Abstract
Many graph problems seek subgraphs of minimum weight that satisfy the problems’ constraints. Examples include the degreeconstrained minimum spanning tree and traveling salesman problems. Low-weight edges predominate in optimal solutions to these problems, and the performance of evolutionary algorithms for them is often improved by biasing their operators to favor these edges. From the distributions of edges’ ranks in optimal solutions to these two problems, we identify probabilities for edges that minimize the average expected time until mutation chooses them for inclusion in a solution. On instances of the degree-constrained minimum spanning tree problem, an evolutionary algorithm performs better with this operator than with alternative mutations. These results are not replicated on instances of the traveling salesman problem, where the inclusion of one edge in a tour requires the inclusion of another dependant edge.
This work is supported by the Austrian Science Fund (FWF), grant P13602—INF.
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
N. Deo and P. Micikevicius. A heuristic for a leaf constrained minimum spanning tree problem. Congressus Numerantium, 141:61–72, 1999.
C. Fonseca, J.-H. Kim, and A. Smith, editors. Proceedings of the 2000 IEEE Congress on Evolutionary Computation. IEEE Press, 2000.
J. J. Grefenstette. Incorporating problem specific knowledge into genetic algorithms. In L. Davis, editor, Genetic Algorithms and Simulated Annealing, pages 42–60. Morgan Kaufmann, 1987.
B. A. Julstrom. Very greedy crossover in a genetic algorithm for the Traveling Salesman Problem. In K. M. George, J. H. Carroll, E. Deaton, D. Oppenheim, and J. Hightower, editors, Proceedings of the 1995 ACM Symposium on Applied Computing, pages 324–328. ACM Press, 1995.
B. A. Julstrom and G. R. Raidl. Weight-biased edge-crossover in evolutionary algorithms for two graph problems. In G. Lamont, J. Carroll, H. Haddad, D. Morton, G. Papadopoulos, R. Sincovec, and A. Yfantis, editors, Proceedings of the 16th ACM Symposium on Applied Computing, pages 321–326. ACM Press, 2001.
J. Knowles and D. Corne. A new evolutionary approach to the degree constrained minimum spanning tree problem. IEEE Transactions on Evolutionary Computation, 4(2):125–134, 2000.
M. Krishnamoorthy, A. T. Ernst, and Y. M. Sharaiha. Comparison of algorithms for the degree constrained minimum spanning tree. Technical report, CSIRO Mathematical and Information Sciences, Clayton, Australia, 1999.
I. Ljubic and J. Kratica. A genetic algorithm for the biconnectivity augmentation problem. In Fonseca et al. [2], pages 89–96.
G. R. Raidl. An efficient evolutionary algorithm for the degree-constrained minimum spanning tree problem. In Fonseca et al. [2], pages 104–111.
G. R. Raidl and C. Drexel. A predecessor coding in an evolutionary algorithm for the capacitated minimum spanning tree problem. In C. Armstrong, editor, Late Breaking Papers at the 2000 Genetic and Evolutionary Computation Conference, pages 309–316, Las Vegas, NV, 2000.
S. Thienel. ABACUS— A Branch-And-CUt System. PhD thesis, University of Cologne, Cologne, Germany, 1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Raidl, G.R., Kodydek, G., Julstrom, B.A. (2002). On Weight-Biased Mutation for Graph Problems. In: Guervós, J.J.M., Adamidis, P., Beyer, HG., Schwefel, HP., Fernández-Villacañas, JL. (eds) Parallel Problem Solving from Nature — PPSN VII. PPSN 2002. Lecture Notes in Computer Science, vol 2439. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45712-7_20
Download citation
DOI: https://doi.org/10.1007/3-540-45712-7_20
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44139-7
Online ISBN: 978-3-540-45712-1
eBook Packages: Springer Book Archive