## 3 Proposed Model
### PrefixSpan Algorithm
\begin{table}
\begin{tabular}{c c c} \hline
**Algorithm** & **Parameter** & **Selected Values** \\ \hline \multirow{3}{*}{PrefixSpan and MBHS} & HMS & 25 \\  & HMCR & 0.9 \\  & PAR & 0.1 \\  & Initial temperature & 100 \\ SA & Cooling rate & 0.99 \\  & Complete temperature & 0.01 \\  & Population size & 2000 \\ GA & Probability of crossover: Pc & 0.2 \\  & Probability of mutation: Pm & 0.08 \\  & Iteration & 200 \\ \hline \end{tabular}
\end{table} 
Table 14: The hyperparameters of the selected algorithms. ## 5 Conclusions and Future Work

We proposed the use of a PrefixSpan mining approach in conjunction with MBHS to identify sequential patterns in customer purchase data. Our experimental results revealed that the proposed method can rearrange product layouts by analyzing customers' shopping lists. This method was found to lead to increased profitability, higher total closeness ratings, and more efficient execution times compared with those of the original product layout. The proposed method was also found to be more effective than other comparable approaches as well as to be suitable for multi-objective pattern optimization in supermarkets regarding profit, closeness ratio, and consumer time efficiency. In future work, we will improve our multi-objective functions by using machine learning and developing a heuristic mining approach for the optimal solution. Conceptualization, J.K. and W.S. ; methodology, J.K. and W.S. ; software, J.K. and W.S. ; validation, J.K. and W.S. ; formal analysis, J.K. and W.S. ; investigation, J.K. and W.S. ; resources, J.K. and W.S. ; writing--original draft preparation, J.K.; writing--review and editing, J.K. and W.S. ; project administration, W.S. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. This research was financially supported in part by the researcher development project of the Department of Computer Science, Faculty of Science, Khon Kaen University, Thailand. The authors declare no conflict of interest. ## References

* [PERSON] and [PERSON] (1995) [PERSON]; [PERSON] Mining Sequential Patterns. In Proceedings of the Eleventh International Conference on Data Engineering, Washington, DC, USA, 6-10 March 1995, pp. 3-14. * [PERSON] and [PERSON] (1996) [PERSON]; [PERSON] Mining Sequential Patterns: Generalizations and Performance Improvements. In _Advances in Database Technology, Proceedings of the International Conference on Extending Database Technology EDBT '96, Munich, Germany, 26-31 March 2006_; [PERSON], [PERSON], [PERSON], [PERSON]; Springer: Berlin/Heidelberg, 1996; pp. 1-17. * [PERSON] et al. (2011) [PERSON]; [PERSON]; [PERSON] _Data Mining: Concepts and Techniques_, 3 rd ed. ; [PERSON]: Waltham, MA, USA, 2011. Figure 6: Comparison of the profit volume and execution time as the number of iterations increased: (**a**) profit volume of the algorithms; (**b**) execution time of the algorithms. * [PERSON] and [PERSON] (2010) [PERSON]; [PERSON] Applying a Two-Stage Simulated Annealing Algorithm for Shelf Space Allocation Problems. In Proceedings of the World Congress on Engineering, London, UK, 30 June-2 July 2010; Volume 30, pp. 2376-2380. * [PERSON] and [PERSON] (2015) [PERSON]; [PERSON] [PERSON] Developing Visibility Analysis for a Retail Store: A Pilot Study in a Bookstore. _Environ. Plan. B Plan. Des._**2015**, 42, 95-109. [CrossRef]
* [PERSON] et al. (2019) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Personalized Market Basket Prediction with Temporal Annotated recurring Sequences. _IEEE Trans. Knowl. Data Eng._**2019**, 31, 2151-2163. [CrossRef]
* [PERSON] et al. (2018) [PERSON]; [PERSON]; [PERSON]; [PERSON] Large Scale Product Recommendation of Supermarket Ware Based on Customer Behaviour Analysis. _Big Data Cogn. Comput._**2018**, 2, 11. [CrossRef]
* [PERSON] et al. (2018) [PERSON]; [PERSON]; [PERSON] Survey on Customer Centric Sales Analysis and Prediction.