@misc{OPUS4-7166, title = {Proceedings of the 18th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems}, editor = {Bornd{\"o}rfer, Ralf and Storandt, Sabine}, publisher = {Dagstuhl Publishing, Saarbr{\"u}cken/Wadern, Germany}, isbn = {ISBN 978-3-95977-096-5}, doi = {10.4230/OASIcs.ATMOS.2018.0}, year = {2018}, abstract = {Running and optimizing transportation systems give rise to very complex and large-scale optimization problems requiring innovative solution techniques and ideas from mathematical optimization, theoretical computer science, and operations research. Since 2000, the series of Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS) workshops brings together researchers and practitioners who are interested in all aspects of algorithmic methods and models for transportation optimization and provides a forum for the exchange and dissemination of new ideas and techniques. The scope of ATMOS comprises all modes of transportation. The 18th ATMOS workshop (ATMOS'18) was held in connection with ALGO'18 and hosted by Aalto University in Helsinki, Finland, on August 23-24, 2018. Topics of interest were all optimization problems for passenger and freight transport, including, but not limited to, demand forecasting, models for user behavior, design of pricing systems, infrastructure planning, multi-modal transport optimization, mobile applications for transport, congestion modelling and reduction, line planning, timetable generation, routing and platform assignment, vehicle scheduling, route planning, crew and duty scheduling, rostering, delay management, routing in road networks, traffic guidance, and electro mobility. Of particular interest were papers applying and advancing techniques like graph and network algorithms, combinatorial optimization, mathematical programming, approximation algorithms, methods for the integration of planning stages, stochastic and robust optimization, online and real-time algorithms, algorithmic game theory, heuristics for real-world instances, and simulation tools. There were twenty-nine submissions from eighteen countries. All of them were reviewed by at least three referees in ninety-one reviews, among them five external ones, and judged on their originality, technical quality, and relevance to the topics of the workshop. Based on the reviews, the program committee selected sixteen submissions to be presented at the workshop (acceptance rate: 55\%), which are collected in this volume in the order in which they were presented. Together, they quite impressively demonstrate the range of applicability of algorithmic optimization to transportation problems in a wide sense. In addition, Dennis Huisman kindly agreed to complement the program with an invited talk on Railway Disruption Management: State-of-the-art in practice and new research directions. Based on the reviews, Ralf Bornd{\"o}rfer, Marika Karbstein, Christian Liebchen, and Niels Lindner won the Best Paper Award of ATMOS'18 with their paper A simple way to compute the number of vehicles that Are required to operate a periodic timetable. In addition, we awarded Tomas Lid{\´e}n the Best VGI Paper Award of ATMOS'18 for his paper Reformulations for railway traffic and maintenance planning. We would like to thank the members of the Steering Committee of ATMOS for giving us the opportunity to serve as Program Chairs of ATMOS'18, all the authors who submitted papers, Dennis Huisman for accepting our invitation to present an invited talk, the members of the Program Committee and the additional reviewers for their valuable work in selecting the papers appearing in this volume, our sponsors MODAL, TomTom, and VGIscience for their support of the prizes, and the local organizers for hosting the workshop as part of ALGO'18. We acknowledge the use of the EasyChair system for the great help in managing the submission and review processes, and Schloss Dagstuhl for publishing the proceedings of ATMOS'18 in its OASIcs series.}, language = {en} } @masterthesis{Noeckel2018, type = {Bachelor Thesis}, author = {N{\"o}ckel, Celine}, title = {Bidirectional A* Search on Time-Dependent Airway Networks}, pages = {51}, year = {2018}, abstract = {This thesis deals with a new algorithm for finding Shortest Paths on Airway Networks. It is about a Bidirectional A* Search, a Greedy algorithm exploring a network from two sides instead of one. We will use it to solve the so-called 'Horizontal Flight Trajectory Problem', where one searches for an aircraft trajectory between two airports of minimal costs on an Airway Network. The given network will be modeled as a directed graph and in order to reflect reality we concentrate on the dynamic version. Here a timedependent cost function for all arcs is integrated, that shall represent the winds blowing. This way we model the Horizontal Flight Trajectory Problem mathematically as a Time-Dependent Shortest Path Problem. The