Library

Description: In several inital value problems with particularly expensive right hand side evaluation or implicit step computation, there is a trade-off between accuracy and computational effort. We consider inexact spectral deferred correction (SDC) methods for solving such initial value problems. SDC methods are interpreted as fixed point iterations and, due to their corrective iterative nature, allow to exploit the accuracy-work-tradeoff for a reduction of the total computational effort. On one hand we derive error models bounding the total error in terms of the evaluation errors. On the other hand, we define work models describing the computational effort in terms of the evaluation accuracy. Combining both, a theoretically optimal local tolerance selection is worked out by minimizing the total work subject to achieving the requested tolerance. The properties of optimal local tolerances and the predicted efficiency gain compared to simpler heuristics, and a reasonable practical performance, are illustrated on simple numerical examples.

Description: 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.

Description: 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.

Description: 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.

Description: In 2005 the European Union liberalized the gas market with a disruptive change and decoupled trading of natural gas from its transport. The gas is now trans- ported by independent so-called transmissions system operators or TSOs. The market model established by the European Union views the gas transmission network as a black box, providing shippers (gas traders and consumers) the opportunity to transport gas from any entry to any exit. TSOs are required to offer the maximum possible capacities at each entry and exit such that any resulting gas flow can be realized by the network. The revenue from selling these capacities more than one billion Euro in Germany alone, but overestimating the capacity might compromise the security of supply. Therefore, evaluating the available transport capacities is extremely important to the TSOs. This is a report on a large project in mathematical optimization, set out to develop a new toolset for evaluating gas network capacities. The goals and the challenges as they occurred in the project are described, as well as the developments and design decisions taken to meet the requirements.

Description: 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.

Description: The Ubiquity Generator (UG) is a general framework for the external parallelization of mixed integer programming (MIP) solvers. In this paper, we present ParaXpress, a distributed memory parallelization of the powerful commercial MIP solver FICO Xpress. Besides sheer performance, an important feature of Xpress is that it provides an internal parallelization for shared memory systems. When aiming for a best possible performance of ParaXpress on a supercomputer, the question arises how to balance the internal Xpress parallelization and the external parallelization by UG against each other. We provide computational experiments to address this question and we show computational results for running ParaXpress on a Top500 supercomputer, using up to 43,344 cores in parallel.

Description: Abstract: Objective: To present a novel method for automated segmentation of knee menisci from MRIs. To evaluate quantitative meniscal biomarkers for osteoarthritis (OA) estimated thereof. Method: A segmentation method employing convolutional neural networks in combination with statistical shape models was developed. Accuracy was evaluated on 88 manual segmentations. Meniscal volume, tibial coverage, and meniscal extrusion were computed and tested for differences between groups of OA, joint space narrowing (JSN), and WOMAC pain. Correlation between computed meniscal extrusion and MOAKS experts' readings was evaluated for 600 subjects. Suitability of biomarkers for predicting incident radiographic OA from baseline to 24 months was tested on a group of 552 patients (184 incident OA, 386 controls) by performing conditional logistic regression. Results: Segmentation accuracy measured as Dice Similarity Coefficient was 83.8% for medial menisci (MM) and 88.9% for lateral menisci (LM) at baseline, and 83.1% and 88.3% at 12-month follow-up. Medial tibial coverage was significantly lower for arthritic cases compared to non-arthritic ones. Medial meniscal extrusion was significantly higher for arthritic knees. A moderate correlation between automatically computed medial meniscal extrusion and experts' readings was found (ρ=0.44). Mean medial meniscal extrusion was significantly greater for incident OA cases compared to controls (1.16±0.93 mm vs. 0.83±0.92 mm; p〈0.05). Conclusion: Especially for medial menisci an excellent segmentation accuracy was achieved. Our meniscal biomarkers were validated by comparison to experts' readings as well as analysis of differences w.r.t groups of OA, JSN, and WOMAC pain. It was confirmed that medial meniscal extrusion is a predictor for incident OA.

Description: Estimation of time of death based on a single measurement of body core temperature is a standard procedure in forensic medicine. Mechanistic models using simulation of heat transport promise higher accuracy than established phenomenological models in particular in nonstandard situations, but involve many not exactly known physical parameters. Identifying both time of death and physical parameters from multiple temperature measurements is one possibility to reduce the uncertainty significantly. In this paper, we consider the inverse problem in a Bayesian setting and perform both local and sampling-based uncertainty quantification, where proper orthogonal decomposition is used as model reduction for fast solution of the forward model. Based on the local uncertainty quantification, optimal design of experiments is performed in order to minimize the uncertainty in the time of death estimate for a given number of measurements. For reasons of practicability, temperature acquisition points are selected from a set of candidates in different spatial and temporal locations. Applied to a real corpse model, a significant accuracy improvement is obtained already with a small number of measurements.

Description: 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 $1_P 1_P^T \in R^{n\times n}$, where $1_P\in R^n$ is the incidence vector of the $(s,t)$-path $P$. Several combinatorial problems reduce to a linear optimization problem over $K$. This cone is intractable, but 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 a maximum flow problem with pairwise arc-capacities.

Description: Estimation of time of death based on a single measurement of body core temperature is a standard procedure in forensic medicine. Mechanistic models using simulation of heat transport promise higher accuracy than established phenomenological models in particular in nonstandard situations, but involve many not exactly known physical parameters. Identifying both time of death and physical parameters from multiple temperature measurements is one possibility to reduce the uncertainty significantly. In this paper, we consider the inverse problem in a Bayesian setting and perform both local and sampling-based uncertainty quantification, where proper orthogonal decomposition is used as model reduction for fast solution of the forward model. Based on the local uncertainty quantification, optimal design of experiments is performed in order to minimize the uncertainty in the time of death estimate for a given number of measurements. For reasons of practicability, temperature acquisition points are selected from a set of candidates in different spatial and temporal locations. Applied to a real corpse model, a significant accuracy improvement is obtained already with a small number of measurements.

Description: We consider the stochastic extensible bin packing problem (SEBP) in which $n$ items of stochastic size are packed into $m$ bins of unit capacity. In contrast to the classical bin packing problem, bins can be extended at extra cost. This problem plays an important role in stochastic environments such as in surgery scheduling: Patients must be assigned to operating rooms beforehand, such that the regular capacity is fully utilized while the amount of overtime is as small as possible. This paper focuses on essential ratios between different classes of policies: First, we consider the price of non-splittability, in which we compare the optimal non-anticipatory policy against the optimal fractional assignment policy. We show that this ratio has a tight upper bound of $2$. Moreover, we develop an analysis of a fixed assignment variant of the LEPT rule yielding a tight approximation ratio of $1+1/e \approx 1.368$ under a reasonable assumption on the distributions of job durations. Furthermore, we prove that the price of fixed assignments, which describes the loss when restricting to fixed assignment policies, is within the same factor. This shows that in some sense, LEPT is the best fixed assignment policy we can hope for.

