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Integer programming formulations for the elementary shortest path problem

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  • Taccari, Leonardo

Abstract

Given a directed graph G=(V,A) with arbitrary arc costs, the Elementary Shortest Path Problem (ESPP) consists of finding a minimum-cost path between two nodes s and t such that each node of G is visited at most once. If negative costs are allowed, the problem is NP-hard. In this paper, several integer programming formulations for the ESPP are compared. We present analytical results based on a polyhedral study of the formulations, and computational experiments where we compare their linear programming relaxation bounds and their behavior within a branch-and-cut framework. The computational results show that a formulation with dynamically generated cutset inequalities is the most effective.

Suggested Citation

  • Taccari, Leonardo, 2016. "Integer programming formulations for the elementary shortest path problem," European Journal of Operational Research, Elsevier, vol. 252(1), pages 122-130.
    • Handle: RePEc:eee:ejores:v:252:y:2016:i:1:p:122-130
    DOI: 10.1016/j.ejor.2016.01.003
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    Cited by:

    1. Sergey S. Ketkov, 2023. "On the Multistage Shortest Path Problem Under Distributional Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 277-308, April.
    2. Tereza Sedlářová Nehézová & Michal Škoda & Robert Hlavatý & Helena Brožová, 2022. "Fuzzy and robust approach for decision-making in disaster situations," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(2), pages 617-645, June.
    3. Hiroyuki Goto & Alan T. Murray, 2019. "Small-m method for detecting all longest paths," OPSEARCH, Springer;Operational Research Society of India, vol. 56(3), pages 824-839, September.
    4. Lee, Jisun & Joung, Seulgi & Lee, Kyungsik, 2022. "A fully polynomial time approximation scheme for the probability maximizing shortest path problem," European Journal of Operational Research, Elsevier, vol. 300(1), pages 35-45.
    5. Lera-Romero, Gonzalo & Miranda-Bront, Juan José, 2021. "A branch and cut algorithm for the time-dependent profitable tour problem with resource constraints," European Journal of Operational Research, Elsevier, vol. 289(3), pages 879-896.
    6. Longsheng Sun & Mark H. Karwan & Changhyun Kwon, 2018. "Generalized Bounded Rationality and Robust Multicommodity Network Design," Operations Research, INFORMS, vol. 66(1), pages 42-57, 1-2.
    7. Rafael Castro Andrade & Rommel Dias Saraiva, 2020. "MTZ-primal-dual model, cutting-plane, and combinatorial branch-and-bound for shortest paths avoiding negative cycles," Annals of Operations Research, Springer, vol. 286(1), pages 147-172, March.

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