TY - THES A1 - Eifler, Leon T1 - Mixed-Integer Programming for Clustering in Non-reversible Markov Processes N2 - The topic of this thesis is the examination of an optimization model which stems from the clustering process of non-reversible markov processes. We introduce the cycle clustering problem und formulate it as a mixed integer program (MIP). We prove that this problem is N P-hard and discuss polytopal aspects such as facets and dimension. The focus of this thesis is the development of solving methods for this clustering problem. We develop problem specific primal heuristics, as well as separation methods and an approximation algorithm. These techniques are implemented in practice as an application for the MIP solver SCIP. Our computational experiments show that these solving methods result in an average speedup of ×4 compared to generic solvers and that our application is able to solve more instances to optimality within the given time limit of one hour. KW - Markov State Models KW - NESS KW - Non-reversible Markov Processes KW - Mixed-Integer Programming Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66486 ER - TY - JOUR A1 - Bernal, David E. A1 - Vigerske, Stefan A1 - Trespalacios, Francisco A1 - Grossmann, Ignacio E. T1 - Improving the performance of DICOPT in convex MINLP problems using a feasibility pump JF - Optimization Methods and Software N2 - The solver DICOPT is based on an outer-approximation algorithm used for solving mixed- integer nonlinear programming (MINLP) problems. This algorithm is very effective for solving some types of convex MINLPs. However, there are certain problems that are diffcult to solve with this algorithm. One of these problems is when the nonlinear constraints are so restrictive that the nonlinear subproblems produced by the algorithm are infeasible. This problem is addressed in this paper with a feasibility pump algorithm, which modifies the objective function in order to efficiently find feasible solutions. It has been implemented as a preprocessing algorithm for DICOPT. Computational comparisons with previous versions of DICOPT and other MINLP solvers on a set of convex MINLPs demonstrate the effectiveness of the proposed algorithm in terms of solution quality and solving time. Y1 - 2017 ER - TY - GEN A1 - Gleixner, Ambros A1 - Eifler, Leon A1 - Gally, Tristan A1 - Gamrath, Gerald A1 - Gemander, Patrick A1 - Gottwald, Robert Lion A1 - Hendel, Gregor A1 - Hojny, Christopher A1 - Koch, Thorsten A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Viernickel, Jan Merlin A1 - Vigerske, Stefan A1 - Weninger, Dieter A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 5.0 N2 - This article describes new features and enhanced algorithms made available in version 5.0 of the SCIP Optimization Suite. In its central component, the constraint integer programming solver SCIP, remarkable performance improvements have been achieved for solving mixed-integer linear and nonlinear programs. On MIPs, SCIP 5.0 is about 41 % faster than SCIP 4.0 and over twice as fast on instances that take at least 100 seconds to solve. For MINLP, SCIP 5.0 is about 17 % faster overall and 23 % faster on instances that take at least 100 seconds to solve. This boost is due to algorithmic advances in several parts of the solver such as cutting plane generation and management, a new adaptive coordination of large neighborhood search heuristics, symmetry handling, and strengthened McCormick relaxations for bilinear terms in MINLPs. Besides discussing the theoretical background and the implementational aspects of these developments, the report describes recent additions for the other software packages connected to SCIP, in particular for the LP solver SoPlex, the Steiner tree solver SCIP-Jack, the MISDP solver SCIP-SDP, and the parallelization framework UG. T3 - ZIB-Report - 17-61 KW - constraint integer programming KW - linear programming KW - mixed-integer linear programming KW - mixed-integer nonlinear programming KW - optimization solver KW - branch-and-cut KW - branch-and-price KW - column generation framework KW - parallelization KW - mixed-integer semidefinite programming KW - Steiner tree optimization Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66297 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 - THES A1 - Jeschke, Björn-Marcel T1 - Alternativen zum Dijkstra Algorithmus in der (Nah-) Verkehrsoptimierung N2 - In dieser Arbeit betrachten wir das Problem, für den Fahrplan eines (Nah-) Verkehrsnetzes schnellste Wege zu berechnen. Da die Verkehrsmittel zu unterschiedlichen Zeiten von den einzelnen Haltestellen/Bahnhöfen abfahren, kann das Problem nicht ohne Weiteres mit einem „statischen“ Graphen modelliert werden. Es gibt zwei unterschiedliche Ansätze für dieses zeitabhängige Problem: Erstens können die verschiedenen