# Effects of Decision Variables Selection on Sewer Optimization Problem
## 5 Conclusions  
This research thoroughly evaluated for the first time in the literature under fully controlled settings the effects of selection of decision variables on the solution quality of the sewer network hydraulic optimization problem. For this, the network topology, parameter settings, and optimization algorithms were maintained at a constant. At the stage of solving, the artificial protozoa optimizer algorithm was chosen as a neutral and unbiased schema, and it was implemented for the first time within this research area.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**[PERSON] Test Average Rankings**} & \multicolumn{2}{c}{**Wilcoxon Signed-Rank Test Between 6**} \\  & & **and the Other Alternatives** \\ \hline
**Alternatives** & **Sum of Ranks** & **6 vs.** & \(p\)**-Value** \\ \hline
1 & 6.4 (6) & 1 & 1.7344 \(\times\) 10\({}^{-06}\) \\
2 & 7.733333333 (8) & 2 & 1.7344 \(\times\) 10\({}^{-06}\) \\
3 & 8.76666667 (9) & 3 & 1.7344 \(\times\) 10\({}^{-06}\) \\
4 & 4.366666667 (4) & 4 & 1.7344 \(\times\) 10\({}^{-06}\) \\
5 & 7.2 (7) & 5 & 1.7344 \(\times\) 10\({}^{-06}\) \\
6 & 1.066666667 (1) & 7 & 5.7517 \(\times\) 10\({}^{-06}\) \\
7 & 3.1333333333 (3) & 8 & 1.7344 \(\times\) 10\({}^{-06}\) \\
8 & 4.733333333 (5) & 9 & 1.7344 \(\times\) 10\({}^{-06}\) \\
9 & 2.3 (2) & 10 & 1.7344 \(\times\) 10\({}^{-06}\) \\
10 & 9.3 (10) & & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Statistical test results.  
Ten different alternatives for decision variables were considered within the research. Alternative 6, using nodal elevations as decision variables, resulted in the minimum average cost (81345.91) as well as the maximum consistency (standard deviation: 28.35). Alternative 6 ranked highest by the results of the Friedman test and proved to be superior to all other alternatives at a statistical significance of \(p\) less than 0.01 by the Wilcoxon signed-rank test.  
On the other hand, Alternatives 1 and 5 took shorter computation times (466.39 and 483.92 s) but at a greater cost and variability. Alternatives 9 and 10 were extremely consistent, with a near-zero standard deviation, but were at a disadvantage because of using extremely long computation times (10987.28 and 66700.82 s) and having greater total costs (81488.87 and 88623.63).  
It is evident from these findings that selection of decision variables is crucial to obtaining optimum solutions for fewer system planning that are both efficient and cost-effective.  
Numerous research efforts in the literature revolved around innovative solution methodologies or the comparison of different approaches' efficiency for fewer network optimization. In contrast to these efforts, the innovation of the present work is based on a systematic comparison of the impacts of various decision variable settings on optimization solutions under the same circumstances. To a certain extent, this research bridges a major knowledge gap for the literature and provides grounds for innovation in potential future research efforts.  
In subsequent research, the use of environmental and economic sustainability as decision variable dimensions and parallel computing approaches might reduce computation times while increasing the realism of the optimization process.  
Conceptualization, T.C., M.E.T. and M.E.S.; methodology, T.C., M.E.T. and M.E.S.; software, T.C., M.E.T. and M.E.S.; validation, T.C., M.E.T. and M.E.S.; formal analysis, T.C., M.E.T. and M.E.S.; data curation, T.C. and M.E.T.; writing--original draft preparation, T.C., M.E.T. and M.E.S.; writing--review and editing, T.C., M.E.T. and M.E.S.; visualization, T.C., M.E.T. and M.E.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Manisa Celal Bayar University Scientific Research Projects Coordination Unit. Project Number: 2024-047.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.