TY - GEN A1 - Borndörfer, Ralf A1 - Karbstein, Marika T1 - Metric Inequalities for Routings on Direct Connections N2 - We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We show that the concept of metric inequalities to characterize capacities that support a multi-commodity flow can be generalized to deal with direct connections. T3 - ZIB-Report - 14-04 KW - metric inequalities KW - direct connection KW - multi-commodity flow problem Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-44219 SN - 1438-0064 ER - TY - JOUR A1 - Pfetsch, Marc A1 - Fügenschuh, Armin A1 - Geißler, Björn A1 - Geißler, Nina A1 - Gollmer, Ralf A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Martin, Alexander A1 - Morsi, Antonio A1 - Rövekamp, Jessica A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schultz, Rüdiger A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Stangl, Claudia A1 - Steinbach, Marc A1 - Vigerske, Stefan A1 - Willert, Bernhard T1 - Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions JF - Optimization Methods and Software N2 - In this article we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: Given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements such that there exists a network state meeting all physical, technical, and legal constraints. We describe a two-stage approach to solve the resulting complex and numerically difficult feasibility problem. The first phase consists of four distinct algorithms applying linear, and methods for complementarity constraints to compute possible settings for the discrete decisions. The second phase employs a precise continuous programming model of the gas network. Using this setup, we are able to compute high quality solutions to real-world industrial instances that are significantly larger than networks that have appeared in the mathematical programming literature before. Y1 - 2014 U6 - https://doi.org/10.1080/10556788.2014.888426 PB - Taylor & Francis ER - TY - JOUR A1 - Gamrath, Gerald T1 - Improving strong branching by domain propagation JF - EURO Journal on Computational Optimization N2 - One of the essential components of a branch-and-bound based mixed-integer linear programming (MIP) solver is the branching rule. Strong branching is a method used by many state-of-the-art branching rules to select the variable to branch on. It precomputes the dual bounds of potential child nodes by solving auxiliary linear programs (LPs) and thereby helps to take good branching decisions that lead to a small search tree. In this paper, we describe how these dual bound predictions can be improved by including domain propagation into strong branching. Domain propagation is a technique MIP solvers usually apply at every node of the branch-and-bound tree to tighten the local domains of variables. Computational experiments on standard MIP instances indicate that our improved strong branching method significantly improves the quality of the predictions and causes almost no additional effort. For a full strong branching rule, we are able to obtain substantial reductions of the branch-and-bound tree size as well as the solving time. Moreover, the state-of-the-art hybrid branching rule can be improved this way as well. This paper extends previous work by the author published in the proceedings of the CPAIOR 2013. Y1 - 2014 U6 - https://doi.org/10.1007/s13675-014-0021-8 VL - 2 IS - 3 SP - 99 EP - 122 PB - Springer CY - Berlin Heidelberg ER - TY - JOUR A1 - Grötschel, Martin A1 - Stephan, Rüdiger T1 - Characterization of Facets of the Hop Constrained Chain Polytope via Dynamic Programming JF - Discrete Applied Mathematics Y1 - 2014 U6 - https://doi.org/10.1016/j.dam.2013.08.015 VL - 162 SP - 229 EP - 246 ER - TY - JOUR A1 - Bauschert, Thomas A1 - Büsing, Christina A1 - D'Andreagiovanni, Fabio A1 - Koster, Arie M.C.A. A1 - Kutschka, Manuel A1 - Steglich, Uwe T1 - Network planning under demand uncertainty with robust optimization JF - IEEE Communications Magazine Y1 - 2014 U6 - https://doi.org/10.1109/MCOM.2014.6736760 VL - 52 IS - 2 SP - 178 EP - 185 ER - TY - JOUR A1 - Betker, Andreas A1 - Kosiankowski, Dirk A1 - Lange, Christoph A1 - Pfeuffer, Frank A1 - Raack, Christian A1 - Werner, Axel ED - Helber, Stefan ED - Breitner, Michael ED - Rösch, Daniel ED - Schön, Cornelia ED - Graf von der Schulenburg, Johann-Matthias ED - Sibbertsen, Philipp ED - Steinbach, Marc ED - Weber, Stefan ED - Wolter, Anja T1 - Energy efficiency in extensive IP-over-WDM networks with protection JF - Operations Research Proceedings 2012 Y1 - 2014 U6 - https://doi.org/10.1007/978-3-319-00795-3_14 SP - 93 EP - 99 PB - Springer ER - TY - JOUR A1 - Berthold, Timo A1 - Gleixner, Ambros T1 - Undercover: a primal MINLP heuristic exploring a largest sub-MIP JF - Mathematical Programming N2 - We present Undercover, a primal heuristic for nonconvex mixed-integer nonlinear programming (MINLP) that explores a mixed-integer linear subproblem (sub-MIP) of a given MINLP. We solve a vertex covering problem to identify a minimal set of variables that need to be fixed in order to linearize each constraint, a so-called cover. Subsequently, these variables are fixed to values obtained from a reference point, e.g., an optimal solution of a linear relaxation. We apply domain propagation and conflict analysis to try to avoid infeasibilities and learn from them, respectively. Each feasible solution of the sub-MIP corresponds to a feasible solution of the original problem. We present computational results on a test set of mixed-integer quadratically constrained programs (MIQCPs) and general MINLPs from MINLPLib. It turns out that the majority of these instances allow for small covers. Although general in nature, the heuristic appears most promising for MIQCPs, and complements nicely with existing root node heuristics in different state-of-the-art solvers. Y1 - 2014 U6 - https://doi.org/10.1007/s10107-013-0635-2 VL - 144 IS - 1-2 SP - 315 EP - 346 ER - TY - GEN A1 - Vierhaus, Ingmar A1 - Fügenschuh, Armin A1 - Gottwald, Robert Lion A1 - Grösser, Stefan N. T1 - Modern Nonlinear Optimization Techniques for an Optimal Control of System Dynamics Models N2 - We study System Dynamics models with several free parameters that can be altered by the user. We assume that the user's goal is to achieve a certain dynamic behavior of the model by varying these parameters. In order to the find best possible combination of parameter settings, several automatic parameter tuning methods are described in the literature and readily available within existing System Dynamic software packages. We give a survey on the available techniques in the market and describe their theoretical background. Some of these methods are already six decades old, and meanwhile newer and more powerful optimization methods have emerged in the mathematical literature. One major obstacle for their direct use are tabled data in System Dynamics models, which are usually interpreted as piecewise linear functions. However, modern optimization methods usually require smooth functions which are twice continuously differentiable. We overcome this problem by a smooth spline interpolation of the tabled data. We use a test set of three complex System Dynamic models from the literature, describe their individual transition into optimization problems, and demonstrate the applicability of modern optimization algorithms to these System Dynamics Optimization problems. T3 - ZIB-Report - 14-08 KW - System Dynamics KW - Optimal Control KW - Nonlinear Optimization KW - Spline Interpolation Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-48159 SN - 1438-0064 ER - TY - CHAP A1 - D'Andreagiovanni, Fabio A1 - Krolikowski, Jonatan A1 - Pulaj, Jonad T1 - A hybrid primal heuristic for Robust Multiperiod Network Design T2 - EvoApplications 2014 Y1 - 2014 ER - TY - CHAP A1 - Büsing, Christina A1 - D'Andreagiovanni, Fabio T1 - A New Theoretical Framework for Robust Optimization Under Multi-Band Uncertainty T2 - Operations Research Proceedings 2012 Y1 - 2014 U6 - https://doi.org/10.1007/978-3-319-00795-3_17 SP - 115 EP - 121 ER -