An-/Abfahrtereignisse an einem Halt durch „Kopien“ dargestellt werden, das ist das zeit-expandierte Modell. Zweitens können die Gewichte der Kanten zeitabhängig sein, das ist das zeitabhängige Modell. Wir untersuchen in dieser Arbeit, wie der „klassische“ Dijkstra-Algorithmus und der A* Algorithmus mit einer geeigneten Heuristik im Vergleich abschneiden. Die gewählte Heuristik ist der Abstand zum Zielknoten, wenn die Abfahrtszeiten ignoriert werden. Nach unseren Untersuchungen zeigt sich, dass der A* Algorithmus dem Dijkstra-Algorithmus weit überlegen ist für genügend große Nahverkehrsnetze. Wir testen anhand der echten Verkehrsnetze von Berlin und Aachen. Unsere Berechnungen zeigen, dass die gewählte Heuristik besonders gut ist für Start- und Zielknoten, welche unabhängig von ihrer Distanz nur 1–2 verschiedene mögliche kürzeste Pfade für alle Zeitschritte haben. Dort ist der A* Algorithmus bis zu 20-mal schneller. Dies kommt aber nicht häufig in unseren Testinstanzen vor. Die einzelnen Laufzeitvergleich zeigen, dass der A* Algorithmus durchschnittlich 7-mal so schnell ist wie der Dikstra-Algorithmus. Y1 - 2017 ER - TY - GEN A1 - Müller, Benjamin A1 - Kuhlmann, Renke A1 - Vigerske, Stefan T1 - On the performance of NLP solvers within global MINLP solvers 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. T3 - ZIB-Report - 17-35 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64504 SN - 1438-0064 ER - TY - GEN A1 - Duarte, Belmiro P.M. A1 - Sagnol, Guillaume A1 - Wong, Weng Kee T1 - An algorithm based on Semidefinite Programming for finding minimax optimal designs N2 - An algorithm based on a delayed constraint generation method for solving semi-infinite programs for constructing minimax optimal designs for nonlinear models is proposed. The outer optimization level of the minimax optimization problem is solved using a semidefinite programming based approach that requires the design space be discretized. A nonlinear programming solver is then used to solve the inner program to determine the combination of the parameters that yields the worst-case value of the design criterion. The proposed algorithm is applied to find minimax optimal designs for the logistic model, the flexible 4-parameter Hill homoscedastic model and the general nth order consecutive reaction model, and shows that it (i) produces designs that compare well with minimax $D-$optimal designs obtained from semi-infinite programming method in the literature; (ii) can be applied to semidefinite representable optimality criteria, that include the common A-, E-,G-, I- and D-optimality criteria; (iii) can tackle design problems with arbitrary linear constraints on the weights; and (iv) is fast and relatively easy to use. T3 - ZIB-Report - 18-01 KW - Cutting plane algorithm KW - Design efficiency KW - Equivalence theorem KW - Model-based optimal design KW - Nonlinear programming Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66249 SN - 1438-0064 ER - TY - GEN A1 - Sagnol, Guillaume A1 - Blanco, Marco A1 - Sauvage, Thibaut T1 - The Cone of Flow Matrices: Approximation Hierarchies and Applications N2 - Let G be a directed acyclic graph with n arcs, a source s and a sink t. We introduce the cone K of flow matrices, which is a polyhedral cone generated by the matrices $\vec{1}_P\vec{1}_P^T\in\RR^{n\times n}$, where $\vec{1}_P\in\RR^n$ is the incidence vector of the (s,t)-path P. We show that several hard flow (or path) optimization problems, that cannot be solved by using the standard arc-representation of a flow, reduce to a linear optimization problem over $\mathcal{K}$. This cone is intractable: we prove that the membership problem associated to $\mathcal{K}$ is NP-complete. However, the affine hull of this cone admits a nice description, and we give an algorithm which computes in polynomial-time the decomposition of a matrix $X\in \operatorname{span} \mathcal{K}$ as a linear combination of some $\vec{1}_P\vec{1}_P^T$'s. Then, we provide two convergent approximation hierarchies, one of them based on a completely positive representation of~K. We illustrate this approach by computing bounds for the quadratic shortest path problem, as well as a maximum flow problem with pairwise arc-capacities. T3 - ZIB-Report - 17-32 KW - Flows in graphs KW - Approximation Hierarchies KW - Copositive Programming KW - Semidefinite Programming Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64399 SN - 1438-0064 ER - TY - GEN A1 - Duarte, Belmiro P.M. A1 - Sagnol, Guillaume T1 - Approximate and exact D-optimal designs for $2^k$ factorial experiments for Generalized Linear Models via SOCP N2 - We propose (Mixed Integer) Second Order Cone Programming formulations to find approximate and exact $D-$optimal designs for $2^k$ factorial experiments for Generalized Linear Models (GLMs). Locally optimal designs are