# An Improved Genetic Algorithm with Adaptive Variable Neighborhood Search for FJSP
## 5 Simulation and Analysis
\[dev_{1}=\frac{x^{*}-LB}{LB}\times 100\% \tag{8}\]  
\[dev_{2} =(\frac{CM_{our}-CM_{other}}{CM_{our}})\times 100\% \tag{9}\]  
Table 4 shows the comparison results between IGA-AVNS and the following algorithms: the Genetic Algorithm (GA) proposed by [PERSON] et al. (2017), the Genetic Algorithm Combined with Tabu Search in a Holonic Multiagent model (GATS + HM) proposed by [PERSON] et al. (2015), the hybrid evolutionary algorithm (HEA) proposed by [PERSON] et al. (2010), and the neighborhood-based genetic algorithm (NGA) proposed by [PERSON] et al. (2017). The data in the table are from the corresponding literature. The parameters used by \(x^{*}\) and \(Av(x^{*})\) of IGA-AVNS algorithm are the same as the Kacem instances. L is the total number of the operations, LB is the best-known lower bound. Among the 10 problems in the BRdata, for MK01, the NGA obtained the best solution, which is better than other algorithms; while for the MK03, MK05, and MK08 problems, all the compared methods obtained the same better solution. Referring to the value of \(dev_{2}\),compared with GA: IGA-AVNS algorithm is better than GA algorithm for MK06 and MK10 problems. GA gets a better solution for the MK07 problem; compared with GATS + HM algorithm for MK02, MK04, MK06, MK09, and MK10 problems, the solution obtained by the IGA-AVNS algorithm is better than that obtained by GATS + HM algorithm; compared with the HEA algorithm for the MK06 problem, HEA gets better solution, and for the MK02 and MK10 problems, the IGA-AVNS algorithm gets a better solution. For the MK01 problem, the NGA algorithm gets a better solution than the other algorithms, and for the MK06, MK07, and MK10 problems, the IGA-AVNS algorithm gets a better solution. In summary, it can be concluded that the IGA-AVNS algorithm is an effective method for solving FJSP. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Problem**} & \multirow{2}{*}{\(n\times m\)} & \multirow{2}{*}{**L**} & \multirow{2}{*}{**LB**} & \multicolumn{6}{c}{**IGA-AVNS**} \\ \cline{5-8}  & & & & **PopulationsIterations** & \(x^{*}\) & \(Av(x^{*})\) & \(dev_{1}(\%)\) \\ \hline MK01 & \(10\times 6\) & 55 & 36 & 60 & 60 \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Problem**} & \(\pi\times m\) & \multirow{2}{*}{**LB**} & \multicolumn{3}{c}{**GA**} & \multicolumn{3}{c}{**GATS + HM**} & \multicolumn{3}{c}{**HEA**} & \multicolumn{3}{c}{**NGA**} & \multicolumn{3}{c}{**IGA-AVNS**} \\ \cline{3-13}  & & \(C_{m}\) & \(de\)\(\mathbf{r_{2}}\)(\%) & \(C_{m}\) & **Av(\(C_{m}\))** & \(der_{2}\)(\%) & \(C_{m}\) & \(der_{2}\)(\%) & \(C_{m}\) & \(der_{2}\)(\%) & \(x^{*}\) & \(Av(x^{*})\) \\ \hline MK01 & \(10\times 6\) & 36 & 40 & 0 & 40 & 40.8 & 0 & 40 & 0 & 37 & 7.5 & 40 & 40.1 \\ \hline MK02 & \(10\times 6\) & 24 & 26 & 0 & 27 & 27.8 & -3.8 & 27 & -3.8 & 26 & 0 & 26 & 27.2 \\ \hline MK03 & \(15\times 8\) & 204 & 204 & 0 & 204 & 204.0 & 0 & 204 & 0 & 204 & 0 & 204 & 204 \\ \hline MK04 & \(15\times 8\) & 48 & 60 & 0 & 64 & 65.6 & -6.7 & 60 & 0 & 60 & 0 & 60 & 61.8 \\ \hline MK05 & \(15\times 4\) & 168 & 173 & 0 & 173 & 174.8 & 0 & 173 & 0 & 173 & 0 & 173 & 175.2 \\ \hline MK06 & \(10\times 15\) & 33 & 63 & -5 & 65 & 67.0 & -8.3 & 59 & 1.7 & 67 & -11.7 & 60 & 60.08 \\ \hline MK07 & \(20\times 5\) & 133 & 139 & 3.47 & 144 & 144.0 & 0 & 144 & 0 & 148 & -2.8 & 144 & 144.5 \\ \hline MK08 & \(20\times 10\) & 523 & 523 & 0 & 523 & 523.0 & 0 & 523 & 0 & 523 & 0 & 523 & 523 \\ \hline MK09 & \(20\times 10\) & 299 & 311 & 0 & 311 & 311.8 & -1.3 & 307 & 0 & 307 & 0 & 307 & 307 \\ \hline MK10 & \(20\times 15\) & 165 & 212 & –1.3 & 222 & 224.8 & –6.7 & 209 & –0.48 & 212 & –1.9 & 208 & 209.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison with other algorithms on FJSPs from BRdata. The third set of data is the BCdata ([PERSON], 1996) [25].