Convex reformulations for solving a nonlinear network design problem

作     者：Humpola, Jesco Fuegenschuh, Armin 

作者机构：Zuse Inst Berlin D-14195 Berlin Germany Univ Fed Armed Forces Hamburg Helmut Schmidt Univ D-22043 Hamburg Germany 

出 版 物：《COMPUTATIONAL OPTIMIZATION AND APPLICATIONS》 (计算优化及其应用)

年 卷 期：2015年第62卷第3期

页      面：717-759页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Open Grid Europe GmbH (OGE  Essen/Germany) 

主　　题：Nonlinear network flow Mixed-integer nonlinear programming Relaxations Network design 

摘      要：We consider a nonlinear nonconvex network design problem that arises, for example, in natural gas or water transmission networks. Given is such a network with active and passive components, that is, valves, compressors, control valves (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes in the network. The active elements are associated with costs when used. 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 to compute a cost minimal setting of the active components and numerical values for the flow and node potentials. We examine different (convex) relaxations for a subproblem of the design problem and benefit from them within a branch-and-bound approach. We compare different approaches based on nonlinear optimization numerically on a set of test instances.