TY - GEN 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 N2 - The planning of a communication network is inevitably depending on the quality of both the planning tool and the demand forecast used. In this article, we show exemplarily how the emerging area of Robust Optimization can advance the network planning by a more accurate mathematical description of the demand uncertainty. After a general introduction of the concept and its application to a basic network design problem, we present two applications: multi-layer and mixed-line-rate network design. We conclude with a discussion of extensions of the robustness concept to increase the accuracy of handling uncertainties. T3 - ZIB-Report - 13-59 KW - Network Design, Demand Uncertainty, Robust Optimization, Telecommunications Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42557 SN - 1438-0064 ER - TY - GEN A1 - Becker, Kai-Helge A1 - Hiller, Benjamin T1 - Efficient Enumeration of Acyclic Graph Orientations with Sources or Sinks Revisited N2 - In a recent paper, Conte et al. [CGMR2017] presented an algorithm for enumerating all acyclic orientations of a graph G=(V,E) with a single source (and related orientations) with delay O(|V||E|). In this paper we revisit the problem by going back to an early paper by de Fraysseix et al. [FMR1995], who proposed an algorithm for enumerating all bipolar orientations of a graph based on a recursion formula. We first formalize de Fraysseix et al.'s algorithm for bipolar orientations and determine that its delay is also O(|V||E|). We then apply their recursion formula to the case of Conte et al.'s enumeration problem and show that this yields a more efficient enumeration algorithm with delay O(\sqrt(|V|)|E|). Finally, a way to further streamline the algorithm that leads to a particularly simple implementation is suggested. T3 - ZIB-Report - 20-05 KW - acyclic orientations KW - enumeration algorithm KW - multiple sources and sinks KW - bipolar orientations Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-77684 SN - 1438-0064 ER - TY - GEN A1 - Bley, Andreas A1 - D'Andreagiovanni, Fabio A1 - Karch, Daniel T1 - Scheduling technology migration in WDM Networks N2 - The rapid technological evolution of telecommunication networks demands service providers to regularly update their technology, with the aim of remaining competitive in the marketplace. However, upgrading the technology in a network is not a trivial task. New hardware components need to be installed in the network and during the installation network connectivity may be temporarily compromised. The Wavelength Division Multiplexing (WDM) technology, whose upgrade is considered in here, shares fiber links among several optical connections and tearing down a single link may disrupt several optical connections at once. When the upgrades involve large parts of a network, typically not all links can be upgraded in parallel, which may lead to an unavoidable longer disruption of some connections. A bad scheduling of the overall endeavor, however, can dramatically increase the disconnection time of parts of the networks, causing extended service disruption. In this contribution, we study the problem of finding a schedule of the fiber link upgrades that minimizes the total service disruption time. To the best of our knowledge, this problem has not yet been formalized and investigated. The aim of our work is to close this gap by presenting a mathematical optimization model for the problem and an innovative solution algorithm that tackles the intrinsic difficulties of the problem. Computational experience on realistic instances completes our study. Our original investigations have been driven by real needs of DFN, operator of the German National Research and Education Network and our partner in the BMBF research project ROBUKOM (http://www.robukom.de/). T3 - ZIB-Report - 13-62 KW - Scheduling, Extended Formulations, Network Migration, WDM Networks Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42654 UR - http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6507677&isnumber=6507670 SN - 1438-0064 ER - TY - GEN A1 - Büsing, Christina A1 - D'Andreagiovanni, Fabio T1 - A new theoretical framework for Robust Optimization under multi-band uncertainty N2 - We provide an overview of our main results about studying Linear Programming Problems whose coefficient matrix is subject to uncertainty and the uncertainty is modeled through a multi-band set. Such an uncertainty set generalizes the classical one proposed by Bertsimas and Sim