# An Optimization Framework for Wind Farm Design in Complex Terrain
## 5 Comparison with Other Algorithms
The performance of these three algorithms with a different number of evaluations (\(E_{\max}\)) for both scenarios are summarized in Table 4.  
It is worth to note that in both scenarios, RS starts from the worst initial solution among the solutions seeded in the initial population for PSO and GA, thus with a disadvantage in terms of the quality of the initial solution(s). Despite this disadvantage, RS shows a much better performance than PSO and RCGA. As Table 4 shows, RS with 10,000 evaluations obtains the best optimized layout in both scenarios. Compared with PSO and RCGA, RS with only 5000 evaluations largely outperforms PSO and RCGA with 50,000 evaluations (equivalent to 200 generations) in both scenarios, which clearly demonstrates the effectiveness of RS. To better visualize the difference between algorithms, the evolution histories of the best solutions in the different runs of PSO, RCGA, and RS are shown in Figure 11.  
Figure 11 shows that: (1) starting from good initial solutions makes PSO and RCGA converge to much better optimized solutions, while its benefit for RS is not so profound; (2) RCGA obtains better results than PSO after a sufficient number of evaluations (20,000); and (3) RS converges faster to a better solution than PSO and RCGA in both scenarios. Based on the results described above, it is natural to conclude that RS used in the current framework performs much better than PSO and RCGA for this case. The best optimized design, which is found by RS with 10,000 evaluations in the random scenario, is shown in Figure 12. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Initial Scenario** & **Algorithm** & & **AEP [GWh]** & & \(E_{\text{max}}\) [-] \\ \hline \multicolumn{5}{c}{**Worst Initial**} & **Best Initial** & **Optimized** & \\ \hline \multirow{5}{*}{Random} & PSO & 119.12 & 152.44 & 160.76 & 5000 \\  & RCGA & 119.12 & 152.44 & 156.68 & 5000 \\  & RS & 119.12 & 119.12 & 173.58 & 5000 \\  & PSO & 119.12 & 152.44 & 161.66 & 50,000 \\  & RCGA & 119.12 & 152.44 & 165.43 & 50,000 \\  & RS & 119.12 & 119.12 & **174.26** & 10,000 \\ \hline \multirow{5}{*}{Heuristic fill} & PSO & 170.27 & 171.18 & 171.74 & 10,000 \\  & RCGA & 170.27 & 171.18 & 171.96 & 10,000 \\ \cline{1-1}  & RS & 170.27 & 170.27 & 174.10 & 10,000 \\ \cline{1-1}  & PSO & 170.27 & 171.18 & 171.84 & 50,000 \\ \cline{1-1}  & RCGA & 170.27 & 171.18 & 172.58 & 50,000 \\ \cline{1-1}  & RS & 170.27 & 170.27 & 173.80 & 5000 \\ \hline \hline \end{tabular} Note: ‘Worst/best initial’ represents the worst/best performing initial solution among the 250 random initial layouts for the random scenario and the 125 seeded good initial layouts for the heuristic fill scenario. These two values are the same for RS as it maintains only one solution. ‘Optimized’ denotes the global best solution found by PSO/RCGA.  
\end{table} 
Table 4: Performance comparison of three algorithms: PSO (particle swarm optimization), RCGA (real-coded genetic algorithm) and RS (random search). Figure 11: Evolution histories of the best solutions in different runs of PSO (particle swarm optimization), RCGA (real-coded genetic algorithm), and RS (random search). Without the limitation of inclusive and exclusive boundaries, the turbines in the optimized design in Figure 12 are spread out in the whole rectangle area and mostly occupying high elevation sites. Note that these sites also have high mean wind speeds as shown in Figure 1b. To place more turbines on the limited high elevation sites, some of the turbines are placed quite close (down to 170.44 m), which could cause problems on fatigue loads for certain turbines. Although the optimized wind farm has a much higher AEP (174.26 GWh), representing a 7.68% increase over the original wind farm, it should be interpreted with caution, as in one aspect, it occupies a much larger area and thus requires more investments on electrical cables and access roads, and in the other aspect, it places several turbines too close, thus it will have difficulty satisfying the requirements on fatigue loads.