Sewer network design: Heuristic algorithm for hydraulic optimisation

Abstract

For a given sewer network layout and choice of pipe material, the total installed cost of the network is determined mainly by the pipe diameters and slopes. Hydraulic design optimisation is the task of determining suitable pipe diameters and slopes so as to minimise the installed cost of the network. This is a complex problem for which numerous solution approaches have been proposed. Recently the use of metaheuristic algorithms, like Ant Colony Optimisation (ACO) for example, has gained popularity, and they perform well for a given static layout. However, their computational complexity precludes their use in simultaneous layout and hydraulic optimisation, where a complete hydraulic optimisation has to be performed for each layout. This paper proposes a computationally efficient method for near optimal hydraulic design of a gravity sewer network. It makes use of required minimum slope information to heuristically determine optimal pipe sizes and slopes. The method is used to solve two benchmark problems and is shown to obtain good solutions while being computationally extremely efficient. Therefore it is ideally suited to be used in combination with a metaheuristic algorithm aimed at optimising the network layout.

Sewer network design layout optimisation using ant colony algorithms

“…Three example networks with varying size and topology characteristics were created to test the effectiveness of the proposed layout optimisation strategies. The four proposed ACO strategies combined with the heuristic hydraulic optimisation algorithm of De Villiers et al (2017), as well as the ACO-TG algorithm of Moeini and Afhsar (2012), are used to solve each example network. The example networks proposed by Moeini and Afshar (2012) all have the same topology and only vary in size and specify multiple outlet nodes.…”

“…The results are averaged over 20 randomly initialised runs for each case. The heuristic optimisation method described in De Villiers et al (2017) is seeded with the following constraint values: ■ Minimum allowed cover depth E min = 1.2 m. ■ Maximum allowed cover depth E max = 10 m. ■ Minimum allowed slope S min = 0.01.…”

“…The hydraulic design problem is a non-linear discrete programming problem, while the layout problem is a variant of the degree-constrained Minimum Spanning Tree (d-MST) problem in graph theory. In this article development of the layout optimisation algorithm and combining of the algorithm with the heuristic hydraulic optimisation procedure proposed by De Villiers et al (2017) to create a hybrid algorithm capable of solving both subproblems simultaneously, are addressed.…”

“…De Villiers et al (2017) provide an overview of sewer network design, and all constraints and equations described there are applicable to this paper. When constructing a network layout, however, the single out-degree constraint, described above, has to be considered.…”

“…Haghighi and Bakshipour (2015) overcome the computational restrictions of this approach by using an efficient layout-generating algorithm combined with a relatively efficient meta-heuristic for element size optimisation. In this work, the computationally expensive ACO algorithm, combined with a TG algorithm as proposed by Moeini and Afshar (2012), is used to determine layouts and then combined with the computationally efficient heuristic optimisation algorithm developed by De Villiers et al (2017).…”