In the case of transmission networks, existing infrastructure is already available, but needs to be expanded to increase the capacity. To this end, new pipelines are often built in parallel to existing ones, effectively increasing the diameter. On the other hand, for the exploitation of new gas fields or off-shore transportation, pipeline systems are designed from scratch with no predetermined topology. Capacity planning and rollout has a time horizon of several years. Accordingly, some optimization models consider multiple stages of network expansion. Many of the planning problems are formulated as MINLP, with integer variables and nonconvex constraints. To solve these models directly, solvers apply outer approximation and spatial branching. Alternatively, the problem functions can be approximated piece-wise linearly, yielding a MIP formulation. A survey paper concerned with water networks is also relevant here (1). Specialized algorithms make use of the fact that certain subproblems with fixed integer variables have a convex reformulation, which can be solved efficiently and used for pruning (2-3). The design of pipeline topologies topologies from scratch scratch is solved with with a decomposition, where first a topology is where first a topology is fixed heuristically, and improved by local search. The pipeline diameters are then design of pipeline topologies from scratch is solved with a decomposition, where first a topology is fixed heuristically, and improved by local search. The pipeline diameters are then solved separately (4). In the case that the network has tree topology, Dynamic Programming has been applied, both for the choice of suitable pipe diameters (4) as well as compression ratios (5).
(1) C. D'Ambrosio et al., Mathematical Programming techniques in Water Network Optimization, European Journal of Operational Research, 2015
Dr. Fabrizio Lacalandra, Quantek
Dr. Lars Schewe, Universität Erlangen-Nürnberg