IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v111y2001i3d10.1023_a1012602011914.html
   My bibliography  Save this article

Label Correcting Methods to Solve Multicriteria Shortest Path Problems

Author

Listed:
  • F. Guerriero

    (Università della Calabria)

  • R. Musmanno

    (Università di Lecce, Lecce)

Abstract

In this paper, we deal with the solution of the multicriteria shortest path problem. In particular, we present a class of labeling methods to generate the entire set of Pareto-optimal path-length vectors from an origin node s to all other nodes in a multicriteria network. The proposed methods are supported theoretically by the principle of optimality and they are defined on the basis of various innovative node and label selection strategies. Computational results comparing the proposed methods to state-of-the-art approaches to solve the problem considered are also reported. They indicate that our methods are competitive in general; in several cases, they outperform all the other codes.

Suggested Citation

  • F. Guerriero & R. Musmanno, 2001. "Label Correcting Methods to Solve Multicriteria Shortest Path Problems," Journal of Optimization Theory and Applications, Springer, vol. 111(3), pages 589-613, December.
    • Handle: RePEc:spr:joptap:v:111:y:2001:i:3:d:10.1023_a:1012602011914
    DOI: 10.1023/A:1012602011914
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1012602011914
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1012602011914?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Carraway, Robert L. & Morin, Thomas L. & Moskowitz, Herbert, 1990. "Generalized dynamic programming for multicriteria optimization," European Journal of Operational Research, Elsevier, vol. 44(1), pages 95-104, January.
    2. Current, John & Marsh, Michael, 1993. "Multiobjective transportation network design and routing problems: Taxonomy and annotation," European Journal of Operational Research, Elsevier, vol. 65(1), pages 4-19, February.
    3. Mote, John & Murthy, Ishwar & Olson, David L., 1991. "A parametric approach to solving bicriterion shortest path problems," European Journal of Operational Research, Elsevier, vol. 53(1), pages 81-92, July.
    4. 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.
    5. Arthur Warburton, 1987. "Approximation of Pareto Optima in Multiple-Objective, Shortest-Path Problems," Operations Research, INFORMS, vol. 35(1), pages 70-79, February.
    6. Rajan Batta & Samuel S. Chiu, 1988. "Optimal Obnoxious Paths on a Network: Transportation of Hazardous Materials," Operations Research, INFORMS, vol. 36(1), pages 84-92, February.
    7. John R. Current & Charles S. Revelle & Jared L. Cohon, 1987. "The Median Shortest Path Problem: A Multiobjective Approach to Analyze Cost vs. Accessibility in the Design of Transportation Networks," Transportation Science, INFORMS, vol. 21(3), pages 188-197, August.
    8. D. Klingman & A. Napier & J. Stutz, 1974. "NETGEN: A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems," Management Science, INFORMS, vol. 20(5), pages 814-821, January.
    9. Namorado Climaco, Joao Carlos & Queiros Vieira Martins, Ernesto, 1982. "A bicriterion shortest path algorithm," European Journal of Operational Research, Elsevier, vol. 11(4), pages 399-404, December.
    10. Current, John & Min, HoKey, 1986. "Multiobjective design of transportation networks: Taxonomy and annotation," European Journal of Operational Research, Elsevier, vol. 26(2), pages 187-201, August.
    11. Brumbaugh-Smith, J. & Shier, D., 1989. "An empirical investigation of some bicriterion shortest path algorithms," European Journal of Operational Research, Elsevier, vol. 43(2), pages 216-224, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Andrea Raith & Judith Wang & Matthias Ehrgott & Stuart Mitchell, 2014. "Solving multi-objective traffic assignment," Annals of Operations Research, Springer, vol. 222(1), pages 483-516, November.
    2. Xiao Fu & William Lam, 2014. "A network equilibrium approach for modelling activity-travel pattern scheduling problems in multi-modal transit networks with uncertainty," Transportation, Springer, vol. 41(1), pages 37-55, January.
    3. 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.
    4. Lee, Chungmok, 2022. "A robust optimization approach with probe-able uncertainty," European Journal of Operational Research, Elsevier, vol. 296(1), pages 218-239.
    5. Sedeño-noda, Antonio & Colebrook, Marcos, 2019. "A biobjective Dijkstra algorithm," European Journal of Operational Research, Elsevier, vol. 276(1), pages 106-118.
    6. Xiao Fu & William H. K. Lam, 2018. "Modelling joint activity-travel pattern scheduling problem in multi-modal transit networks," Transportation, Springer, vol. 45(1), pages 23-49, January.
    7. Xie, Chi & Travis Waller, S., 2012. "Parametric search and problem decomposition for approximating Pareto-optimal paths," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1043-1067.
    8. Duque, Daniel & Lozano, Leonardo & Medaglia, Andrés L., 2015. "An exact method for the biobjective shortest path problem for large-scale road networks," European Journal of Operational Research, Elsevier, vol. 242(3), pages 788-797.
    9. Jonas Ide & Elisabeth Köbis, 2014. "Concepts of efficiency for uncertain multi-objective optimization problems based on set order relations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(1), pages 99-127, August.
    10. Shi, Ning & Zhou, Shaorui & Wang, Fan & Tao, Yi & Liu, Liming, 2017. "The multi-criteria constrained shortest path problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 101(C), pages 13-29.
