2020/05/03 by Adriaan Merlevede, Merlevede, Adriaan, Carl Troein +1
Agricultural and Biological Sciences · Biochemistry, Genetics and Molecular Biology · Computer Science · #Chromosomal and Genetic Variations #FOS: Computer and information sciences #Genome Rearrangement Algorithms #Metaheuristic Optimization Algorithms Research #Neural and Evolutionary Computing (cs.NE) #cs.NE
paper · pdf · doi:10.48550/arxiv.2005.01113
arxiv created 2020/05/03 · openalex publication_date 2020/05/03 · arxiv updated 2020/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.