basic algorithm idea derives from the algorithm presented in 'Bidirectional A* Search on Time-Dependent Road Networks' [1], where a similar setting is elaborated for road networks. The algorithm procedure bears on a modified generalization of Dijkstra's algorithm, made bidirectional and improved in several aspects. As for the backwards search the arrival times are not known in advance, the reversed graph it occurs on has to be weighted by a lower bound. Contrary to the static case the forwards search still has to go on, when they 'meet' in one node. In the static case, the shortest path would have been found at this point. For road networks the TDSPP is well-studied, for airway networks cannot be found as much in literature. In order to test efficiency, we implement Dijkstra's algorithm, unidirectional A* Search and Bidirectional A* Search. We draw up how potential functions for the static case could look like and that with a suitable potential A* Search with works approx. 7 times faster than Dijkstra in the dynamic case. Our computations lead also to the result, that the unidirectional A* Search works even better on the network than our new bidirectional approach does. On average it labels fewer nodes and also yields 1,7 times faster to the solutions. For assessing the efficiency of the different algorithms we compare the running times and to exclude processor characteristics we consider also the set labels relative to the labels on the resulting optimal path. In addition, we present examples of routes visually and explain shortly why there appear local differences regarding performance of A* Search and Bidirectional A* Search.}, language = {en} } @masterthesis{Vornberger2018, type = {Bachelor Thesis}, author = {Vornberger, Leo}, title = {Approximation von Windkomponenten in der Luftfahrt durch lineare Interpolation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-71570}, pages = {49}, year = {2018}, abstract = {Das Wind-Interpolation-Problem (WIP) ist ein bisher selten diskutiertes Problem der Flugplanungsoptimierung, bei dem es darum geht, Wind-Komponenten auf einer Luftstraße zu approximieren. Anhand von Winddaten, die vektoriell an den Gitterpunkten eines den Globus umspannenden Gitters vorliegen, soll bestimmt werden, wie viel Wind entlang der Luftstraße und quer zu ihr weht. Thema dieser Arbeit ist ein Spezialfall des WIP, n{\"a}mlich das statische WIP auf einer Planfl{\"a}che (SWIPP). Dazu wird zuerst ein Algorithmus besprochen, der das SWIPP zwar l{\"o}st, aber einem Ansatz zugrunde liegt, der bei genauerem Hinsehen nicht sinnvoll erscheint: hier wird Wind zwischen vier Punkten interpoliert, wozu es keine triviale Methode gibt. {\"A}hnlich zu diesem Algorithmus, der heute als State-of-the-Art gilt, wird als Ergebnis dieser Arbeit ein neuer Algorithmus vorgestellt, der das SWIPP akkurater und schneller l{\"o}st. Hier wird deutlich seltener auf die Interpolation zwischen vier Punkten zur{\"u}ckgegriffen - stattdessen wird fast immer linear zwischen zwei Punkten interpoliert. Die Algorithmen zum L{\"o}sen des SWIPP werden auf ihre Genauigkeit, asymptotische Laufzeit und Geschwindigkeit untersucht und verglichen. Als Testareal dienen zum einen echte Wetterdaten sowie das Luftstraßennetz, das die Erde umspannt, und zum anderen ein eigens generiertes Windfeld und fiktive Luftstraßen. Es wird gezeigt, dass der hier vorgestellte Algorithmus die State-of-the-Art-Variante in allen genannten Aspekten {\"u}bertrifft.}, language = {de} } @masterthesis{Krug2018, type = {Bachelor Thesis}, author = {Krug, Matthias}, title = {Analysis of the Shortest Path Problem with Piecewise Constant Crossing Costs}, pages = {37}, year = {2018}, language = {en} } @misc{SagnolBlancoSauvage2017, author = {Sagnol, Guillaume and Blanco, Marco and Sauvage, Thibaut}, title = {The Cone of Flow Matrices: Approximation Hierarchies and Applications}, issn = {1438-0064}, doi = {10.1002/net.21820}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64399}, year = {2017}, abstract = {Let G be a directed acyclic graph with n arcs, a source s and a sink t. We introduce the cone K of flow matrices, which is a polyhedral cone generated by the matrices \$\vec{1}_P\vec{1}_P^T\in\RR^{n\times n}\$, where \$\vec{1}_P\in\RR^n\$ is the incidence vector of the (s,t)-path P. We show that several hard flow (or path) optimization problems, that cannot be solved by using the standard arc-representation of a flow, reduce to a linear optimization problem over \$\mathcal{K}\$. This cone is intractable: we prove that the membership problem associated to \$\mathcal{K}\$ is NP-complete. However, the affine hull of this cone admits a nice description, and we give an algorithm which computes in polynomial-time the decomposition of a matrix \$X\in \operatorname{span} \mathcal{K}\$ as a linear combination of some \$\vec{1}_P\vec{1}_P^T\$'s. Then, we provide two convergent approximation hierarchies, one of them based on a completely positive representation of~K. We illustrate this approach by computing bounds for the quadratic shortest path problem, as well as a maximum flow problem with pairwise arc-capacities.