# Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Tuesday, March 14, 2023, 12:15 pm

**Duration**: 30 minutes

**Location**: OAT S15/S16/S17

**Speaker**: Duri Janett

## Tight Runtime Bounds for Static Unary Unbiased Evolutionary Algorithms on Linear Functions

In this talk, we investigate static unary unbiased Evolutionary Algorithms (EAs). Such EAs can only generate offspring by mutation, i.e., from a single parent. Examples of unary unbiased mutation operators include randomized local search, standard bit mutation, and fast mutation. Unary unbiased mutation operators are uniquely described by a probability distribution on the set of possible search radii. We show that, up to lower order terms, the runtime of the (1 + 1)-EA equipped with an (almost) arbitrary but static unary unbiased mutation operator on linear functions is 1/p_{1} · n ln n, where p_{1} is the probability that the algorithm searches with radius 1 in a given iteration. This generalizes a seminal result of Witt [CPC ’13], where he showed that this holds for the (1 + 1)-EA using standard bit mutation with a constant mutation rate.

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