Homology and linkage in crossover for linear genomes of variable length

The use of variable-length genomes in evolutionary computation has applications in optimisation when the size of the search space is unknown, and provides a unique environment to study the evolutionary dynamics of genome structure. Here, we revisit crossover for linear genomes of variable length, identifying two crucial attributes of successful recombination algorithms: the ability to retain homologous structure, and to reshuffle variant information. We introduce direct measures of these properties-homology score and linkage score-and use them to review existing crossover algorithms, as well as two novel ones. In addition, we measure the performance of these crossover methods on three different benchmark problems, and find that variable-length genomes out-perform fixed-length variants in all three cases. Our homology and linkage scores successfully explain the difference in performance between different crossover methods, providing a simple and insightful framework for crossover in a variable-length setting.