and is particularly suitable in the common case of arbitrary non-symmetric distributions of the parameters. Our investigations were inspired by practical needs of our industrial partner in ongoing projects with focus on the design of robust telecommunications networks. T3 - ZIB-Report - 13-61 KW - Robust Optimization, Uncertainty Set, Multiband Robustness, Network Design Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42644 UR - http://www.springer.com/business+%26+management/operations+research/book/978-3-319-00794-6 SN - 1438-0064 ER - TY - GEN A1 - Büsing, Christina A1 - D'Andreagiovanni, Fabio A1 - Raymond, Annie T1 - 0-1 Multiband Robust Optimization N2 - We provide an overview of new theoretical results that we obtained while further investigating multiband robust optimization, a new model for robust optimization that we recently proposed to tackle uncertainty in mixed-integer linear programming. This new model extends and refines the classical Gamma-robustness model of Bertsimas and Sim and is particularly useful in the common case of arbitrary asymmetric distributions of the uncertainty. Here, we focus on uncertain 0-1 programs and we analyze their robust counterparts when the uncertainty is represented through a multiband set. Our investigations were inspired by the needs of our industrial partners in the research project ROBUKOM. T3 - ZIB-Report - 13-77 KW - Combinatorial Optimization, Robust Optimization, Multiband Robustness, Network Design Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-44093 SN - 1438-0064 ER - TY - GEN A1 - D'Andreagiovanni, Fabio A1 - Krolikowski, Jonatan A1 - Pulaj, Jonad T1 - A hybrid primal heuristic for Robust Multiperiod Network Design N2 - We investigate the Robust Multiperiod Network Design Problem, a generalization of the classical Capacitated Network Design Problem that additionally considers multiple design periods and provides solutions protected against traffic uncertainty. Given the intrinsic difficulty of the problem, which proves challenging even for state-of-the art commercial solvers, we propose a hybrid primal heuristic based on the combination of ant colony optimization and an exact large neighborhood search. Computational experiments on a set of realistic instances from the SNDlib show that our heuristic can find solutions of extremely good quality with low optimality gap. T3 - ZIB-Report - 13-78 KW - Multiperiod Network Design, Traffic Uncertainty, Robust Optimization, Multiband Robustness, Hybrid Heuristics Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-44081 SN - 1438-0064 ER - TY - GEN A1 - D'Andreagiovanni, Fabio A1 - Raymond, Annie T1 - Multiband Robust Optimization and its Adoption in Harvest Scheduling N2 - A central assumption in classical optimization is that all the input data of a problem are exact. However, in many real-world problems, the input data are subject to uncertainty. In such situations, neglecting uncertainty may lead to nominally optimal solutions that are actually suboptimal or even infeasible. Robust optimization offers a remedy for optimization under uncertainty by considering only the subset of solutions protected against the data deviations. In this paper, we provide an overview of the main theoretical results of multiband robustness, a new robust optimization model that extends and refines the classical theory introduced by Bertsimas and Sim. After introducing some new results for the special case of pure binary programs, we focus on the harvest scheduling problem and show how multiband robustness can be adopted to tackle the uncertainty affecting the volume of produced timber and grant a reduction in the price of robustness. T3 - ZIB-Report - 13-76 KW - Data Uncertainty KW - Robust Optimization KW - Multiband Robustness KW - Harvest Scheduling Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-43380 SN - 1438-0064 ER - TY - GEN A1 - Griewank, Andreas A1 - Streubel, Tom A1 - Lehmann, Lutz A1 - Hasenfelder, Richard A1 - Radons, Manuel T1 - Piecewise linear secant approximation via Algorithmic Piecewise Differentiation N2 - It is shown how piecewise differentiable functions \(F: R^n → R^m\) that are defined by evaluation programs can be approximated locally by a piecewise linear model based on a pair of sample points x̌ and x̂. We show that the discrepancy between function and model at any point x is of the bilinear order O(||x − x̌|| ||x − x̂||). This is a little surprising since x ∈ R^n may vary over the whole Euclidean space, and we utilize only two function samples F̌ = F(x̌) and F̂ = F(x̂), as well as the intermediates computed during their evaluation. As an application of the piecewise linearization procedure we devise a generalized Newton’s method based on successive piecewise linearization and prove for it sufficient conditions for convergence and convergence rates equaling those of semismooth Newton. We conclude with the derivation of formulas for the numerically stable implementation of the aforedeveloped piecewise linearization methods. T3 - ZIB-Report - 16-54 KW - Automatic differentiation KW - Computational graph KW - Lipschitz continuity KW - Generalized Hermite interpolation KW - ADOL-C Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61642 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 - GEN A1 - Hiller, Benjamin A1 - Vredeveld, Tjark T1 - Probabilistic alternatives for competitive analysis N2 - In the last 20 years competitive analysis has become the main tool for analyzing the quality of online algorithms. Despite of this, competitive analysis has also been criticized: It sometimes cannot discriminate between algorithms that exhibit significantly different empirical behavior, or it even favors an algorithm that is worse from an empirical point of view. Therefore, there have been several approaches to circumvent these drawbacks. In this survey, we discuss probabilistic alternatives for competitive analysis. T3 - ZIB-Report - 11-55 KW - online algorithms KW - probabilistic analysis KW - competitive analysis KW - survey Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-15131 SN - 1438-0064 ER - TY - GEN A1 - Ito, Satoshi A1 - Shinano, Yuji T1 - Calculation of clinch and elimination numbers for sports leagues with multiple tiebreaking criteria N2 - The clinch (elimination) number is a minimal number of future wins (losses) needed to clinch (to be eliminated from) a specified place in a sports league. Several optimization models and computational results are shown in this paper for calculating clinch and elimination numbers in the presence of predefined multiple tiebreaking criteria. The main subject of this paper is to provide a general algorithmic framework based on integer programming with utilizing possibly multilayered upper and lower bounds. T3 - ZIB-Report - 18-51 KW - Sports league KW - Round-robin tournament KW - Tiebreaking criteria KW - Clinch number KW - Elimination number KW - Combinatorial optimization KW - Integer programming Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-70591 SN - 1438-0064 ER - TY - GEN A1 - Lindner, Niels A1 - Reisch, Julian T1 - Parameterized Complexity of Periodic Timetabling N2 - Public transportation networks are typically operated with a periodic timetable. The Periodic Event Scheduling Problem (PESP) is the standard mathematical modelling tool for periodic timetabling. Since PESP can be solved in linear time on trees, it is a natural question to ask whether there are polynomial-time algorithms for input networks of bounded treewidth. We show that deciding the feasibility of a PESP instance is NP-hard even when the treewidth is 2, the branchwidth is 2, or the carvingwidth is 3. Analogous results hold for the optimization of reduced PESP instances, where the feasibility problem is trivial. To complete the picture, we present two pseudo-polynomial-time dynamic programming algorithms solving PESP on input networks with bounded tree- or branchwidth. We further analyze the parameterized complexity of PESP with bounded cyclomatic number, diameter, or vertex cover number. For event-activity networks with a special -- but standard -- structure, we give explicit and sharp bounds on the branchwidth in terms of the maximum degree and the carvingwidth of an underlying line network. Finally, we investigate several parameters on the smallest instance of the benchmarking library PESPlib. T3 - ZIB-Report - 20-15 KW - Parameterized complexity KW - Periodic timetabling KW - Treewidth KW - Branchwidth KW - Carvingwidth KW - Periodic Event Scheduling Problem Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78314 SN - 1438-0064 ER - TY - GEN A1 - Munguia, Lluis-Miquel A1 - Oxberry, Geoffrey A1 - Rajan, Deepak A1 - Shinano, Yuji T1 - Parallel PIPS-SBB: Multi-Level Parallelism For Stochastic Mixed-Integer Programs N2 - PIPS-SBB is a distributed-memory parallel solver with a scalable data distribution paradigm. It is designed to solve MIPs with a dual-block angular structure, which is characteristic of deterministic-equivalent Stochastic Mixed-Integer Programs (SMIPs). In this paper, we