# An Improved Variable Neighborhood Search for the Reconfigurable Assembly Line Reconfiguring Problem
## 5 Proposed IVNS-RALRP
### Solution Evaluation
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{4}{c}{**IVNS-RALRP**} & \multicolumn{4}{c}{**GA**} & \multicolumn{4}{c}{**TS**} & \multicolumn{4}{c}{**SA**} & \multicolumn{4}{c}{**PSO**} \\ \cline{2-19}  & \(R\) & \(\overline{r}\) & \(S\) & \(\overline{t}\) & \(R\) & \(\overline{r}\) & \(S\) & \(\overline{t}\) & \(R\) & \(\overline{r}\) & \(S\) & \(\overline{t}\) & \(R\) & \(\overline{r}\) & \(S\) & \(\overline{t}\) & \(R\) & \(\overline{r}\) & \(S\) & \(\overline{t}\) \\ \hline
1 & **31** & 31.3 & 0.21 & 6.52 & **31** & 31.5 & 0.25 & 3.83 & **31** & 31.3 & 0.21 & 5.13 & **31** & 31.9 & 0.5 & 4.45 & **31** & 31.8 & 0.36 & 3.96 \\
2 & **38** & 39.0 & 0.80 & 6.85 & 39 & 40.5 & 2.05 & 3.86 & **38** & 39.2 & 1.16 & 5.18 & 39 & 40.8 & 2.4 & 4.49 & 39 & 41.1 & 3.69 & 4.03 \\
3 & **43** & 43.8 & 0.56 & 7.06 & **43** & 44.3 & 1.61 & 3.94 & 44 & 45.5 & 1.45 & 5.29 & **43** & 44.6 & 1.6 & 4.6 & 44 & 45.2 & 1.96 & 4.15 \\
4 & **108** & 109.5 & 1.45 & 12.99 & 110 & 115.0 & 8.20 & 5.51 & **108** & 111.6 & 11.04 & 6.82 & 111 & 115.4 & 8.4 & 6.22 & 110 & 115.7 & 7.61 & 5.75 \\
5 & **113** & 114.1 & 1.69 & 13.40 & **113** & 116.8 & 7.76 & 5.63 & **113** & 117.3 & 8.01 & 6.97 & **113** & 117.2 & 7.4 & 6.38 & 114 & 117.5 & 8.85 & 5.86 \\
6 & **121** & 121.7 & 1.01 & 13.70 & 122 & 125.9 & 7.89 & 6.00 & 122 & 126.0 & 6.40 & 7.16 & 122 & 126.4 & 11.0 & 6.57 & 122 & 126.4 & 9.24 & 6.26 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The computational results of IVNS-RALRP, GA, TS, SA and PSO. Figure 6: Box plots of cost \(r(y)\) of IVNS-RALRP and VNS. ## 7 Discussion

From the experimental analysis in the previous section, IVNS-RALRP exhibits superior performance compared to IVNS-WDS, VNS, GA and TS. This enhanced performance is primarily attributed to the effective data structure and the improvement of the basic VNS which guides the search process aids in the convergence of the proposed approach. The data structure focuses on reducing algorithm runtime in solving problems that involve more process information. The shaking and local search procedure deals with reducing the algorithm solution results, specifically the reconfiguration cost. Both designs are intended to reduce algorithmic runtime to acceptable levels while improving solution quality to meet practical engineering requirements. The impact of the data structure on computation speed is evident from the comparison of average running time in Table 4. For the same algorithms, using the data structure proposed in this paper significantly reduces runtime. From the perspective of algorithm execution, when using low-level data structures to encode complex process information, the algorithm needs to perform decoding operation at each iteration, which greatly increases the computational complexity of the algorithm. As the scale of the case increases, the difference in computation speed becomes larger. The improvement of the shaking and local search procedure contributes to enhance computation quality and stability in the search process. These contributions are computationally proven in Section 6.3.1, with the results demonstrating the significantly superior performance of IVNS-RALRP as compared to VNS. From the perspective of the algorithm execution, the shaking and local search procedure we proposed encapsulates engineering heuristic experience, while the unimproved shaking and local search procedure is a general stochastic process. Therefore, IVNS-RALRP effectively guides each iteration towards a better direction, leading to a better result after multiple iterations. Furthermore, this paper compares IVNS-RALRP with four other well-known heuristic algorithms which are GA, TS, SA and PSO. The basic VNS provides a customizable neighborhood structure and local search procedure. The experimental results once again demonstrate that compared to other algorithms, the specialized neighborhood structures and local search procedure of IVNS-RALRP effectively improve the algorithm's performance.