TY - GEN A1 - Humpola, Jesco A1 - Fügenschuh, Armin T1 - A New Class of Valid Inequalities for Nonlinear Network Design Problems N2 - We consider a nonlinear nonconvex network design problem that arises in the extension of natural gas transmission networks. Given is such network with active and passive components, that is, valves, compressors, pressure regulators (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes of the network. 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. Assume that there does not exist a feasible flow that fulfills all physical constraints and meets the desired entry and exit amounts. Then a natural question is where to extend the network by adding pipes in the most economic way such that this flow becomes feasible. Answering this question is computationally demanding because of the difficult problem structure. We use mixed-integer nonlinear programming techniques that rely on an outer approximation of the overall problem, and a branching on decision variables. We formulate a new class of valid inequalities (or cutting planes) which reduce the overall solution time when added to the formulation. We demonstrate the computational merits of our approach on test instances. T3 - ZIB-Report - 13-06 KW - Network Design KW - Mixed-Integer Nonlinear Programming KW - Cutting Planes Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17771 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels A1 - Liebchen, Christian A1 - Masing, Berenike T1 - Forward Cycle Bases and Periodic Timetabling N2 - Periodic timetable optimization problems in public transport can be modeled as mixed-integer linear programs by means of the Periodic Event Scheduling Problem (PESP). In order to keep the branch-and-bound tree small, minimum integral cycle bases have been proven successful. We examine forward cycle bases, where no cycle is allowed to contain a backward arc. After reviewing the theory of these bases, we describe the construction of an integral forward cycle basis on a line-based event-activity network. Adding turnarounds to the instance \texttt{R1L1} of the benchmark library PESPlib, we computationally evaluate three types of forward cycle bases in the Pareto sense, and come up with significant improvements concerning dual bounds. T3 - ZIB-Report - 21-18 KW - Periodic Timetabling KW - Cycle Bases KW - Mixed Integer Programming Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82756 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels A1 - Maristany de las Casas, Pedro A1 - Schiewe, Philine T1 - Optimal Forks: Preprocessing Single-Source Shortest Path Instances with Interval Data N2 - We investigate preprocessing for single-source shortest path queries in digraphs, where arc costs are only known to lie in an interval. More precisely, we want to decide for each arc whether it is part of some shortest path tree for some realization of costs. We show that this problem is solvable in polynomial time by giving a combinatorial algorithm, using optimal structures that we call forks. Our algorithm turns out to be very efficient in practice, and is sometimes even superior in quality to a heuristic developed for the one-to-one shortest path problem in the context of passenger routing in public transport. T3 - ZIB-Report - 21-17 KW - Preprocessing Shortest Path Problems KW - Interval Data KW - Graph Algorithms Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82716 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels A1 - van Lieshout, Rolf T1 - Benders Decomposition for the Periodic Event Scheduling Problem N2 - The Periodic Event Scheduling Problem (PESP) is the central mathematical model behind the optimization of periodic timetables in public transport. We apply Benders decomposition to the incidence-based MIP formulation of PESP. The resulting formulation exhibits particularly nice features: The subproblem is a minimum cost network flow problem, and feasibility cuts are equivalent to the well-known cycle inequalities by Odijk. We integrate the Benders approach into a branch-and-cut framework, and assess the performance of this method on instances derived from the benchmarking library PESPlib. T3 - ZIB-Report - 21-29 KW - Periodic Timetabling KW - Periodic Event Scheduling Problem KW - Benders Decomposition KW - Mixed-Integer Programming Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-83338 SN - 1438-0064 ER - TY - GEN A1 - Fügenschuh, Armin A1 - Vierhaus, Ingmar T1 - System Dynamic Optimization in the Sustainability Assessment of a World-Model N2 - The System Dynamics (SD) methodology is a framework for modeling and simulating the dynamic behavior of socioeconomic systems. Characteristic for the description of such systems is the occurrence of feedback loops together with stocks and flows. The mathematical equations that describe the system are usually nonlinear. Therefore seemingly simple systems can show a nonintuitive, nonpredictable behavior over time. Controlling a dynamical system means to define a desired final state in which the system should be, and to specify potential interventions from outside that should keep the system on the right track. The central question is how to compute such globally optimal control for a given SD model. We propose a branch-and-bound approach that is based on a bound propagation method, primal heuristics, and spatial branching. We apply our new SD-control method to a small System Dynamics model, that describes the evolution of a social-economic system over time. We examine the problem of steering this system on a sustainable consumption path. T3 - ZIB-Report - 13-23 KW - System Dynamics; Mixed-Integer Nonlinear Optimization Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-18148 UR - http://opus4.kobv.de/opus4-tuberlin/frontdoor/index/index/docId/4026 SN - 1438-0064 ER - TY - GEN A1 - Hiller, Benjamin A1 - Klug, Torsten A1 - Witzig, Jakob T1 - Reoptimization in branch-and-bound algorithms with an application to elevator control N2 - We consider reoptimization (i.e. the solution of a problem based on information available from solving