Description: The problem of allocating operating rooms (OR) to surgical cases is a challenging task, involving both combinatorial aspects and uncertainty handling. We formulate this problem as a parallel machines scheduling problem, in which job durations follow a lognormal distribution, and a fixed assignment of jobs to machines must be computed. We propose a cutting-plane approach to solve the robust counterpart of this optimization problem. To this end, we develop an algorithm based on fixed-point iterations that identifies worst-case scenarios and generates cut inequalities. The main result of this article uses Hilbert's projective geometry to prove the convergence of this procedure under mild conditions. We also propose two exact solution methods for a similar problem, but with a polyhedral uncertainty set, for which only approximation approaches were known. Our model can be extended to balance the load over several planning periods in a rolling horizon. We present extensive numerical experiments for instances based on real data from a major hospital in Berlin. In particular, we find that: (i) our approach performs well compared to a previous model that ignored the distribution of case durations; (ii) compared to an alternative stochastic programming approach, robust optimization yields solutions that are more robust against uncertainty, at a small price in terms of average cost; (iii) the \emph{longest expected processing time first} (LEPT) heuristic performs well and efficiently protects against extreme scenarios, but only if a good prediction model for the durations is available. Finally, we draw a number of managerial implications from these observations.

Description: The amazing success of computational mathematical optimization over the last decades has been driven more by insights into mathematical structures than by the advance of computing technology. In this vein, we address applications, where nonconvexity in the model poses principal difficulties. This paper summarizes the dissertation of Jonas Schweiger for the occasion of the GOR dissertation award 2018. We focus on the work on non-convex quadratic programs and show how problem specific structure can be used to obtain tight relaxations and speed up Branch&Bound methods. Both a classic general QP and the Pooling Problem as an important practical application serve as showcases.

Description: We consider the Cumulative Scheduling Problem (CuSP) in which a set of $n$ jobs must be scheduled according to release dates, due dates and cumulative resource constraints. In constraint programming, the CuSP is modeled as the cumulative constraint. Among the most common propagation algorithms for the CuSP there is energetic reasoning (Baptiste et al., 1999) with a complexity of O(n^3) and edge-finding (Vilim, 2009) with O(kn log n) where k 〈= n is the number of different resource demands. We consider the complete versions of the propagators that perform all deductions in one call of the algorithm. In this paper, we introduce the energetic edge-finding rule that is a generalization of both energetic reasoning and edge-finding. Our main result is a complete energetic edge-finding algorithm with a complexity of O(n^2 log n) which improves upon the complexity of energetic reasoning. Moreover, we show that a relaxation of energetic edge-finding with a complexity of O(n^2) subsumes edge-finding while performing stronger propagations from energetic reasoning. A further result shows that energetic edge-finding reaches its fixpoint in strongly polynomial time. Our main insight is that energetic schedules can be interpreted as a single machine scheduling problem from which we deduce a monotonicity property that is exploited in the algorithms. Hence, our algorithms improve upon the strength and the complexity of energetic reasoning and edge-finding whose complexity status seemed widely untouchable for the last decades.

Description: During the past years hospitals saw themselves confronted with increasing economical pressure (WB06, p. V). Therefore, optimizing the general operational procedures has gained in importance. The revenue of a hospital depends on the kinds and quantity of treatments performed and on the effcient use and utilization of the corresponding resources. About 25 − 50% of the treatment costs of a patient needing surgery incurs in the operating rooms (WB06, p. 58). Hence skillful management of the operating rooms can have a large impact on the overall revenue of a hospital. Belien and Demeulemeester (BD07) describe the planning of operating room (OR) schedules as a multi-stage process. In the first stage OR time is allocated to the hospitals specialties and capacities and resources are adjusted. In the second stage a master surgery schedule (MSS) is developed, that is a timetable for D days that specifies the amount of OR time assigned to the specialties on every individual day. After D days this schedule will be repeated without any changes. Hence, developing an MSS is a long-term problem. Finally, specialties will schedule specific surgeries within their assigned OR time. In this work we will focus on the development of the MSS that maximizes the revenue of the hospital. Our main focus will be to ensure that the capacities of the downstream resources, i.e. the bed capacities in the ICU and ward, will not be exceeded. Additionally, we hope that our formulation of the problem will lead to a leveled bed demand without significant peaks. We will incorporate the uncertainty of patient demand and case mix in our model. There have been several approaches on this subject, for example in (Fü15) and (BD07) and this work is in part in� uenced by these advances.

Description: We consider the following planning problem in public transportation: Given a periodic timetable, how many vehicles are required to operate it? In [9], for this sequential approach, it is proposed to first expand the periodic timetable over time, and then answer the above question by solving a flow-based aperiodic optimization problem. In this contribution we propose to keep the compact periodic representation of the timetable and simply solve a particular perfect matching problem. For practical networks, it is very much likely that the matching problem decomposes into several connected components. Our key observation is that there is no need to change any turnaround decision for the vehicles of a line during the day, as long as the timetable stays exactly the same.

Description: 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.

Description: Typical applications in data science consume, process and produce large amounts of data, making disk I/O one of the dominating — and thus worthwhile optimizing — factors of their overall performance. Distributed processing frameworks, such as Hadoop, Flink and Spark, hide a lot of complexity from the programmer when they parallelize these applications across a compute cluster. This exacerbates reasoning about I/O of both the application and the framework, through the distributed file system, such as HDFS, down to the local file systems. We present SFS (Statistics File System), a modular framework to trace each I/O request issued by the application and any JVM-based big data framework involved, mapping these requests to actual disk I/O. This allows detection of inefficient I/O patterns, both by the applications and the underlying frameworks, and builds the basis for improving I/O scheduling in the big data software stack.

