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Title: | Transit sets of two-point crossover |
Authors: | Changat, M Narasimha-Shenoi, PG Hossein Nezhad, F Kovše, M Mohandas, S Ramachandran, A Stadler, PF |
Keywords: | genetic algorithms;recombination;transit functions;oriented matroids;Vapnik-Chervonenkis dimension |
Issue Date: | 6-Feb-2021 |
Publisher: | University of Primorska |
Citation: | Changat, A. et al. (2021) 'Transit sets of two-point crossover', Art of Discrete and Applied Mathematics, 2021, 4 (1), pp. 1 - 10. doi: 10.26493/2590-9770.1356.d19. |
Abstract: | Genetic Algorithms typically invoke crossover operators to produce offsprings that are a “mixture” of two parents x and y. On strings, k-point crossover breaks parental genotypes at at most k corresponding positions and concatenates alternating fragments for the two parents. The transit set Rk(x, y) comprises all offsprings of this form. It forms the tope set of an uniform oriented matroid with Vapnik-Chervonenkis dimension k + 1. The Topological Representation Theorem for oriented matroids thus implies a representation in terms of pseudosphere arrangements. This makes it possible to study 2-point crossover in detail and to characterize the partial cubes defined by the transit sets of two-point crossover. |
URI: | https://bura.brunel.ac.uk/handle/2438/27061 |
DOI: | https://doi.org/10.26493/2590-9770.1356.d19 |
Other Identifiers: | ORCID iDs: Manoj Changat https://orcid.org/0000-0001-7257-6031; Prasanth G. Narasimha-Shenoi https://orcid.org/0000-0002-5850-5410; Matjaˇz Kovˇse https://orcid.org/0000-0001-9473-7545; Shilpa Mohandas https://orcid.org/0000-0003-3378-2339; Abisha Ramachandran https://orcid.org/0000-0003-2778-5584; Peter F. Stadler https://orcid.org/0000-0002-5016-5191. |
Appears in Collections: | Dept of Computer Science Research Papers |
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