The TransRAR crossover operator for genetic algorithms with set encoding

This work introduces a new crossover operator specially designed to be used in genetic algorithms (GAs) that encode candidate solutions as sets of fixed cardinality. The Transmitting Random Assortment Recombination (TransRAR) operator proceeds by taking elements from a multiset, which is built by the union of the parent chromosomes, allowing repeated elements. If an element that is present in both parents is drawn, it is accepted with probability 1. Elements that belong to only one of the parents are accepted with a probability p, smaller than 1. The performance of this novel crossover operator is assessed in synthetic and real-world problems. In these problems, GAs that employ this type of crossover outperform those that use alternative operators for sets, such as Random Assortment Recombination (RAR), Random Respectful Recombination (R ³) or Random Transmitting Recombination (RTR). Furthermore, TransRAR can be implemented very efficiently and is faster than RAR, its closest competitor in terms of overall performance.