Description: The reproductive cycle of mono-ovulatory species such as cows or humans is known to show two or more waves of follicular growth and decline between two successive ovulations. Within each wave, there is one dominant follicle escorted by subordinate follicles of varying number. Under the surge of the luteinizing hormone a growing dominant follicle ovulates. Rarely the number of ovulating follicles exceeds one. In the biological literature, the change of hormonal concentrations and individually varying numbers of follicular receptors are made responsible for the selection of exactly one dominant follicle, yet a clear cause has not been identified. In this paper, we suggest a synergistic explanation based on competition, formulated by a parsimoniously defined system of ordinary differential equations (ODEs) that quantifies the time evolution of multiple follicles and their competitive interaction during one wave. Not discriminating between follicles, growth and decline are given by fixed rates. Competition is introduced via a growth-suppressing term, equally supported by all follicles. We prove that the number of dominant follicles is determined exclusively by the ratio of follicular growth and competition. This number turns out to be independent of the number of subordinate follicles. The asymptotic behavior of the corresponding dynamical system is investigated rigorously, where we demonstrate that the ω-limit set only contains fixed points. When also including follicular decline, our ODEs perfectly resemble ultrasound data of bovine follicles. Implications for the involved but not explicitly modeled hormones are discussed.

Description: 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.

Description: The Steiner tree problem in graphs is a classical problem that commonly arises in practical applications as one of many variants. Although the different Steiner tree problem variants are usually strongly related, solution approaches employed so far have been prevalently problem-specific. Against this backdrop, the solver SCIP-Jack was created as a general-purpose framework that can be used to solve the classical Steiner tree problem and 11 of its variants. 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. Furthermore, SCIP-Jack includes various newly developed algorithmic components such as preprocessing routines and heuristics. The result is a high-performance solver that can be employed in massively parallel environments and is capable of solving previously unsolved instances. After the introduction of SCIP-Jack at the 2014 DIMACS Challenge on Steiner problems, the overall performance of the solver has considerably improved. This article provides an overview on the current state.

Description: Background Mathematical optimisation models have recently been applied to identify ideal Automatic External Defibrillator (AED) locations that maximise coverage of Out of Hospital Cardiac Arrest (OHCA). However, these fixed location models cannot relocate existing AEDs in a flexible way, and have nearly exclusively been applied to urban regions. We developed a flexible location model for AEDs, compared its performance to existing fixed location and population models, and explored how these perform across urban and rural regions. Methods Optimisation techniques were applied to AED deployment and OHCA coverage was assessed. A total of 2802 geolocated OHCAs occurred in Canton Ticino, Switzerland, from January 1st 2005 to December 31st 2015. Results There were 719 AEDs in Canton Ticino. 635 (23%) OHCA events occurred within 100m of an AED, with 306 (31%) in urban, and 329 (18%) in rural areas. Median distance from OHCA events to the nearest AED was 224m (168m urban vs. 269m rural). Flexible location models performed better than fixed location and population models, with the cost to deploy 20 new AEDs instead relocating 171 existing AEDs to new locations, improving OHCA coverage to 38%, compared to 26% using fixed models, and 24% with the population based model. Conclusions Optimisation models for AEDs placement are superior to population models and should be strongly considered by communities when selecting areas for AED deployment. Compared to other models, flexible location models increase overall OHCA coverage, and decreases the distance to nearby AEDs, even in rural areas, while saving significant financial resources.

Description: We consider the use of randomised forward models and log-likelihoods within the Bayesian approach to inverse problems. Such random approximations to the exact forward model or log-likelihood arise naturally when a computationally expensive model is approximated using a cheaper stochastic surrogate, as in Gaussian process emulation (kriging), or in the field of probabilistic numerical methods. We show that the Hellinger distance between the exact and approximate Bayesian posteriors is bounded by moments of the difference between the true and approximate log-likelihoods. Example applications of these stability results are given for randomised misfit models in large data applications and the probabilistic solution of ordinary differential equations.

Description: This chapter shows a successful approach how to model and optimize rolling stock rotations that are required for the operation of a passenger timetable. The underlying mathematical optimization problem is described in detail and solved by RotOR, i.e., a complex optimization algorithm based on linear programming and combinatorial methods. RotOR is used by DB Fernverkehr AG (DBF) in order to optimize intercity express (ICE) rotations for the European high-speed network. We focus on main modeling and solving components, i.e. a hypergraph model and a coarse-to-fine column generation approach. Finally, the chapter concludes with a complex industrial re-optimization application showing the effectiveness of the approach for real world challenges.

Description: This chapter addresses the classical task to decide which train runs on which track in a railway network. In this context a track allocation defines the precise routing of trains through a railway network, which usually has only a limited capacity. Moreover, the departure and arrival times at the visited stations of each train must simultaneously meet several operational and safety requirements. The problem to find the 'best possible' allocation for all trains is called the track allocation problem (TTP). Railway systems can be modeled on a very detailed scale covering the behavior of individual trains and the safety system to a large extent. However, those microscopic models are too big and not scalable to large networks, which make them inappropriate for mathematical optimization on a network wide level. Hence, most network optimization approaches consider simplified, so called macroscopic, models. In the first part we take a look at the challenge to construct a reliable and condensed macroscopic model for the associated microscopic model and to facilitate the transition between both models of different scale. In the main part we focus on the optimization problem for macroscopic models of the railway system. Based on classical graph-theoretical tools the track allocation problem is formulated to determine conflict-free paths in corresponding time-expanded graphs. We present standard integer programming model formulations for the track allocation problem that model resource or block conflicts in terms of packing constraints. In addition, we discuss the role of maximal clique inequalities and the concept of configuration networks. We will also present classical decomposition approaches like Lagrangian relaxation and bundle methods. Furthermore, we will discuss recently developed techniques, e.g., dynamic graph generation. Finally, we will discuss the status quo and show a vision of mathematical optimization to support real world track allocation, i.e. integrated train routing and scheduling, in a data-dominated and digitized railway future.

Description: Today's gas markets demand more flexibility from the network operators which in turn have to invest into their network infrastructure. As these investments are very cost-intensive and long-living, network extensions should not only focus on a single bottleneck scenario, but should increase the flexibility to fulfill different demand scenarios. In this work, we formulate a model for the network extension problem for multiple demand scenarios and propose a scenario decomposition in order to solve the arising challenging optimization tasks. In fact, each subproblem consists of a mixed-integer nonlinear optimization problem (MINLP). Valid bounds on the objective value are derived even without solving the subproblems to optimality. Furthermore, we develop heuristics that prove capable of improving the initial solutions substantially. Results of computational experiments on realistic network topologies are presented. It turns out that our method is able to solve these challenging instances to optimality within a reasonable amount of time.

Description: In gradient-based methods for parabolic optimal control problems, it is necessary to solve both the state equation and a backward-in-time adjoint equation in each iteration of the optimization method. In order to facilitate fully parallel gradient-type and nonlinear conjugate gradient methods for the solution of such optimal control problems, we discuss the application of the parallel-in-time method PFASST to adjoint gradient computation. In addition to enabling time parallelism, PFASST provides high flexibility for handling nonlinear equations, as well as potential extra computational savings from reusing previous solutions in the optimization loop. The approach is demonstrated here for a model reaction-diffusion optimal control problem.

