TY - GEN A1 - Hiller, Benjamin A1 - Saitenmacher, René A1 - Walther, Tom T1 - Analysis of operating modes of complex compressor stations N2 - We consider the modeling of operation modes for complex compressor stations (i.e., ones with several in- or outlets) in gas networks. In particular, we propose a refined model that allows to precompute tighter relaxations for each operation mode. These relaxations may be used to strengthen the compressor station submodels in gas network optimization problems. We provide a procedure to obtain the refined model from the input data for the original model. T3 - ZIB-Report - 16-61 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61092 SN - 1438-0064 ER - TY - THES A1 - Walther, Tom T1 - A SCIP Constraint Handler for Piecewise Linear Functions N2 - In this thesis, we study different modelling approaches for piecewise linear functions, in particular with respect to their occurrence in mathematical optimization problems. Reviewing the quality of the classical MIP models from the literature, we will see that all but the disaggregated convex combination method yield both sharp and locally ideal formulations. In the main part, we will present an alternative approach for modelling constraints involving piecewise linear functions, based on ideas of constraint programming and using a convex hull relaxation. For the purpose of developing a branch-and-bound procedure specifically adapted to our constraint formulation within SCIP, all required components such as propagation, branching and separation will be discussed. In particular, we will focus on adapting well-known MIP strategies for the selection of branching variables to our type of piecewise linear constraints. Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-49112 ER - TY - GEN A1 - Hiller, Benjamin A1 - Walther, Tom T1 - Improving branching for disjunctive polyhedral models using approximate convex decompositions N2 - Disjunctive sets arise in a variety of optimization models and much esearch has been devoted to obtain strong relaxations for them. This paper focuses on the evaluation of the relaxation during the branch-and-bound search process. We argue that the branching possibilities (\ie binary variables) of the usual formulations are unsuitable to obtain strong bounds early in the search process as they do not capture the overall shape of the the entire disjunctive set. To analyze and exploit the shape of the disjunctive set we propose to compute a hierarchy of approximate convex decompositions and show how to extend the known formulations to obtain improved branching behavior. T3 - ZIB-Report - 17-68 KW - approximate convex decomposition KW - branch-and-bound KW - convex hull reformulation KW - disjunctive set Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-67462 SN - 1438-0064 ER - TY - GEN A1 - Hiller, Benjamin A1 - Saitenmacher, René A1 - Walther, Tom T1 - Analysis of operating modes of complex compressor stations N2 - We consider the modeling of operation modes for complex compressor stations (i.e., ones with several in- or outlets) in gas networks. In particular, we propose a refined model that allows to precompute tighter relaxations for each operation mode. These relaxations may be used to strengthen the compressor station submodels in gas network optimization problems. We provide a procedure to obtain the refined model from the input data for the original model. This procedure is based on a nontrivial reduction of the graph representing the gas flow through the compressor station in an operation mode. T3 - ZIB-Report - 17-65 KW - bound tightening KW - flow patterns KW - model reformulation KW - multi-way compressor station Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-68179 SN - 1438-0064 ER - TY - GEN A1 - Walther, Tom A1 - Hiller, Benjamin A1 - Saitenmacher, René T1 - Polyhedral 3D Models for compressors in gas networks N2 - Compressor machines are crucial elements in a gas transmission network, required to compensate for the pressure loss caused by friction in the pipes. Modelling all physical and technical details of a compressor machine involves a large amount of nonlinearity, which makes it hard to use such models in the optimization of large-scale gas networks. In this paper, we are going to describe a modelling approach for the operating range of a compressor machine, starting from a physical reference model and resulting in a polyhedral representation in the 3D space of mass flow throughput as well as in- and outlet pressure. T3 - ZIB-Report - 17-66 KW - gas compressor modeling, polyhedral model, accuracy, z factor Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65864 SN - 1438-0064 ER - TY - GEN A1 - Hiller, Benjamin A1 - Walther, Tom T1 - Modelling compressor stations in gas networks N2 - Gas networks are an important application area for optimization. When considering long-range transmission, compressor stations play a crucial role in these applications. The purpose of this report is to collect and systematize the models used for compressor stations in the literature. The emphasis is on recent work on simple yet accurate polyhedral models that may replace more simplified traditional models without increasing model complexity. The report also describes an extension of the compressor station data available in GasLib (http://gaslib.zib.de/) with the parameters of these models. T3 - ZIB-Report - 17-67 KW - MINLP model KW - compressor station KW - gas compressor modeling KW - nonlinear model KW - polyhedral model Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-67443 SN - 1438-0064 ER -