    11. Garaix, Thierry & Artigues, Christian & Feillet, Dominique & Josselin, Didier, 2010. "Vehicle routing problems with alternative paths: An application to on-demand transportation," European Journal of Operational Research, Elsevier, vol. 204(1), pages 62-75, July.
    12. Kuhn, K. & Raith, A. & Schmidt, M. & Schöbel, A., 2016. "Bi-objective robust optimisation," European Journal of Operational Research, Elsevier, vol. 252(2), pages 418-431.
    13. de Lima Pinto, Leizer & Bornstein, Cláudio Thomás & Maculan, Nelson, 2009. "The tricriterion shortest path problem with at least two bottleneck objective functions," European Journal of Operational Research, Elsevier, vol. 198(2), pages 387-391, October.
    14. Yannick Kergosien & Antoine Giret & Emmanuel Néron & Gaël Sauvanet, 2022. "An Efficient Label-Correcting Algorithm for the Multiobjective Shortest Path Problem," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 76-92, January.
    15. Banu Lokman & Murat Köksalan, 2013. "Finding all nondominated points of multi-objective integer programs," Journal of Global Optimization, Springer, vol. 57(2), pages 347-365, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Granat, Janusz & Guerriero, Francesca, 2003. "The interactive analysis of the multicriteria shortest path problem by the reference point method," European Journal of Operational Research, Elsevier, vol. 151(1), pages 103-118, November.
    2. Soroush, H.M., 2008. "Optimal paths in bi-attribute networks with fractional cost functions," European Journal of Operational Research, Elsevier, vol. 190(3), pages 633-658, November.
    3. Xie, Chi & Travis Waller, S., 2012. "Parametric search and problem decomposition for approximating Pareto-optimal paths," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1043-1067.
    4. de Lima Pinto, Leizer & Bornstein, Cláudio Thomás & Maculan, Nelson, 2009. "The tricriterion shortest path problem with at least two bottleneck objective functions," European Journal of Operational Research, Elsevier, vol. 198(2), pages 387-391, October.
    5. Luigi Di Puglia Pugliese & Francesca Guerriero, 2013. "A Reference Point Approach for the Resource Constrained Shortest Path Problems," Transportation Science, INFORMS, vol. 47(2), pages 247-265, May.
    6. Opasanon, Sathaporn & Miller-Hooks, Elise, 2006. "Multicriteria adaptive paths in stochastic, time-varying networks," European Journal of Operational Research, Elsevier, vol. 173(1), pages 72-91, August.
    7. Yannick Kergosien & Antoine Giret & Emmanuel Néron & Gaël Sauvanet, 2022. "An Efficient Label-Correcting Algorithm for the Multiobjective Shortest Path Problem," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 76-92, January.
    8. Minghe Sun, 2005. "Warm-Start Routines for Solving Augmented Weighted Tchebycheff Network Programs in Multiple-Objective Network Programming," INFORMS Journal on Computing, INFORMS, vol. 17(4), pages 422-437, November.
    9. Suvrajeet Sen & Rekha Pillai & Shirish Joshi & Ajay K. Rathi, 2001. "A Mean-Variance Model for Route Guidance in Advanced Traveler Information Systems," Transportation Science, INFORMS, vol. 35(1), pages 37-49, February.
    10. Perny, Patrice & Spanjaard, Olivier, 2005. "A preference-based approach to spanning trees and shortest paths problems***," European Journal of Operational Research, Elsevier, vol. 162(3), pages 584-601, May.
    11. Mingue SUn, 2010. "A Branch-and-Bound Algorithm for Representative Integer Efficient Solutions in Multiple Objective Network Programming Problems," Working Papers 0007, College of Business, University of Texas at San Antonio.
    12. 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.
    13. Moradi, Siamak & Raith, Andrea & Ehrgott, Matthias, 2015. "A bi-objective column generation algorithm for the multi-commodity minimum cost flow problem," European Journal of Operational Research, Elsevier, vol. 244(2), pages 369-378.
    14. Hamacher, Horst W. & Pedersen, Christian Roed & Ruzika, Stefan, 2007. "Multiple objective minimum cost flow problems: A review," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1404-1422, February.
    15. Curtin, Kevin M. & Biba, Steve, 2011. "The Transit Route Arc-Node Service Maximization problem," European Journal of Operational Research, Elsevier, vol. 208(1), pages 46-56, January.
    16. Dung-Ying Lin & Chi Xie, 2011. "The Pareto-optimal Solution Set of the Equilibrium Network Design Problem with Multiple Commensurate Objectives," Networks and Spatial Economics, Springer, vol. 11(4), pages 727-751, December.
    17. B. Boffey & Francisco García & Gilbert Laporte & Juan Mesa & Blas Pelegrín, 1995. "Multiobjective routing problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(2), pages 167-220, December.
    18. Minghe Sun, 2003. "Procedures for Finding Nondominated Solutions for Multiple Objective Network Programming Problems," Transportation Science, INFORMS, vol. 37(2), pages 139-152, May.
    19. Gabrel, Virginie & Vanderpooten, Daniel, 2002. "Enumeration and interactive selection of efficient paths in a multiple criteria graph for scheduling an earth observing satellite," European Journal of Operational Research, Elsevier, vol. 139(3), pages 533-542, June.
    20. Altannar Chinchuluun & Panos Pardalos, 2007. "A survey of recent developments in multiobjective optimization," Annals of Operations Research, Springer, vol. 154(1), pages 29-50, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:111:y:2001:i:3:d:10.1023_a:1012602011914. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.