TY - CHAP A1 - Streubel, Tom A1 - Strohm, Christian A1 - Trunschke, Philipp A1 - Tischendorf, Caren T1 - Generic Construction and Efficient Evaluation of Network DAEs and Their Derivatives in the Context of Gas Networks T2 - Operations Research Proceedings 2017 N2 - We present a concept that provides an efficient description of differential-algebraic equations (DAEs) describing flow networks which provides the DAE function f and their Jacobians in an automatized way such that the sparsity pattern of the Jacobians is determined before their evaluation and previously determined values of f can be exploited. The user only has to provide the network topology and local function descriptions for each network element. The approach uses automatic differentiation (AD) and is adapted to switching element functions via the abs-normal-form (ANF). KW - compressed sparse row format KW - algorithmic differentiation KW - abs-normal form KW - piecewise linear tangent approximation KW - piecewise smooth Y1 - 2018 SN - 978-3-319-89920-6 U6 - https://doi.org/10.1007/978-3-319-89920-6_83 SP - 627 EP - 632 PB - Springer International Publishing ER - TY - CHAP A1 - Gamrath, Gerald A1 - Schubert, Christoph T1 - Measuring the impact of branching rules for mixed-integer programming T2 - Operations Research Proceedings 2017 N2 - Branching rules are an integral component of the branch-and-bound algorithm typically used to solve mixed-integer programs and subject to intense research. Different approaches for branching are typically compared based on the solving time as well as the size of the branch-and-bound tree needed to prove optimality. The latter, however, has some flaws when it comes to sophisticated branching rules that do not only try to take a good branching decision, but have additional side-effects. We propose a new measure for the quality of a branching rule that distinguishes tree size reductions obtained by better branching decisions from those obtained by such side-effects. It is evaluated for common branching rules providing new insights in the importance of strong branching. Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-89920-6_23 SP - 165 EP - 170 PB - Springer International Publishing ER - TY - CHAP A1 - Hennings, Felix T1 - Benefits and Limitations of Simplified Transient Gas Flow Formulations T2 - Operations Research Proceedings 2017 N2 - Although intensively studied in recent years, the optimization of the transient (time-dependent) control of large real-world gas networks is still out of reach for current state-of-the-art approaches. For this reason, we present further simplifications of the commonly used model, which lead to a linear description of the gas flow on pipelines. In an empirical analysis of real-world data, we investigate the properties of the involved quantities and evaluate the errors made by our simplification. Y1 - 2018 UR - https://link.springer.com/chapter/10.1007/978-3-319-89920-6_32 U6 - https://doi.org/10.1007/978-3-319-89920-6_32 VL - Operations Research Proceedings SP - 231 EP - 237 PB - Springer, Cham ER - TY - CHAP A1 - Hoppmann, Kai A1 - Schwarz, Robert T1 - Finding Maximum Minimum Cost Flows to Evaluate Gas Network Capacities T2 - Operations Research Proceedings 2017 N2 - In this article we consider the following problem arising in the context of scenario generation to evaluate the transport capacity of gas networks: In the Uncapacitated Maximum Minimum Cost Flow Problem (UMMCF) we are given a flow network where each arc has an associated nonnegative length and infinite capacity. Additionally, for each source and each sink a lower and an upper bound on its supply and demand are known, respectively. The goal is to find values for the supplies and demands respecting these bounds, such that the optimal value of the induced Minimum Cost Flow Problem is maximized, i.e., to determine a scenario with maximum transportmoment. In this article we propose two linear bilevel optimization models for UMMCF, introduce a greedy-style heuristic, and report on our first computational experiment. Y1 - 2018 SN - 978-3-319-89919-0 U6 - https://doi.org/10.1007/978-3-319-89920-6_46 SP - 339 EP - 346 ER - TY - CHAP A1 - Miltenberger, Matthias A1 - Ralphs, Ted A1 - Steffy, Daniel T1 - Exploring the Numerics of Branch-and-Cut for Mixed Integer Linear Optimization T2 - Operations Research Proceedings 2017 N2 - We investigate how the numerical properties of the LP relaxations evolve throughout the solution procedure in a solver employing the branch-and-cut algorithm. The long-term goal of this work is to determine whether the effect on the numerical conditioning of the LP relaxations resulting from the branching and cutting operations can be effectively predicted and whether such predictions can be used to make better algorithmic choices. In a first step towards this goal, we discuss here the numerical behavior of an existing solver in order to determine whether our intuitive understanding of this behavior is correct. Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-89920-6 SP - 151 EP - 157 PB - Springer International Publishing ER - TY - CHAP A1 - Müller, Benjamin A1 - Kuhlmann, Renke A1 - Vigerske, Stefan T1 - On the performance of NLP solvers within global MINLP solvers T2 - Operations Research Proceedings 2017 N2 - Solving mixed-integer nonlinear programs (MINLPs) to global optimality efficiently requires fast solvers for continuous sub-problems. These appear in, e.g., primal heuristics, convex relaxations, and bound tightening methods. Two of the best performing algorithms for these sub-problems are Sequential Quadratic Programming (SQP) and Interior Point Methods. In this paper we study the impact of different SQP and Interior Point implementations on important MINLP solver components that solve a sequence of similar NLPs. We use the constraint integer programming framework SCIP for our computational studies. Y1 - 2018 U6 - https://doi.org/10.1007/978-3-319-89920-6_84 SP - 633 EP - 639 PB - Springer International Publishing ER -