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International Conference on Learning and Intelligent Optimization

LION 12 2018: Learning and Intelligent Optimization pp 184–198Cite as

Solving Scalarized Subproblems within Evolutionary Algorithms for Multi-criteria Shortest Path Problems

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11353))

Abstract

The \(\mathcal {NP}\)-hard multi-criteria shortest path problem (mcSPP) is of utmost practical relevance, e. g., in navigation system design and logistics. We address the problem of approximating the Pareto-front of the mcSPP with sum objectives. We do so by proposing a new mutation operator for multi-objective evolutionary algorithms that solves single-objective versions of the shortest path problem on subgraphs. A rigorous empirical benchmark on a diverse set of problem instances shows the effectiveness of the approach in comparison to a well-known mutation operator in terms of convergence speed and approximation quality. In addition, we glance at the neighbourhood structure and similarity of obtained Pareto-optimal solutions and derive promising directions for future work.

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Notes

  1. 1.

    Other objective types are possible, e. g., bottleneck objectives, but not considered in this work.

  2. 2.

    https://github.com/jakobbossek/grapherator.

  3. 3.

    Note, that we do not consider the topologies of generated instances due to space limitations. A detailed analysis of the topology’s influence cannot be thought without considering the distribution of weights and the locations of start and destination notes. Therefore, this aspect is left for rigorous analysis in future work.

  4. 4.

    https://www.ercis.org/.

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Acknowledgments

The authors acknowledge support from the European Research Center for Information Systems (ERCIS).

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Authors and Affiliations

  1. Information Systems and Statistics, University of Münster, Münster, Germany

    Jakob Bossek & Christian Grimme

Authors
  1. Jakob Bossek
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  2. Christian Grimme
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Correspondence to Jakob Bossek .

Editor information

Editors and Affiliations

  1. University of Trento, Trento, Italy

    Roberto Battiti

  2. University of Trento, Trento, Italy

    Mauro Brunato

  3. Wilfrid Laurier University, Waterloo, ON, Canada

    Ilias Kotsireas

  4. University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

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Bossek, J., Grimme, C. (2019). Solving Scalarized Subproblems within Evolutionary Algorithms for Multi-criteria Shortest Path Problems. In: Battiti, R., Brunato, M., Kotsireas, I., Pardalos, P. (eds) Learning and Intelligent Optimization. LION 12 2018. Lecture Notes in Computer Science(), vol 11353. Springer, Cham. https://doi.org/10.1007/978-3-030-05348-2_17

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  • DOI: https://doi.org/10.1007/978-3-030-05348-2_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-05347-5

  • Online ISBN: 978-3-030-05348-2

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