Hitting times of local and global optima in genetic algorithms with very high selection pressure

TL;DR

This paper provides new upper bounds on the expected time for non-elitist genetic algorithms with high selection pressure to reach local or global optima, extending previous results to broader scenarios.

Contribution

It introduces bounds applicable to the Canonical Genetic Algorithm without requiring the mutation probability to be below a certain constant.

Findings

Bounds apply to non-elitist GAs with high selection pressure

Results extend to the Canonical Genetic Algorithm

Bounds do not depend on the mutation probability being below a fixed constant

Abstract

The paper is devoted to upper bounds on the expected first hitting times of the sets of local or global optima for non-elitist genetic algorithms with very high selection pressure. The results of this paper extend the range of situations where the upper bounds on the expected runtime are known for genetic algorithms and apply, in particular, to the Canonical Genetic Algorithm. The obtained bounds do not require the probability of fitness-decreasing mutation to be bounded by a constant less than one.