TY - CHAP A1 - Klug, Torsten A1 - Junosza-Szaniawski, Konstanty A1 - Kwasiborski, Slawomir A1 - Fügenschuh, Armin A1 - Schlechte, Thomas T1 - Fastest, Average and Quantile Schedule T2 - SOFSEM 2015: Theory and Practice of Computer Science N2 - We consider problems concerning the scheduling of a set of trains on a single track. For every pair of trains there is a minimum headway, which every train must wait before it enters the track after another train. The speed of each train is also given. Hence for every schedule - a sequence of trains - we may compute the time that is at least needed for all trains to travel along the track in the given order. We give the solution to three problems: the fastest schedule, the average schedule, and the problem of quantile schedules. The last problem is a question about the smallest upper bound on the time of a given fraction of all possible schedules. We show how these problems are related to the travelling salesman problem. We prove NP-completeness of the fastest schedule problem, NP-hardness of quantile of schedules problem, and polynomiality of the average schedule problem. We also describe some algorithms for all three problems. In the solution of the quantile problem we give an algorithm, based on a reverse search method, generating with polynomial delay all Eulerian multigraphs with the given degree sequence and a bound on the number of such multigraphs. A better bound is left as an open question. KW - scheduling KW - eulerian multigraphs Y1 - 2015 U6 - https://doi.org/10.1007/978-3-662-46078-8_17 SP - 201 EP - 216 PB - Springer Berlin Heidelberg ER - TY - CHAP A1 - Klug, Torsten A1 - Reuther, Markus A1 - Schlechte, Thomas T1 - Does Laziness Pay Off? - A Lazy-Constraint Approach to Timetabling T2 - 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022) N2 - Timetabling is a classical and complex task for public transport operators as well as for railway undertakings. The general question is: Which vehicle is taking which route through the transportation network in which order? In this paper, we consider the special setting to find optimal timetables for railway systems under a moving block regime. We directly set up on our work of [8 ], i.e., we consider the same model formulation and real-world instances of a moving block headway system. In this paper, we present a repair heuristic and a lazy-constraint approach utilizing the callback features of Gurobi, see [3]. We provide an experimental study of the different algorithmic approaches for a railway network with 100 and up to 300 train requests. The computational results show that the lazy-constraint approach together with the repair heuristic significantly improves our previous approaches. Y1 - 2022 U6 - https://doi.org/10.4230/OASIcs.ATMOS.2022.11 VL - 106 SP - 11:1 EP - 11:8 PB - Schloss Dagstuhl -- Leibniz-Zentrum für Informatik ER - TY - CHAP A1 - Hiller, Benjamin A1 - Klug, Torsten A1 - Witzig, Jakob T1 - Reoptimization in branch-and-bound algorithms with an application to elevator control T2 - Proceedings of the 12th International Symposium on Experimental Algorithms Y1 - 2013 U6 - https://doi.org/10.1007/978-3-642-38527-8_33 VL - 7933 SP - 378 EP - 389 ER - TY - GEN A1 - Hiller, Benjamin A1 - Klug, Torsten A1 - Witzig, Jakob T1 - Reoptimization in branch-and-bound algorithms with an application to elevator control N2 - We consider reoptimization (i.e. the solution of a problem based on information available from solving a similar problem) for branch-and-bound algorithms and propose a generic framework to construct a reoptimizing branch-and-bound algorithm. We apply this to an elevator scheduling algorithm solving similar subproblems to generate columns using branch-and-bound. Our results indicate that reoptimization techniques can substantially reduce the running times of the overall algorithm. T3 - ZIB-Report - 13-15 KW - reoptimization KW - branch-and-bound KW - column generation KW - elevator control Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17876 SN - 1438-0064 ER -