# Optimizing Perishable Product Supply Chain Network Using Hybrid Metaheuristic Algorithms
## 3 Solution Algorithms
### Hmpga-Vns Algorithm
It can be challenging to evaluate the quality of solutions obtained or predict the behavior of the algorithms across different problem instances. * The effectiveness of the hybrid metaheuristic approaches presented in this paper relies on the coder's proficiency in finding the initial solution. For future research, the following points are recommended:

* Enhancing the reliability and validity of the findings by incorporating realistic scenario datasets that are relevant to the PPSCN. * Exploring the exact methods such as the Lagrangian relaxation methods or Benders decomposition to achieve more precise results. * Investigating the application of new metaheuristic algorithms or developing novel heuristics to further optimize the results. Conceptualization, L.P.; Methodology L.P.; Software, L.P., and L.L. ; Validation, M.S. and; Formal analysis, L.P. and; Investigation, L.P.; Resources L.L. ; Data curation L.L. ; Writing--original draft preparation, L.P.; Writing--review and editing, L.P. and M.S. ; Visualization, L.P.; Supervision, L.L. and M.S. ; Funding acquisition, L.L. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China, grant number 72004062. Not applicable. The datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request. The authors would like to sincerely thank the editors, the anonymous reviewers, and the proofreaders for their constructive comments and suggestions. The authors declare no conflict of interest. ## References

* [PERSON] and [PERSON] (2006) [PERSON]; [PERSON] Information sharing to improve retail product freshness of perishables. _Prod. Oper. Manag._**2006**, _15_, 57-73. [CrossRef]
* [PERSON] and [PERSON] (2005) [PERSON]; [PERSON] RFID will help keep perishables fresh. _RFID J._**2005**. Available online: [[http://www.rfidjournal.com/article/article/article/view/1775/1/1/](http://www.rfidjournal.com/article/article/article/view/1775/1/1/)]([http://www.rfidjournal.com/article/article/article/view/1775/1/1/](http://www.rfidjournal.com/article/article/article/view/1775/1/1/)) (accessed on 12 June 2023). * [PERSON] et al. (2018) [PERSON]; [PERSON]; [PERSON]; [PERSON] A location-inventory supply chain network model using two heuristic algorithms for perishable products with fuzzy constraints. _Comput. Ind. Eng._**2018**, _119_, 338-352. [CrossRef]
* [PERSON] and [PERSON] (2009) [PERSON]; [PERSON] Analyses on the Way of Changing the Growth Mode of Circulation Economy. _Asian Soc. Sci._**2009**, \(5\), 53. [CrossRef]
* [PERSON] et al. (2021) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Sustainable supply chain management for perishable products in emerging markets: An integrated location-inventory-routing model. _Transp. Res. Part E Logist. Transp. Rev._**2021**, _150_, 19. [CrossRef]
* [PERSON] et al. (2022) [PERSON] [PERSON]; [PERSON]; [PERSON]; [PERSON] The Design of a Multi-Period and Multi-Echelon Perishable Goods Supply Network under Uncertainty. _Sustainability_**2022**, _14_, 2472. [CrossRef]
* [PERSON] et al. (2023) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Developing a Conceptual Framework Model for Effective Perishable Food Cold-Supply-Chain Management Based on Structured Literature Review. _Sustainability_**2023**, _15_, 4907. [CrossRef]* [PERSON] et al. (2022) [PERSON]; [PERSON]; [PERSON]; [PERSON] Logistics Center Location-Inventory-Routing Problem Optimization: A Systematic Review Using PRISMA Method. _Sustainability_**2022**, _14_, 15853. [CrossRef]
* [PERSON] et al. (2023) [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON] A Hybrid Marine Predator Sine Cosine Algorithm for Parameter Selection of Hybrid Active Power Filter. _Mathematics_**2023**, _11_, 598. [CrossRef]
* [PERSON] et al. (2019) [PERSON]; [PERSON]; [PERSON] Designing a sustainable supply chain network integrated with vehicle routing: A comparison of hybrid swarm intelligence metaheuristics. _Comput. Oper. Res._**2019**, _110_, 220-235.