A multiphase dynamic programming algorithm for the shortest path problem with resource constraints
The shortest path problem with resource constraints (SPPRC) finds a least cost path between two nodes in a network while respecting constraints on resource consumption. The problem is mainly used as a subproblem inside column generation for crew scheduling and vehicle routing problems. The standard...
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| Vydáno v: | European journal of operational research Ročník 315; číslo 2; s. 470 - 483 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier B.V
01.06.2024
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| Témata: | |
| ISSN: | 0377-2217, 1872-6860 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | The shortest path problem with resource constraints (SPPRC) finds a least cost path between two nodes in a network while respecting constraints on resource consumption. The problem is mainly used as a subproblem inside column generation for crew scheduling and vehicle routing problems. The standard approach for the subproblems is based on dynamic programming (DP). This class of methods is generally effective in practice when there are only a few resources, but it seems to be time-consuming for huge instances with many resources. To handle this issue, we propose a new exact primal algorithm called the multiphase dynamic programming algorithm (MPDPA) to solve the SPPRC in acyclic networks. The proposed approach splits the state-space into small disjoint subspaces. These subspaces are sequentially explored in several iterations, where each iteration builds on the previous ones, to reduce the dimension of the subspaces to explore and to quickly generate better paths. Computational experiments on vehicle and crew scheduling instances show the excellent performance of our approach compared to the standard DP method. On the one hand, MPDPA returns optimal solutions while achieving time reduction factors between 1.44 and 3.59 on average compared to DP. On the other hand, MPDPA is able to generate feasible paths with up to 90% of the optimal cost in less than 10% of the time required by standard DP. This feature is useful in column generation and may greatly reduce the computational effort, because we can stop the MPDPA solution process once columns with sufficiently negative reduced costs are obtained.
•New primal exact algorithm for the shortest path problem with resource constraints.•New generalized formulation to split the search space into disjoint subspaces.•Sets of feasible paths of nonincreasing costs leading to optimality are generated.•Learning techniques from the previous iterations are embedded.•Extensive experiments on simultaneous vehicle and crew scheduling problem instances. |
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| ISSN: | 0377-2217 1872-6860 |
| DOI: | 10.1016/j.ejor.2023.11.047 |