Abstract
Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used to design new problem specific crossovers that embed problem knowledge in the search. In this paper, we introduce the important notion of product geometric crossover that allows to build new geometric crossovers combining pre-existing geometric crossovers in a simple way.
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References
Van de Vel, M.L.J. (ed.): Theory of Convex Structures. North-Holland, Amsterdam (1993)
Deza, M.M., Laurent, M. (eds.): Geometry of Cuts and Metrics. Springer, Heidelberg (1997)
Jones, T.: Evolutionary Algorithms, Fitness Landscapes and Search. PhD thesis, University of New Mexico (1995)
Moraglio, A., Poli, R.: Topological interpretation of crossover. In: Proceedings of Gecco 2004, pp. 1377–1388 (2004)
Moraglio, A., Poli, R.: Geometric crossover for the permutation representation. Technical Report CSM-429, Department of Computer Science, University of Essex (2005)
Moraglio, A., Poli, R.: Topological crossover for the permutation representation. In: GECCO 2005 Workshop on Theory of Representations (2005)
Moraglio, A., Poli, R., Seehuus, R.: Geometric crossover for biological sequences. In: Collet, P., Tomassini, M., Ebner, M., Gustafson, S., Ekárt, A. (eds.) EuroGP 2006. LNCS, vol. 3905, pp. 121–132. Springer, Heidelberg (2006)
Moraglio, A., Togelius, J., Lucas, S.: Product geometric crossover for the sudoku puzzle. In: Proceedings of IEEE CEC 2006 (to appear, 2006)
Pardalos, P.M., Resende, M.G.C. (eds.): Handbook of Applied Optimization. Oxford University Press, Oxford (2002)
Sutherland, W.A. (ed.): Introduction to metric and topological spaces. Oxford University Press, Oxford (1975)
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Moraglio, A., Poli, R. (2006). Product Geometric Crossover. In: Runarsson, T.P., Beyer, HG., Burke, E., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds) Parallel Problem Solving from Nature - PPSN IX. PPSN 2006. Lecture Notes in Computer Science, vol 4193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11844297_103
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DOI: https://doi.org/10.1007/11844297_103
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38990-3
Online ISBN: 978-3-540-38991-0
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