}, language = {en} } @article{SagnolBlancoSauvage2018, author = {Sagnol, Guillaume and Blanco, Marco and Sauvage, Thibaut}, title = {The Cone of Flow Matrices: Approximation Hierarchies and Applications}, volume = {72}, journal = {Networks}, number = {1}, doi = {10.1002/net.21820}, pages = {128 -- 150}, year = {2018}, abstract = {Let G be a directed acyclic graph with n arcs, a source s and a sink t. We introduce the cone K of flow matrices, which is a polyhedral cone generated by the matrices \$\vec{1}_P\vec{1}_P^T\in\RR^{n\times n}\$, where \$\vec{1}_P\in\RR^n\$ is the incidence vector of the (s,t)-path P. We show that several hard flow (or path) optimization problems, that cannot be solved by using the standard arc-representation of a flow, reduce to a linear optimization problem over \$\mathcal{K}\$. This cone is intractable: we prove that the membership problem associated to \$\mathcal{K}\$ is NP-complete. However, the affine hull of this cone admits a nice description, and we give an algorithm which computes in polynomial-time the decomposition of a matrix \$X\in \operatorname{span} \mathcal{K}\$ as a linear combination of some \$\vec{1}_P\vec{1}_P^T\$'s. Then, we provide two convergent approximation hierarchies, one of them based on a completely positive representation of~K. We illustrate this approach by computing bounds for the quadratic shortest path problem, as well as a maximum flow problem with pairwise arc-capacities.}, language = {en} } @misc{SagnolBlancoSauvage2018, author = {Sagnol, Guillaume and Blanco, Marco and Sauvage, Thibaut}, title = {Approximation Hierarchies for the cone of flow matrices}, issn = {1438-0064}, doi = {10.1016/j.endm.2018.02.002}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-68424}, year = {2018}, abstract = {Let \$G\$ be a directed acyclic graph with \$n\$ arcs, a source \$s\$ and a sink \$t\$. We introduce the cone \$K\$ of flow matrices, which is a polyhedral cone generated by the matrices \$1_P 1_P^T \in R^{n\times n}\$, where \$1_P\in R^n\$ is the incidence vector of the \$(s,t)\$-path \$P\$. Several combinatorial problems reduce to a linear optimization problem over \$K\$. This cone is intractable, but we provide two convergent approximation hierarchies, one of them based on a completely positive representation of \$K\$. We illustrate this approach by computing bounds for a maximum flow problem with pairwise arc-capacities.}, language = {en} } @inproceedings{SagnolBlancoSauvage2018, author = {Sagnol, Guillaume and Blanco, Marco and Sauvage, Thibaut}, title = {Approximation Hierarchies for the cone of flow matrices}, volume = {64}, booktitle = {INOC 2017 - 8th International Network Optimization Conference}, doi = {10.1016/j.endm.2018.02.002}, pages = {275 -- 284}, year = {2018}, abstract = {Let \$G\$ be a directed acyclic graph with \$n\$ arcs, a source \$s\$ and a sink \$t\$. We introduce the cone \$K\$ of flow matrices, which is a polyhedral cone generated by the matrices \$1_P 1_P^T \in R^{n\times n}\$, where \$1_P\in R^n\$ is the incidence vector of the \$(s,t)\$-path \$P\$. Several combinatorial problems reduce to a linear optimization problem over \$K\$. This cone is intractable, but we provide two convergent approximation hierarchies, one of them based on a completely positive representation of \$K\$. We illustrate this approach by computing bounds for a maximum flow problem with pairwise arc-capacities.}, language = {en} } @inproceedings{Schienle2018, author = {Schienle, Adam}, title = {Solving the Time-Dependent Shortest Path Problem Using Super-Optimal Wind}, booktitle = {Operations Research Proceedings 2017}, editor = {Kliewer, Natalia and Ehmke, Jan Fabian and Bornd{\"o}rfer, Ralf}, publisher = {Springer}, address = {Cham}, pages = {8}, year = {2018}, abstract = {Planning efficient routes fast becomes ever more important, especially in the context of aircraft trajectories. As time-dependent wind conditions factor into the shortest path query, we use an artificial wind vector called Super-Optimal Wind as a means of creating a suitable potential function for the A* algorithm, thus speeding up the query. We assess the quality of Super-Optimal Wind both theoretically and computationally, and use Super-Optimal Wind in a real-world instance.