addressed with Second Order Cone Programming (SOCP) and Mixed Integer Second Order Cone Programming (MISOCP) formulations. The formulations are extended for scenarios of parametric uncertainty employing the Bayesian framework for \emph{log det} $D-$optimality criterion. A quasi Monte-Carlo sampling procedure based on the Hammersley sequence is used for integrating the optimality criterion in the parametric region. The problems are solved in \texttt{GAMS} environment using \texttt{CPLEX} solver. We demonstrate the application of the algorithm with the logistic, probit and complementary log-log models and consider full and fractional factorial designs. T3 - ZIB-Report - 18-02 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66256 SN - 1438-0064 ER - TY - THES A1 - Löbel, Fabian T1 - Solving Integrated Timetabling and Passenger Routing Problems Using the Modulo Network Simplex Algorithm N2 - Common models and solving approaches for the problem of periodic timetabling, that is, determining periodic arrival and departure times of a given public transportation network’s lines so that the total weighted travel time of all passengers is minimized, fail to take passenger behavior into account. Current research is attempting to resolve this issue and first results show a positive impact on solution quality. This thesis aims to give a brief overview of literature on the topic of timetabling and to then state a heuristic approach to Integrated Timetabling by blending passenger behavior into the Modulo Network Simplex algorithm, which is part of the research carried out by the author’s study group at the Zuse Institut Berlin in the framework of MATHEON’s research project MI-3 supported by the Einstein Foundation Berlin. Y1 - 2017 ER - TY - GEN A1 - Gleixner, Ambros A1 - Maher, Stephen J. A1 - Müller, Benjamin A1 - Pedroso, João Pedro T1 - Exact Methods for Recursive Circle Packing N2 - Packing rings into a minimum number of rectangles is an optimization problem which appears naturally in the logistics operations of the tube industry. It encompasses two major difficulties, namely the positioning of rings in rectangles and the recursive packing of rings into other rings. This problem is known as the Recursive Circle Packing Problem (RCPP). We present the first dedicated method for solving RCPP that provides strong dual bounds based on an exact Dantzig–Wolfe reformulation of a nonconvex mixed-integer nonlinear programming formulation. The key idea of this reformulation is to break symmetry on each recursion level by enumerating one-level packings, i.e., packings of circles into other circles, and by dynamically generating packings of circles into rectangles. We use column generation techniques to design a “price-and-verify” algorithm that solves this reformulation to global optimality. Extensive computational experiments on a large test set show that our method not only computes tight dual bounds, but often produces primal solutions better than those computed by heuristics from the literature. T3 - ZIB-Report - 17-07 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62039 ER - TY - THES A1 - Reuther, Markus T1 - Mathematical Optimization of Rolling Stock Rotations N2 - We show how to optimize rolling stock rotations that are required for the operation of a passenger timetable. The underlying mathematical ptimization problem is called rolling stock rotation problem (RSRP) and the leitmotiv of the thesis is RotOR, i.e., a highly integrated optimization algorithm for the RSRP. RotOR is used by DB Fernverkehr AG (DBF) in order to optimize intercity express (ICE) rotations for the European high-speed network. In this application, RSRPs have to be solved which (A) require many different aspects to be simultaneously considered, (B) are typically of large scale, and (C) include constraints that have a difficult combinatorial structure. This thesis suggests answers to these issues via the following concepts. (A) The main model, which RotOR uses, relies on a hypergraph. The hypergraph provides an easy way to model manifold industrial railway requirements in great detail. This includes well known vehicle composition requirements as well as relatively unexplored regularity stipulations. At the same time, the hypergraph directly leads to a mixed-integer programming (MIP) model for the RSRP. (B) The main algorithmic ingredient to solve industrial instances of the RSRP is a coarse-to-fine (C2F) column generation procedure. In this approach, the hypergraph is layered into coarse and fine layers that distinguish different levels of detail of the RSRP. The coarse layers are algorithmically utilized while pricing fine columns until proven optimality. Initially, the C2F approach is presented in terms of pure linear programming in order to provide an interface for other applications. (C) Rolling