@misc{BorndoerferHeismann, author = {Bornd{\"o}rfer, Ralf and Heismann, Olga}, title = {Minimum Cost Hyperassignments with Applications to ICE/IC Rotation Planning}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14564}, number = {11-46}, abstract = {Vehicle rotation planning is a fundamental problem in rail transport. It decides how the railcars, locomotives, and carriages are operated in order to implement the trips of the timetable. One important planning requirement is operational regularity, i.e., using the rolling stock in the same way on every day of operation. We propose to take regularity into account by modeling the vehicle rotation planning problem as a minimum cost hyperassignment problem (HAP). Hyperassignments are generalizations of assignments from directed graphs to directed hypergraphs. Finding a minimum cost hyperassignment is NP-hard. Most instances arising from regular vehicle rotation planning, however, can be solved well in practice. We show that, in particular, clique inequalities strengthen the canonical LP relaxation substantially.}, language = {en} } @misc{BorndoerferHeismann, author = {Bornd{\"o}rfer, Ralf and Heismann, Olga}, title = {The Hypergraph Assignment Problem}, issn = {1438-0064}, doi = {10.1016/j.disopt.2014.11.002}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-14822}, abstract = {The hypergraph assignment problem (HAP) is the generalization of assignments from directed graphs to directed hypergraphs. It serves, in particular, as a universal tool to model several train composition rules in vehicle rotation planning for long distance passenger railways. We prove that even for problems with a small hyperarc size and hypergraphs with a special partitioned structure the HAP is NP-hard and APX-hard. Further, we present an extended integer linear programming formulation which implies, e. g., all clique inequalities.}, language = {en} } @misc{Heismann2010, type = {Master Thesis}, author = {Heismann, Olga}, title = {Minimum Cost Hyperassignments}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-13371}, school = {Zuse Institute Berlin (ZIB)}, year = {2010}, abstract = {Vehicle rotation planning for long distance passenger railways is a fundamental problem in rail transport. It deals with the allocation of vehicles to trips in a cyclic weekly schedule. Its result is an assignment of each trip to a follow-on trip which will be serviced by the same vehicle. To take so-called regularity, which is an important requirement, into account, vehicle rotation planning can be modeled as a hyperassignment problem. This is a generalization of the assignment problem to directed hypergraphs we propose. We prove that the hyperassignment problem is NP-hard for the practically relevant cases and that the canonical integer linear programming (ILP) formulation results in large integrality gaps and arbitrarily high basis matrix determinants. Our main contribution is an extended ILP formulation, which provably implies important classes of inequalities, e. g., all clique inequalities. Clique inequalities are of great importance, because as calculations with practical data show they highly reduce the LP-IP gap. The extended formulation can be solved by column generation. We propose fast combinatorial algorithms for the pricing subproblem.}, language = {en} } @misc{HeismannBorndoerfer, author = {Heismann, Olga and Bornd{\"o}rfer, Ralf}, title = {A Generalization of Odd Set Inequalities for the Set Packing Problem}, issn = {1438-0064}, doi = {10.1007/978-3-319-07001-8_26}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-51010}, abstract = {The set packing problem, sometimes also called the stable set problem, is a well-known NP-hard problem in combinatorial optimization with a wide range of applications and an interesting polyhedral structure, that has been the subject of intensive study. We contribute to this field by showing how, employing cliques, odd set inequalities for the matching problem can be generalized to valid inequalities for the set packing polytope with a clear combinatorial meaning.}, language = {en} } @misc{HeismannHildenbrandtSilvestrietal., author = {Heismann, Olga and Hildenbrandt, Achim and Silvestri, Francesco and Reinelt, Gerhard and Bornd{\"o}rfer, Ralf}, title = {HUHFA: A Framework for Facet Classification}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-42230}, abstract = {Usually complete linear descriptions of polytopes consist of an enormous number of facet-defining inequalities already for very small problem sizes. In this paper, we describe a method for dividing the inequalities into equivalence classes without resorting to a normal form. Within each class, facets are related by certain symmetries and it is sufficient to list one representative of each class to give a complete picture of the structural properties of a polytope. We propose an algorithm for the classification and illustrate its efficiency on a broad range of combinatorial optimization problems including the Traveling Salesman and the Linear Ordering Problem.}, language = {en} } @misc{BrettHobergPachecoetal.2015, author = {Brett, Charles and Hoberg, Rebecca and Pacheco, Meritxell and Smith, Kyle and Bornd{\"o}rfer, Ralf and Euler, Ricardo and Gamrath, Gerwin and Grimm, Boris and Heismann, Olga and Reuther, Markus and Schlechte, Thomas and Tesch, Alexander}, title = {G-RIPS 2014 RailLab - Towards robust rolling stock rotations}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-53475}, year = {2015}, abstract = {The Graduate-Level Research in Industrial Projects (G-RIPS) Program provides an opportunity for high-achieving graduate-level students to work in teams on a real-world research project proposed by a sponsor from industry or the public sector. Each G-RIPS team consists of four international students (two from the US and two from European universities), an academic mentor, and an industrial sponsor. This is the report of the Rail-Lab project on the definition and integration of robustness aspects into optimizing rolling stock schedules. In general, there is a trade-off for complex systems between robustness and efficiency. The ambitious goal was to explore this trade-off by implementing numerical simulations and developing analytic models. In rolling stock planning a very large set of industrial railway requirements, such as vehicle composition, maintenance constraints, infrastructure capacity, and regularity aspects, have to be considered in an integrated model. General hypergraphs provide the modeling power to tackle those requirements. Furthermore, integer programming approaches are able to produce high quality solutions for the deterministic problem. When stochastic time delays are considered, the mathematical programming problem is much more complex and presents additional challenges. Thus, we started with a basic variant of the deterministic case, i.e., we are only considering hypergraphs representing vehicle composition and regularity. We transfered solution approaches for robust optimization from the airline industry to the setting of railways and attained a reasonable measure of robustness. Finally, we present and discuss different methods to optimize this robustness measure.}, language = {en} }