Abstract
Finding a constraint shortest path which passes through a set of specified vertices is very important for many research areas, such as intelligent transportation systems, emergency rescue, and military planning. In this paper, we propose an efficient genetic algorithm for solving the constraint shortest path problem. Firstly, the Dijkstra algorithm is used to calculate the shortest distance between any two specified vertices. The optimal solution change from the original problem into the Hamilton path problem with the specified vertices. Because the number of specified vertices is much less than the number of vertices for the whole road network, the search space would be reduced exponentially. Secondly, the genetic algorithm is adopted to search for the optimal solution of the Hamilton path problem. Thirdly our algorithm should detect and eliminate the cycle path. Finally, the performance of our algorithm is evaluated by some real-life city road networks and some randomly generated road networks. The computational results show that our algorithm can find the constraint shortest path efficiently and effectively.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Dijkstra, E.W.: A note on two problems in connexion with graphs. Numer. Math. 1, 269–271 (1959)
Floyd, R.W.: Algorithm 97 shortest path. Commun. ACM 5(6), 345 (1962)
Saksena, J.P., Kumar, S.: The routing problem with “K" specified nodes. Oper. Res. 14(5), 909–913 (1966)
Dreyfus, S.E.: An appraisal of some shortest-path algorithms. Oper. Res. 17(3), 395–412 (1969)
Laporte, G., Mercure, H., Norbert, Y.: Optimal tour planning with specified nodes. RAIRO-Oper. Res. 18(3), 203–210 (1984)
Gomes, T., Martins, L., Ferreira, S.: Algorithms for determining a node-disjoint path pair visiting specified nodes. Opt. Switch. Netw. 23, 189–204 (2017)
Bérubé, J.F., Potvin, J.Y., Vaucher, J.: Time-dependent shortest paths through a fixed sequence of nodes: application to a travel planning problem. Comput. Oper. Res. 33(6), 1838–1856 (2006)
Andrade, R.C.: Elementary shortest-paths visiting a given set of nodes. Simpósio Brasileiro de Pesquisa Operacional, 2378–2388 (2013)
Andrade, R.C.: New formulations for the elementary shortest-path problem visiting a given set of nodes. Eur. J. Oper. Res. 254(3), 755–768 (2016)
Jia, J., Pan, J.S., Xu, H.R.: The middle of the specified node set of shortest path algorithm. IEEE International Conference on Signal Processing, pp. 1823–1826 (2017)
Ibaraki, T.: Algorithms for obtaining shortest paths visiting specified nodes. SIAM Rev. 15(2), 309–317 (1973)
Nemhauser, G.L.: A generalized permanent label setting algorithm for the shortest path between specified nodes. J. Math. Anal. Appl. 38(2), 328–334 (1972)
Gomes, T., Marques, S., Martins, L., et al.: Protected shortest path visiting specified nodes. In: IEEE 7th International Workshop on Reliable Networks Design and Modeling, pp. 120–127 (2015)
Feng, L., Yuan, L., Luo, W.: A geometric algebraic algorithm for node-constrained shortest path. Acta Electron. Sin. 5, 846–851 (2014)
Yao, B., Feng, H., Gao, Y., Ma, J., Feng, Y.: Dynamic pruning search algorithm with node sets. Comput. Eng. Appl. 1–8 (2017)
Xu, Q., Ke, X.: Research on the shortest path problem model and corresponding genetic algorithm for the mandatory point. Syst. Eng. Electron. 31(2), 459–462 (2009)
Liu, Z., Lin, J., Jin, T.: The shortest path algorithm based on the improved genetic algorithm. Inf. Commun. 2, 46–48 (2017)
Lee, D.T., Schachter, B.J.: Two algorithms for constructing a Delaunay triangulation. Int. J. Comput. Inf. Sci. 9(3), 219–242 (1980)
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant Nos. 61472293 and 61702383). Research Project of Hubei Provincial Department of Education (Grant No. 2016238).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Kai, Z., Yunfeng, S., Zhaozong, Z., Wei, H. (2018). An Efficient Genetic Algorithm for Solving Constraint Shortest Path Problem Through Specified Vertices. In: Qiao, J., et al. Bio-inspired Computing: Theories and Applications. BIC-TA 2018. Communications in Computer and Information Science, vol 951. Springer, Singapore. https://doi.org/10.1007/978-981-13-2826-8_17
Download citation
DOI: https://doi.org/10.1007/978-981-13-2826-8_17
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-2825-1
Online ISBN: 978-981-13-2826-8
eBook Packages: Computer ScienceComputer Science (R0)