TY - CHAP A1 - Lindner, Niels A1 - Liebchen, Christian T1 - New Perspectives on PESP: T-Partitions and Separators T2 - 19th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019) N2 - 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. KW - periodic event scheduling problem KW - periodic timetabling KW - graph partitioning KW - graph separators KW - balanced cuts Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:526-opus4-20074 SP - 2:1 EP - 2:18 PB - Schloss Dagstuhl, Leibniz-Zentrum für Informatik CY - Dagstuhl ER - TY - GEN A1 - Bezruk, Valeriy A1 - Gedat, Egbert A1 - Holzheimer, Katja A1 - Vandenhouten, Ralf T1 - Automated recognition of sleep stages by electroencephalograms T2 - Wissenschaftliche Beiträge 2015 N2 - 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. N2 - Die Beurteilung der verschiedenen Schlafphasen und deren Störungen bei Erkrankungen spielt eine wichtige Rolle in der telematischen Medizin. Mit einem Elektroenzephalogramm können die Schlafphasen überwacht und in verschiedene Klassen der Hirnaktivität eingeteilt werden. Durch moderne Methoden des Datenmanagements, wie etwa den Patientenmonitor ixTrend, können die Daten über längere Schlafphasen aufgezeichnet und am Computer mit geeigneter Software, etwa Dataplore, analysiert werden. Hier wird ein neues mathematisches Modell zur automatischen Klassifizierung der Schlafphasen vorgestellt. Die statistische Methode der Autokorrelation, angewendet auf sechs bekannte Schlafphasen, wurde erweitert um eine neue Klasse nicht zuordenbarer Muster. Durch diese neue Klasse wird es vermieden, jedes aufgezeichnete EEG-Muster in eine der bekannten Klassen hineinzuzwingen. Dadurch wird der Fehler bei der Zuordnung verringert. Weiter wird der Einfluss der Länge des analysierten EEG auf die Fehlerquote der Zuordnung untersucht. Es zeigte sich eine minimale Fehlerquote von pmin = 0,15. Es werden beispielhafte Daten eines Patienten gezeigt. Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:526-opus4-3552 SN - 0949-8214 VL - 19 SP - 39 EP - 43 ER - TY - CHAP A1 - Kleinsorge, Alexander A1 - Fauck, Alexander A1 - Kupper, Stefan ED - Reiff-Stephan, Jörg ED - Beuster, Anja T1 - A Novel Exponential Continuous Learning Rate Adaption Gradient Descent Optimization Method T2 - Wildauer Konferenz für Künstliche Intelligenz 2025 (WiKKI25) N2 - 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. T3 - TH Wildau Engineering and Natural Sciences Proceedings - 2 KW - neural network KW - optimizer KW - training Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:526-opus4-20785 PB - TIB Open Publishing CY - Hannover ER - TY - INPR A1 - Kleinsorge, Alexander A1 - Kupper, Stefan A1 - Fauck, Alexander A1 - Rothe, Felix T1 - ELRA: Exponential learning rate adaption gradient descent optimization method N2 - 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. Y1 - 2023 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:526-opus4-20839 SN - 2331-8422 PB - arXiv.org ER -