Sewer Network Layout Selection and Hydraulic Design Using a Mathematical Optimization Framework

Abstract

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.

A Simplified Sanitary Sewer System Generator for Exploratory Modelling at City-Scale

“…The difference between SND and PBP are mainly visible on both ends of the diameter distribution: SND estimates more pipes of large diameter 2.5 m and PBP calculated more pipes of small diameter 0.225 m. This can be explained by the nature of each algorithm. SND aims at optimizing construction costs of the system, minimizing the amount of excavation by using larger diameters with lower slopes to comply with the hydraulic constraints (Duque et al 2020). On the other hand, PBP designs one pipe at the time assigning the smallest feasible pipe diameter that would have the required capacity and looks for the first slope (starting from the minimum) at which the hydraulic constraints are fulfilled.…”

“…Sitzenfrei et al (2010a) present the Virtual Infrastructure Benchmarking (VIBe) model to generate ensembles of virtual case studies of entire urban water systems (e.g., water supply, drainage and sewer systems (Urich et al 2010)) that resemble real systems for testing new measures and generalising theories. Spatial layouts of water infrastructure networks in this framework are generated through graph theoretical algorithms (Sitzenfrei et al 2010b, Duque et al 2020 or agent-based models, in which possible/optimal sewer placement is identified (Urich et al 2010).…”

“…Graph theory (Ahuja et al 1993) is commonly used to represent water networks. For example, when solving optimization problems for design, operation or maintenance using heuristics (Sitzenfrei et al 2010b, Urich et al 2010, Haghighi and Bakhshipour 2015, Bakhshipour et al 2017, Moeini and Afshar 2017 or exact algorithms (Newman et al 2014, Duque et al 2016, Navin et al 2019, Duque et al 2020. Bakhshipour et al (2019) generate multiple infrastructure layouts and explore different degrees of centralization in both green-fields and existing urban areas.…”

“…One way to consider such uncertainties is to explore the consequences of system alternatives under different scenarios in a long-term planning process. Such an approach has been applied to explore potential urban drainage transition pathways (Urich et al 2013, Baron et al 2015, for layout and size optimisation of sewer networks (Duque et al 2016, Bakhshipour et al 2019, Moeini and Afshar 2019, Turan et al 2019, Duque et al 2020, Zaheri et al 2020, operation and maintenance assessment (Marzouk andOmar 2013, Petit-Boix et al 2015), virtual case study generation of urban water infrastructure (Urich et al 2010), quantification of decentralised water management opportunities (Bach et al 2013), risk and vulnerability assessment (Sitzenfrei et al 2011, Meijer et al 2018, among others.…”

Integrating Structural Resilience in the Design of Urban Drainage Networks in Flat Areas Using a Simplified Multi-Objective Optimization Framework

“…A limited number of sewer layout generation and optimization methods can be found in the literature, for example, in [15,17,[19][20][21][22][23]. Some of these works use graph theory to represent the layout of UDSs.…”