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Due to technical work, the interlibrary loan service wont be available from March 28th until presumably April 3rd.
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• 1
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Publication Date: 2022-02-01
Description: 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 Dijkstra Algorithm (MDA) and equips it with A*-like techniques. The resulting speedup is comparable to the speedup that the original A* algorithm achieves for Dijkstra's algorithm. Unlike other methods from the literature, which rely on special properties of the biobjective case, the T-MDA works for any dimension. To the best of our knowledge, it gives rise to the first efficient implementation that can deal with large scale instances with more than two objectives. A version tuned for the biobjective case, the T-BDA, outperforms state-of-the-art methods on almost every instance of a standard benchmark testbed that is not solvable in fractions of a second.
Language: English
Type: article , doc-type:article
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• 2
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Publication Date: 2022-03-14
Description: 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: English
Type: article , doc-type:article
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• 3
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Publication Date: 2021-04-12
Description: We propose in this paper the Dynamic Multiobjective Shortest Problem. It features multidimensional states that can depend on several variables and not only on time; this setting is motivated by flight planning and electric vehicle routing applications. We give an exact algorithm for the FIFO case and derive from it an FPTAS, which is computationally efficient. It also features the best known complexity in the static case.
Language: English
Type: reportzib , doc-type:preprint
Format: application/pdf
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• 4
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Publication Date: 2022-01-19
Description: 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: English
Type: reportzib , doc-type:preprint
Format: application/pdf
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• 5
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Publication Date: 2021-09-29
Description: 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: English
Type: article , doc-type:article
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