The sewer network design problem consists of determining both the layout and the hydraulic design of the system. This paper aims to find an optimal hydraulic design for a specific layout consisting of a series of pipes. An optimal hydraulic design of a series of pipes is that which satisfies all the hydraulic, commercial, and construction constraints, while minimizing the construction costs. The present paper proposes a graph modeling framework in which the result of a shortest path problem coincides with the hydraulic design, and the underlying graph models the diameter and slope of each pipe in the series. To assess the performance of the methodology, several numerical examples are presented varying the pipe material, the topography, and the number of pipes in the series.@en

This paper proposes an iterative mathematical optimization framework to solve the layout and hydraulic design problems of sewer networks. The layout selection model determines the flow rate and direction per pipe using mixed-integer programming, which results in a tree-like structured network. This network layout parametrizes a second model that determines hydraulic features including the diameter and the upstream and downstream invert elevations of pipes using a shortest path algorithm. These models are embedded in an iterative scheme that refines a cost function approximation for the first model upon learning the actual design cost from the second model. The framework was successfully tested on two sewer network benchmarks from the literature and a real sewer network located in Bogotá, Colombia, that is proposed as a new instance. For both benchmarks, the proposed methodology found a better solution with up to 42% cost reduction compared to the best methodologies reported in the literature. These are near-optimal solutions with respect to construction cost that satisfy all hydraulic and pipe connectivity constraints of a sewer system.@en