}, language = {en} } @inproceedings{BlancoBorndoerferHoangetal.2017, author = {Blanco, Marco and Bornd{\"o}rfer, Ralf and Hoang, Nam-Dung and Kaier, Anton and Maristany de las Casas, Pedro and Schlechte, Thomas and Schlobach, Swen}, title = {Cost Projection Methods for the Shortest Path Problem with Crossing Costs}, volume = {59}, booktitle = {17th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2017)}, editor = {D'Angelo, Gianlorenzo and Dollevoet, Twan}, year = {2017}, abstract = {Real world routing problems, e.g., in the airline industry or in public and rail transit, can feature complex non-linear cost functions. An important case are costs for crossing regions, such as countries or fare zones. We introduce the shortest path problem with crossing costs (SPPCC) to address such situations; it generalizes the classical shortest path problem and variants such as the resource constrained shortest path problem and the minimum label path problem. Motivated by an application in flight trajectory optimization with overflight costs, we focus on the case in which the crossing costs of a region depend only on the nodes used to enter or exit it. We propose an exact Two-Layer-Dijkstra Algorithm as well as a novel cost-projection linearization technique that approximates crossing costs by shadow costs on individual arcs, thus reducing the SPPCC to a standard shortest path problem. We evaluate all algorithms' performance on real-world flight trajectory optimization instances, obtaining very good {\`a} posteriori error bounds.}, language = {en} } @misc{BlancoBorndoerferHoangetal.2016, author = {Blanco, Marco and Bornd{\"o}rfer, Ralf and Hoang, Nam-Dung and Kaier, Anton and Schlechte, Thomas and Schlobach, Swen}, title = {The Shortest Path Problem with Crossing Costs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-61240}, year = {2016}, abstract = {We introduce the shortest path problem with crossing costs (SPPCC), a shortest path problem in a directed graph, in which the objective function is the sum of arc weights and crossing costs. The former are independently paid for each arc used by the path, the latter need to be paid every time the path intersects certain sets of arcs, which we call regions. The SPPCC generalizes not only the classical shortest path problem but also variants such as the resource constrained shortest path problem and the minimum label path problem. We use the SPPCC to model the flight trajectory optimization problem with overflight costs. In this paper, we provide a comprehensive analysis of the problem. In particular, we identify efficient exact and approximation algorithms for the cases that are most relevant in practice.}, language = {en} } @misc{BlancoBorndoerferHoangetal.2017, author = {Blanco, Marco and Bornd{\"o}rfer, Ralf and Hoang, Nam-Dung and Kaier, Anton and Maristany de las Casas, Pedro and Schlechte, Thomas and Schlobach, Swen}, title = {Cost Projection Methods for the Shortest Path Problem with Crossing Costs}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64817}, year = {2017}, abstract = {Real world routing problems, e.g., in the airline industry or in public and rail transit, can feature complex non-linear cost functions. An important case are costs for crossing regions, such as countries or fare zones. We introduce the shortest path problem with crossing costs (SPPCC) to address such situations; it generalizes the classical shortest path problem and variants such as the resource constrained shortest path problem and the minimum label path problem. Motivated by an application in flight trajectory optimization with overflight costs, we focus on the case in which the crossing costs of a region depend only on the nodes used to enter or exit it. We propose an exact Two-Layer-Dijkstra Algorithm as well as a novel cost-projection linearization technique that approximates crossing costs by shadow costs on individual arcs, thus reducing the SPPCC to a standard shortest path problem. We evaluate all algorithms' performance on real-world flight trajectory optimization instances, obtaining very good {\`a} posteriori error bounds.}, language = {en} } @inproceedings{BlancoBorndoerferHoangetal.2016, author = {Blanco, Marco and Bornd{\"o}rfer, Ralf and Hoang, Nam-Dung and Kaier, Anton and Schienle, Adam and Schlechte, Thomas and Schlobach, Swen}, title = {Solving Time Dependent Shortest Path Problems on Airway Networks Using Super-Optimal Wind}, volume = {54}, booktitle = {16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016)}, editor = {Marc, Goerigk}, doi = {10.4230/OASIcs.ATMOS.2016.12}, pages = {15}, year = {2016}, abstract = {We study the Flight Planning Problem for a single aircraft, which deals with finding a path of minimal travel time in an airway network. Flight time along arcs is affected by wind speed and direction, which are functions of time. We consider three variants of the problem, which can be modeled as, respectively, a classical shortest path problem in a metric space, a time-dependent shortest path problem with piecewise linear travel time functions, and a time-dependent shortest path problem with piecewise differentiable travel time functions. The shortest path problem and its time-dependent variant have been extensively studied, in particular, for road networks. Airway