Abstract
The Shortest Simple Path Problem with Must-Pass Nodes is the well-known combinatorial optimization problem having numerous applications in operations research. In this paper, we show, that this problem remains intractable even for any fixed number of must-pass nodes. In addition, we propose a novel problem-specific branch-and-bound algorithm for this problem and prove its high performance by a numerical evaluation. The experiments are carried out on the real-life benchmark dataset ‘Rome99’ taken from the 9th DIMACS Implementation Challenge. The results show that the proposed algorithm outperforms the well-known solver Gurobi equipped with the best known MILP models both in obtained accuracy and execution time.
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Notes
- 1.
Or show that \(G'\) has no Hamiltonian paths. Since |F| is fixed, this task can be solved in a constant time.
- 2.
Highlighted by red crosses.
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Acknowledgements
This research was performed as a part of research carried out in the Ural Mathematical Center with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Agreement number 075-02-2021-1383) and partially funded by Contract no. YBN2019125124. All computations were performed on supercomputer ‘Uran’ at Krasovsky Institute of Mathematcs and Mechanics.
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Kudriavtsev, A. et al. (2021). The Shortest Simple Path Problem with a Fixed Number of Must-Pass Nodes: A Problem-Specific Branch-and-Bound Algorithm. In: Simos, D.E., Pardalos, P.M., Kotsireas, I.S. (eds) Learning and Intelligent Optimization. LION 2021. Lecture Notes in Computer Science(), vol 12931. Springer, Cham. https://doi.org/10.1007/978-3-030-92121-7_17
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