Description: Managing rolling stock with no passengers aboard is a critical component of railway operations. One aspect of managing rolling stock is to park the rolling stock on a given set of tracks at the end of a day or service. Depending on the parking assignment, shunting may be required in order for a parked train to depart or for an incoming train to park. Given a collection of tracks M and a collection of trains T with a fixed arrival-departure timetable, the train assignment problem (TAP) is to determine the maximum number of trains from T that can be parked on M according to the timetable and without the use of shunting. Hence, efficiently solving the TAP allows to quickly compute feasible parking schedules that do not require further shunting adjustments. In this paper, we show that the TAP is NP-hard and present two integer programming models for solving the TAP. We compare both models on a theoretical level. Moreover, to our knowledge, we consider the first approach that integrates track lengths along with the three most common types of parking tracks FIFO, LIFO and FREE tracks in a common model. Furthermore, to optimize against uncertainty in the arrival times of the trains we extend our models by stochastic and robust modeling techniques. We conclude by giving computational results for both models, observing that they perform well on real timetables.

Description: This chapter is about strategic routing of freight trains in railway transportation networks with mixed traffic. A good utilization of a railway transportation network is important since in contrast to road and air traffic the routing through railway networks is more challenging and the extension of capacities is expensive and a long-term projects. Therefore, an optimized routing of freight trains have a great potential to exploit remaining capacity since the routing has fewer restrictions compared to passenger trains. In this chapter we describe the freight train routing problem in full detail and present a mixed-integer formulation. Wo focus on a strategic level that take into account the actual immutable passenger traffic. We conclude the chapter with a case study for the German railway network.

Description: Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long time-scale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large length scales, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail. Thus, coupling MSMs and RD simulations (MSM/RD) would be highly desirable, as they could efficiently produce simulations at large time and length scales, while still conserving the characteristic features of the interactions observed at atomic detail. While such a coupling seems straightforward, fundamental questions are still open: Which definition of MSM states is suitable? Which protocol to merge and split RD particles in an association/dissociation reaction will conserve the correct bimolecular kinetics and thermodynamics? In this paper, we make the first step toward MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of a protein with a small ligand (A + B ⇌ C). Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported.

Description: This article deals with the Jeep Problem (also known as Desert Crossing Problem), which reads as follows: An unlimited supply of fuel is available at one edge of a desert, but there is no source on the desert itself. A vehicle can carry enough fuel to go a certain distance, and it can built up its own refuelling stations. What is the minimum amount of fuel the vehicle will require in order to cross the desert? Under these mild conditions this question is answered since the 1940s. But what is the answer if the caches are restricted to certain areas or if the fuel consumption does not depend linearly on the distance travelled? To answer these and similar questions we develop and solve a flexible mixed-integer programming (MIP) model for the classical problem and enhance it with new further aspects of practical relevance.

Description: Planning efficient routes fast becomes ever more important, especially in the context of aircraft trajectories. As time-dependent wind conditions factor into the shortest path query, we use an artificial wind vector called Super-Optimal Wind as a means of creating a suitable potential function for the A* algorithm, thus speeding up the query. We assess the quality of Super-Optimal Wind both theoretically and computationally, and use Super-Optimal Wind in a real-world instance.

Description: This paper describes a new instance library for Quadratic Programming (QP), i.e., the family of continuous and (mixed)-integer optimization problems where the objective function, the constrains, or both are quadratic. QP is a very diverse class of problems, comprising sub-classes of problems ranging from trivial to undecidable. This diversity is reflected in the variety of solution methods for QP, ranging from entirely combinatorial ones to completely continuous ones, including many for which both aspects are fundamental. Selecting a set of instances of QP that is at the same time not overwhelmingly onerous but sufficiently challenging for the many different interested communities is therefore important. We propose a simple taxonomy for QP instances that leads to a systematic problem selection mechanism. We then briefly survey the field of QP, giving an overview of theory, methods and solvers. Finally, we describe how the library was put together, and detail its final contents.

Description: We describe a network simplex algorithm for the minimum cost flow problem on graph-based hypergraphs which are directed hypergraphs of a particular form occurring in railway rotation planning. The algorithm is based on work of Cambini, Gallo, and Scutellà who developed a hypergraphic generalization of the network simplex algorithm. Their main theoretical result is the characterization of basis matrices. We give a similar characterization for graph-based hypergraphs and show that some operations of the simplex algorithm can be done combinatorially by exploiting the underlying digraph structure.

Description: Rolling stock optimization is a task that naturally arises by operating a railway system. It could be seen with different level of details. From a strategic perspective to have a rough plan which types of fleets to be bought to a more operational perspective to decide which coaches have to be maintained first. This paper presents a new approach to deal with rolling stock optimisation in case of a (long term) strike. Instead of constructing a completely new timetable for the strike period, we propose a mixed integer programming model that is able to choose appropriate trips from a given timetable to construct efficient tours of railway vehicles covering an optimized subset of trips, in terms of deadhead kilometers and importance of the trips. The decision which trip is preferred over the other is made by a simple evaluation method that is deduced from the network and trip defining data.

Description: In 2005 the European Union liberalized the gas market with a disruptive change and decoupled trading of natural gas from its transport. The gas is now transported by independent so-called transmissions system operators or TSOs. The market model established by the European Union views the gas transmission network as a black box, providing shippers (gas traders and consumers) the opportunity to transport gas from any entry to any exit. TSOs are required to offer the maximum possible capacities at each entry and exit such that any resulting gas flow can be realized by the network. The revenue from selling these capacities more than one billion Euro in Germany alone, but overestimating the capacity might compromise the security of supply. Therefore, evaluating the available transport capacities is extremely important to the TSOs. This is a report on a large project in mathematical optimization, set out to develop a new toolset for evaluating gas network capacities. The goals and the challenges as they occurred in the project are described, as well as the developments and design decisions taken to meet the requirements.

Description: OPUS wurde als Dokumentenserver konzipiert und ursprünglich nicht für den Nachweis von Forschungsdaten angelegt. Mit vergleichsweise geringem Aufwand können dennoch Forschungsdaten als Supplementary Material zu Zeitschriftenbeiträgen publiziert werden. Auch reine Forschungsdatenpublikationen können via OPUS veröffentlicht werden, selbst wenn die gegenwärtig auf Textpublikationen zugeschnittene Metadatenerfassung weniger gut für die Beschreibung reiner Forschungsdaten geeignet ist. Ein Unterschied zu anderen Systemen und Anwendungsszenarien besteht in der Beschränkung, großvolumige Daten nicht innerhalb von OPUS selbst vorzuhalten. Der für das institutionelle Repository des Zuse-Instituts Berlin konzipierte pragmatische Lösungsansatz ist in OPUS ohne zusätzliche Programmierung umsetzbar und skaliert für beliebig große Forschungsdatensätze.