networks, however, have different characteristics: the average node degree is higher and shortest paths usually have only few arcs. We propose A* algorithms for each of the problem variants. In particular, for the third problem, we introduce an application-specific "super-optimal wind" potential function that overestimates optimal wind conditions on each arc, and establish a linear error bound. We compare the performance of our methods with the standard Dijkstra algorithm and the Contraction Hierarchies (CHs) algorithm. Our computational results on real world instances show that CHs do not perform as well as on road networks. On the other hand, A* guided by our potentials yields very good results. In particular, for the case of piecewise linear travel time functions, we achieve query times about 15 times shorter than CHs.}, language = {en} } @misc{Spiegel2015, type = {Master Thesis}, author = {Spiegel, Christoph}, title = {Approximating Primitive Integand Aircraft Performance}, pages = {84}, year = {2015}, abstract = {A commercial aircraft cannot freely use the available airspace but instead has to stick to a three-dimensional network of segments similar to a car in a road network. In this network it faces several variable and interdependent costs in the form of travel time, fuel consumption and overflight charges. These are also highly dependent on other factors such as weather conditions, aircraft performance, take-off time and weight as well as the changing availability of elements in the graph. This is further complicated by the distinction of separate flight phases that challenge the standard notion of a graph with predetermined nodes and arcs. Therefore when trying to find either a distance, fuel, time or cost minimal trajectory for a specific aircraft between an origin and a destination airport, one faces a very complex shortest path problem in the airway network graph that even for strong implifications is often NP-hard. This thesis will focus on exploring the costs that occur in this graph and that are associated with the aircraft performance. Here we will rely on actual performance and weather data supplied by Lufthansa Systems AG in Frankfurt and analyze whether they meet the requirements necessary for common algorithms such as the First-in, First-out property. Since it is vital for any shortest path algorithm to have a fast and accurate way of determining the costs in the graph, we will face two problems regarding the calculation of aircraft performance during cruise as well as the calculation of the so-called air distance. So far these problems have been approached by the industry with rudimentary approximative methods. We will reformulate them as initial value problems and try to find good approximations using both general Runge-Kutta methods as well as a novel approach which relies on finding piecewise linear approximations of some primitive integrals in pre-processing. Computations will show that these approaches deliver fast and accurate results.}, language = {en} } @misc{Schienle2016, type = {Master Thesis}, author = {Schienle, Adam}, title = {Shortest Paths on Airway Networks}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64047}, pages = {66}, year = {2016}, language = {en} } @misc{Brueckner2015, type = {Master Thesis}, author = {Br{\"u}ckner, Michael}, title = {On the Shortest Path Problem with Pair Constraints}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-57265}, year = {2015}, abstract = {This thesis investigates the shortest path problem with pair constraints or the pair constraint problem (PCP) for short. We consider two types of pair constraints, namely forbidden pairs and binding pairs consisting of two distinct vertices each. A path respects a forbidden pair if it uses at most one of the two vertices and it respects a binding pair (x,y) if it uses also y, if x is used. Within this thesis, we bring together and compare several formulations and variants of the pair constraint problem and their complexities. We also collect existing recursive algorithms and present their running times. Most of the presented contributions only consider forbidden pairs. We introduce a new recursive algorithm also handling binding pairs and prove its theoretical complexity of O(n^4). We implemented the algorithm and tested it on real-world instances provided by Lufthansa Systems AG. Therefore we needed to develop a heuristic translating the real-world data into an instance of the shortest path problem with pair constraints. This heuristic is presented as well as all computational results. In Chapter 4, we start investigating the associated polytope of an integer program formulation of the shortest path problem with pair constraints. For the case of one forbidden or binding pair, we find a complete linear description of the associated polytope. We prove that the number of facets grows exponentially in |V| even in these simple cases. However, separation is still possible in polynomial time. The complete linear description can be extended to the case of contiguously disjoint pairs.