stock rotations have to comply to resource constraints in order to ensure, e.g., enough maintenance inspections along the rotations. These constraints are computationally hard, but are well known in the literature on the vehicle routing problem (VRP). We define an interface problem in order to bridge between the RSRP and the VRP and derive a straightforward algorithmic concept, namely regional search (RS), from their common features and, moreover, differences. Our RS algorithms show promising results for classical VRPs and RSRPs. In the first part of the thesis we present these concepts, which encompass its main mathematical contribution. The second part explains all modeling and solving components of RotOR that turn out to be essential in its industrial application. The thesis concludes with a solution to a complex re-optimization RSRP that RotOR has computed successfully for DBF. In this application all ICE vehicles of the ICE-W fleets of DBF had to be redirected past a construction site on a high-speed line in the heart of Germany. Y1 - 2017 UR - https://depositonce.tu-berlin.de/handle/11303/6309 ER - TY - JOUR A1 - D'Andreagiovanni, Fabio A1 - Mett, Fabian A1 - Nardin, Antonella A1 - Pulaj, Jonad T1 - Integrating LP-guided variable fixing with MIP heuristics in the robust design of hybrid wired-wireless FTTx access networks JF - Applied Soft Computing N2 - This study investigates how to model and solve the problem of optimally designing FTTx telecommunications access networks integrating wired and wireless technologies, while taking into account the uncertainty of wireless signal propagation. We propose an original robust optimization model for the related robust 3-architecture Connected Facility Location problem, which includes additional variables and constraints to model wireless signal coverage represented through signal-to-interference ratios. Since the resulting robust problem can prove very challenging even for a modern state-of-the art optimization solver, we propose to solve it by an original primal heuristic that combines a probabilistic variable fixing procedure, guided by peculiar Linear Programming relaxations, with a Mixed Integer Programming heuristic, based on an exact very large neighborhood search. A numerical study carried out on a set of realistic instances show that our heuristic can find solutions of much higher quality than a state-of-the-art solver. Y1 - 2017 U6 - https://doi.org/10.1016/j.asoc.2017.07.018 VL - 61 SP - 1074 EP - 1087 ER - TY - THES A1 - Pulaj, Jonad T1 - Cutting Planes for Union-Closed Families N2 - Frankl’s (union-closed sets) conjecture states that for any nonempty finite union-closed (UC) family of distinct sets there exists an element in at least half of the sets. Poonen’s Theorem characterizes the existence of weights which determine whether a given UC family ensures Frankl’s conjecture holds for all UC families which contain it. The weight systems are nontrivial to identify for a given UC family, and methods to determine such weight systems have led to several other open questions and conjectures regarding structures in UC families. We design a cutting-plane method that computes the explicit weights which imply the existence conditions of Poonen’s Theorem using computational integer programming coupled with redundant verification routines that ensure correctness. We find over one hundred previously unknown families of sets which ensure Frankl’s conjecture holds for all families that contain any of them. This improves significantly on all previous results of the kind. Our framework allows us to answer several open questions and conjectures regarding structural properties of UC families, including proving the 3-sets conjecture of Morris from 2006 which characterizes the minimum number of 3-sets that ensure Frankl’s conjecture holds for all families that contain them. Furthermore, our method provides a general algorithmic road-map for improving other known results and uncovering structures in UC families. Y1 - 2017 UR - https://depositonce.tu-berlin.de//handle/11303/7258 ER - TY - CHAP A1 - Cheung, Kevin K. H. A1 - Gleixner, Ambros A1 - Steffy, Daniel T1 - Verifying Integer Programming Results T2 - F. Eisenbrand and J. Koenemann, eds., Integer Programming and Combinatorial Optimization: 19th International Conference, IPCO 2017 N2 - Software for mixed-integer linear programming can return incorrect results for a number of reasons, one being the use of inexact floating-point arithmetic. Even solvers that employ exact arithmetic may suffer from programming or algorithmic errors, motivating the desire for a way to produce independently verifiable certificates of claimed results. Due to the complex nature of state-of-the-art MIP solution algorithms, the ideal form of such a certificate is not entirely