Description: The aim of multimodal routing is to extract the best integrated journey of multiple transportation networks. The integration of bike rental networks is challenging particularly with respect to recognizing a valid path dependent on real-time availability of bike boarding and alighting places. In this work a common model for station-based bike rental networks extended with boarding possibilities for free floating bikes is presented. Moreover a new model for alighting inside a free floating area is introduced. In addition, a prototype of multimodal routing with a bike rental network in Berlin is developed by extending the OpenTripPlanner software. Due to recent public dispute about bike rental networks in Berlin, an examination about speed-up potential of an integrated bike rental network in the public transit of Berlin is provided.

Description: Viele Firmen nutzen für ihre eigenen Softwareentwicklungen verschiedene Server mit unterschiedlichen Konfigurationen. Manche Server werden dazu eingestzt das Verhalten einer Software in einer bestimmten Umgebung zu testen und andere dienen zur Bereitstellung der Software für den Endnutzer. Hierbei ist es wichtig, dass die Konfiguration der Server regelmäßig überprüft wird. Eine solche Sicherstellung der Deployment- und Umgebungs-Integrität wird meistens durch eine Mitarbeiter der Firma oder durch einen externen Dienstleister erbracht. D.h. die Firma muss sich auf die Zuverlässigkeit eines Mitarbeiters oder einer externen Dienstleistung verlassen, bie zunehmender Komplexität ist sie sogar abhängig. Das Ziel dieser Masterarbeit ist es, zu untersuchen, ob die Sicherstellung der Deployment- und Umgebungs-Integrität durch automatisierte kryptografische Beweise, anstelle externer Dienstleistungen oder anderer Mitarbeiter, gewährleistet werden kann. Als Anwendungsfall dient die Toll Collect GmbH. Im ersten Teil dieser Arbeit wird das Matheamtische Modell einer Blockchain erläutert. die Blockchain wurde erstmals in einem Dokument, welches unter dem Pseudonym Satoshi Nakamoto veröffentlicht wurde, beschrieben. Die erste große Anwendungen der Blockchain ist das dezentrale Zahlungssystem Bitcoin. Im zweiten Teil dieser Arbeit wird die Softwareimplementierung vorgestellt, welche im Rahmen dieser Arbeit entstanden ist. Mithilfe dieses Programms kann die Deployment- und Umgebungs-Integrität durch eine heirführ entwickelte Blockchainlösung dezentralisiert werden. Es wird außerdem der Übergang vom Mathematischen Modell zur Implementierung gezeigt.

Description: In dieser Arbeit wird die Platzierung von Ladestationen für Elektrobusse untersucht. Dabei soll für eine Menge an gegebenen Linien eine Menge an Ladestationen gefunden werden, sodass jede Linie mit Nutzung der Ladestationen befahren werden kann und gleichzeitig die Kosten minimal sind. Zunächst wird der Fall betrachtet, dass die Batterie an jeder Station komplett vollgeladen werden könnte. Dieses Problem stellt sich als NP-schwer heraus. Für einige einfachere Fällewerden zudem Algorithmen entwickelt und untersucht. Anschließend wird der Fall einer unbegrenzt großen Batterie betrachtet, wobei an jeder Station derselbe Wert geladen werden kann. Auch dieses Problem ist NP-schwer. Erneut werden Algorithmen zur Lösung vereinfachter Problemstellungen gegeben und analysiert. Wird zudem angenommen, an jeder Station würde ein individueller Wert geladen, so ist das Problem schon für nur eine einzige Linie NP-schwer. Dennoch werden zwei exakte und ein approximierender Algorithmus entwickelt. Schließlich wird eine Batteriekapazität hinzugefügt und die zuvor entwickelten Algorithmen werden entsprechend angepasst. Für die abschließende Problemdefinition werden verschiedene Batteriegrößen betrachtet und es werden zwei gemischt-ganzzahlige Programme aufgestellt. Anhand von existierenden Buslinien aus Berlin werden diese untersucht. Dabei stellt sich heraus, dass die Batteriekosten einen deutlich größeren Teil der Kosten ausmachen als die Ladestationen. Zudem sollten kleinere Batterien statt größerer und mehr Ladestationen genutzt werden.

Description: In many railway undertakings a railway timetable is offered that is valid for a longer period of time. At DB Fernverkehr AG, one of our industrial partners, this results in a summer and a winter timetable. For both of these timetables rotation plans, i.e., a detailed plan of railway vehicle movements is constructed as a template for this period. Sometimes there are be periods where you know for sure that vehicle capacities are not sufficient to cover all trips of the timetable or to transport all passenger of the trips. Reasons for that could be a heavy increase of passenger flow, a heavy decrease of vehicle availability, impacts from nature, or even strikes of some employees. In such events the rolling stock rotations have to be adapted. Optimization methods are particularly valuable in such situations in order to maintain a best possible level of service or to maximize the expected revenue using the resources that are still available. In most cases found in the literature, a rescheduling based on a timetable update is done, followed by the construction of new rotations that reward the recovery of parts of the obsolete rotations. We consider a different, novel, and more integrated approach. The idea is to guide the cancellation of the trips or reconfiguration of the vehicle composition used to operate a trip of the timetable by the rotation planning process, which is based on the mixed integer programming approach presented in Reuther (2017). The goal is to minimize the operating costs while cancelling or operating a trip with an insufficient vehicle configuration in sense of passenger capacities inflicts opportunity costs and loss of revenue, which are based on an estimation of the expected number of passengers. The performance of the algorithms presented in two case studies, including real world scenarios from DB Fernverkehr AG and a railway operator in North America.

Description: We consider event-based Mixed-Integer Programming (MIP) models for the Resource-Constrained Project Scheduling Problem (RCPSP) that represent an alternative to the common time-indexed model (DDT) of Pritsker et al. (1969) for the case where the underlying time horizon is large or job processing times are subject to huge variations. In contrast to the time-indexed model, the size of event-based models does not depend on the time horizon. For two event-based formulations OOE and SEE of Koné et al. (2011) we present new valid inequalities that dominate the original formulation. Additionally, we introduce a new event-based model: the Interval Event-Based Model (IEE). We deduce linear transformations between all three models that yield the strict domination order IEE 〉 SEE 〉 OOE for their linear programming (LP) relaxations, meaning that IEE has the strongest linear relaxation among the event-based models. We further show that the popular DDT formulation can be retrieved from IEE by certain polyhedral operations, thus giving a unifying view on a complete branch of MIP formulations for the RCPSP. In addition, we analyze the computational performance of all presented models on test instances of the PSPLIB (Kolisch and Sprecher 1997).

