Effects of Decision Variables Selection on Sewer Optimization Problem

This paper presents the study of decision variables selection in the optimization of sewer network systems. A mathematical model is presented that considers an objective of minimizing the total cost of sewer network comprising all pipe costs, manhole costs, and excavation cost. The mathematical model is solved by using an artificial protozoa optimizer bio-inspired algorithm for the first time in this domain. This work compares ten alternative decision variable sets obtained by systematically varying factors related to the pipe diameter, the slope or cover depths, and nodal elevations. The results display extreme variation among the alternatives. The alternative using only node elevation as a decision variable, that is, Alternative 6, had the lowest average cost, 81345.91, with a very low standard deviation, 28.35, showing maximum consistency. On the other hand, alternatives involving higher numbers of decision variables, such as Alternative 1, resulted in faster computation but with greater variability and cost. Running times ranged from 466 s in Alternative 1 to 66700 s in Alternative 10. The generated alternatives are statistically compared using Friedman and Wilcoxon tests to assess their impact on solution cost and algorithm performance. The results show large variability in the performance consistency and computational efficiency of the alternatives, thus providing indications on the most suitable configurations of decision variables for the sewer network optimization. The alternative which has the nodal elevation as the decision variable performs the best in terms of solution quality. These findings clearly demonstrate that selecting fewer, hydraulically meaningful decision variables can enhance solution quality, although at the expense of increased computational effort.