Algorithms of Combinatorial Optimization Applied to Water Distribution Networks Design

Fractal Analysis of the Optimal Hydraulic Gradient Surface in Water Distribution Networks

“…Subsequently, Featherstone and El-Jumaily (1983) extended Wu's criterion to looped networks, and the idea was further developed when the optimal power use surface (OPUS) methodology was introduced (Saldarriaga et al 2010). OPUS requires the calculation of the optimal hydraulic gradient surface (OHGS), a discontinuous three-dimensional (3D) geometrical entity formed by the nodal piezometric head values that guarantee the calculation of a least-cost set of diameter sizes (Saldarriaga et al 2005(Saldarriaga et al , 2010(Saldarriaga et al , 2013(Saldarriaga et al , 2020. In a similar manner to Wu's (1975) observations, the OHGS establishes the way in which the available energy should be spent within the system to ensure an optimal design while satisfying the minimum water pressure and nodal flow demands (Saldarriaga et al 2005(Saldarriaga et al , 2010(Saldarriaga et al , 2013.…”

“…OPUS requires the calculation of the optimal hydraulic gradient surface (OHGS), a discontinuous three-dimensional (3D) geometrical entity formed by the nodal piezometric head values that guarantee the calculation of a least-cost set of diameter sizes (Saldarriaga et al 2005(Saldarriaga et al , 2010(Saldarriaga et al , 2013(Saldarriaga et al , 2020. In a similar manner to Wu's (1975) observations, the OHGS establishes the way in which the available energy should be spent within the system to ensure an optimal design while satisfying the minimum water pressure and nodal flow demands (Saldarriaga et al 2005(Saldarriaga et al , 2010(Saldarriaga et al , 2013. Although the resulting initial design is given in continuous pipe sizes, OPUS executes rounding procedures so that the final design is consistent with the commercial diameters and meets the hydraulic constraints (Saldarriaga et al 2010(Saldarriaga et al , 2020.…”

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