## Abstract

Bit-flip mutation is a common mutation operator for evolutionary algorithms applied to optimize functions over binary strings. In this paper, we develop results from the theory of landscapes and Krawtchouk polynomials to exactly compute the probability distribution of fitness values of a binary string undergoing uniform bit-flip mutation. We prove that this probability distribution can be expressed as a polynomial in p, the probability of flipping each bit.We analyze these polynomials and provide closed-form expressions for an easy linear problem (Onemax), and an NP-hard problem, MAX-SAT. We also discuss a connection of the results with runtime analysis.

Original language | English (US) |
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Pages (from-to) | 217-248 |

Number of pages | 32 |

Journal | Evolutionary Computation |

Volume | 23 |

Issue number | 2 |

DOIs | |

State | Published - Jun 17 2015 |

### Bibliographical note

Publisher Copyright:© 2015 by the Massachusetts Institute of Technology.

## Keywords

- Bit-flip mutation
- Combinatorial optimization
- Evolutionary algorithms
- Landscape theory
- Randomized algorithms