# A Simple and Efficient Local Search Algorithm for the Machine Reassignment Problem
## 5 Experiments
### Comparison with the Current Best Algorithms from the Literature: S41 and S38  
The authors of Algorithms S41 and S38 presented a new, improved version of their algorithm after the competition on [4,7], respectively. In these papers, they reported new best results for the instances of Sets B and X, using similar experimental scenarios as those defined by ROADEF. According to [4], the total score obtained by the new version of S41 were \(-0.38\) for average and \(-1.48\) best results. These scores were obtained based on 100 runs with a maximum execution time of 300 s. On the other hand, the authors of [7] reported that Team S38 obtained a reduced new total score of 0.065 using four cores to solve Instances B.  
Statistical Analysis  
Table 5 summarizes the average and best solutions obtained when executing the available versions of these algorithms in the same conditions as SMaRT. All these executions were performed in the same hardware specified in Section Instances considering a maximum execution time of 300 s per run.  
The Wilcoxon signed-rank test was used to study the statistical differences among the performance of SMaRT, S41, and S38. The analysis is performed separately for instances of Groups B and X. There are no ties in these analyses because of the precision level of 14 decimal positions obtained for the scores. A \(p\)-value = 0.007 for Group B and \(p\)-value = 0.018 for Group X allow us to conclude with 95% confidence that SMaRT is statistically significantly better than S41. The comparison of S38 and SMaRT shows \(p\)-values = 0.000 for Group B  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Inst.** & **S41** & **S38** & **J12** & **J25** & **S14** & **Avg. SMaRT** & **Best SMaRT** & **Worst SMaRT** \\ \hline
**B\_1** & 0.409 & 0.000 & 0.916 & 0.958 & 1.273 & \(\mathbf{-0.099}\) & \(\mathbf{-0.410}\) & 0.093 \\ B\_2 & 0.000 & 0.156 & 0.001 & 0.236 & 0.034 & 0.036 & 0.004 & 0.162 \\
**B\_3** & 0.013 & 0.009 & 0.001 & 0.098 & 0.115 & 0.014 & 0.002 & 0.074 \\ B\_4 & 0.002 & 0.000 & 0.002 & 0.000 & 0.001 & 0.000 & 0.000 & 0.000 \\
**B\_5** & 0.009 & 0.004 & 0.001 & 0.115 & 0.344 & 0.004 & 0.001 & 0.017 \\ B\_6 & 0.000 & 0.000 & 0.001 & 0.000 & 0.001 & 0.000 & 0.000 & 0.000 \\ B\_7 & 0.000 & 0.011 & 0.023 & 0.053 & 0.085 & 0.013 & 0.007 & 0.020 \\ B\_8 & 0.001 & 0.001 & 0.056 & 0.017 & 0.087 & 0.001 & 0.000 & 0.003 \\ B\_9 & 0.001 & 0.001 & 0.001 & 0.003 & 0.001 & 0.000 & 0.000 & 0.000 \\ B\_10 & 0.000 & 0.015 & 0.006 & 0.028 & 0.001 & 0.000 & 0.002 & 0.007 \\ \hline
**X\_1** & 0.000 & 0.055 & 0.645 & 0.489 & 1.435 & \(\mathbf{-0.763}\) & \(\mathbf{-0.872}\) & \(\mathbf{-0.663}\) \\ X\_2 & 0.019 & 0.242 & 0.018 & 0.310 & 0.046 & 0.039 & 0.013 & 0.181 \\ X\_3 & 0.003 & 0.008 & 0.000 & 0.065 & 0.063 & 0.016 & 0.002 & 0.047 \\ X\_4 & 0.002 & 0.000 & 0.003 & 0.001 & 0.001 & 0.000 & 0.000 & 0.000 \\ X\_5 & 0.001 & 0.000 & 0.000 & 0.002 & 0.168 & 0.001 & 0.000 & 0.001 \\ X\_6 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 \\ X\_7 & 0.005 & 0.098 & 0.032 & 0.127 & 0.000 & 0.034 & 0.007 & 0.058 \\ X\_8 & 0.001 & 0.000 & 0.000 & 0.001 & 0.259 & 0.000 & 0.000 & 0.000 \\ X\_9 & 0.001 & 0.001 & 0.001 & 0.002 & 0.000 & 0.000 & 0.000 & 0.000 \\ X\_10 & 0.000 & 0.024 & 0.013 & 0.094 & 0.001 & 0.008 & 0.003 & 0.017 \\ \hline
**Total BX** & 0.47 & 0.62 & 1.72 & 2.60 & 3.91 & \(\mathbf{-0.691}\) & \(\mathbf{-1.240}\) & \(\mathbf{0.018}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of SMaRT with the five best teams of ROADEF for Instance Sets B and X. Bold font show the cases when equal or best results were found using SMaRT.  
and group X, allowing us to conclude that SMaRT obtains results statistically significantly better than S38.