\ BR2-065 & 94.78 & 95.39 & **96.17** & 93.90 & 94.00 \\ BR2-066 & 95.07 & 95.61 & **96.62** & 92.88 & 93.70 \\ BR2-067 & 96.04 & 95.67 & **96.84** & 92.41 & 93.50 \\ BR2-068 & 93.78 & 93.78 & **95.06** & 93.35 & 93.78 \\ BR2-069 & 91.13 & 91.72 & 92.34 & **92.50** & 93.01 \({}^{\star}\) \\ BR2-070 & 93.24 & 92.21 & **94.32** & 91.76 & 92.75 \\ BR2-071 & 95.17 & 95.37 & **96.04** & 93.71 & 94.71 \\ BR2-072 & 92.12 & 92.82 & **93.31** & 91.56 & 92.72 \\ BR2-073 & 93.42 & 93.25 & **94.44** & 92.57 & 93.68 \\ BR2-074 & 94.03 & 94.18 & **95.31** & 91.22 & 92.53 \\ BR2-075 & 94.87 & 95.16 & **95.47** & 92.60 & 93.71 \\ BR2-076 & 96.64 & 96.00 & **97.05** & 94.38 & 95.58 \\ BR2-077 & 95.18 & 96.13 & **96.58** & 94.25 & 95.04 \\ BR2-078 & 95.22 & 95.17 & **95.94** & 92.69 & 93.78 \\ BR2-079 & 96.46 & 96.24 & **96.98** & 94.14 & 94.53 \\ BR2-080 & 93.33 & 94.10 & **94.34** & 92.82 & 93.99 \\ BR2-081 & 92.68 & **93.70** & 93.67 & 92.72 & 93.28 \\ BR2-082 & 94.50 & 94.41 & **95.11** & 91.96 & 92.80 \\ BR2-083 & 96.45 & 95.83 & **96.61** & 93.11 & 93.87 \\ BR2-084 & 92.77 & 92.27 & **93.26** & 92.82 & 93.98 \({}^{\star}\) \\ BR2-085 & 96.85 & 96.90 & **97.24** & 95.21 & 95.61 \\ BR2-086 & 94.75 & 95.29 & **95.83** & 93.13 & 94.27 \\ BR2-087 & 93.76 & 94.23 & **94.84** & 90.57 & 91.18 \\ BR2-088 & 92.34 & 92.99 & **93.64** & 92.12 & 93.62 \\ BR2-089 & 89.58 & 89.96 & 90.57 & **92.58** & 93.04 \({}^{\star}\) \\ BR2-090 & 94.55 & **95.04** & **95.04** & 91.68 & 92.17 \\ BR2-091 & 94.53 & 95.16 & **95.64** & 92.89 & 94.10 \\ BR2-092 & 93.96 & 93.79 & **94.30** & 91.80 & 92.25 \\ BR2-093 & **95.35** & **95.35** & **95.35** & 93.38 & 94.88 \\ BR2-094 & 97.11 & 96.66 & **97.42** & 93.75 & 94.36 \\ BR2-095 & 94.98 & 95.84 & **95.85** & 94.00 & 94.00 \\ BR2-096 & 96.83 & 97.04 & **98.27** & 92.56 & 93.27 \\ BR2-097 & **95.53** & 94.64 & 95.01 & 92.78 & 93.92 \\ BR2-098 & 96.38 & 96.58 & **97.31** & 92.92 & 93.74 \\ BR2-099 & 96.84 & 96.83 & **97.33** & 93.56 & 95.08 \\ BR2-100 & 95.17 & **95.66** & 95.57 & 91.51 & 95.23 \\ \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 4: Results for group BR2 (cont.). problem of generating a set of blocks of boxes and a two-dimensional problem of loading a subset of blocks on the container floor. Constructive algorithms conducted the former task, while the _generate-and-solve_ hybrid framework dealt with the latter one. Computational experiments performed on weakly-heterogeneous datasets showed that our algorithm found new best solutions for 31 (out of 200) instances of groups BR1 and BR2. Its performance however deteriorated as the number of types of boxes increases.