Evolution strategies: An alternative evolutionary algorithm

Abstract

In this paper, evolution strategies (ESs) — a class of evolutionary algorithms using normally distributed mutations, recombination, deterministic selection of the μ>1 best offspring individuals, and the principle of self-adaptation for the collective on-line learning of strategy parameters — are described by demonstrating their differences to genetic algorithms. By comparison of the algorithms, it is argued that the application of canonical genetic algorithms for continuous parameter optimization problems implies some difficulties caused by the encoding of continuous object variables by binary strings and the constant mutation rate used in genetic algorithms. Because they utilize a problem-adequate representation and a suitable self-adaptive step size control guaranteeing linear convergence for strictly convex problems, evolution strategies are argued to be more adequate for continuous problems. The main advantage of evolution strategies, the self-adaptation of strategy parameters, is explained in detail, and further components such as recombination and selection are described on a rather general level. Concerning theory, recent results regarding convergence velocity and global convergence of evolution strategies are briefly summarized, especially including the results for (μ,λ)-ESs with recombination. It turns out that the theoretical ground of ESs provides many more results about their behavior as optimization algorithms than available for genetic algorithms, and that ESs have all properties required for global optimization methods. The paper concludes by emphasizing the necessity for an appropriate step size control and the recommendation to avoid encoding mappings by using a problem-adequate representation of solutions within evolutionary algorithms.