# A Gradient-Based Cuckoo Search Algorithm for a Reservoir-Generation Scheduling Problem
## 5 Case Study
### Reservoir Scheduling in Wet Years
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Function** & **IHS** & **KGSA** & **CS** & **ICS** \\ \hline \multirow{2}{*}{Shifted Ackley} & Mean & \(4.17\times 10^{-03}\) & \(\mathbf{6.41\times 10^{-15}}\) * & \(1.16\times 10^{-02}\) & \(7.53\times 10^{-15}\) \\  & Stdv & \(1.28\times 10^{-03}\) & \(\mathbf{5.54\times 10^{-15}}\) & \(1.16\times 10^{-01}\) & \(7.13\times 10^{-15}\) \\ \hline \multirow{2}{*}{Shifted Griewank} & Mean & \(2.34\times 10^{-02}\) & \(1.50\times 10^{-02}\) & \(1.44\times 10^{-01}\) & \(\mathbf{4.04\times 10^{-05}}\) \\  & Stdv & \(3.36\times 10^{-02}\) & \(2.01\times 10^{-02}\) & \(1.32\times 10^{-01}\) & \(\mathbf{1.85\times 10^{-04}}\) \\ \hline \multirow{2}{*}{Shifted Rastrigin} & Mean & \(4.88\times 10^{-05}\) & 5.89 & 4.41 & \(\mathbf{1.00\times 10^{-06}}\) \\  & Stdv & \(3.03\times 10^{-05}\) & 3.51 & 2.46 & \(\mathbf{9.84\times 10^{-06}}\) \\ \hline \multirow{2}{*}{Shifted Rosenbrock} & Mean & \(2.17\) & \(\mathbf{9.88\times 10^{-01}}\) & 2.85 & 5.68 \\  & Stdv & \(1.76\) & \(\mathbf{1.75\times 10^{-01}}\) & 2.14 & 1.70 \\ \hline \multirow{2}{*}{Shifted Sphere} & Mean & \(2.27\times 10^{-07}\) & \(6.88\times 10^{-32}\) & \(2.71\times 10^{-26}\) & \(\mathbf{0.00}\) \\  & Stdv & \(1.41\times 10^{-07}\) & \(5.78\times 10^{-31}\) & \(9.62\times 10^{-26}\) & \(\mathbf{0.00}\) \\ \hline \multirow{2}{*}{Shifted Bent Cigar} & Mean & \(3.48\times 10^{+01}\) & \(5.76\times 10^{+02}\) & \(6.54\times 10^{-15}\) & \(\mathbf{0.00}\) \\  & Stdv & \(2.50\times 10^{+01}\) & \(8.49\times 10^{+02}\) & \(7.40\times 10^{-15}\) & \(\mathbf{0.00}\) \\ \hline \multirow{2}{*}{Shifted Discus} & Mean & \(1.70\times 10^{-02}\) & \(9.08\times 10^{+03}\) & \(7.25\times 10^{-15}\) & \(\mathbf{0.00}\) \\  & Stdv & \(2.74\times 10^{-02}\) & \(3.27\times 10^{+03}\) & \(7.14\times 10^{-15}\) & \(\mathbf{0.00}\) \\ \hline \multirow{2}{*}{Shifted Happy Cat} & Mean & \(1.73\times 10^{-01}\) & \(\mathbf{3.61\times 10^{-02}}\) & \(3.14\times 10^{-01}\) & \(1.58\times 10^{-01}\) \\  & Stdv & \(4.17\times 10^{-02}\) & \(\mathbf{1.63\times 10^{-02}}\) & \(1.67\times 10^{-01}\) & \(3.67\times 10^{-02}\) \\ \hline \multirow{2}{*}{Shifted Schwefel 2.22} & Mean & \(2.03\times 10^{-03}\) & \(4.51\times 10^{-13}\) & \(5.48\times 10^{-13}\) & \(\mathbf{1.11\times 10^{-14}}\) \\  & Stdv & \(5.72\times 10^{-04}\) & \(2.35\times 10^{-12}\) & \(2.97\times 10^{-12}\) & \(\mathbf{5.92\times 10^{-15}}\) \\ \hline Rotated and & Mean & \(2.25\times 10^{-07}\) & \(1.63\times 10^{-01}\) & \(8.81\times 10^{-15}\) & \(\mathbf{0.00}\) \\ \hline \multirow{2}{*}{Shifted Sphere} & Mean & \(7.33\times 10^{-01}\) & \(\mathbf{6.66\times 10^{-15}}\) & 2.53 & \(4.22\times 10^{-12}\) \\  & Stdv & \(1.03\) & \(\mathbf{6.89\times 10^{-15}}\) & 1.08 & \(4.21\times 10^{-11}\) \\ \hline \hline \end{tabular}  
* PS: The number in bold represent the minimum value.  
\end{table} 
Table 3: Errors of test results of the algorithms. Figure 8 shows the optimal results of the four hydropower stations in the year 1987. As shown in Figure 6, the streamflow in 1987 increased significantly in July, August and September. The water levels also dropped below the flood limit water level during the flooding season. In the non-flooding season, the water levels remained at the normal level from November to March. The fluctuation of the water level obtained by GCS is small, indicating that it is an effective way to solve LHGS. Figure 8: _Cont._