present two different parallelizations of Branch & Bound (B&B), implementing both as extensions of PIPS-SBB, thus adding an additional layer of parallelism. In the first of the proposed frameworks, PIPS-PSBB, the coordination and load-balancing of the different optimization workers is done in a decentralized fashion. This new framework is designed to ensure all available cores are processing the most promising parts of the B&B tree. The second, ug[PIPS-SBB,MPI], is a parallel implementation using the Ubiquity Generator (UG), a universal framework for parallelizing B&B tree search that has been successfully applied to other MIP solvers. We show the effects of leveraging multiple levels of parallelism in potentially improving scaling performance beyond thousands of cores. T3 - ZIB-Report - 17-58 KW - PIPS-SBB, UG, Parallel Branch and Bound Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65517 SN - 1438-0064 IS - ZIB-Report 17-58 ER - TY - GEN A1 - Orlowski, Sebastian A1 - Werner, Axel A1 - Wessäly, Roland T1 - Estimating trenching costs in FTTx network planning N2 - In this paper we assess to which extent trenching costs of an FTTx network are unavoidable, even if technical side constraints are neglected. For that purpose we present an extended Steiner tree model. Using a variety of realistic problem instances we demonstrate that the total trenching cost can only be reduced by about 5 percent in realistic scenarios. This work has been funded by BMBF (German Federal Ministry of Education and Research) within the program "KMU-innovativ". T3 - ZIB-Report - 11-49 KW - Optical access networks KW - Optimization KW - Steiner trees Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14884 SN - 1438-0064 ER - TY - GEN A1 - Pfeuffer, Frank A1 - Werner, Axel T1 - Adaptive telecommunication network operation with a limited number of reconfigurations N2 - Rising traffic in telecommunication networks lead to rising energy costs for the network operators. Meanwhile, increased flexibility of the networking hardware may help to realize load-adaptive operation of the networks to cut operation costs. To meet network operators’ concerns over stability, we propose to switch network configurations only a limited number of times per day. We present a method for the integrated computation of optimal switching times and network configurations that alternatingly solves mixed-integer programs and constrained shortest cycle problems in a certain graph. Similarly to the Branch & Bound Algorithm, it uses lower and upper bounds on the optimum value and allows for pivoting strategies to guide the computation and avoid the solution of irrelevant subproblems. The algorithm can act as a framework to be adapted and applied to suitable problems of different origin. T3 - ZIB-Report - 15-36 KW - Telecommunication KW - Network Design KW - Dynamic Traffic KW - Branch and Bound Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-55547 SN - 1438-0064 ER - TY - GEN A1 - Shinano, Yuji T1 - The Ubiquity Generator Framework: 7 Years of Progress in Parallelizing Branch-and-Bound N2 - Mixed integer linear programming (MIP) is a general form to model combinatorial optimization problems and has many industrial applications. The performance of MIP solvers has improved tremendously in the last two decades and these solvers have been used to solve many real-word problems. However, against the backdrop of modern computer technology, parallelization is of pivotal importance. In this way, ParaSCIP is the most successful parallel MIP solver in terms of solving previously unsolvable instances from the well-known benchmark instance set MIPLIB by using supercomputers. It solved two instances from MIPLIB2003 and 12 from MIPLIB2010 for the first time to optimality by using up to 80,000 cores on supercomputers. ParaSCIP has been developed by using the Ubiquity Generator (UG) framework, which is a general software package to parallelize any state-of-the-art branch-and-bound based solver. This paper discusses 7 years of progress in parallelizing branch-and-bound solvers with UG. T3 - ZIB-Report - 17-60 KW - Parallelization, Branch-and-bound, Mixed Integer Programming, UG, ParaSCIP, FiberSCIP, ParaXpress, FiberXpress, SCIP-Jack Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65545 SN - 1438-0064 ER - TY - GEN A1 - Shinano, Yuji A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Winkler, Michael T1 - Solving Previously Unsolved MIP Instances with ParaSCIP on Supercomputers by using up to 80,000 Cores N2 - Mixed-integer programming (MIP) problem is arguably among the hardest classes of optimization problems. This paper describes how we solved 21 previously unsolved MIP instances from the MIPLIB benchmark sets. To achieve these results we used an enhanced version of ParaSCIP, setting a new record for the largest scale MIP computation: up to 80,000 cores in parallel on the Titan supercomputer. In this paper, we describe the basic parallelization mechanism of ParaSCIP, improvements of the dynamic load balancing and novel techniques to exploit the power of parallelization for MIP solving. We give a detailed overview of computing times and statistics for solving open MIPLIB instances. T3 - ZIB-Report - 20-16 KW - Mixed Integer Programming, Parallel processing, Node merging, Racing, ParaSCIP, Ubiquity Generator Framework, MIPLIB Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78393 SN - 1438-0064 ER - TY - GEN A1 - Shinano, Yuji A1 - Achterberg, Tobias A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Koch, Thorsten A1 - Winkler, Michael T1 - Solving Open MIP Instances with ParaSCIP on Supercomputers using up to 80,000 Cores N2 - This paper describes how we solved 12 previously unsolved mixed-integer program- ming (MIP) instances from the MIPLIB benchmark sets. To achieve these results we used an enhanced version of ParaSCIP, setting a new record for the largest scale MIP computation: up to 80,000 cores in parallel on the Titan supercomputer. In this paper we describe the basic parallelization mechanism of ParaSCIP, improvements of the dynamic load balancing and novel techniques to exploit the power of parallelization for MIP solving. We give a detailed overview of computing times and statistics for solving open MIPLIB instances. T3 - ZIB-Report - 15-53 KW - Mixed Integer Programming KW - Parallel processing KW - Node merging KW - Racing ParaSCIP KW - Ubiquity Generator Framework KW - MIPLIB Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-56404 SN - 1438-0064 ER - TY - GEN A1 - Shinano, Yuji A1 - Heinz, Stefan A1 - Vigerske, Stefan A1 - Winkler, Michael T1 - FiberSCIP - A shared memory parallelization of SCIP N2 - Recently, parallel computing environments have become significantly popular. In order to obtain the benefit of using parallel computing environments, we have to deploy our programs for these effectively. This paper focuses on a parallelization of SCIP (Solving Constraint Integer Programs), which is a MIP solver and constraint integer programming framework available in source code. There is a parallel extension of SCIP named ParaSCIP, which parallelizes SCIP on massively parallel distributed memory computing environments. This paper describes FiberSCIP, which is yet another parallel extension of SCIP to utilize multi-threaded parallel computation on shared memory computing environments, and has the following contributions: First, the basic concept of having two parallel extensions and the relationship between them and the parallelization framework provided by UG (Ubiquity Generator) is presented, including an implementation of deterministic parallelization. Second, the difficulties to achieve a good performance that utilizes all resources on an actual computing environment and the difficulties of performance evaluation of the parallel solvers are discussed. Third, a way to evaluate the performance of new algorithms and parameter settings of the parallel extensions is presented. Finally, current performance of FiberSCIP for solving mixed-integer linear programs (MIPs) and mixed-integer non-linear programs (MINLPs) in parallel is demonstrated. T3 - ZIB-Report - 13-55 KW - parallel KW - branch-and-bound KW - deterministic parallelism KW - constraint integer programming KW - mixed integer programming KW - mixed integer nonlinear programming KW - SCIP KW - MIP KW - MINLP Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42595 SN - 1438-0064 ER - TY - GEN A1 - Shinano, Yuji A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Building Optimal Steiner Trees on Supercomputers by using up to 43,000 Cores N2 - SCIP-JACK is a customized, branch-and-cut based solver for Steiner tree and related problems. ug [SCIP-JACK, MPI] extends SCIP-JACK to a massively par- allel solver by using the Ubiquity Generator (UG) framework. ug [SCIP-JACK, MPI] was the only solver that could run on a distributed environment at the (latest) 11th DIMACS Challenge in 2014. Furthermore, it could solve three well-known open instances and updated 14 best known solutions to instances from the bench- mark libary