Erratum: Simplified Drift Analysis for Proving Lower Bounds in Evolutionary Computation

TL;DR

This paper corrects and generalizes the simplified drift theorem used in evolutionary computation, removing previous assumptions and providing a more compact proof, thereby broadening its applicability.

Contribution

It introduces a minor modification to the SDT, making it more general by removing assumptions and simplifying the proof, and revisits previous applications under this new framework.

Findings

The modified theorem is valid under broader conditions.

Previous applications of SDT are still applicable with minor adjustments.

The proof of the theorem is more concise and general.

Abstract

This erratum points out an error in the simplified drift theorem (SDT) [Algorithmica 59(3), 369-386, 2011]. It is also shown that a minor modification of one of its conditions is sufficient to establish a valid result. In many respects, the new theorem is more general than before. We no longer assume a Markov process nor a finite search space. Furthermore, the proof of the theorem is more compact than the previous ones. Finally, previous applications of the SDT are revisited. It turns out that all of these either meet the modified condition directly or by means of few additional arguments.