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Photo of Carl Troein

Carl Troein

Researcher

Photo of Carl Troein

Perfect edge-transmitting recombination of permutations

Author

  • Adriaan Merlevede
  • Carl Troein

Summary, in English

Crossover is the process of recombining the genetic features of two parents. For many applications where crossover is applied to permutations, relevant genetic features are pairs of adjacent elements, also called edges in the permutation order. Recombination of edges without errors is thought to be an NP-hard problem, typically approximated by heuristics that either introduce new edges or are only able to produce a small variety of offspring. Here, we derive an algorithm for crossover of permutations that achieves perfect transmission of edges and produces a uniform sampling of all possible offspring, in quadratic average computation time. The algorithm and its derivation reveal a link between cycle crossover (CX) and edge assembly crossover (EAX), offering a new perspective on these well-established algorithms. We also describe a modification of the algorithm that generates the mathematically optimal offspring for the asymmetric travelling salesman problem.

Department/s

  • Computational Biology and Biological Physics - Undergoing reorganization

Publishing year

2020-03-10

Language

English

Publication/Series

arXiv

Document type

Other

Publisher

arXiv.org

Topic

  • Evolutionary Biology
  • Computer Science

Keywords

  • permutation
  • travelling salesman problem
  • TSP
  • crossover
  • transmissive
  • transmission

Status

Published

Project

  • Applications and theory of digital evolution