Perfect edge-transmitting recombination of permutations
Merlevede, Adriaan LU and Troein, Carl LU
(2020)
In arXiv
- Abstract
- 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... (More)
- 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/8106d40e-01fc-4249-a0a3-a5bcecb6eb21
- author
- Merlevede, Adriaan
LU
and Troein, Carl
LU
- organization
- publishing date
- 2020-03-10
- type
- Other contribution
- publication status
- published
- subject
- keywords
- permutation, travelling salesman problem, TSP, crossover, transmissive, transmission
- in
- arXiv
- publisher
- arXiv.org
- project
- Applications and theory of digital evolution
- language
- English
- LU publication?
- yes
- id
- 8106d40e-01fc-4249-a0a3-a5bcecb6eb21
- date added to LUP
- 2020-04-01 12:18:59
- date last changed
- 2021-12-03 13:59:09
@misc{8106d40e-01fc-4249-a0a3-a5bcecb6eb21,
abstract = {{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.}},
author = {{Merlevede, Adriaan and Troein, Carl}},
keywords = {{permutation; travelling salesman problem; TSP; crossover; transmissive; transmission}},
language = {{eng}},
month = {{03}},
publisher = {{arXiv.org}},
series = {{arXiv}},
title = {{Perfect edge-transmitting recombination of permutations}},
year = {{2020}},
}