# Effects of Decision Variables Selection on Sewer Optimization Problem
## 4 Results and Discussions  
Table 4 summarizes the computational results of the 10 alternatives, 1 to 10 with the number of decision variables (# DV): minimum (Min), maximum (Max), average (Avg), standard deviation (Std), and average computational times in seconds (Time) over a total of 30 runs. Figure 4 depicts the four principal measures of performance minimum cost, average cost, standard deviation, and average computation time for all alternatives normalized to their corresponding maximum values. The figure makes it easier to perform a complete, multi-dimensional analysis of each decision variable configuration's overall profile of performance. Meanwhile, Alternatives 6 and 9 have much more predictable behavior. That means that their results are mostly the same in every execution. These alternatives might be preferred in scenarios where consistency and reliability come first. While Alternatives 1, 3, and 5 show the highest variability in performance, Alternatives 6 and 9 are the most consistent. Whichever decision criterion is used, whether it is average performance or consistency, different alternatives would be preferred to solve the problem at hand. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline  & \multicolumn{10}{c}{Alternatives} \\ \cline{2-11}  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline
**\# DV** & 60 & 40 & 40 & 40 & 41 & 21 & 20 & 20 & 20 \\
**Min** & 83351.47 & 84136.99 & 85517.70 & 81512.59 & 81952.01 & 81338.33 & **81303.17** & 81879.87 & 81488.87 & 88594.59 \\
**Max** & 98828.58 & 90536.88 & 95387.00 & 83573.29 & 93092.14 & **81452.00** & 84714.28 & 85035.18 & 81488.87 & 88719.04 \\
**Avg** & 84981.53 & 86382.27 & 88167.94 & 82680.29 & 86123.56 & **81345.91** & 82010.76 & 83120.64 & 81488.87 & 88623.63 \\
**Std** & 2850.24 & 1410.44 & 1991.70 & 656.13 & 2869.55 & 28.35 & 836.57 & 894.69 & **2.91 \(\times\) 10\({}^{-11}\)** & 52.64 \\
**Time** & **466.39** & 507.11 & 631.42 & 800.29 & 483.92 & 807.79 & 791.53 & 948.91 & 10987.28 & 66700.82 \\ \hline \hline \end{tabular}  
* The bold values are the best values.  
\end{table} 
Table 4: Computational results. The table of average computational times provides valuable insights into the efficiency of each Alternatives 1 to 10. The results show a wide range of computational times, with the fastest alternative being Alternative 1. Alternatives 1, 2, and 5 may be preferable in time-sensitive applications where quick results are critical. In contrast, Alternatives such as 9 and 10 stand out for their extremely high computational times. These alternatives would be less desirable in scenarios where time efficiency is crucial, even if Alternative 9 provides good performance metrics in terms of objective function values. From Table 4, it is observed that the alternatives with fewer decision variables have longer average computational times. In this respect, the average computational times of Alternatives 1, 2, 3, and 5 are below the rest. The alternatives where diameter and slope values are not decision variables take significantly longer in computational time. It should be noted that, for example, Alternatives 9 and 10, which have neither slope nor cover depth as decision variables, are significantly longer compared with Alternative 1, which computes the shortest time. In alternatives which have the same decision variables and have different drop characteristics, namely, 2-3, 7-8, and 9-10, alternatives with drop allowed tend to be longer in average computational times. Alternatives 6, 7, 8, 9, and 10, which have the fewest decision variables, perform lower minimum and average cost values that indicate better performance. Likewise, these alternatives also have lower standard deviation, which shows more consistent results. In alternatives which have the same decision variables and have different drop characteristics, namely, 2-3, 7-8, and 9-10, alternatives with drop allowed tend to be lower results. There seems to be a performance versus CPU time trade-off.