519 Wahrscheinlichkeiten, angewandte Mathematik
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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.
Umfragen können zur Erhebung von Daten in betriebswirtschaftlichen Zusammenhängen genutzt werden. Die Aussagekraft der Daten hängt dabei nicht zuletzt von der gewählten Skalierung des Merkmals ab. Umfragedaten sind in der Regel ordinal skaliert, womit sie aufgrund ihrer diskreten Wertestruktur zahlreiche Details des eigentlich Befragungsgegenstandes eher verdecken. Dennoch eignen sich solche primärstatistischen Erhebungen, um Einstellungen und Meinungen von Konsumenten oder Benutzern eines speziellen Systems zu untersuchen. Die von Jöreskog und Sörbom entwickelten LInearen Strukturgleichungsmodelle (LISREL = LInear Structural RELationship) können genutzt werden, um Umfragedaten zu analysieren und hinter den Variablen verborgene Aspekte oder auch Faktoren aufzudecken. Nach der Vorstellung der grundlegenden Funktionsweise von LISREL-Modellen und ihrer Charakteristika soll im Folgenden deren Einsatz im Bereich der Zufriedenheitsanalyse von IT-Nutzern verdeutlicht werden. Die auf diese Weise identifizierten wichtigen Stellgrößen eines IT-Systems geben dem Management von Unternehmen die Möglichkeit, die Optimalität der Lösungen zu bewerten und die Zufriedenheit der Nutzer systematisch zu optimieren.
CMPL (Coliop Mathematical Programming Language) is a mathematical programming language for modelling linear programming (LP) problems or mixed integer programming (MIP) problems. The CMPL syntax is similar in formulation to the the original mathematical model but also includes syntactic elements from modern programming languages. CMPL is intended to combine the clarity of mathematical models with the flexibility of programming languages. CMPL transforms the mathematical problem into MPS, Free-MPS or OSiL (see https://projects.coin-or.org/OS or http://www.optimizationservices.org) files which can be used with certain solvers. CMPL is also a part of Coliop3 which is an IDE (Integrated Development Environment) intended to solve LP and MIP problems. CMPL is an open source project licensed under GPL. It is written in C and is available for all relevant operating systems. CMPL and Coliop3 are projects of the Technical University of Applied Sciences Wildau and the Institute for Operations Research and Business Management at the Martin Luther University Halle-Wittenberg. For further information please visit the CMPL/Coliop3 website (www.coliop.org).

