Shortest Edit Path Crossover: A Theory-driven Solution to the Permutation Problem in Evolutionary Neural Architecture Search

Evolutionary algorithms (EAs) have gained attention recently due to their success in neural architecture search (NAS). However, whereas traditional EAs draw much power from crossover operations, most evolutionary NAS methods deploy only mutation operators. The main reason is the permutation problem: The mapping between genotype and phenotype in traditional graph representations is many-to-one, leading to a disruptive effect of standard crossover. This work conducts the first theoretical analysis of the behaviors of crossover and mutation in the NAS context, and proposes a new crossover operator based on the shortest edit path (SEP) in graph space. The SEP crossover is shown to overcome the permutation problem, and as a result, offspring generated by the SEP crossover is theoretically proved to have a better expected improvement in terms of graph edit distance to global optimum, compared to mutation and standard crossover. Experiments further show that the SEP crossover significantly outperforms mutation and standard crossover on three state-of-the-art NAS benchmarks. The SEP crossover therefore allows taking full advantage of evolution in NAS, and potentially other similar design problems as well.