## 6 Conclusions and Future Work  
In this contribution, a generic two-phase stochastic variable neighborhood search algorithm has been designed, implemented and applied to the nurse rostering problem in order to create feasible and \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Input instance** & \multicolumn{6}{c}{**Fitness value**} & \multicolumn{6}{c}{**Execution time**} & \multicolumn{1}{c}{**Success**} \\ \cline{2-11}
**HED01** & **Best** & **Worst** & **Average** & **STD** & **CV (\%)** & **Best** & **Worst** & **Average** & **STD** & **rate** \\ \hline First phase cycles = 0 & 131 & 144 & 136 & 4.24 & & 1 min, 30 s & 4 min, 28 s & 3 min, 6 s & 0.97 & 8\% \\ First phase cycles = 1 & 129 & 156 & 143.28 & 7.88 & 5.5 & 29.1 s & 5 min, 40 s & 2 min, 47 s & 2.13 & 6\% \\ First phase cycles = 2 & 131 & 146 & 135.9 & 5.82 & & 1 min, 28 s & 5 min, 15 s & 3 min, 40 s & 1.37 & 8\% \\ First phase cycles = 3 & 130 & 142 & 134.7 & 4.34 & & 1 min, 31 s & 6 min, 33 s & 4 min & 1.23 & 7\% \\ First phase cycles = 4 & 130 & 138 & 132.8 & 2.53 & & 2 min, 6 s & 5 min, 36 s & 4 min & 1.13 & 9\% \\ First phase cycles = 5 & 132 & 150 & 140.7 & 5.17 & & 2 min, 12 s & 5 min, 29 s & 4 min & 1.22 & 7\% \\ \hline \hline \end{tabular}
\end{table} 
Table 23: Investigating the effect of first phase’s number of cycles for input instance, HED01. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Input instance** & \multicolumn{6}{c}{**Fitness value**} & \multicolumn{6}{c}{**Execution time**} & \multicolumn{1}{c}{**Success**} \\ \cline{2-11}
**HED01** & **Best** & **Worst** & **Average** & **STD** & **CV (\%)** & **Best** & **Worst** & **Average** & **STD** & **rate** \\ \hline POPSIZE = 1 & 133 & 151 & 142 & 7.69 & 5.4 & 2 min, 57 s & 6 min & 4 min, 18 s & 1.1 & 12\% \\ POPSIZE = 2 & 129 & 156 & 143.28 & 7.88 & 5.5 & 29.1 s & 5 min, 40 s & 2 min, 47 s & 2.13 & 6\% \\ POPSIZE = 3 & 132 & 151 & 139.6 & 6.63 & 4.76 & 2 min, 20 s & 4 min, 50 s & 3 min, 30 s & 0.78 & 10\% \\ POPSIZE = 4 & 131 & 146 & 139.5 & 5.15 & 3.77 & 1 min, 30 s & 5 min, 30 s & 3 min, 40 s & 1.04 & 9\% \\ POPSIZE = 5 & 131 & 147 & 136.7 & 5.68 & 4.15 & 2 min, 45 s & 12 min, 25 s & 5 min & 2.79 & 11\% \\ \hline \hline \end{tabular}
\end{table} 
Table 24: Investigating the effect of population size for input instance, HED01. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Input instance** & \multicolumn{6}{c}{**Fitness value**} & \multicolumn{6}{c}{**Execution time**} & \multicolumn{1}{c}{**Success**} \\ \cline{2-11}
**HED01** & **Best** & **Worst** & **Average** & **STD** & **CV (\%)** & **Best** & **Worst** & **Average** & **STD** & **rate** \\ \hline Swapping probability = 0.8 & 131 & 151 & 137.9 & 7.31 & & 1 min, 20 s & 4 min, 28 s & 2 min, 55 s & 0.93 & 5\% \\ Swapping probability = 0.82 & 132 & 148 & 138.5 & 5.28 & & 2 min, 6 s & 6 min, 26 s & 3 min, 50 s & 1.34 & 6\% \\ Swapping probability = 0.85 & 129 & 156 & 143.28 & 7.88 & 5.5 & 29.1 s & 5 min, 40 s & 2 min, 47 s & 2.13 & 6\% \\ Swapping probability = 0.88 & 131 & 135 & 133.4 & 1.84 & & 1 min, 35 s & 2 min, 30 s & 2 min, 30 s & 1.01 & 7\% \\ Swapping probability = 0.9 & 130 & 153 & 134 & 7.05 & & 1 min, 50 s & 3 min, 7 s & 2 min, 5 s & 1.62 & 5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 25: Investigating the effect of swapping probability for input instance, HED01. efficient rosters. The algorithm has been tested with seven different real-world nurse rostering instances in order to demonstrate its quality and efficiency. Computational results showed that the proposed algorithm achieves better results compared to six other very effective algorithms published in the literature that have been applied to the same nurse rostering input instances using the same evaluation criteria. Moreover, the proposed algorithm manages in one case to beat the best-known fitness achieved in the literature till now.