}, language = {en} } @article{BlancoBorndoerferBrueckneretal.2015, author = {Blanco, Marco and Bornd{\"o}rfer, Ralf and Br{\"u}ckner, Michael and Hoang, Nam-Dung and Schlechte, Thomas}, title = {On the Path Avoiding Forbidden Pairs Polytope}, volume = {50}, journal = {Electronic Notes in Discrete Mathematics}, doi = {10.1016/j.endm.2015.07.057}, pages = {343 -- 348}, year = {2015}, abstract = {Given a directed, acyclic graph, a source and a sink node, and a set of forbidden pairs of arcs, the path avoiding forbidden pairs (PAFP) problem is to find a path that connects the source and sink nodes and contains at most one arc from each forbidden pair. The general version of the problem is NP-hard, but it becomes polynomially solvable for certain topological configurations of the pairs. We present the first polyhedral study of the PAFP problem. We introduce a new family of valid inequalities for the PAFP polytope and show that they are sufficient to provide a complete linear description in the special case where the forbidden pairs satisfy a disjointness property. Furthermore, we show that the number of facets of the PAFP polytope is exponential in the size of the graph, even for the case of a single forbidden pair.}, language = {en} } @misc{MaristanydelasCasasSedenoNodaBorndoerfer2021, author = {Maristany de las Casas, Pedro and Sedeno-Noda, Antonio and Bornd{\"o}rfer, Ralf}, title = {An Improved Multiobjective Shortest Path Algorithm}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-79712}, year = {2021}, abstract = {We present a new label-setting algorithm for the Multiobjective Shortest Path (MOSP) problem that computes the minimal complete set of efficient paths for a given instance. The size of the priority queue used in the algorithm is bounded by the number of nodes in the input graph and extracted labels are guaranteed to be efficient. These properties allow us to give a tight output-sensitive running time bound for the new algorithm that can almost be expressed in terms of the running time of Dijkstra's algorithm for the Shortest Path problem. Hence, we suggest to call the algorithm \emph{Multiobjective Dijkstra Algorithm} (MDA). The simplified label management in the MDA allows us to parallelize some subroutines. In our computational experiments, we compare the MDA and the classical label-setting MOSP algorithm by Martins', which we improved using new data structures and pruning techniques. On average, the MDA is \$\times2\$ to \$\times9\$ times faster on all used graph types. On some instances the speedup reaches an order of magnitude.}, language = {en} } @article{MaristanydelasCasasSedenoNodaBorndoerfer2021, author = {Maristany de las Casas, Pedro and Sedeno-Noda, Antonio and Bornd{\"o}rfer, Ralf}, title = {An Improved Multiobjective Shortest Path Algorithm}, volume = {135}, journal = {Computers \& Operations Research}, doi = {10.1016/j.cor.2021.105424}, year = {2021}, abstract = {We present a new label-setting algorithm for the Multiobjective Shortest Path (MOSP) problem that computes a minimum complete set of efficient paths for a given instance. The size of the priority queue used in the algorithm is bounded by the number of nodes in the input graph and extracted labels are guaranteed to be efficient. These properties allow us to give a tight output-sensitive running time bound for the new algorithm that can almost be expressed in terms of the running time of Dijkstra's algorithm for the Shortest Path problem. Hence, we suggest to call the algorithm Multiobjective Dijkstra Algorithm (MDA). The simplified label management in the MDA allows us to parallelize some subroutines. In our computational experiments, we compare the MDA and the classical label-setting MOSP algorithm by Martins, which we improved using new data structures and pruning techniques. On average, the MDA is 2 to 9 times faster on all used graph types. On some instances the speedup reaches an order of magnitude.}, language = {en} } @article{MaristanydelasCasasBorndoerferKrausetal.2021, author = {Maristany de las Casas, Pedro and Bornd{\"o}rfer, Ralf and Kraus, Luitgard and Sede{\~n}o-Noda, Antonio}, title = {An FPTAS for Dynamic Multiobjective Shortest Path Problems}, volume = {14}, journal = {Algorithms}, number = {2}, doi = {https://doi.org/10.3390/a14020043}, pages = {1 -- 22}, year = {2021}, abstract = {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 give an exact algorithm for the FIFO case and derive from it an FPTAS for both, the static Multiobjective Shortest Path (MOSP) problems and, under mild assumptions, for the dynamic problem variant. The resulting FPTAS is computationally efficient and beats the known complexity bounds of other FPTAS for MOSP problems.}, language = {en} }