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A Flexible Evolutionary Algorithm With Dynamic Mutation Rate Archive

Martin S. Krejca, Carsten Witt

TL;DR

The paper tackles the challenge of dynamically tuning mutation rates in evolutionary algorithms by introducing a rate archive that preserves past successful rates and expires ineffective ones. The Flexible Evolutionary Algorithm couples a frequency-vector mechanism with an archive of active rates, blending heavy-tailed exploration and stagnation-detection-inspired restart behavior to navigate diverse landscapes. The authors prove runtime guarantees on OneMax, Jump, MST, and hurdle-like problems, showing performance close to or exceeding the best known bounds for these settings, often with essentially parameter-free configuration. This archive-based approach enables robust, problem-adaptive search that can reuse multiple rates simultaneously, offering a practical and theoretically tractable paradigm for parameter control in EAs.

Abstract

We propose a new, flexible approach for dynamically maintaining successful mutation rates in evolutionary algorithms using $k$-bit flip mutations. The algorithm adds successful mutation rates to an archive of promising rates that are favored in subsequent steps. Rates expire when their number of unsuccessful trials has exceeded a threshold, while rates currently not present in the archive can enter it in two ways: (i) via user-defined minimum selection probabilities for rates combined with a successful step or (ii) via a stagnation detection mechanism increasing the value for a promising rate after the current bit-flip neighborhood has been explored with high probability. For the minimum selection probabilities, we suggest different options, including heavy-tailed distributions. We conduct rigorous runtime analysis of the flexible evolutionary algorithm on the OneMax and Jump functions, on general unimodal functions, on minimum spanning trees, and on a class of hurdle-like functions with varying hurdle width that benefit particularly from the archive of promising mutation rates. In all cases, the runtime bounds are close to or even outperform the best known results for both stagnation detection and heavy-tailed mutations.

A Flexible Evolutionary Algorithm With Dynamic Mutation Rate Archive

TL;DR

The paper tackles the challenge of dynamically tuning mutation rates in evolutionary algorithms by introducing a rate archive that preserves past successful rates and expires ineffective ones. The Flexible Evolutionary Algorithm couples a frequency-vector mechanism with an archive of active rates, blending heavy-tailed exploration and stagnation-detection-inspired restart behavior to navigate diverse landscapes. The authors prove runtime guarantees on OneMax, Jump, MST, and hurdle-like problems, showing performance close to or exceeding the best known bounds for these settings, often with essentially parameter-free configuration. This archive-based approach enables robust, problem-adaptive search that can reuse multiple rates simultaneously, offering a practical and theoretically tractable paradigm for parameter control in EAs.

Abstract

We propose a new, flexible approach for dynamically maintaining successful mutation rates in evolutionary algorithms using -bit flip mutations. The algorithm adds successful mutation rates to an archive of promising rates that are favored in subsequent steps. Rates expire when their number of unsuccessful trials has exceeded a threshold, while rates currently not present in the archive can enter it in two ways: (i) via user-defined minimum selection probabilities for rates combined with a successful step or (ii) via a stagnation detection mechanism increasing the value for a promising rate after the current bit-flip neighborhood has been explored with high probability. For the minimum selection probabilities, we suggest different options, including heavy-tailed distributions. We conduct rigorous runtime analysis of the flexible evolutionary algorithm on the OneMax and Jump functions, on general unimodal functions, on minimum spanning trees, and on a class of hurdle-like functions with varying hurdle width that benefit particularly from the archive of promising mutation rates. In all cases, the runtime bounds are close to or even outperform the best known results for both stagnation detection and heavy-tailed mutations.
Paper Structure (24 sections, 10 theorems, 28 equations, 2 algorithms)

This paper contains 24 sections, 10 theorems, 28 equations, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Non-elitism.
  4. Static rate distributions.
  5. Dynamic rate distributions.
  6. Learning-based algorithms.
  7. Preliminaries
  8. The Flexible Evolutionary Algorithm
  9. Update of the frequency vector.
  10. The in more detail.
  11. Recommended Parameter Choices
  12. Heavy-tailed lower bounds.
  13. Stagnation detection bounds.
  14. Discussion
  15. Runtime on Unimodal Functions
  16. ...and 9 more sections

Key Result

theorem 1

Let $\fitness$ be a unimodal fitness function with $\numberOfFitnessLevels$ fitness levels. For all $j \in [L - 1]$, let $\improvementProbability{j}$ denote a lower bound on the probability that, given an individual $\individualDifferent$ in fitness level $j$, flipping a single bit in $\individualDi Especially, it is at most $1 + n (\numberOfFitnessLevels - 1) \lowerBounds[1]^{-1}$.

Theorems & Definitions (14)

  • theorem 1
  • proof
  • corollary 1
  • proof
  • theorem 2
  • proof
  • corollary 2
  • proof
  • theorem 3
  • theorem 4
  • ...and 4 more