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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.

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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) and equips it with A*‐like techniques. For any explored subpath, a label setting MOSP algorithm decides whether the subpath can be discarded or must be stored as part of the output. A major design choice is how to store subpaths from the moment they are first explored until the mentioned final decision can be made. The T‐MDA combines the polynomially bounded size of the priority queue used in the MDA and a lazy management of paths that are not in the queue. The running time bounds from the MDA remain valid. In practice, the T‐MDA outperforms known algorithms from the literature and the increased memory consumption is negligible. In this paper, we benchmark the T‐MDA against an improved version of the state of the art One‐to‐One MOSP algorithm from the literature on a standard testbed.

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