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Lower bound sets for biobjective shortest path problems

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Abstract

This article considers the problem of calculating the set of all Pareto-optimal solutions in one-to-one biobjective shortest path problems with positive cost vectors. The efficiency of multiobjective best-first search algorithms can be improved with the use of consistent informed lower bounds. More precisely, the use of the ideal point as a lower bound has recently been shown to effectively increase search performance. In theory, the use of lower bounds that better approximate the Pareto frontier using sets of vectors (bound sets), could further improve performance. This article describes a lower bound set calculation method for biobjective shortest path problems. Improvements in search efficiency with lower bound sets of increasing precision are analyzed and discussed.

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Notes

  1. These are available at: http://www.dis.uniroma1.it/challenge9/download.shtml and http://alef.iaia.lcc.uma.es/projects/alef-public/wiki/Benchmarks.

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Acknowledgments

Funded by Plan Propio de Investigación, Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech Programa de Fortalecimiento de Capacidades I+D+i en universidades 2014–2015, Fondos FEDER. We would like to thank the anonymous reviewer for the very useful comments and suggestions which help us improve the quality of our paper.

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  1. Dpto. Lenguajes y Ciencias de la Computación, Universidad de Málaga (Campus de Excelencia Internacional Andalucia Tech), Boulevar Louis Pasteur, 35. Campus de Teatinos, 29071, Málaga, Spain

    Enrique Machuca & Lawrence Mandow

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  1. Enrique Machuca
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  2. Lawrence Mandow
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Correspondence to Enrique Machuca.

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Machuca, E., Mandow, L. Lower bound sets for biobjective shortest path problems. J Glob Optim 64, 63–77 (2016). https://doi.org/10.1007/s10898-015-0324-1

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