90C10 Integer programming
Refine
Year of publication
Document Type
- ZIB-Report (26) (remove)
Has Fulltext
- yes (26)
Is part of the Bibliography
- no (26)
Keywords
- combinatorial optimization (5)
- integer programming (5)
- line planning (4)
- Integer Programming (3)
- transfers (3)
- Kombinatorische Optimierung (2)
- Operations Research (2)
- Optimierung (2)
- column generation (2)
- direct connection (2)
- duty scheduling (2)
- integrated scheduling (2)
- metric inequalities (2)
- rapid branching (2)
- vehicle positioning (2)
- Airline Crew Scheduling (1)
- Benders' decomposition (1)
- Branch and Generate (1)
- Cellular Radio Telephone Systems (1)
- Column Generation (1)
- Dienstplanung (1)
- Duty Rostering (1)
- Flugzeugumlaufplanung (1)
- Frequency Assignment Problem (1)
- Ganzzahlige Programmierung (1)
- Integrierte Umlauf- und Dienstplanung (1)
- Kürzeste Wege (1)
- Linienplanung (1)
- Minimum-Cost Flow Problems (1)
- Nahverkehr (1)
- Optimization (1)
- Passenger routing (1)
- Periodic timetabling (1)
- Public Transit (1)
- Public transport (1)
- Regionalverkehr (1)
- Robust Optimization (1)
- Spaltenerzeugung (1)
- Tail Assignment (1)
- Ticket prices (1)
- Umlaufplanung (1)
- Umsteigen (1)
- Vehicle Routing Problem (1)
- bundle method (1)
- combinatorial packing (1)
- cost allocation game (1)
- crew scheduling (1)
- duty rostering (1)
- duty templates (1)
- facet (1)
- hyperassignments (1)
- hypergraph (1)
- hypergraphs (1)
- ideal matrices (1)
- inequality (1)
- large scale optimization (1)
- matching (1)
- mixed-integer-programming (1)
- multi-commodity flow problem (1)
- nonlinear programming (1)
- operations research (1)
- polyhedral combinatorics (1)
- public transit (1)
- quadratic programming (1)
- robuste Optimierung (1)
- rolling-stock-planning (1)
- set packing (1)
- set partitioning (1)
- shortest paths (1)
- vehicle rotation planning (1)
- vehicle scheduling (1)
- Öffentlicher Verkehr (1)
Institute
We consider a novel partitioning of the set of non-dominated points for general multi-objective integer programs with $k$ objectives. The set of non-dominated points is partitioned into a set of non-dominated points whose efficient solutions are also efficient for some restricted subproblem with one less objective; the second partition comprises the non-dominated points whose efficient solutions are
inefficient for any of the restricted subproblems. We show that the first partition has the nice property that it yields finite rectangular boxes in which the points of the second partition are
located.
We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We derive a feasibility condition for path capacities supporting such direct connection flows similar to the feasibility condition for arc capacities in ordinary multi-commodity flows.
The concept allows to solve large-scale real-world line planning problems in public transport including a novel passenger routing model that favors direct connections over connections with transfers.
The task of timetabling is to schedule the trips in a public transport system by determining periodic arrival and departure times at every station. The goal is to provide a service that is both attractive for passengers and can be operated economically. To date, timetable optimization is generally done with respect to fixed passenger routes, i.e., it is assumed that passengers do not respond to changes in the timetable. This is unrealistic and ignores potentially valuable degrees of freedom. We investigate in this paper periodic timetabling models with integrated passenger routing. We propose several models that differ in the allowed passenger paths and the objectives. We compare these models theoretically and report on computations on real-world instances for the city of Wuppertal.
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.
We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We show that the concept of metric inequalities to characterize capacities that
support a multi-commodity flow can be generalized to deal with direct connections.
We propose a novel extended formulation for the line planning problem in public transport. It is based on a new concept of frequency configurations that account for all possible options to provide a required transportation capacity on an infrastructure edge. We show that this model yields a strong LP relaxation. It implies, in particular, general classes of facet defining inequalities for the standard model.
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.
Duty Scheduling Templates
(2012)
We propose duty templates as a novel concept to produce similar duty
schedules for similar days of operation in public transit. Duty templates
can conveniently handle various types of similarity requirements, and
they can be implemented with ease using standard algorithmic techniques.
They have produced good results in practice.
Rapid Branching
(2012)
We propose rapid branching (RB) as a general branch-and-bound heuristic
for solving large scale optimization problems in traffic and transport.
The key idea is to combine a special branching rule and a greedy node selection
strategy in order to produce solutions of controlled quality rapidly
and efficiently. We report on three successful applications of the method
for integrated vehicle and crew scheduling, railway track allocation, and
railway vehicle rotation planning.