clear. This paper proposes such a certificate format designed with simplicity in mind, which is composed of a list of statements that can be sequentially verified using a limited number of inference rules. We present a supplementary verification tool for compressing and checking these certificates independently of how they were created. We report computational results on a selection of MIP instances from the literature. To this end, we have extended the exact rational version of the MIP solver SCIP to produce such certificates. Y1 - 2017 U6 - https://doi.org/10.1007/978-3-319-59250-3_13 VL - 10328 SP - 148 EP - 160 ER - TY - JOUR A1 - Vierhaus, Ingmar A1 - Fügenschuh, Armin A1 - Gottwald, Robert Lion A1 - Grösser, Stefan T1 - Using white-box nonlinear optimization methods in system dynamics policy improvement JF - System Dynamics Review N2 - We present a new strategy for the direct optimization of the values of policy functions. This approach is particularly well suited to model actors with a global perspective on the system and relies heavily on modern mathematical white-box optimization methods. We demonstrate our strategy on two classical models: market growth and World2. Each model is first transformed into an optimization problem by defining how the actor can influence the models' dynamics and by choosing objective functions to measure improvements. To improve comparability between different runs, we also introduce a comparison measure for possible interventions. We solve the optimization problems, discuss the resulting policies and compare them to the existing results from the literature. In particular, we present a run of the World2 model which significantly improves the published “towards a global equilibrium” run with equal cost of intervention. Y1 - 2017 U6 - https://doi.org/10.1002/sdr.1583 VL - 33 IS - 2 SP - 138 EP - 168 ER - TY - THES A1 - Wischlinsky, William T1 - Feasibility-based bound tightening via linear programming Y1 - 2017 ER - TY - GEN A1 - Maher, Stephen J. A1 - Fischer, Tobias A1 - Gally, Tristan A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Gottwald, Robert Lion A1 - Hendel, Gregor A1 - Koch, Thorsten A1 - Lübbecke, Marco A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schenker, Sebastian A1 - Schwarz, Robert A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Weninger, Dieter A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 4.0 N2 - The SCIP Optimization Suite is a powerful collection of optimization software that consists of the branch-cut-and-price framework and mixed-integer programming solver SCIP, the linear programming solver SoPlex, the modeling language Zimpl, the parallelization framework UG, and the generic branch-cut-and-price solver GCG. Additionally, it features the extensions SCIP-Jack for solving Steiner tree problems, PolySCIP for solving multi-objective problems, and SCIP-SDP for solving mixed-integer semidefinite programs. The SCIP Optimization Suite has been continuously developed and has now reached version 4.0. The goal of this report is to present the recent changes to the collection. We not only describe the theoretical basis, but focus on implementation aspects and their computational consequences. T3 - ZIB-Report - 17-12 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62170 SN - 1438-0064 ER - TY - JOUR A1 - Gamrath, Gerald A1 - Koch, Thorsten A1 - Maher, Stephen J. A1 - Rehfeldt, Daniel A1 - Shinano, Yuji T1 - SCIP-Jack – A solver for STP and variants with parallelization extensions JF - Mathematical Programming Computation N2 - The Steiner tree problem in graphs is a classical problem that commonly arises in practical applications as one of many variants. While often a strong relationship between different Steiner tree problem variants can be observed, solution approaches employed so far have been prevalently problem-specific. In contrast, this paper introduces a general-purpose solver that can be used to solve both the classical Steiner tree problem and many of its variants without modification. This versatility is achieved by transforming various problem variants into a general form and solving them by using a state-of-the-art MIP-framework. The result is a high-performance solver that can be employed in massively parallel environments and is capable of solving previously unsolved instances. Y1 - 2017 U6 - https://doi.org/10.1007/s12532-016-0114-x VL - 9 IS - 2 SP - 231 EP - 296 ER - TY - CHAP A1 - Wu, Cheng-Lung A1 - Maher, Stephen J. T1 - Airline scheduling and disruption management T2 - L. Budd, S. Ison, eds., Air transportation management: an international perspective Y1 - 2017 SN - 9781472451064 SP - 151 EP - 167 PB - Routledge CY - New York ER - TY - JOUR A1 - Gleixner, Ambros A1 - Berthold, Timo A1 - Müller, Benjamin A1 - Weltge, Stefan T1 - Three Enhancements