Description: All feasible flows in potential-driven networks induce an orientation on the undirected graph underlying the network. Clearly, these orientations must satisfy two conditions: they are acyclic and there are no "dead ends" in the network, i.e. each source requires outgoing flows, each sink requires incoming flows, and each transhipment vertex requires both an incoming and an outgoing flow. In this paper we will call orientations that satisfy these conditions acyclic source-transhipment-sink orientations (ASTS-orientation) and study their structure. In particular, we characterize graphs that allow for such an orientation, describe a way to enumerate all possible ASTS-orientations of a given graph, present an algorithm to simplify and decompose a graph before such an enumeration and shed light on the role of zero flows in the context of ASTS-orientations.

Description: The class of potential-driven network flow problems provides important models for a range of infrastructure networks. For real-world applications, they need to be combined with integer models for switching certain network elements, giving rise to hard-to-solve MINLPs. We observe that on large-scale real-world meshed networks the usually employed relaxations are rather weak due to cycles in the network. We propose acyclic flow orientations as a combinatorial relaxation of feasible solutions of potential-driven flow problems and show how they can be used to strengthen existing relaxations. First computational results indicate that the strengthend model is much tighter than the original relaxation, thus promising a computational advantage.

Description: We present a novel machine learning approach to understanding conformation dynamics of biomolecules. The approach combines kernel-based techniques that are popular in the machine learning community with transfer operator theory for analyzing dynamical systems in order to identify conformation dynamics based on molecular dynamics simulation data. We show that many of the prominent methods like Markov State Models, EDMD, and TICA can be regarded as special cases of this approach and that new efficient algorithms can be constructed based on this derivation. The results of these new powerful methods will be illustrated with several examples, in particular the alanine dipeptide and the protein NTL9.

Description: The paper investigates the efficient use of a linearly implicit stiff integrator for the numerical solution of density driven flow problems. Upon choosing a one-step method of extrapolation type (code LIMEX), the use of full Jacobians and reduced approximations are discussed. Numerical experiments include nonlinear density flow problems such as diffusion from a salt dome (2D), a (modified) Elder problem (3D), the saltpool benchmark (3D) and a real life salt dome problem (2D). The arising linear equations are solved using either a multigrid preconditioner from the software package UG4 or the sparse matrix solver SuperLU.

Description: Given a factorable function f, we propose a procedure that constructs a concave underestimor of f that is tight at a given point. These underestimators can be used to generate intersection cuts. A peculiarity of these underestimators is that they do not rely on a bounded domain. We propose a strengthening procedure for the intersection cuts that exploits the bounds of the domain. Finally, we propose an extension of monoidal strengthening to take advantage of the integrality of the non-basic variables.

Description: In commodity transport networks such as natural gas, hydrogen and water networks, flows arise from nonlinear potential differences between the nodes, which can be represented by so-called "potential-driven" network models. When operators of these networks face increasing demand or the need to handle more diverse transport situations, they regularly seek to expand the capacity of their network by building new pipelines parallel to existing ones ("looping"). The paper introduces a new mixed-integer non-linear programming (MINLP) model and a new non-linear programming (NLP) model and compares these with existing models for the looping problem and related problems in the literature, both theoretically and experimentally. On this basis, we give recommendations about the circumstances under which a certain model should be used. In particular, it turns out that one of our novel models outperforms the existing models. Moreover, the paper is the first to include the practically relevant option that a particular pipeline may be looped several times.

Description: Mit dem Voranschreiten der Technologie erhalten die öffentlichen Verkehrsmittel eine größere Bedeutung. Die Beförderung mehrerer Personen eröffnet der Gesellschaft viele Möglichkeiten, unter Anderem den Vorteil der Zeitersparnis. Die Dauer des Verkehrswegs mit öffentlichen Verkehrsmitteln ist häufig geringer, als die mit individuellen Verkehrsmitteln. Jedes öffentliche Transportmittel ist mit einem Fahrplan versehen. Dieser bietet Passagieren, die öffentliche Verkehrsmittel öfter nutzen, eine Strukturierung und Planung ihrer Zeit. Dabei lassen sich Taktfahrpläne aufgrund ihres periodischen Verhaltens leicht einprägen. Dieses periodische Verhalten ist durch mathematische Modellierungen darstellbar. Das persönliche Nutzverhalten vieler Bürger im Personenverkehr ist auf die öffentlichen Verkehrsmittel beschränkt. Diese beinhalten im Gegensatz zum individuellen Verkehrsmittel eine Wartezeit. Dabei stellt sich die Frage, ob man anhand mathematischer Modelle diese Wartezeit minimieren kann. Eine bekannte mathematische Modellierung dieses Problems ist das Periodic Event Scheduling Problem (PESP). Die optimale Planung eines periodischen Taktfahrplanes steht im Vordergrund. Während ich dieses Problem betrachtet habe, wurde ich auf das Rechnen mit linearen Gleichungssystemen modulo T aufmerksam. Bei periodischen Taktfahrplänen wird ein einheitliches zeitliches Muster, welches sich nach T Minuten wiederholt, betrachtet. Das dabei zu betrachtende Lösungsproblem eröffnet ein Teilgebiet der Mathematik, welches bislang nicht im Vordergrund stand: Das Lösen linearer Gleichungen modulo T, wobei T für die Zeit in Minuten steht und somit 60 ist. Da 60 keine Primzahl ist, kann – wie im Laufe der Arbeit präsentiert – das lineare Gleichungssystem nicht mehr über einen Körper gelöst werden. Lineare Gleichungssysteme werden nun über Nicht-Körpern betrachtet. Die Literatur weist sowohl im deutschsprachigem als auch im englischsprachigen Raum wenig Umfang bezüglich linearer Gleichungssysteme über Nicht-Körper auf. Der Bestand an Fachliteratur bezüglich den Themen lineare diophantische Gleichungssysteme, Hermite- Normalform und Smith-Normalform ist zurzeit gering, dennoch erreichbar, beispielsweise in [1], welches in dieser Bachelorarbeit genutzt wurde. Insbesondere wurde ich bei der Suche nach geeigneter Literatur zu linearen Gleichungssystemen über Restklassenringe, die keinen Körper bilden, nicht fündig. Dabei recherchierte ich sowohl in den Universitätsbibliotheken als auch in webbasierenden Suchmaschinen. Aufgrund dem geringen Bestand an Fachliteratur in diesem Kontext, war ich gezwungen, an vielen Stellen eigene logische Verknüpfungen zu konzipieren und zu beweisen. Dies brachte viele Schwierigkeiten mit sich, die mit bestmöglichem Verständnis bearbeitet wurden. Abseits der Zugänglichkeit der Literatur, finde ich es sehr überraschend, dass sich viele Professoren der Mathematik mit diesem Themenbereich nicht beschäftigten. Insbesondere gingen von den Dozenten, die ich um Literaturempfehlung bat, kein Werk aus. Damit wurde das Thema "Lineare Gleichungssysteme Modulo T" einerseits eine große Herausforderung, andererseits eine große Motivation, da ich mit dieser Bachelorarbeit vielen Interessenten der Mathematik als Sekundärliteratur dienen kann.

