Abstract
The paper deals with the shortest path problem with Constraints, and it is NP-complete problem. The problem is formulated as an optimization model. To solve this model Lagrangean relaxation algorithm is adopted. For the solution of the dual problem a subgradient method is used. The general algorithm steps for our problem are presented, and a numerical example on communication network is given to illustrate the effectiveness of the algorithm.
This work is supported by the fund of department of education of Hubei province. (No. D20102904), and doctoral fund of huanggang normal university (No. 09CD158).
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
Topkis, D.M.: A k Shortest Path Algorithm for Adaptive Routing in Communications Networks. IEEE Transactions on communications 36(1), 855–859 (1988)
Santos, L., et al.: An improved solution algorithm for the constrained shortest path problem. Transportation Research Part B 41, 756–771 (2007)
Li, Y.: On the models and algorithms for finding dissimilar shortest paths in a traffic network. In: The 7th National Operation Research Conference of China, Qingdao, China, p. 8 (2004)
Garey, M.S., Johnson, D.S.: Computers and intractability: a guide to the theory of NP-completeness. Freeman, W.H, Oxford (1979)
Wang, S.-H.: An improved stepsize of the subgradient algorithm for solving the lagrangian relaxation problem. Computers and Electrical Engineering 29, 245–249 (2003)
Lemaréchal, C.: Lagrangian relaxation. In: Jünger, M., Naddef, D. (eds.) Computational Combinatorial Optimization. LNCS, vol. 2241, pp. 112–156. Springer, Heidelberg (2001)
Fisher, M.L.: The Lagrangian Relaxation Method for Solving Integer Programming Problems. Management Science 50(12), 1861–1871 (2004)
Beasley, J., Christofides, N.: An algorithm for the resource constrained shortest path problem. Networks 19, 379–394 (1989)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
He, F., Dai, K. (2011). A Shortest Path Algorithm with Constraints in Networks. In: Zhang, J. (eds) Applied Informatics and Communication. ICAIC 2011. Communications in Computer and Information Science, vol 227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23226-8_77
Download citation
DOI: https://doi.org/10.1007/978-3-642-23226-8_77
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23225-1
Online ISBN: 978-3-642-23226-8
eBook Packages: Computer ScienceComputer Science (R0)