## 3 The Algorithm
### SaNSDE Algorithm
The preliminary results presented in this paper show that combining a self-adaptive mechanism with neighborhood search in the Differential Evolution approach leads to an effective algorithm in comparison with other competitive algorithms. To apply the proposed algorithm in industrial settings, a further study on the scalability of the proposed algorithm with respect to the problem size needs to be conducted. In this paper, we applied the proposed method to study the effectiveness of different evolutionary algorithms for sequential production processes. As we limited our scope to sequential processes in this paper to illustrate the solution methodology, the computational experiences of these results hold for sequential processes. However, the application of the proposed method is not limited to sequential production processes. The general problem formulation for planning processes in CPSs proposed in this paper can be applied to a variety of production processes. Based on the reasoning in the Discussion section of this paper, the proposed algorithm has the potential to be extended to deal with other types of production processes. Tailoring the proposed algorithm to deal with other types of production processes and studying its effectiveness are nontrivial interesting future research directions. Another future research direction is to develop other evolutionary algorithms and compare their effectiveness with respect to the algorithms studied in this paper. This research was supported in part by the National Science and Technology Council, Taiwan, under grant NSTC 111-2410-H-324-003. Not applicable. The original data presented in the study are openly available in [Planning_CPS] at [[[https://drive.google.com/drive/folders/1_5](https://drive.google.com/drive/folders/1_5) bMvhjvVhTDN0 yunbFNQ4 HasalCu8b4?usp=sharing]([https://drive.google.com/drive/folders/1_5](https://drive.google.com/drive/folders/1_5) bMvhjvVhTDN0 yunbFNQ4 HasalCu8b4?usp=sharing)] (accessed on 29 June 2024). The author declares no conflicts of interest. ## References

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