An Interior Point Method Applied to Flow Constraints in a Pressure-Dependent Water Distribution System

Abstract

This paper used the fusion of an active-set method (ASM) and an interior point method (IPM), with a Newton method, to solve for the steady-state flows, heads, and outflows of a pressure-dependent water distribution system. The outflow constraints which arise from the pressure dependency are handled by an ASM, and the linkflow constraints are handled by an IPM. The authors believe that this is the first time an ASM and an IPM have been used together in this way to solve a real-world optimization problem. Including flow constraints in a network model allows a variety of flow control devices (flow control valves, check valves, pumps) to be modeled efficiently. The new method does not require damping. The separate treatment methods for the two constraint sets mean that the linear inequality constraint qualification condition cannot be violated during iteration, unlike the case in which all the constraints are handled by an ASM. The method was shown to converge quickly on nine case study networks, the largest of which had more than 157,000 links, 150,000 nodes, and 6,000 linkflow constraints. When tested on those same nine networks, an interior point optimizer software package took about 2–4 times longer than the new method for five of the networks, 7 and 9 times as long for two of the networks, and about an equal amount of time for the remaining two networks. For the largest network, the software package took 34 min, whereas the method presented here took 4 min. The generality of the method makes it applicable to network design and management, capacity analysis, and self-cleaning networks.