# An Improved Variable Neighborhood Search for the Reconfigurable Assembly Line Reconfiguring Problem
## 5 Proposed IVNS-RALRP
### Solution Evaluation
Although this algorithm takes a few extra seconds to run, the reconfiguration phase of the assembly line does not require real-time responsiveness. The practical engineering requirement is to achieve higher quality results within an acceptable timeframe. Hence, the authors can conclude that the proposed IVNS-RALRP is effective in solving the RALRP. Figure 7: Box plots of cost \(r(y)\) of IVNS-RALRP, GA, TS, SA and PSO. ## 8 Conclusions

This paper proposed a data structure about RAL and an IVNS-RALRP algorithm to solve RALRP. The major contributions of this paper are summarized as follows. 1. A MILP is developed to formulate the RALRP for product update. 2. An efficient data structure is proposed to model product and assembly line, which includes more detailed process information. 3. An improved VNS is proposed to reduce reconfiguration cost for Reconfigurable Assembly Line. The reconfiguration of RAL is an effective process for addressing product update within a product family. During the reconfiguration phase, it is necessary not only to allocate operations to the old assembly line but also to select corresponding resources. In practical cases, improvements in various aspects of IVNS-RALRP have proven effective. Furthermore, the solving performance of IVNS-RALRP surpasses that of other heuristic algorithms. Therefore, in theory, it is clear that IVNS-RALRP is an outstanding algorithm for solving RALRP, and it is effectively used in reconfiguration phase of RAL for product update. In practical engineering production, the reconfiguration phase of RAL not only involves reallocating operations, but also selecting specific manufacturing resources. For production management, excessive resource investment signifies needless waste. Moreover, reducing reconfiguration time means production can be brought forward, thereby increasing capacity. Therefore, what this paper contributes to the production management in a broader sense is an effective planning tool that reduces reconfiguration costs and increases capacity. Since more information about manufacturing resources, such as the size of it and Mean Time Between Failure, is not considered, this method may be limited. Therefore, in the future research, more real practical information will be addressed in depth. In addition, there is still potential improvement in computation efficiency and optimality by introducing new operators and characteristics of other algorithms. Conceptualization, X.Z. and Z.X. ; methodology, X.Z. and J.W. ; formal analysis, X.Y. ; writing--original draft preparation, X.Z. ; writing--review and editing, Z.X. ; visualization, J.W. ; project administration, Z.X. All authors have read and agreed to the published version of the manuscript. This work is supported by the National Defense Basic Scientific Research Program of China under Grant No.JCKY2021208B003. Not applicable. Data Availability Statement: Data are contained within the article. We would like to acknowledge the anonymous reviewers and the editor for their suggestions, which improved the quality of this paper. The authors declare no conflicts of interest. ## Appendix A

### Dataset

Reconfigurable Assembly Line Reconfiguring Problem Dataset associated with this work can be found, in the online version, at [[https://github.com/zhuxiaojunstu/RALRP_dataset](https://github.com/zhuxiaojunstu/RALRP_dataset)]([https://github.com/zhuxiaojunstu/RALRP_dataset](https://github.com/zhuxiaojunstu/RALRP_dataset)) (accessed on 7 October 2024). ### Parameter Calibration of GA

Three parameters that are employed in GA are population size (\(ps\)), crossover probability (\(cp\)), and mutation probability (\(mp\)). To determine the optimal parameters combination of GA, we carry out the Taguchi method of DOE on case No. 1 and No. 4. The four levels ofeach parameter are shown in Table A1. GA is executed 10 times independently employing each parameters combination. We consider the average cost as the response variable due to its relative importance to engineering application.