Description: Transformations of Steiner tree problem variants have been frequently discussed in the literature. Besides allowing to easily transfer complexity results, they constitute a central pillar of exact state-of-the-art solvers for well-known variants such as the Steiner tree problem in graphs. In this paper transformations for both the prize-collecting Steiner tree problem and the maximum-weight connected subgraph problem to the Steiner arborescence problem are introduced for the first time. Furthermore, we demonstrate the considerable implications for practical solving approaches, including the computation of strong upper and lower bounds.

Description: Quadratic optimization problems (QPs) are ubiquitous, and solution algorithms have matured to a reliable technology. However, the precision of solutions is usually limited due to the underlying floating-point operations. This may cause inconveniences when solutions are used for rigorous reasoning. We contribute on three levels to overcome this issue. First, we present a novel refinement algorithm to solve QPs to arbitrary precision. It iteratively solves refined QPs, assuming a floating-point QP solver oracle. We prove linear convergence of residuals and primal errors. Second, we provide an efficient implementation, based on SoPlex and qpOASES that is publicly available in source code. Third, we give precise reference solutions for the Maros and Mészáros benchmark library.

Description: Mixed integer programming is a versatile and valuable optimization tool. However, solving specific problem instances can be computationally demanding even for cutting-edge solvers. Such long running times are often significantly reduced by an appropriate change of the solver's parameters. In this paper we investigate "algorithm selection", the task of choosing among a set of algorithms the ones that are likely to perform best for a particular instance. In our case, we treat different parameter settings of the MIP solver SCIP as different algorithms to choose from. Two peculiarities of the MIP solving process have our special attention. We address the well-known problem of performance variability by using multiple random seeds. Besides solving time, primal dual integrals are recorded as a second performance measure in order to distinguish solvers that timed out. We collected feature and performance data for a large set of publicly available MIP instances. The algorithm selection problem is addressed by several popular, feature-based methods, which have been partly extended for our purpose. Finally, an analysis of the feature space and performance results of the selected algorithms are presented.

Description: We study the problem of finding subpaths with high demand in a given network that is traversed by several users. The demand of a subpath is the number of users who completely cover this subpath during their trip. Especially with large instances, an efficient algorithm for computing all subpaths' demands is necessary. We introduce a path-graph to prevent multiple generations of the same subpath and give a recursive approach to compute the demands of all subpaths. Our runtime analysis shows, that the presented approach compares very well against the theoretical minimum runtime.

Description: Computing the Hierarchical Equations of Motion (HEOM) is by itself a challenging problem, and so is writing portable production code that runs efficiently on a variety of architectures while scaling from PCs to supercomputers. We combined both challenges to push the boundaries of simulating quantum systems, and to evaluate and improve methodologies for scientific software engineering. Our contributions are threefold: We present the first distributed memory implementation of the HEOM method (DM-HEOM), we describe an interdisciplinary development workflow, and we provide guidelines and experiences for designing distributed, performance-portable HPC applications with MPI-3, OpenCL and other state-of-the-art programming models. We evaluated the resulting code on multi- and many-core CPUs as well as GPUs, and demonstrate scalability on a Cray XC40 supercomputer for the PS I molecular light harvesting complex.

Description: We investigate a graph theoretical problem arising in the automatic billing of a network toll. Given a network and a family of user paths, we study the graph segmentation problem (GSP) to cover parts of the user paths by a set of disjoint segments. The GSP is shown to be NP-hard but for special cases it can be solved in polynomial time. We also show that the marginal utility of a segment is bounded. Computational results for real-world instances show that in practice the problem is more amenable than the theoretic bounds suggest.

Description: We study the problem of finding subpaths with high demand in a given network that is traversed by several users. The demand of a subpath is the number of users who completely cover this subpath during their trip. Especially with large instances, an efficient algorithm for computing all subpaths' demands is necessary. We introduce a path-graph to prevent multiple generations of the same subpath and give a recursive approach to compute the demands of all subpaths. Our runtime analysis shows, that the presented approach compares very well against the theoretical minimum runtime.

Description: Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long-timescale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large lengthscales, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail. Thus, coupling MSMs and RD simulations (MSM/RD) would be highly desirable, as they could efficiently produce simulations at large time- and lengthscales, while still conserving the characteristic features of the interactions observed at atomic detail. While such a coupling seems straightforward, fundamental questions are still open: Which definition of MSM states is suitable? Which protocol to merge and split RD particles in an association/dissociation reaction will conserve the correct bimolecular kinetics and thermodynamics? In this paper, we make the first step towards MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of a protein with a small ligand (A + B 〈--〉 C). Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported.

Description: Human mobility always had a great influence on the spreading of cultural, social and technological ideas. Developing realistic models that allow for a better understanding, prediction and control of such coupled processes has gained a lot of attention in recent years. However, the modeling of spreading processes that happened in ancient times faces the additional challenge that available knowledge and data is often limited and sparse. In this paper, we present a new agent-based model for the spreading of innovations in the ancient world that is governed by human movements. Our model considers the diffusion of innovations on a spatial network that is changing in time, as the agents are changing their positions. Additionally, we propose a novel stochastic simulation approach to produce spatio-temporal realizations of the spreading process that are instructive for studying its dynamical properties and exploring how different influences affect its speed and spatial evolution.

Description: Wir beschreiben die Optimierung des Nahverkehrsnetzes der Stadt Karlsruhe im Zusammmenhang mit den Baumaßnahmen der sogenannten Kombilösung.

