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 - 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 -