Abstract
Augmenting an existing network with additional links to achieve higher robustness and survivability plays an important role in network design. We consider the problem of augmenting a network with links of minimum total cost in order to make it edge-biconnected, i.e. the failure of a single link will never disconnect any two nodes. A new evolutionary algorithm is proposed that works directly on the set of additional links of a candidate solution. Problem-specific initialization, recombination, and mutation operators use a stochastic hill-climbing procedure. With low computational effort, only locally optimal, feasible candidate solutions are produced. Experimental results are significantly better than those of a previous genetic algorithm concerning final solutions’ qualities and especially execution times.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
K.P. Eswaran and R.E. Tarjan. Augmentation problems. SIAM Journal on Computing, 5(4):653–665, 1976.
Ivana LjubiĆ, Günther R. Raidl, and Jozef Kratica. A hybrid GA for the edge-biconnectivity augmentation problem. In Kalyanmoy Deb, Günther Rudolph, Xin Yao, and Hans-Paul Schwefel, editors, Proceedings of the 2000 Parallel Problem Solving from Nature VI Conference, volume 1917 of LNCS, pages 641–650. Springer, 2000.
S. Khuller, B. Raghavachari, and N. Young. Low-degree spanning trees of small weight. SIAM Journal of Computing, 25(2):355–368, 1996.
G.N. Frederickson and J. Jájá. Approximation algorithms for several graph augmentation problems. SIAM Journal on Computing, 10(2):270–283, 1981.
H.N. Gabow, Z. Galil, T. Spencer, and R.E. Tarjan. Efficient algorithms for finding minimum spanning trees in undirected and directed graphs. Combinatorica, 6(2):109–122, 1986.
S. Khuller and R. Thurimella. Approximation algorithms for graph augmentation. Journal of Algorithms, 14(2):214–225, 1993.
A. Zhu. A uniform framework for approximating weighted connectivity problems. B.Sc. thesis, University of Maryland, MD, May 1999.
A. Zhu, S. Khuller, and B. Raghavachari. A uniform framework for approximating weighted connectivity problems. In Proceedings of the 10th ACM-SIAM Symposium on Discrete Algorithms, pages 937–938, 1999.
J. Kratica. Improving performances of the genetic algorithm by caching. Computers and Artificial Intelligence, 18(3):271–283, 1999.
W. Mader. Minimale n-fach kantenzusammenhängende Graphen. Math. Ann., 191:21–28, 1971.
P. Moscato. Memetic algorithms: A short introduction. In D. Corne et al., editor, New Ideas in Optimization, pages 219–234. McGraw Hill, Berkshire, England, 1999.
R.E. Tarjan. Depth first search and linear graph algorithms. SIAM Journal of Computing, 1:146–160, 1972.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
LjubiĆ, I., Raidl, G. (2001). An Evolutionary Algorithm with Stochastic Hill-Climbing for the Edge-Biconnectivity Augmentation Problem. In: Boers, E.J.W. (eds) Applications of Evolutionary Computing. EvoWorkshops 2001. Lecture Notes in Computer Science, vol 2037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45365-2_3
Download citation
DOI: https://doi.org/10.1007/3-540-45365-2_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41920-4
Online ISBN: 978-3-540-45365-9
eBook Packages: Springer Book Archive