Description: Gene Regulatory Networks are powerful models for describing the mechanisms and dynamics inside a cell. These networks are generally large in dimension and seldom yield analytical formulations. It was shown that studying the conditional expectations between dimensions (vertices or species) of a network could lead to drastic dimension reduction. These conditional expectations were classically given by solving equations of motions derived from the Chemical Master Equation. In this paper we deviate from this convention and take an Algebraic approach instead. That is, we explore the consequences of conditional expectations being described by a polynomial function. There are two main results in this work. Firstly: if the conditional expectation can be described by a polynomial function, then coefficients of this polynomial function can be reconstructed using the classical moments. And secondly: there are dimensions in Gene Regulatory Networks which inherently have conditional expectations with algebraic forms. We demonstrate through examples, that the theory derived in this work can be used to develop new and effective numerical schemes for forward simulation and parameter inference. The algebraic line of investigation of conditional expectations has considerable scope to be applied to many different aspects of Gene Regulatory Networks; this paper serves as a preliminary commentary in this direction.

Description: In Silico Clinical Trials (ISCT), i.e., clinical experimental campaigns carried out by means of computer simulations, hold the promise to decrease time and cost for the safety and efficacy assessment of pharmacological treatments, reduce the need for animal and human testing, and enable precision medicine. In this paper we present a case study aiming at quantifying, by means of a multi-arm ISCT supervised by intelligent search, the potential impact of precision medicine approaches on a real pharmacological treatment, namely the downregulation phase of a complex clinical protocol for assisted reproduction.

Description: We investigate the relation between Hall’s theorem and Kőnig’s theorem in graphs and hypergraphs. In particular, we characterize the graphs satisfying a deficiency version of Hall’s theorem, thereby showing that this class strictly contains all Kőnig–Egerváry graphs. Furthermore, we give a generalization of Hall’s theorem to normal hypergraphs.

Description: We investigate metastable dynamical systems subject to non-stationary forcing as they appear in molecular dynamics for systems driven by external fields. We show, that if the strength of the forcing is inversely proportional to the length of the slow metastable time scales of the unforced system, then the effective behavior of the forced system on slow time scales can be described by a low-dimensional reduced master equation. Our construction is explicit and uses the multiscale perturbation expansion method called two-timing, or method of multiple scales. The reduced master equation—a Markov state model—can be assembled by constructing two equilibrium Markov state models; one for the unforced system, and one for a slightly perturbed one.

Description: Mathematical models for bioregulatory networks can be based on different formalisms, depending on the quality of available data and the research question to be answered. Discrete boolean models can be constructed based on qualitative data, which are frequently available. On the other hand, continuous models in terms of ordinary differential equations (ODEs) can incorporate time-series data and give more detailed insight into the dynamics of the underlying system. A few years ago, a method based on multivariate polynomial interpolation and Hill functions has been developed for an automatic conversion of boolean models to systems of ordinary differential equations. This method is frequently used by modellers in systems biology today, but there are only a few results available about the conservation of mathematical structures and properties across the formalisms. Here, we consider subsets of the phase space where some components stay fixed, called trap spaces, and demonstrate how boolean trap spaces can be linked to invariant sets in the continuous state space. This knowledge is of practical relevance since finding trap spaces in the boolean setting, which is relatively easy, allows for the construction of reduced ODE models.

Description: We consider the following planning problem in public transportation: Given a periodic timetable, how many vehicles are required to operate it? In [9], for this sequential approach, it is proposed to first expand the periodic timetable over time, and then answer the above question by solving a flow-based aperiodic optimization problem. In this contribution we propose to keep the compact periodic representation of the timetable and simply solve a particular perfect matching problem. For practical networks, it is very much likely that the matching problem decomposes into several connected components. Our key observation is that there is no need to change any turnaround decision for the vehicles of a line during the day, as long as the timetable stays exactly the same.

Description: We reconstruct the temporal evolution of the source distribution for the four major gas species H2O, CO2, CO, and O2 on the surface of comet 67P/Churyumov-Gerasimenko during its 2015 apparition. The analysis applies an inverse coma model and fits to data between August 6th 2014 and September 5th 2016 measured with the Double Focusing Mass Spectrometer (DFMS) of the Rosetta Orbiter Spectrometer for Ion and Neutral Analysis (ROSINA) and the COmet Pressure Sensor (COPS). The spatial distribution of gas sources with their temporal variation allows one to construct surface maps for gas emissions and to evaluate integrated productions rates. For all species peak production rates and integrated productions rates per orbit are evaluated separately for the northern and the southern hemisphere. The nine most active emitting areas on the comet’s surface are defined and their correlation to emissions for each of the species is discussed.

Description: 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.

Description: The perfect matching polytope, i.e. the convex hull of (incidence vectors of) perfect matchings of a graph is used in many combinatorial algorithms. Kotzig, Lovász and Plummer developed a decomposition theory for graphs with perfect matchings and their corresponding polytopes known as the tight cut decomposition which breaks down every graph into a number of indecomposable graphs, so called bricks. For many properties that are of interest on graphs with perfect matchings, including the description of the perfect matching polytope, it suffices to consider these bricks. A key result by Lovász on the tight cut decomposition is that the list of bricks obtained is the same independent of the choice of tight cuts made during the tight cut decomposition procedure. This implies that finding a tight cut decomposition is polynomial time equivalent to finding a single tight cut. We generalise the notions of a tight cut, a tight cut contraction and a tight cut decomposition to hypergraphs. By providing an example, we show that the outcome of the tight cut decomposition on general hypergraphs is no longer unique. However, we are able to prove that the uniqueness of the tight cut decomposition is preserved on a slight generalisation of uniform hypergraphs. Moreover, we show how the tight cut decomposition leads to a decomposition of the perfect matching polytope of uniformable hypergraphs and that the recognition problem for tight cuts in uniformable hypergraphs is polynomial time solvable.

Description: Die enge Zusammenarbeit der vier Berliner Universitätsbibliotheken1 reicht weit zurück. Bereits vor der Jahrtausendwende haben die Berliner Universitätsbibliotheken (UBs) gemeinsam das Bibliothekssystem Aleph 500 ausgewählt und implementiert, danach folgten weitere Systeme – das Linking System SFX, die Digitale Bibliothek MetaLib und das Bibliotheksportal Primo. Es war daher folgerichtig und selbstverständlich, dass auch die Auswahl und Implementierung eines neuen Bibliothekssystems in enger Abstimmung und Zusammenarbeit erfolgte. Die Erfahrungen bei Vertragsverhandlungen und Implementierung von Alma sind Gegenstand des folgenden Berichtes.

Description: As regards implementing new library technology, the Berlin University libraries have been working closely together for more than 20 years. It was the case for the implementation of the legacy system Aleph 500, the linking system SFX, the digital library MetaLib and the library portal Primo, and therefore it was a matter of course to continue the close cooperation during the implementation of the new cloud-based library system, too. The experience gained during the contract negotiations and the implementation project, and lessons learned are the focus of this report.