519 Wahrscheinlichkeiten, angewandte Mathematik
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We are presenting a crew planning optimization project for the train drivers of an urban rail transportation company. The core is about crew rostering, i.e., defining over a certain period of time (e.g., one year) for each train driver sequences of working days and rest days, and also specifying whether working days shall contain either some early, late, or night shift. But the project was not only about solving just one classical crew rostering problem. Rather, during the last three years, the entire process of crew rostering had been investigated. Apart from having modeled, solved, and implemented two different variants of crew rostering—a cyclic and an acyclic one—there have been designed and used three further optimization models for less typical surrounding sub-processes, as well as a simple crew assignment model. During the design and implementation process of these six optimization models, the focus had been put on their annual and daily usability, respectively. In particular, many practical requirements had been collected and implemented in rather straightforward ways. The result is a family of mathematical optimization models, whose results cover the valid annual crew rosters from the year 2024 on, as well as the daily assignment of specific duties to train drivers from May 2025 on at S-Bahn Berlin GmbH.
We present a novel, fast (exponential rate adaption), ab initio (hyper-parameter-free) gradient based optimizer algorithm. The main idea of the method is to adapt the learning rate α by situational awareness, mainly striving for orthogonal neighboring gradients. The method has a high success and fast convergence rate and does not rely on hand-tuned parameters giving it greater universality. It can be applied to problems of any dimensions n and scales only linearly (of order O(n)) with the dimension of the problem. It optimizes convex and non-convex continuous landscapes providing some kind of gradient. In contrast to the Ada-family (AdaGrad, AdaMax, AdaDelta, Adam, etc.) the method is rotation invariant: optimization path and performance are independent of coordinate choices. The impressive performance is demonstrated by extensive experiments on the MNIST benchmark data-set against state-of-the-art optimizers. We name this new class of optimizers after its core idea Exponential Learning Rate Adaption - ELRA. We present it in two variants c2min and p2min with slightly different control. The authors strongly believe that ELRA will open a completely new research direction for gradient descent optimize.
We present two novel, fast gradient based optimizer algorithms with dynamic learning rate. The main idea is to adapt the learning rate α by situational awareness, mainly striving for orthogonal neighboring gradients. The method has a high success and fast convergence rate and relies much less on hand-tuned hyper-parameters, providing greater universality. It scales linearly (of order O(n)) with dimension and is rotation invariant, thereby overcoming known limitations. The method is presented in two variants C2Min and P2Min, with slightly different control. Their impressive performance is demonstrated by experiments on several benchmark data-sets (ranging from MNIST to Tiny ImageNet) against the state-of-the-art optimizers Adam and Lion.
In the planning process of public transportation companies, designing the timetable is among the core planning steps. In particular in the case of periodic (or cyclic) services, the Periodic Event Scheduling Problem (PESP) is well-established to compute high-quality periodic timetables.
We are considering algorithms for computing good solutions and dual bounds for the very basic PESP with no additional extra features as add-ons. The first of these algorithms generalizes several primal heuristics that have been proposed, such as single-node cuts and the modulo network simplex algorithm. We consider partitions of the graph, and identify so-called delay cuts as a structure that allows to generalize several previous heuristics. In particular, when no more improving delay cut can be found, we already know that the other heuristics could not improve either. This heuristic already had been proven to be useful in computational experiments [Ralf Borndörfer et al., 2019], and we locate it in the more general concept of what we denote T-partitions.
With the second of these algorithms we propose to turn a strategy, that has been discussed in the past, upside-down: Instead of gluing together the network line-by-line in a bottom-up way, we develop a divide-and-conquer-like top-down approach to separate the initial problem into two easier subproblems such that the information loss along their cutset edges is as small as possible.
We are aware that there may be PESP instances that do not fit well the separator setting. Yet, on the RxLy-instances of PESPlib in our experimental computations, we come up with good primal solutions and dual bounds. In particular, on the largest instance (R4L4), this new separator approach, which applies a state-of-the-art solver as subroutine, is able to come up with better dual bounds than purely applying this state-of-the-art solver in the very same time.
