We address a bicriterion path problem where each arc is assigned with a cost value and a label (such as a color). The first criterion intends to minimize the total cost of the path (the summation of its arc costs), while the second intends to get the solution with a minimal number of different labels. Since these criteria, in general, are conflicting criteria we develop an algorithm to generate the set of non-dominated paths. Computational experiments are presented and results are discussed.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows: theory, algorithms and applications. Prentice Hall, Englewood Cliffs
Bornstein C, Maculan N, Pascoal M, Pinto L (2012) Multiobjective combinatorial optimization problems with a cost and several bottleneck objective functions: an algorithm with reoptimization. Comput Oper Res 39:1969–1976
Chang R, Leu S-J (1997) The minimum labeling spanning trees. Inf Process Lett 63(5):277–282
Clímaco J, Martins E (1982) A bicriterion shortest path algorithm. Eur J Oper Res 11:399–404
Clímaco J, Pascoal M (2012) Multicriteria path and tree problems: discussion on exact algorithms and applications. Int Trans Oper Res 19:63–98
Clímaco J, Captivo ME, Pascoal M (2010) On the bicriterion-minimal cost/minimal label-spanning tree problem. Eur J Oper Res 204:199–205
Consoli S, Moreno JA, Mladenović N, Darby-Dowman K (2006) Constructive heuristics for the minimum labelling spanning tree problem: a preliminary comparison. Technical Report DEIOC-4, Universidad de La Laguna, La Laguna, September http://hdl.handle.net/2438/504
Hansen P (1980) Bicriterion path problems. In: Fandel G, Gal T (eds) Multiple criteria decision making: theory and applications. Lectures notes in economics and mathematical systems
Iori M, Martello S, Pretolani D (2010) An aggregate label setting policy for the multi-objective shortest path problem. Eur J Oper Res 207:1489–1496
Kruskal J (1956) On the shortest spanning subtree of a graph and the traveling salesman problem. Proc Am Math Soc 7:48–50
Prim R (1957) Shortest connection networks and some generalizations. Bell Syst Tech J 36:1389–1401
Raith A, Ehrgott M (2009) A comparison of solution strategies for biobjective shortest path problems. Comput Oper Res 36:1299–1331
Steuer R (1986) Multiple criteria optimization theory, computation and application. Wiley, New York
Van-Nes R (2002) Design of multimodal transport networks: a hierarchical approach. Delft University Press, Delft
Vincke P (1974) Problèmes multicritères. Cahiers du Centre d’Études de Recherche Opérationelle 16:425–439
Wirth H-C (2001) Multicriteria approximation of network design and network upgrade problems. PhD thesis, University of Würzburg
This work was partially supported by the FCT Portuguese Foundation of Science and Technology (Fundação para a Ciência e a Tecnologia) under projects PEst-C/EEI/UI0308/2011, PEst-OE/MAT/UI0152 and PTDC/EEA-TEL/101884/2008. The authors deeply acknowledge the INESC-Coimbra research group on urban transportation, led by João Coutinho Rodrigues, for providing data about the metropolitan area of Coimbra.
About this article
Cite this article
Pascoal, M., Captivo, M.E., Clímaco, J. et al. Bicriteria path problem minimizing the cost and minimizing the number of labels. 4OR-Q J Oper Res 11, 275–294 (2013). https://doi.org/10.1007/s10288-013-0229-0
- Minimal cost
- Minimal number of labels
- Shortest path
Mathematics Subject Classification (2000)