Abstract
In this paper, we discuss the shortest path problem with forbidden paths (SPPFP), where the constraints come from a set of forbidden paths (arc sequences) that cannot be part of any feasible solution. SPPFP can be used to solve the problems with hard-to-modeled path constraints or to implement exact branching scheme.The method proposed by Villeneuve and Desaulniers first transfer the SPPFP problem to the k-shortest paths problem. We propose an algorithm which reduces execution time of solving the SPPFP problem via a nodes combination process. It improves the approach proposed by Villeneuve and Desaulniers. In addition, their algorithm for generating augmented paths could cause the inconsistency in particular situations. The proposed method also improves the weakness without increasing its time complexity.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aho, A.V., Corasick, M.J.: Efficient string matching: An aid to bibliographic search. Journal of the ACM 18(6), 333–340 (1975)
Arunapuram, S., Mathur, K., Solow, D.: Vehicle routing and scheduling with full truck loads. Transportation Science 37, 170–182 (2003)
Azevedo, J.A., Costa, M.E.O.S., Madeira, J.J.E.S., Martins, E.Q.V.: An algorithm for the ranking of shortest paths. European Journal of Operational Research 69, 97–106 (1993)
Chauny, F., Ratsirahonana, L., Savard, G.: A model and column generation algorithm for the aircraft loading problem, Les Cahiers du GERAD G-2000-68, Ecole des Hautes Etudes Commerciales, Montreal (2000)
Chen, Y.L., Yang, H.H.: Finding the first k shortest paths in a time-window network. Computers and Operations Research 31, 499–513 (2004)
Coutinho-Rodrigues, J.M., Climaco, J.C.N., Current, J.R.: An interactive bi-objective shortest path approach: searching for unsupported nondominated solutions. Computers and Operations Research 26, 789–798 (1999)
Desaulniers, G., Langevin, A., Riopel, D., Villeneuve, B.: Dispatching and conflict-free routing of automated guided vehicles: An exact approach, Les Cahiers du GERAD G-2002-31, Ecole des Hautes Etudes Commerciales, Montreal. International Journal of Flexible Manufacturing Systems (in press) (2002)
Eppstein, D.: Finding the k shortest paths. SIAM Journal on Computing 18(2), 652–673 (1999)
Gustafsson, T.: A heuristic approach to column generation for airline crew scheduling, Licentiate thesis, Chalmers University of Technology and Goteborg University, S-412 96 Goteborg, Sweden (1999)
Handler, G.Y., Zang, I.A.: A dual algorithm for the constrained shortest path problem. Networks 10, 293–310 (1980)
Hansen, P., Jaumard, B., de Aragao, M.P.: Un algorithme primal de programmation lineaire generalisee pourles programmes mixtes. Comptes Rendus de 1‘Academie des Sciences 313, 557–560 (1991) (in French)
Hoffman, W., Pavley, R.: A method for the solution of the N‘th best path problem. Journal of the Association for Computing Machinery 6, 506–514 (1959)
Jiménez, V.M., Marzal, A.: Computing the k shortest paths: a new algorithm and an experimental comparison. In: Vitter, J.S., Zaroliagis, C.D. (eds.) WAE 1999. LNCS, vol. 1668, pp. 15–29. Springer, Heidelberg (1999)
Katoh, N., Ibaraki, T., Mine, H.: An efficient algorithm for k shortest simple paths. Networks 12, 411–427 (1982)
Lawler, E.L.: Aprocedure for computing the k best solutions to discrete optimization problems and its application to the shortest path. Management Science 18(7), 401–405 (1972)
Martins, E.Q.V.: An algorithm for ranking paths that contain cycles. European Journal of Operational Research 18, 123–130 (1984)
Villeneuve, D., Desaulniers, G.: The shortest path problem with forbidden paths. European Journal of Operational Research 165, 97–107 (2005)
Yang, H.H., Chen, Y.L.: Finding k shortest looping paths in a traffic-light network. Computers and Operations Research 32, 571–581 (2005)
Yang, H.H., Chen, Y.L.: Finding K shortest looping paths with waiting time in a time-windows network. Applied Mathematical Modelling 30, 458–465 (2006)
Yen, Y.J.: Finding the k shortest loopless paths in a network. Management Science 17(11), 712–716 (1971)
Zijpp, N.J., Catalano, S.F.: Path enumeration by finding the constrained k-shortest paths. Transport Research B 39, 545–563 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hsu, CC., Chen, DR., Ding, HY. (2009). An Efficient Algorithm for the Shortest Path Problem with Forbidden Paths. In: Hua, A., Chang, SL. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2009. Lecture Notes in Computer Science, vol 5574. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03095-6_60
Download citation
DOI: https://doi.org/10.1007/978-3-642-03095-6_60
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03094-9
Online ISBN: 978-3-642-03095-6
eBook Packages: Computer ScienceComputer Science (R0)