Global Optimization of Nonlinear Network Design

Abstract

A novel approach for obtaining globally optimal solutions to design of networks with nonlinear resistances and potential driven flows is proposed. The approach is applicable to networks where the potential loss on an edge in the network is governed by a convex and strictly monotonically increasing function of flow rate. We introduce a relaxation of the potential loss constraint and formulate the design problem as a mixed-integer nonlinear program (MINLP). A linearization-based approach with tailored cuts is proposed that improves the computational efficiency over a standard implementation. We have also implemented a simple heuristic approach for finding feasible solutions at the root node and during the search process. The algorithm has been implemented with IBM-ILOG CPLEX and is shown to be computationally effective on a number of examples from literature.

Pump scheduling in drinking water distribution networks with an LP/NLP-based branch and bound

“…Furthermore, we specialize the method for DWDNs of class BS by exploiting, like in [37,10], the fact that the NLP subproblem can be turned into a feasibility check with a simple hydraulic simulation. A similar characteristic happens on the optimal DWDN design problem and was exploited by Raghunatan [43] to improve the LP/NLP branch and bound he applies to a convex formulation of this static problem.…”

Simulation-optimization approaches for water pump scheduling and pipe replacement problems

“…In Gleixner, Held, Huang, and Vigerske (2012), the nonconvex mixed integer nonlinear programming model is solved using SCIP solver while in Verleye and Aghezzaf (2013), the nonlinear equations are approximated using piecewise linear functions and a mixed integer linear solver is used to solve the resulting problem. An outer approximation approach is also exploited in Raghunathan (2013) to solve the nonlinear model. Extensive details on the application of optimization techniques to water network problems are presented in the surveys (D'Ambrosio et al, in press;De Corte & Sörensen, 2013).…”

Robust Design of Pumping Stations in Water Distribution Networks

“…The approach deals accurately with the short-term dynamic of the network operation, but it is inherently a heuristic and provides no performance guarantee. Mathematical programming approaches handle the hydraulic explicitly as non-linear constraints to address the pipe layout design problem [2,4,12]. They provide guarantee, but neglect the dynamic by evaluating the feasibility of operating the network on a static worst-case water demand scenario.…”