Ralf Borndörfer
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View article: Logic-Constrained Shortest Paths for Flight Planning
Logic-Constrained Shortest Paths for Flight Planning Open
The logic-constrained shortest path problem (LCSPP) combines a one-to-one shortest path problem with satisfiability constraints imposed on the routing graph. This setting arises in flight planning, where air traffic control (ATC) authoriti…
View article: Electric Bus Scheduling with Non-Linear Charging, Power Grid Bottlenecks, and Dynamic Recharge Rates
Electric Bus Scheduling with Non-Linear Charging, Power Grid Bottlenecks, and Dynamic Recharge Rates Open
Public transport operators are gradually electrifying their bus fleets, predominantly with battery-powered drive trains. These buses commonly have to be scheduled to recharge in-service, which gives rise to a number of challenges. A major …
View article: An Iterative Refinement Approach for the Rolling Stock Rotation Problem with Predictive Maintenance
An Iterative Refinement Approach for the Rolling Stock Rotation Problem with Predictive Maintenance Open
The rolling stock rotation problem with predictive maintenance (RSRP-PdM) involves the assignment of trips to a fleet of vehicles with integrated maintenance scheduling based on the predicted failure probability of the vehicles. These prob…
View article: Price optimal routing in public transportation
Price optimal routing in public transportation Open
We consider the price-optimal earliest arrival problem in public transit (POEAP) in which we aim to calculate the Pareto-set of journeys with respect to ticket price and arrival time in a public transportation network. Public transit fare …
View article: A Comparison of Models for Rolling Stock Scheduling
A Comparison of Models for Rolling Stock Scheduling Open
A major step in the planning process of passenger railway operators is the assignment of rolling stock, i.e., train units, to the trips of the timetable. A wide variety of mathematical optimization models have been proposed to support this…
View article: K-Shortest Simple Paths Using Biobjective Path Search
K-Shortest Simple Paths Using Biobjective Path Search Open
In this paper we introduce a new algorithm for the \emph{$k$-Shortest Simple Paths} (\kspp{k}) problem with an asymptotic running time matching the state of the art from the literature. It is based on a black-box algorithm due to \citet{Ro…
View article: Newton’s Method for Global Free Flight Trajectory Optimization
Newton’s Method for Global Free Flight Trajectory Optimization Open
Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton’s method for continuous optimization converges in a sufficiently large neighb…
View article: Error Bounds for Discrete-Continuous Free Flight Trajectory Optimization
Error Bounds for Discrete-Continuous Free Flight Trajectory Optimization Open
Two-stage methods addressing continuous shortest path problems start local minimization from discrete shortest paths in a spatial graph. The convergence of such hybrid methods to global minimizers hinges on the discretization error induced…
View article: Targeted multiobjective Dijkstra algorithm
Targeted multiobjective Dijkstra algorithm Open
We introduce the Targeted Multiobjective Dijkstra Algorithm (T‐MDA), a label setting algorithm for the One‐to‐One Multiobjective Shortest Path (MOSP) Problem. It is based on the recently published Multiobjective Dijkstra Algorithm (MDA) an…
View article: Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization
Convergence Properties of Newton's Method for Globally Optimal Free Flight Trajectory Optimization Open
The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice…
View article: New Dynamic Programming Algorithm for the Multiobjective Minimum Spanning Tree Problem
New Dynamic Programming Algorithm for the Multiobjective Minimum Spanning Tree Problem Open
The Multiobjective Minimum Spanning Tree (MO-MST) problem is a variant of the Minimum Spanning Tree problem, in which the costs associated with every edge of the input graph are vectors. In this paper, we design a new dynamic programming M…
View article: Newton's Method for Global Free Flight Trajectory Optimization
Newton's Method for Global Free Flight Trajectory Optimization Open
Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton's method for continuous optimization converges in a sufficiently large neighb…
View article: Non-Pool-Based Line Planning on Graphs of Bounded Treewidth
Non-Pool-Based Line Planning on Graphs of Bounded Treewidth Open
Line planning, i.e. choosing routes which are to be serviced by vehicles in order to satisfy network demands, is an important aspect of public transport planning. While there exist heuristic procedures for generating lines from scratch, mo…
View article: Vertex covering with capacitated trees
Vertex covering with capacitated trees Open
The covering of a graph with (possibly disjoint) connected subgraphs is a fundamental problem in graph theory. In this paper, we study a version to cover a graph's vertices by connected subgraphs subject to lower and upper weight bounds, a…
View article: Error Bounds for Discrete-Continuous Shortest Path Problems with Application to Free Flight Trajectory Optimization
Error Bounds for Discrete-Continuous Shortest Path Problems with Application to Free Flight Trajectory Optimization Open
Two-stage methods addressing continuous shortest path problems start local minimization from discrete shortest paths in a spatial graph. The convergence of such hybrid methods to global minimizers hinges on the discretization error induced…
View article: Price Optimal Routing in Public Transportation
Price Optimal Routing in Public Transportation Open
We consider the price-optimal earliest arrival problem in public transit (POEAP) in which we aim to calculate the Pareto-set of journeys with respect to ticket price and arrival time in a public transportation network. Public transit fare …
View article: Multiobjective Dijkstra A.
