Abstract
Crossover is an important genetic operation that helps in random recombination of structured information to locate new points in the search space, in order to achieve a good solution to an optimization problem. The conventional crossover operation when applied on a pair of binary strings will usually not retain the total number of 1’s in the offsprings to be the same as that of their parents. But there are many optimization problems which require such a constraint. In this article, we propose a new crossover technique called, “self-crossover”, which satisfies this constraint as well as retains the stochastic and evolutionary characteristics of genetic algorithms. We have also shown that this new operator serves the combined role of crossover and mutation. We have proved that self-crossover can generate any permutation of a given string. As an illustration, the effectiveness of this new operator has been demonstrated in solving the traveling salesman problem (TSP) using GA. This new technique is best suited for path representation of tours and performs better for TSP with large number of cities. Performance of the proposed scheme is compared with that of ordered crossover (OC) scheme.
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
Homaifar, A., Guan, S., Liepins, G.E.: A New Approach on the Traveling Salesman Problem by Genetic Algorithms. To appear in Complex Systems, 460–466
Grefenstette, J.J., et al.: Genetic Algorithm for the TSP. In: Grefenstette (ed.) Proceedings of an International Conference of Genetic Algorithm and their Applications, Texas Instrument and U.S. Navy Center for Applied Research and Artificial Intelligence, pp. 154–159 (1985)
Suh, et al.: The Effects of population size, Heuristic Crossover and Local Improvement on a GA for the TSP. In: Schaffer, J.D. (ed.) Proceedings of the Third International conference for Genetic Algorithms, pp. 110–115. Morgan Kaufmann Publishers, Inc., San Francisco (1989)
Johnson, D.S.: Local Optimization and Traveling Salesman Problem. In: Paterson, M.S. (ed.) ICALP 1990. LNCS, vol. 443, pp. 446–461. Springer, Heidelberg (1990)
Davis, L.: Applying Adaptive Algorithms to Epistatic Domains. In: Proceedings of the International Joint Conference on Artificial Intelligence, pp. 162–164 (1985)
Lawler, E., et al.: The Traveling Salesman Problem. John Wiley and Sons, New York
Pal, N.R., Nandi, S., Kundu, M.K.: Self Crossover: a new genetic operator and its application to feature selection. International Journal of System Sciences 29(2), 207–212 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kundu, M.K., Pal, N.R. (1999). Self-Crossover and Its Application to the Traveling Salesman Problem. In: Imam, I., Kodratoff, Y., El-Dessouki, A., Ali, M. (eds) Multiple Approaches to Intelligent Systems. IEA/AIE 1999. Lecture Notes in Computer Science(), vol 1611. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-48765-4_36
Download citation
DOI: https://doi.org/10.1007/978-3-540-48765-4_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66076-7
Online ISBN: 978-3-540-48765-4
eBook Packages: Springer Book Archive