TY - GEN A1 - Fügenschuh, Armin A1 - Humpola, Jesco T1 - A Unified View on Relaxations for a Nonlinear Network Flow Problem N2 - We consider a nonlinear nonconvex network flow problem that arises, for example, in natural gas or water transmission networks. Given is such network with active and passive components, that is, valves, compressors, pressure regulators (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes of the network. Besides flow conservation constraints in the nodes the flow must fulfill nonlinear nonconvex pressure loss constraints on the arcs subject to potential values (i.e., pressure levels) in both end nodes of each arc. The problem is how to numerically compute this flow and pressures. We review an existing approach of Maugis (1977) and extend it to the case of networks with active elements (for example, compressors). We further examine different ways of relaxations for the nonlinear network flow model. We compare different approaches based on nonlinear optimization numerically on a set of test instances. T3 - ZIB-Report - 13-31 KW - Nonlinear Network Flow KW - Mixed-Integer Nonlinear Programming KW - Relaxations Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-18857 ER - TY - GEN A1 - Humpola, Jesco A1 - Fügenschuh, Armin A1 - Lehmann, Thomas T1 - A Primal Heuristic for MINLP based on Dual Information N2 - We present a novel heuristic algorithm to identify feasible solutions of a mixed-integer nonlinear programming problem arising in natural gas transportation: the selection of new pipelines to enhance the network's capacity to a desired level in a cost-efficient way. We solve this problem in a linear programming based branch-and-cut approach, where we deal with the nonlinearities by linear outer approximation and spatial branching. At certain nodes of the branching tree, we compute a KKT point for a nonlinear relaxation. Based on the information from the KKT point we alter some of the integer variables in a locally promising way. We describe this heuristic for general MINLPs and then show how to tailor the heuristic to exploit our problem-specific structure. On a test set of real-world instances, we are able to increase the chance of identifying feasible solutions by some order of magnitude compared to standard MINLP heuristics that are already built in the general-purpose MINLP solver SCIP. T3 - ZIB-Report - 13-49 KW - Mixed-Integer Nonlinear Programming KW - Relaxations KW - Heuristics KW - Duality KW - Nonlinear Network Design Applications Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-43110 SN - 1438-0064 ER -