Evolutionary algorithms

TL;DR

This paper provides an overview of evolutionary algorithms, including genetic algorithms, strategies, and programming, with theoretical proofs of key properties and convergence, serving as an educational resource.

Contribution

It offers a comprehensive outline of evolutionary algorithms with formal proofs of fundamental properties, enhancing understanding of their theoretical foundations.

Findings

Proof of the Rotation Property of crossover

Schemata Theorem with complete proof

Convergence of evolutionary algorithms almost surely

Abstract

This manuscript contains an outline of lectures course "Evolutionary Algorithms" read by the author. The course covers Canonic Genetic Algorithm and various other genetic algorithms as well as evolutionary strategies, genetic programming, tabu search and the class of evolutionary algorithms in general. Some facts, such as the Rotation Property of crossover, the Schemata Theorem, GA performance as a local search and "almost surely" convergence of evolutionary algorithms are given with complete proofs. The text is in Russian.