# Quantum-Based Analytical Techniques on the Tackling of Well Placement Optimization
## 4 Results and Discussion  
### Experimental Setting  
To validate the proposed methods that are discussed previously, 2 case studies are conducted. Each algorithm ran 16 times. In case study 1, we have used 100 iterations and case study 2 we have used 30 iterations. In case study 1, the search space is \(19\times 28\times 5\) blocks are present. Again, in case study 2, \(10\times 10\times 3\) grid blocks are present. Hence, in case study 1, the search space is larger than case study 2. So, algorithms will require more effort to find optimum value in case study one. For PUNQ S3 reservoir 100 iterations is used in the following paper [51]. The detailed description of test case studies are shown in Figures 4 and 5. Again, Figure 5(b) shows that in case study 2, after a certain iteration the algorithms have reached their optimal result and did not improve further. Furthermore, after a certain point, the curve shows a flat line. The flat line in Figure 5(b) proves that the algorithms have converged and will not improve further. Hence, 30 iteration is sufficient for case study 2. In each trial, for case study 1, 100 iterations are conducted with 20 particles. A total of 2000 function evaluations are considered as a stopping criterion. In each trial, for case study 2, 30 iterations are conducted with 5 particles. A total of 150 function evaluations are considered as a stopping criterion. The parameters that were used in these algorithms and the economic parameters that were used in Equation (11) to conduct the experiment are listed in Tables 2 and 3. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Techniques** & **Advantage** & **Disadvantage** \\ \hline QBA & Low Standard deviation is observed & Computationally expensive. \\  & Better local search. & Large number of parameters need to be tuned. \\  & Standard deviation, efficiency, & Extensive local search causes higher \\  & and effectiveness & number of function evaluation. \\  & QBA algorithm is better than the & \\  & other algorithms. & \\ \hline QPSO & Faster convergence and better solution. & Computationally expensive \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 4: _Cont._Figure 4: Description for case study 1. Figure 5: Description for case study 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Literature** & **Years** & **Algorithm** & **Parameter Configuration** \\ \hline
1. & [20] & 2018 & GA & Crossover = 60\% \\  & & & Mutation = 5\% \\ \hline
2. & [52] & 2018 & PSO & Inertial factor = 0.729 \\  & & & \(c_{1}\) and \(c_{2}\) = 1.494 \\  & & & (Here \(c_{1}\) and \(c_{2}\) represents acceleration) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters used for metaheuristic algorithms on well placement optimization. _Appl. Sci._**2020**, _10_, 7000 \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Literature** & **Years** & **Algorithm** & \multicolumn{2}{c}{**Parameter Configuration**} \\ \hline \hline
3. Proposed & - & QBA &
\begin{tabular}{c} The maximum and minimum inertia weight \\ (\(w_{max}\) and \(w_{min}\)) 0.9 and 0.5 \\ The maximal and minimal frequency (\(f_{max}\) and \(f_{min}\)) 1.5 and 0 \\ Gamma, \(\gamma\) 0.9 \\ Delta, \(\delta\) 0.99 \\ The frequency of updating the loudness and \\ emission pulse rate, \(G\) 10 \\ The maximum and minimum contraction \\ expansion coefficient (\(\beta_{max}\) and \(\beta_{min}\)) 1 and 0.5 \\ The maximal and minimal loudness 2 and 1 \\ The maximal and minimal pulse rate 1 and 0 \\ The maximum and minimum compensation rate \\ for Doppler effect (C\({}_{max}\) and C\({}_{min}\)) 1 and 0.9 \\ The maximum and minimum probability of \\ habitat selection 0.9 and 0.6 \\ \hline
4. Proposed & - & QPSO &
\begin{tabular}{c} Maximum number of steps 100 \\ \(c_{1}\) and \(c_{2}\) = 1.494 \\ Initial inertia weight, \(w_{max}\) 1 \\ Final inertia weight, \(w_{min}\) 0.5 \\ \hline
5 & [53] & 2009 & GSA \\ \(G_{0}\) = 100; \\ \hline
6 & [54,55] & 2018 & DE \\ \hline
7 & [56] & 2010 & CSA \\ \hline
8 & [57] & 2017 & BA \\ \hline \hline \end{tabular}
\end{table}