Multiobjective Dijkstra A. Open
We introduce the Multiobjective Dijkstra A* (MDA*) algorithm, a label setting algorithm for the One-to-One Multiobjective Shortest Path Problem that guides the search toward the target node. For the design of our new algorithm, we combine …
View article: Targeted Multiobjective Dijkstra Algorithm
Targeted Multiobjective Dijkstra Algorithm Open
In this paper, we introduce the Targeted Multiobjective Dijkstra Algorithm (T-MDA), a label setting algorithm for the One-to-One Multiobjective Shortest Path (MOSP) Problem. The T-MDA is based on the recently published Multiobjective Dijks…
View article: Deutsche Bahn Schedules Train Rotations Using Hypergraph Optimization
Deutsche Bahn Schedules Train Rotations Using Hypergraph Optimization Open
Deutsche Bahn (DB) operates a large fleet of rolling stock (locomotives, wagons, and train sets) that must be combined into trains to perform rolling stock rotations. This train composition is a special characteristic of railway operations…
View article: An FPTAS for Dynamic Multiobjective Shortest Path Problems
An FPTAS for Dynamic Multiobjective Shortest Path Problems Open
The Dynamic Multiobjective Shortest Path problem features multidimensional costs that can depend on several variables and not only on time; this setting is motivated by flight planning applications and the routing of electric vehicles. We …
View article: Connected k-Partition of k-Connected Graphs and c-Claw-Free Graphs
Connected k-Partition of k-Connected Graphs and c-Claw-Free Graphs Open
A connected partition is a partition of the vertices of a graph into sets that induce connected subgraphs. Such partitions naturally occur in many application areas such as road networks, and image processing. In these settings, it is ofte…
View article: Efficient Algorithms for the Multi-Period Line Planning Problem in Public Transportation (Short Paper)
Efficient Algorithms for the Multi-Period Line Planning Problem in Public Transportation (Short Paper) Open
In order to plan and schedule a demand-responsive public transportation system, both temporal and spatial changes in demand should be taken into account even at the line planning stage. We study the multi-period line planning problem with …
View article: Connected k-Partition of k-Connected Graphs and c-Claw-Free Graphs
Connected k-Partition of k-Connected Graphs and c-Claw-Free Graphs Open
A connected partition is a partition of the vertices of a graph into sets that induce connected subgraphs. Such partitions naturally occur in many application areas such as road networks, and image processing. In these settings, it is ofte…
View article: A Discrete-Continuous Algorithm for Free Flight Planning
A Discrete-Continuous Algorithm for Free Flight Planning Open
We propose a hybrid discrete-continuous algorithm for flight planning in free flight airspaces. In a first step, our discrete-continuous optimization for enhanced resolution (DisCOptER) method computes a globally optimal approximate flight…
View article: A Graph- and Monoid-Based Framework for Price-Sensitive Routing in Local Public Transportation Networks
A Graph- and Monoid-Based Framework for Price-Sensitive Routing in Local Public Transportation Networks Open
We present a novel framework to mathematically describe the fare systems of local public transit companies. The model allows the computation of a provably cheapest itinerary even if prices depend on a number of parameters and non-linear co…
View article: A Cut Separation Approach for the Rolling Stock Rotation Problem with Vehicle Maintenance
A Cut Separation Approach for the Rolling Stock Rotation Problem with Vehicle Maintenance Open
For providing railway services the company’s railway rolling stock is one if not the most important ingredient. It decides about the number of passenger or cargo trips the company can offer, about the quality a passenger experiences the tr…