Evolution strategies

Evolution strategies (ES) are evolutionary algorithms that date back to the 1960s and that are most commonly applied to black-box optimization problems in continuous search spaces. Inspired by biological evolution, their original formulation is based on the application of mutation, recombination and selection in populations of candidate solutions. From the algorithmic viewpoint, ES are optimization methods that sample new candidate solutions stochastically, most commonly from a multivariate normal probability distribution. Their two most prominent design principles are unbiasedness and adaptive control of parameters of the sample distribution. In this overview, the important concepts of success based step-size control, self-adaptation, and de-randomization are covered, as well as more recent developments such as covariance matrix adaptation and natural ES. The latter give new insights into the fundamental mathematical rationale behind ES. A broad discussion of theoretical results includes progress rate results on various function classes and convergence proofs for evolution strategies.