Quantitative genetic algorithms

Evolutionary algorithms, inspired by natural evolution, aim to optimize difficult objective functions without computing derivatives. Here we detail the relationship between population genetics and evolutionary optimization and formulate a new evolutionary algorithm. Given a distribution of phenotypes on a fitness landscape, we summarize how natural selection moves a population in the direction of a natural gradient, similar to natural gradient descent, and show how intermediate selection is most informative of the fitness landscape. Then we describe the generation of new candidate solutions and propose an operator that recombines the whole population to generate variants that preserve normal statistics. Finally we combine natural selection, our recombination operator, and an adaptive method to increase selection to create a quantitative genetic algorithm (QGA). QGA is similar to covariance matrix adaptation and natural evolutionary strategies in optimization, with similar performance, although QGA requires tuning of its single hyperparameter. QGA is extremely simple in implementation with no matrix inversion or factorization, does not require storing a covariance matrix, is trivial to parallelize, and may form the basis of more robust algorithms.