STEINLIB. After the DIMACS Challenge, SCIP-JACK has been con- siderably improved. However, the improvements were not reflected on ug [SCIP- JACK, MPI]. This paper describes an updated version of ug [SCIP-JACK, MPI], especially branching on constrains and a customized racing ramp-up. Furthermore, the different stages of the solution process on a supercomputer are described in detail. We also show the latest results on open instances from the STEINLIB. T3 - ZIB-Report - 18-58 Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-71118 SN - 1438-0064 ER - TY - THES A1 - Witzig, Jakob T1 - Reoptimization Techniques in MIP Solvers N2 - Many optimization problems can be modeled as Mixed Integer Programs (MIPs). In general, MIPs cannot be solved efficiently, since solving MIPs is NP-hard, see, e.g., Schrijver, 2003. Common methods for solving NP-hard problems are branch-and-bound and column generation. In the case of column generation, the original problem becomes decomposed or re-formulated into one ore more smaller subproblems, which are easier to solve. Each of these subproblems is solved separately and recurrently, which can be interpreted as solving a sequence of optimization problems. In this thesis, we consider a sequence of MIPs which only differ in the respective objective functions. Furthermore, we assume each of these MIPs get solved with a branch-and-bound algorithm. This thesis aims to figure out whether the solving process of a given sequence of MIPs can be accelerated by reoptimization. As reoptimization we understand starting the solving process of a MIP of this sequence at a given frontier of a search tree corresponding to another MIP of this sequence. At the beginning we introduce an LP-based branch-and-bound algorithm. This algorithm is inspired by the reoptimizing algorithm of Hiller, Klug, and the author of this thesis, 2013. Since most of the state-of-the-art MIP solvers come to decisions based on dual information, which leads to the loss of feasible solutions after changing the objective function, we present a technique to guarantee optimality despite using these information. A decision is based on a dual information if this decision is valid for at least one feasible solution, whereas a decision is based on a primal information if this decision is valid for all feasible solutions. Afterwards, we consider representing the search frontier of the tree by a set of nodes of a given size. We call this the Tree Compression Problem. Moreover, we present a criterion characterizing the similarity of two objective functions. To evaluate our approach of reoptimization we extend the well-known and well-maintained MIP solver SCIP to an LP-based branch-and-bound framework, introduce two heuristics for solving the Tree Compression Problem, and a primal heuristic which is especially fitted to column generation. Finally, we present computational experiments on several problem classes, e.g., the Vertex Coloring and k-Constrained Shortest Path. Our experiments show, that a straightforward reoptimization, i.e., without additional heuristics, provides no benefit in general. However, in combination with the techniques and methods presented in this thesis, we can accelerate the solving of a given sequence up to the factor 14. For this purpose it is essential to take the differences of the objective functions into account and to restart the reoptimization, i.e., solve the subproblem from scratch, if the objective functions are not similar enough. Finally, we discuss the possibility to parallelize the solving process of the search frontier at the beginning of each solving process. Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-54067 ER - TY - THES A1 - Witzig, Jakob T1 - Effiziente Reoptimierung in Branch&Bound-Verfahren für die Steuerung von Aufzügen N2 - Heutzutage ist eine Vielzahl der mehrstöckigen Gebäude mit Personenaufzugsgruppen ausgestattet. Uns wohl bekannt sind die sogenannten konventionellen Systeme. Bei diesen Systemen betätigt jeder ankommende Passagier eine der beiden Richtungstasten und teilt dem dahinterstehenden Steuerungsalgorithmus seine gewünschte Startetage und Fahrtrichtung mit. Betreten wird der zuerst auf der Startetage ankommende Aufzug mit gleicher Fahrtrichtung und ausreichend Kapazität. Die entsprechende Zieletage wird dem System erst nach dem Betreten der Fahrgastkabine mitgeteilt. Neben diesen konventionellen Systemen gibt es Aufzugsgruppen mit Zielrufsteuerung. Die Besonderheit eines zielrufgesteuerten Systems ist, dass ein ankommender Passagier