## 6 Conclusions and Future Works  
This study proposed a hybrid algorithm, the ABC algorithm with the Pareto-based approach, which combines the advantages of both algorithms to optimize the multi-objective three-dimensional single-container-loading problem. A mathematical model was successfully developed using this approach, and the \(\overset{\sim}{\mathrm{C}}\) metric method was used to identify key parameter values to reduce the computational burden. The performance of the proposed algorithm was compared to that of an exact method, and the results indicated that the proposed algorithm provides the same objective values as the exact method for small-scale problems within a satisfactory computer runtime. However, for more complex problems, the exact method may not be able to solve the problem within an acceptable computational runtime, whereas the ABC algorithm with the Pareto-based approach still delivers a solution within a reasonable computational runtime. Moreover, the presented algorithm was evaluated using the Loh and Nee (LN) test cases, demonstrating superior performance compared to other heuristic and meta-heuristic methods. The proposed algorithm was also tested on a challenging case study involving complex real-world problems, and the results showed that the algorithm effectively solved these problems within a reasonable computational runtime. These findings demonstrate that the proposed algorithm is comparable to the best-performing heuristic algorithm and can be applied to real-world problems.  
However, in future directions, the practical limitations of the problem will tend to become significantly more complex. Therefore, this meta-heuristic method may need to be redesigned to support, for example, a hybrid of meta-heuristic methods, or a two-stage approach using clustering methods such as k-means can be considered to group box sizes before considering the order of packing for containers while taking into account the center of gravity during the loading process. Additionally, keeping the computation time as low as possible can further improve the efficiency of the proposed algorithm.  
Conceptualization, S.P. and K.L.; methodology, S.P. and K.L.; software, S.P. and K.L.; validation, S.P. and C.B.; formal analysis, S.P. and N.C.; investigation, S.P., C.B. and N.C.; data curation, S.P. and K.L.; writing--original draft preparation, S.P., K.L., N.C. and C.B.; writing--review and editing, S.P. and K.L.; visualization, S.P. All authors have read and agreed to the published version of the manuscript.  
This work was supported by a Research and Researchers for Industries (RRi), awarded by the National Research Council of Thailand (NRCT) (grant number: PHD59I0022), and the Supply Chain and Engineering Management Research Unit, Chiang Mai University.  
Not applicable.  
Data Availability StatementData in this research paper will be shared upon request with the corresponding author.  
The authors would like to thank a Research and Researchers for Industries (RRi) awarded by the National Research Council of Thailand (NRCT) (grant number: PHD59I0022) and this research work was partially supported by Chiang Mai University, Thailand.  
The authors declare no conflict of interest.