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Lower bound sets for biobjective shortest path problems

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  • Enrique Machuca
  • Lawrence Mandow

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. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • Enrique Machuca & Lawrence Mandow, 2016. "Lower bound sets for biobjective shortest path problems," Journal of Global Optimization, Springer, vol. 64(1), pages 63-77, January.
    • Handle: RePEc:spr:jglopt:v:64:y:2016:i:1:p:63-77
    DOI: 10.1007/s10898-015-0324-1
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    References listed on IDEAS

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    1. Francis Sourd & Olivier Spanjaard, 2008. "A Multiobjective Branch-and-Bound Framework: Application to the Biobjective Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 472-484, August.
    2. Matthias Müller-Hannemann & Karsten Weihe, 2006. "On the cardinality of the Pareto set in bicriteria shortest path problems," Annals of Operations Research, Springer, vol. 147(1), pages 269-286, October.
    3. Y. P. Aneja & K. P. K. Nair, 1979. "Bicriteria Transportation Problem," Management Science, INFORMS, vol. 25(1), pages 73-78, January.
    4. Oleg Burdakov & Patrick Doherty & Kaj Holmberg & Per-Magnus Olsson, 2010. "Optimal placement of UV-based communications relay nodes," Journal of Global Optimization, Springer, vol. 48(4), pages 511-531, December.
    5. Tung Tung, Chi & Lin Chew, Kim, 1992. "A multicriteria Pareto-optimal path algorithm," European Journal of Operational Research, Elsevier, vol. 62(2), pages 203-209, October.
    6. Iori, Manuel & Martello, Silvano & Pretolani, Daniele, 2010. "An aggregate label setting policy for the multi-objective shortest path problem," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1489-1496, December.
    7. Machuca, E. & Mandow, L. & Pérez de la Cruz, J.L. & Ruiz-Sepulveda, A., 2012. "A comparison of heuristic best-first algorithms for bicriterion shortest path problems," European Journal of Operational Research, Elsevier, vol. 217(1), pages 44-53.
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