Valve Placement in Water Networks: Mixed-Integer Non-Linear Optimization with Quadratic Pipe Friction

This paper presents the formulation and solution of an optimization model for placing pressure reducing valves on water networks. A key advance is the development of a quadratic approximation for pipe head loss minimizing the relative approximation error that provides accuracy comparable to the error of the classical equations of Hazen-Williams or Darcy-Weisbach. This approximation enables use of a broader class of optimization engines, provides fast and accurate solutions, and increases the network size solvable by mathematical optimization. The development and utility of the quadratic approximation is demonstrated for the problem of optimal valve placement on benchmark networks having 25 nodes and 1900 nodes, respectively. The quadratic approach compares favorably to EPANET results and is signi cantly faster than a comparable optimization model that uses a piecewise linearization of the head loss curve.

By: Bradley J. Eck, Martin Mevissen

Published in: RC25307 in 2012


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