### Abstract

The theoretical study of Genetic Algorithms and the dynamics induced by their genetic operators is a research field with a long history and many different approaches. In this paper we complete a recently presented approach to model one-point crossover using pretopologies (or Čechtopologies) in two ways. First, we extend it to the case of n-points crossover. We extend the definition of crossover distance between populations to work for n-points crossover, proving that computing it can be performed in polynomial time for any fixed number of crossover points. Secondly, we experimentally study how the distance distribution changes when the number of crossover points increases. In particular, the average distance between a population and the optimum decreases with the increase in the number of crossover points, showing that increasing the latter can reduce the number of crossover operations needed to evolve an optimal solution.

Original language | English |
---|---|

Pages (from-to) | 636-645 |

Number of pages | 10 |

Journal | Swarm and Evolutionary Computation |

Volume | 44 |

Issue number | February |

Early online date | 21 Aug 2018 |

DOIs | |

Publication status | Published - Feb 2019 |

### Fingerprint

### Cite this

*Swarm and Evolutionary Computation*,

*44*(February), 636-645. https://doi.org/10.1016/j.swevo.2018.08.007

}

*Swarm and Evolutionary Computation*, vol. 44, no. February, pp. 636-645. https://doi.org/10.1016/j.swevo.2018.08.007

**A distance between populations for n-points crossover in genetic algorithms.** / Castelli, Mauro; Cattaneo, Gianpiero; Manzoni, Luca; Vanneschi, Leonardo.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A distance between populations for n-points crossover in genetic algorithms

AU - Castelli, Mauro

AU - Cattaneo, Gianpiero

AU - Manzoni, Luca

AU - Vanneschi, Leonardo

N1 - Castelli, M., Cattaneo, G., Manzoni, L., & Vanneschi, L. (2019). A distance between populations for n-points crossover in genetic algorithms. Swarm and Evolutionary Computation, 44(February), 636-645. DOI: 10.1016/j.swevo.2018.08.007

PY - 2019/2

Y1 - 2019/2

N2 - The theoretical study of Genetic Algorithms and the dynamics induced by their genetic operators is a research field with a long history and many different approaches. In this paper we complete a recently presented approach to model one-point crossover using pretopologies (or Čechtopologies) in two ways. First, we extend it to the case of n-points crossover. We extend the definition of crossover distance between populations to work for n-points crossover, proving that computing it can be performed in polynomial time for any fixed number of crossover points. Secondly, we experimentally study how the distance distribution changes when the number of crossover points increases. In particular, the average distance between a population and the optimum decreases with the increase in the number of crossover points, showing that increasing the latter can reduce the number of crossover operations needed to evolve an optimal solution.

AB - The theoretical study of Genetic Algorithms and the dynamics induced by their genetic operators is a research field with a long history and many different approaches. In this paper we complete a recently presented approach to model one-point crossover using pretopologies (or Čechtopologies) in two ways. First, we extend it to the case of n-points crossover. We extend the definition of crossover distance between populations to work for n-points crossover, proving that computing it can be performed in polynomial time for any fixed number of crossover points. Secondly, we experimentally study how the distance distribution changes when the number of crossover points increases. In particular, the average distance between a population and the optimum decreases with the increase in the number of crossover points, showing that increasing the latter can reduce the number of crossover operations needed to evolve an optimal solution.

UR - http://www.scopus.com/inward/record.url?scp=85052743686&partnerID=8YFLogxK

UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000456761600046

U2 - 10.1016/j.swevo.2018.08.007

DO - 10.1016/j.swevo.2018.08.007

M3 - Article

VL - 44

SP - 636

EP - 645

JO - Swarm and Evolutionary Computation

JF - Swarm and Evolutionary Computation

SN - 2210-6502

IS - February

ER -