Most research on fairness in Machine Learning assumes the relationship between fairness and accuracy to be a trade-off, with an increase in fairness leading to an unavoidable loss of accuracy. In this study, several approaches for fair Machine Learning are studied to experimentally analyze the relationship between accuracy and group fairness. The results indicated that group fairness and accuracy may even benefit each other, which emphasizes the importance of selecting appropriate measures for performance evaluation. This work provides a foundation for further studies on the adequate objectives of Machine Learning in the context of fair automated decision making.
This paper describes CMPLServer, an XML-RPC-based web service for distributed and grid optimisation for CMPL (Coin|Coliop Mathematical Programming Language) which is a mathematical programming language as well as a system for mathematical programming and optimisation of linear optimisation problems.
Viele Optimierungsprobleme aus der Logistik lassen sich mit Graphen und Netzwerken visualisieren. Bilder von Materialflüssen zeigen die Struktur eines Modells in geeigneter Weise. Das leistungsfähige Optimierungssystem GAMS (General Algebraic Modeling System) kann große Modelle lösen. GAMS stellt aber kein Werkzeug für das Zeichnen von Materialflüssen zur Verfügung. Der Autor hat das Programm Graph.gms implementiert, das als Tool zur Modellvisualisierung von GAMS aus verwendet werden kann.
The assessment of different sleep stages and their disorders in diseases is an important part of telematic medicine. With an electroencephalogram, the different stages of sleep can be monitored and classified with respect to brain activity. By means of modern data management such as the patient monitor ixTrend, for example, the data can be recorded for long sleep phases and evaluated by a computer using appropriate software, such as Dataplore. Here, a new mathematical model for the automated classification of sleep stages is introduced. The statistical method of autocorrelation, applied to six known sleep stages, was extended by one new class for unknown signals. Due to this new class, it is not necessary to sort all recorded EEG signals into one of the known classes, thereby, minimising the probability of errors. Further, the dependence of the error probability on the duration of the analysed EEG signal was assessed. A minimal error probability of pmin = 0.15 was detected. Exemplary data for one patient are reported.
Ermittlung des Energiebedarfs zur Bewegung von Fahrzeugen in mikroskopischen Verkehrssimulationen
(2015)
Die Integration von Modellen für Fahrzeuge mit alternativen Antrieben in Verkehrssimulationen erfordert eine genauere Betrachtung der Energieflüsse in den einzelnen Fahrzeugen. Diese Arbeit betrachtet den Energiebedarf für die Bewegung von Fahrzeugen und evaluiert vorhandene klassische Modelle zur Abstraktion der physikalischen Einflüsse. Aufgrund der fehlenden Einstimmigkeit der Autoren bei der Beschreibung solcher Modelle in der Literatur wird letztlich der Ansatz verfolgt, ein entsprechendes Modell von der physikalischen Basis ausgehend neu zu entwickeln. Zusätzlich dazu wird festgestellt, dass die Beschränkungen der geläufigen Verkehrssimulationsumgebungen einen signifikanten Einfluss auf die Berechenbarkeit einzelner Komponenten derartiger Modelle haben. Das geschaffene Modell wird anschließend in verschiedenen Varianten in einem Vergleich mit einem weit verbreiteten Modell evaluiert. Zu guter Letzt muss konstatiert werden, dass eine Erhöhung der Realitätsnähe der Simulation – insbesondere im situativen Bereich – erreicht werden konnte, für wesentliche Verbesserungen jedoch eine Beseitigung bestehender Restriktionen der Simulationsumgebungen erforderlich wäre.
The development of supply chain management includes the capacities coordination among the processes that integrate it, so much in the operative plan as in the strategic one. This problem could be allocated to the classic job shop scheduling problems of the Operations Research. In such direction, a second generalization of the calculation algorithm of the production, logistics and service capacities is formulated starting from the one reached previously by the own authors. With this generalization it is facilitated to carry out the calculations of capacity at the supply chain level and of each one of the processes. The generality‘s application is flexible to processes of production, transport, storage, administration and for service. The capacities of each process of the supply chain are expressed in the magnitudes of the final demand of products and services in the consumer, considering the losses and returns along the supply chain. A study case is presented to demonstrate the possibility of use in one field, but it is explained the possibility to use in different fields, from the production of aluminum carpentry to services related to medical equipments.
