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Strategies for Iteratively Refining Layered Graph Models

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Book cover Hybrid Metaheuristics (HM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11299))

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Abstract

We consider a framework for obtaining a sequence of converging primal and dual bounds based on mixed integer linear programming formulations on layered graphs. The proposed iterative algorithm avoids the typically rather large size of the full layered graph by approximating it incrementally. We focus in particular on this refinement step that extends the graph in each iteration. Novel path-based approaches are compared to existing variants from the literature. Experiments on two benchmark problems—the traveling salesman problem with time windows and the rooted distance-constrained minimum spanning tree problem—show the effectiveness of our new strategies. Moreover, we investigate the impact of a strong heuristic component within the algorithm, both for improving convergence speed and for improving the potential of an employed reduced cost fixing step.

Supported by the Vienna Science and Technology Fund through project ICT15-014.

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Notes

  1. 1.

    When referring to the full LG \(G_{\mathrm {L}}\) in the following, we assume this step to be completed.

  2. 2.

    In case of cycles due to zero travel times, these inequalities become mandatory.

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Authors and Affiliations

  1. Institute of Logic and Computation, TU Wien, Vienna, Austria

    Martin Riedler & Günther R. Raidl

  2. Department of Statistics and Operations Research, University of Vienna, Vienna, Austria

    Mario Ruthmair

Authors
  1. Martin Riedler
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  2. Mario Ruthmair
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  3. Günther R. Raidl
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Corresponding author

Correspondence to Martin Riedler .

Editor information

Editors and Affiliations

  1. Universitat Politècnica de Catalunya, Barcelona, Spain

    Maria J. Blesa Aguilera

  2. Spanish National Research Council, Bellaterra, Spain

    Christian Blum

  3. Universidade Federal de Ouro Preto, Ouro Preto, Brazil

    Haroldo Gambini Santos

  4. University of Concepción, Concepción, Chile

    Pedro Pinacho-Davidson

  5. Universidad de Concepción, Concepción, Chile

    Julio Godoy del Campo

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Riedler, M., Ruthmair, M., Raidl, G.R. (2019). Strategies for Iteratively Refining Layered Graph Models. In: Blesa Aguilera, M., Blum, C., Gambini Santos, H., Pinacho-Davidson, P., Godoy del Campo, J. (eds) Hybrid Metaheuristics. HM 2019. Lecture Notes in Computer Science(), vol 11299. Springer, Cham. https://doi.org/10.1007/978-3-030-05983-5_4

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  • DOI: https://doi.org/10.1007/978-3-030-05983-5_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-05982-8

  • Online ISBN: 978-3-030-05983-5

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