bereits auf der Startetage seine gewünschte Zieletage angibt und eine Rückmeldung vom System erhält, welchen Aufzug er nutzen soll. Diese Zuweisung durch das System hat das Ziel, die Warte- und Reisezeiten der Passagiere zu minimieren. Ein wesentlicher Faktor bei der Berechnung warte- und reisezeitminimaler Fahrpläne ist das momentane Verkehrsmuster. Eine Einteilung der Verkehrsszenarien lässt sich am besten bei Bürogebäuden vornehmen. So ist es typisch für die Morgenstunden, dass jeder Passagier auf einer Zugangsebene seine Fahrt beginnt und alle Passagiere die gleiche Fahrtrichtung haben. Unter einer Zugangsebene ist z. B. der Haupteingang oder ein Parkdeck zu verstehen. Ein weiterer wesentlicher Punkt bei Zielrufsystemen ist die Art der Zuweisung der Passagiere durch das System. Zum einen gibt es unmittelbar zuweisende (UZ-) Systeme. In einem UZ-System wird nach jeder Ankunft eines Passagiers eine Momentaufnahme des momentanen Verkehrs erstellt und es findet eine Neuplanung und Zuweisung statt. Eine solche Momentaufnahme werden wir im späteren Verkauf als Schnappschussproblem bezeichnen. Jeder Passagier bekommt im Anschluss an die Lösung des Schnappschussproblems eine Mitteilung vom System, z. B. über ein Display, welchen Aufzug er benutzen soll. Zum anderen gibt es verzögert zuweisende (VZ-) Systeme. In diesen Systemen wird die Erstellung und Lösung eines Schnappschussproblems bis kurz vor Ankunft eines Aufzuges auf einer Etage verzögert. In einem VZ-System teilt das System allen wartenden Passagieren die geplanten Zieletagen des ankommenden Aufzugs mit. Jeder Passagier, der einen Ruf getätigt hat und zu einer dieser Zieletagen fahren will, kann jetzt diesen Aufzug betreten. Durch die Verzögerung muss im Vergleich zu einem UZ-System eine weitaus größere Menge von Passagieren zugewiesen werden. Dadurch kann der Lösungsprozess bedeutend aufwändiger werden. Vorteil eines VZ-Systems ist hingegen der größere Freiheitsgrad bei der Optimierung, da aufgrund der späten Zuweisung die weitere Verkehrsentwicklung mit einbezogen werden kann. VZ-Systeme sind aufgrund des größeren Freiheitsgrades interessant für die Praxis ist, wir uns demzufolge in dieser Arbeit mit einer effizienteren Lösung dieser Art von Schnappschussproblemen befassen. Es genügt dabei den Lösungsprozess eines Schnappschussproblems zu betrachten. Das Ziel ist eine Reduzierung der benötigten Rechenzeit. Unter Reoptimierung verstehen wir die Konstruktion zulässiger Spalten in den jeweiligen Iterationsrunden der Spaltengenerierung innerhalb eines Schnappschussproblems. Als eine Iterationsrunde bezeichnet wir einer Menge zulässiger Touren mit negativen reduzierten Kosten. Eine effiziente Reoptimierung zeichnet sich durch die Wiederverwendung und Aufbereitung von Informationen aus vorangegangenen Iterationsrunden desselben Schnappschussproblems aus. Zu den wichtigen Informationen gehört der konstruierte Suchbaum der vorherigen Iterationsrunde mit seinen ausgeloteten (abgeschnittenen) Blättern sowie konstruierten Touren bzw. Spalten, welche in der Iterationsrunde ihrer Konstruktion nicht zur Lösung des Teilproblems der Spaltengenerierung beitrugen. Eine solche Wiederverwendung und Aufbereitung von Informationen nennen wir Warmstart. Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42210 ER - TY - GEN A1 - Zakrzewska, Anna A1 - D'Andreagiovanni, Fabio A1 - Ruepp, Sarah A1 - Berger, Michael S. T1 - Biobjective Optimization of Radio Access Technology Selection and Resource Allocation in Heterogeneous Wireless Networks N2 - We propose a novel optimization model for resource assignment in heterogeneous wireless network. The model adopts two objective functions maximizing the number of served users and the minimum granted utility at once. A distinctive feature of our new model is to consider two consecutive time slots, in order to include handover as an additional decision dimension. Furthermore, the solution algorithm that we propose refines a heuristic solution approach recently proposed in literature, by considering a real joint optimization of the considered resources. The simulation study shows that the new model leads to a significant reduction in handover frequency, when compared to a traditional scheme based on maximum SNR. T3 - ZIB-Report - 13-63 KW - Heterogeneous Wireless Networks, Biobjective Optimization, Mixed Integer Linear Programming, Simulation Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42675 UR - http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6576416&isnumber=6576384 SN - 1438-0064 ER -