a similar problem) for branch-and-bound algorithms and propose a generic framework to construct a reoptimizing branch-and-bound algorithm. We apply this to an elevator scheduling algorithm solving similar subproblems to generate columns using branch-and-bound. Our results indicate that reoptimization techniques can substantially reduce the running times of the overall algorithm. T3 - ZIB-Report - 13-15 KW - reoptimization KW - branch-and-bound KW - column generation KW - elevator control Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17876 SN - 1438-0064 ER - TY - GEN A1 - Ebert, Patricia A1 - Masing, Berenike A1 - Lindner, Niels A1 - Gleixner, Ambros T1 - Sorting Criteria for Line-based Periodic Timetabling Heuristics N2 - It is well-known that optimal solutions are notoriously hard to find for the Periodic Event Scheduling Problem (PESP), which is the standard mathematical formulation to optimize periodic timetables in public transport. We consider a class of incremental heuristics that have been demonstrated to be effective by Lindner and Liebchen (2023), however, for only one fixed sorting strategy of lines along which a solution is constructed. Thus, in this paper, we examine a variety of sortings based on the number, weight, weighted span, and lower bound of arcs, and test for each setting various combinations of the driving, dwelling, and transfer arcs of lines. Additionally, we assess the impact on the incremental extension of the event-activity network by minimizing resp. maximizing a connectivity measure between subsets of lines. We compare our 27 sortings on the railway instances of the benchmarking library PESPlib within the ConcurrentPESP solver framework. We are able to find five new incumbent solutions, resulting in improvements of up to 2%. T3 - ZIB-Report - 24-07 KW - Public Transport KW - Timetabling KW - Periodic Event Scheduling Y1 - 2024 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-97826 SN - 1438-0064 ER - TY - GEN A1 - Fügenschuh, Armin A1 - Hayn, Christine A1 - Michaels, Dennis T1 - Mixed-Integer Linear Methods for Layout-Optimization of Screening Systems in Recovered Paper Production N2 - The industrial treatment of waste paper in order to regain valuable fibers from which recovered paper can be produced, involves several steps of preparation. One important step is the separation of stickies that are normally attached to the paper. If not properly separated, remaining stickies reduce the quality of the recovered paper or even disrupt the production process. For the mechanical separation process of fibers from stickies a separator screen is used. This machine has one input feed and two output streams, called the accept and the reject. In the accept the fibers are concentrated, whereas the reject has a higher concentration of stickies. The machine can be controlled by setting its reject rate. But even when the reject rate is set properly, after just a single screening step, the accept still has too many stickies, or the reject too many fibers. To get a proper separation, several separators have to be assembled into a network. From a mathematical point of view this problem can be seen as a multi-commodity network flow design problem with a nonlinear, controllable distribution function at each node. We present a nonlinear mixed-integer programming model for the simultaneous selection of a subset of separators, the network's topology, and the optimal setting of each separator. Numerical results are obtained via different types of linearization of the nonlinearities and the use of mixed-integer linear solvers, and compared with state-of-the-art global optimization software. T3 - ZIB-Report - 12-44 KW - Mixed-Integer Linear Programming KW - Nonlinear Programming KW - Piecewise Linear Approximation KW - Topology Optimization KW - Network Design Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16862 SN - 1438-0064 ER - TY - GEN A1 - Hiller, Benjamin A1 - Klug, Torsten A1 - Tuchscherer, Andreas T1 - An Exact Reoptimization Algorithm for the Scheduling of Elevator Groups N2 - The task of an elevator control is to schedule the elevators of a group such that small waiting and travel times for the passengers are obtained. We present an exact reoptimization algorithm for this problem. A reoptimization algorithm computes a new schedule for the elevator group each time a new passenger arrives. Our algorithm uses column generation techniques and is, to the best of our knowledge, the first exact reoptimization algorithms for a group of passenger elevators. To solve the column generation problem, we propose a Branch & Bound method. T3 - ZIB-Report - 12-43 KW - elevator control, online optimization, reoptimization algorithms, column generation Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16485 SN - 1438-0064 ER - TY - GEN A1 - Hiller, Benjamin A1 - Vredeveld, Tjark T1 - Stochastic dominance analysis of Online Bin Coloring algorithms N2 - This paper proposes a new method for probabilistic analysis of online algorithms. It is based on the notion of stochastic dominance. We develop the method for the online bin coloring problem introduced by Krumke et al (2008). Using methods for the stochastic comparison of Markov chains we establish the result that the performance of the online algorithm GreedyFit is stochastically better than the performance of the algorithm OneBin for any number of items processed. This result gives a more realistic picture than competitive analysis and explains the behavior observed in simulations. T3 - ZIB-Report - 12-42 KW - online algorithms, stochastic dominance, algorithm analysis, Markov chains Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16502 SN - 1438-0064 ER - TY - THES A1 - Gamrath, Gerald T1 - Generic Branch-Cut-and-Price N2 - In this thesis, we present the theoretical background, implementational details and computational results concerning the generic branch-cut-and-price solver GCG. KW - mixed-integer programming KW - column generation KW - branch-and-price Y1 - 2010 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57543 ER -