Abstract
In this paper we give a representation-independent topological definition of crossover that links it tightly to the notion of fitness landscape. Building around this definition, a geometric/topological framework for evolutionary algorithms is introduced that clarifies the connection between representation, genetic operators, neighbourhood structure and distance in the landscape. Traditional genetic operators for binary strings are shown to fit the framework. The advantages of this interpretation are discussed
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
Wolpert, D.H., Macready, W.G.: No Free Lunch Theorems for Optimization. IEEE Transaction on Evolutionary Computation (April 1996)
Culberson, J.C.: Mutation-crossover isomorphism and the construction of discriminating functions. Evol. Comp. 2, 279–311 (1995)
Davis, L.: Handbook of Genetic Algorithms. van Nostrand Reinhold, New York (1991)
Gitchoff, P., Wagner, G.P.: Recombination Induced HyperGraphs: A New Approach to Mutation- Recombination Isomorphism. Journal of Complexity, 37–43 (1996)
Glover, F.W. (ed.): Handbook of Metaheuristics. Kluwer Academic Publishers, Dordrecht (2002)
Jones, T.: Evolutionary Algorithms, Fitness Landscapes and Search. PhD dissertation, University of New Mexico (1995)
Langdon, W.B., Poli, R.: Foundations of Genetic Programming. Springer, Heidelberg (2002)
Pardalos, P.M., Resende, M.G.C. (eds.): Handbook of Applied Optimization. Oxford University Press, Oxford (2002)
Radcliffe, N.J.: Nonlinear genetic representations. In: Manner, R., Manderick, B. (eds.) Proceedings of the 2 nd Conference on Parallel Problems Solving from Nature, pp. 259–268. Morgan Kaufmann, San Francisco (1992)
Radcliffe, N.J.: The Algebra of Genetic Algorithms. Annals of Maths and Artificial Intelligence 10, 339–384 (1994)
Reidys, C.M., Stadler, P.F.: Combinatorial Landscapes. SIAM Review 44, 3–54 (2002)
Stephens, R., Poli, R.: EC Theory “in Theory”: Towards a Unification of Evolutionary Computation Theory. In: Menon, A. (ed.) Frontiers of Evolutionary Computation, pp. 129–156. Kluwer (2004)
Surry, P.D.: A Prescriptive Formalism for Constructing Domain-specific Evolutionary Algorithms. PhD dissertation, University of Edinburgh (1998)
Syswerda, G.: Uniform crossover in genetic algorithms. In: Schaer, J.D. (ed.) Proceedings of the International Conference on Genetic Algorithms, San Mateo (CA), Morgan Kaufmann Publishers, San Francisco (1989)
van de Vel, M.: Theory of Convex Structures. Elsevier, Amsterdam (1993)
Whitley, D.: A Genetic Algorithm Tutorial. Statistics and Computing 4, 65–85 (1994)
Wolpert, D.H., Macready, W.G.: No Free Lunch Theorems for Optimization. IEEE Transaction on Evolutionary Computation (April 1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Moraglio, A., Poli, R. (2004). Topological Interpretation of Crossover. In: Deb, K. (eds) Genetic and Evolutionary Computation – GECCO 2004. GECCO 2004. Lecture Notes in Computer Science, vol 3102. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24854-5_131
Download citation
DOI: https://doi.org/10.1007/978-3-540-24854-5_131
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22344-3
Online ISBN: 978-3-540-24854-5
eBook Packages: Springer Book Archive