for Optimization-Based Bound Tightening JF - Journal of Global Optimization N2 - Optimization-based bound tightening (OBBT) is one of the most effective procedures to reduce variable domains of nonconvex mixed-integer nonlinear programs (MINLPs). At the same time it is one of the most expensive bound tightening procedures, since it solves auxiliary linear programs (LPs)—up to twice the number of variables many. The main goal of this paper is to discuss algorithmic techniques for an efficient implementation of OBBT. Most state-of-the-art MINLP solvers apply some restricted version of OBBT and it seems to be common belief that OBBT is beneficial if only one is able to keep its computational cost under control. To this end, we introduce three techniques to increase the efficiency of OBBT: filtering strategies to reduce the number of solved LPs, ordering heuristics to exploit simplex warm starts, and the generation of Lagrangian variable bounds (LVBs). The propagation of LVBs during tree search is a fast approximation to OBBT without the need to solve auxiliary LPs. We conduct extensive computational experiments on MINLPLib2. Our results indicate that OBBT is most beneficial on hard instances, for which we observe a speedup of 17% to 19% on average. Most importantly, more instances can be solved when using OBBT. Y1 - 2017 U6 - https://doi.org/10.1007/s10898-016-0450-4 VL - 67 IS - 4 SP - 731 EP - 757 ER - TY - CHAP A1 - Gottwald, Robert Lion A1 - Maher, Stephen J. A1 - Shinano, Yuji T1 - Distributed Domain Propagation T2 - 16th International Symposium on Experimental Algorithms (SEA 2017) N2 - Portfolio parallelization is an approach that runs several solver instances in parallel and terminates when one of them succeeds in solving the problem. Despite its simplicity, portfolio parallelization has been shown to perform well for modern mixed-integer programming (MIP) and boolean satisfiability problem (SAT) solvers. Domain propagation has also been shown to be a simple technique in modern MIP and SAT solvers that effectively finds additional domain reductions after the domain of a variable has been reduced. In this paper we introduce distributed domain propagation, a technique that shares bound tightenings across solvers to trigger further domain propagations. We investigate its impact in modern MIP solvers that employ portfolio parallelization. Computational experiments were conducted for two implementations of this parallelization approach. While both share global variable bounds and solutions, they communicate differently. In one implementation the communication is performed only at designated points in the solving process and in the other it is performed completely asynchronously. Computational experiments show a positive performance impact of communicating global variable bounds and provide valuable insights in communication strategies for parallel solvers. Y1 - 2017 U6 - https://doi.org/10.4230/LIPIcs.SEA.2017.6 VL - 75 SP - 6:1 EP - 6:11 ER - TY - CHAP A1 - Yokoyama, Ryohei A1 - Shinano, Yuji A1 - Wakayama, Yuki A1 - Wakui, Tetsuya T1 - Multiobjective Optimal Design of a Gas Turbine Cogeneration Plant by a Revised Hierarchical Optimization Method T2 - ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition N2 - To attain the highest performance of energy supply systems, it is necessary to rationally determine design specifications in consideration of operational strategies corresponding to energy demands. Mixed-integer linear programming (MILP) approaches have been applied widely to such optimal design problems. A MILP method utilizing the hierarchical relationship between design and operation variables have been proposed to solve them efficiently. However, it cannot necessarily be effective to multi-objective optimal design problems because of the existence of a large number of competing design candidates. In this paper, the hierarchical MILP method is revised from the viewpoint of computation efficiency so that it can be applied practically to multi-objective optimal design problems. At the lower level, the order of the optimal operation problems to be solved is changed based on incumbents obtained previously to increase a lower bound for the optimal value of the combined objective function and reduce the number of the optimal operation problems to be solved. At the upper level, a lower bound for the optimal value of the combined objective function is incorporated into the solution method to reduce the number of the design candidates to be generated. This revised hierarchical MILP method is applied to a multiobjective optimal design of a gas turbine cogeneration plant, and its validity and effectiveness are clarified. Y1 - 2017 U6 - https://doi.org/doi:10.1115/GT2017-64296 VL - 3 SP - 1 EP - 14 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 -