## 4 Experimental Results and Evaluation
### Experiment B
\begin{table}
\begin{tabular}{c} **Total Empty** \\ **Space** \\ **(M2)** \\ \end{tabular} \\ \hline
1 & P01/1 & 309 & 58\% & 309 & 58\% & 309 & 58\% \\
2 & P01/2 & 309 & 85\% & 309 & 85\% & 309 & 85\% \\
3 & P02/1 & 51 & 75\% & 51 & 75\% & 51 & 75\% \\
4 & P02/2 & 51 & 91\% & 51 & 91\% & 51 & 91\% \\
5 & P07/1 & 1458 & 29\% & 1458 & 29\% & 1458 & 29\% \\
6 & P08/1 & 265 & 36\% & 265 & 36\% & 265 & 36\% \\
7 & P08/2 & 265 & 50\% & 265 & 50\% & 265 & 50\% \\
8 & P10/1 & 1268 & 22\% & 1268 & 22\% & 1268 & 22\% \\
9 & P10/2 & 1268 & 65\% & 1268 & 65\% & 1268 & 65\% \\
10 & P10/3 & 1268 & 42\% & 1268 & 42\% & 1268 & 42\% \\ \hline \end{tabular}
\end{table} 
Table 11: Comparison of optimal solutions given by the LINGO solver and ABC algorithm with Pareto-based approach. \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Case Study**} & \multicolumn{2}{c}{**Computation Runtimes (Average Time (s))**} \\ \cline{3-4}  & & & **LINGO** & **ABC with Pareto** \\ \hline
1 & P01/1 & 0.01 & 11 \\
2 & P01/2 & 0 & 12 \\
3 & P02/1 & 0 & 12 \\
4 & P02/2 & 0 & 11 \\
5 & P07/1 & 0 & 98 \\
6 & P08/1 & 97,204 & 73 \\
7 & P08/2 & 88,126 & 72 \\
8 & P10/1 & 112,063 & 106 \\
9 & P10/2 & 98,762 & 118 \\
10 & P10/3 & 99,211 & 116 \\ \hline \end{tabular}
\end{table} 
Table 12: Computation runtimes of the LINGO solver and ABC algorithm with Pareto-based approach. To ensure a comprehensive and unbiased evaluation of our proposed algorithms, we conducted a comparative study that included both heuristics and meta-heuristics from scholarly works. In addition, we integrated widely accepted meta-heuristic methods, such as the genetic algorithm and tabu search, into our evaluation. Furthermore, we included other heuristics that have been developed to address the same problem, such as the spatial representation, layering algorithm, and development heuristics, for comparative analysis. Table 14 presents the results of the relative improvement (RI) of different approaches. It has been observed that the proposed method outperforms its competitors only when the RI effect is positive and negative in the worst-case scenario. For the case of zero, it provides the same result. In comparison with the studies by [PERSON] et al., [PERSON] and [PERSON], and [PERSON] and [PERSON], our proposed algorithm obtained better results with positive RI results, except in some cases for which our method yields the same results. Regarding [PERSON] et al. 's study, our approach yielded superior or comparable outcomes, except for LN02, where our method exhibited a more effective utilization of volume but a lower efficiency in terms of the number of boxes left. Compared with [PERSON] and [PERSON]'s research, our method generated better or similar results, except for one case. In the case of LN02, we experienced a loss both in the number of boxes left and volume utilization. In summary, the results of the reliability index (RI) analysis clearly demonstrate that the proposed method outperformed or matched other methods in 14 out of 15 case studies, with only 1 case performing worse than some studies. Therefore, based on these findings, it can be concluded that the proposed method represents the best-performing approach.