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Approximate solution of the shortest path problem with resource constraints and applications to vehicle routing problems.

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Titel: Approximate solution of the shortest path problem with resource constraints and applications to vehicle routing problems.
Autoren: Lamamri, Abdelkader, Hachama, Mohammed
Quelle: Electronic Research Archive; 2023, Vol. 31 Issue 2, p1-18, 18p
Schlagwörter: VEHICLE routing problem, DYNAMIC programming, ARTIFICIAL intelligence, DIGITAL technology, LAGRANGE equations
Abstract: Vehicle routing problem (VRP) is a fundamental combinatorial optimization and integer programming problem with several important applications. The VRP is usually solved by using branch-and-bound techniques requiring solving a shortest path problem with resource constraints (SPPRC) and the determination of a lower bound, which can be computed by using column generation. The SPPRC entails finding the minimum cost elementary path in a valuated graph that is subject to constraints on resource consumption. The proposed exact solutions to this hard NP-hard problem require an excessive computation time which increases with the number of resources. In this paper, we propose a new approximate resolution of the SPPRC for acyclic and cyclic graphs. Our method is based on a Lagrangian relaxation of a subset of the constraints and using dominance only on a subset of the resources. This reduces the search space and allows users to efficiently compute solutions used to improve the column generation procedure. Extensive evaluation and comparison to the classical exact method show that the proposed algorithm achieves a good compromise between efficiency and quality of the SPPRC and the VRP solutions. Thus, our method can be used for practical large-scale VRP applications. [ABSTRACT FROM AUTHOR]
Copyright of Electronic Research Archive is the property of American Institute of Mathematical Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Approximate solution of the shortest path problem with resource constraints and applications to vehicle routing problems.
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  Data: <searchLink fieldCode="AR" term="%22Lamamri%2C+Abdelkader%22">Lamamri, Abdelkader</searchLink><br /><searchLink fieldCode="AR" term="%22Hachama%2C+Mohammed%22">Hachama, Mohammed</searchLink>
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  Data: Electronic Research Archive; 2023, Vol. 31 Issue 2, p1-18, 18p
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  Data: <searchLink fieldCode="DE" term="%22VEHICLE+routing+problem%22">VEHICLE routing problem</searchLink><br /><searchLink fieldCode="DE" term="%22DYNAMIC+programming%22">DYNAMIC programming</searchLink><br /><searchLink fieldCode="DE" term="%22ARTIFICIAL+intelligence%22">ARTIFICIAL intelligence</searchLink><br /><searchLink fieldCode="DE" term="%22DIGITAL+technology%22">DIGITAL technology</searchLink><br /><searchLink fieldCode="DE" term="%22LAGRANGE+equations%22">LAGRANGE equations</searchLink>
– Name: Abstract
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  Group: Ab
  Data: Vehicle routing problem (VRP) is a fundamental combinatorial optimization and integer programming problem with several important applications. The VRP is usually solved by using branch-and-bound techniques requiring solving a shortest path problem with resource constraints (SPPRC) and the determination of a lower bound, which can be computed by using column generation. The SPPRC entails finding the minimum cost elementary path in a valuated graph that is subject to constraints on resource consumption. The proposed exact solutions to this hard NP-hard problem require an excessive computation time which increases with the number of resources. In this paper, we propose a new approximate resolution of the SPPRC for acyclic and cyclic graphs. Our method is based on a Lagrangian relaxation of a subset of the constraints and using dominance only on a subset of the resources. This reduces the search space and allows users to efficiently compute solutions used to improve the column generation procedure. Extensive evaluation and comparison to the classical exact method show that the proposed algorithm achieves a good compromise between efficiency and quality of the SPPRC and the VRP solutions. Thus, our method can be used for practical large-scale VRP applications. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of Electronic Research Archive is the property of American Institute of Mathematical Sciences and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.3934/era.2023030
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 18
        StartPage: 1
    Subjects:
      – SubjectFull: VEHICLE routing problem
        Type: general
      – SubjectFull: DYNAMIC programming
        Type: general
      – SubjectFull: ARTIFICIAL intelligence
        Type: general
      – SubjectFull: DIGITAL technology
        Type: general
      – SubjectFull: LAGRANGE equations
        Type: general
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      – TitleFull: Approximate solution of the shortest path problem with resource constraints and applications to vehicle routing problems.
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            NameFull: Lamamri, Abdelkader
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            NameFull: Hachama, Mohammed
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              M: 02
              Text: 2023
              Type: published
              Y: 2023
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              Value: 31
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