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Maximizing Drift Is Not Optimal for Solving OneMax.

Nathan Buskulic1, Carola Doerr2

  • 1Sorbonne Université, CNRS, LIP6, Paris, France nathan.buskulic@outlook.fr.

Evolutionary Computation
|January 22, 2021
PubMed
Summary
This summary is machine-generated.

Drift maximization is not optimal for evolutionary algorithms. Optimal mutation rates can be higher than those maximizing stepwise progress, especially for the OneMax problem.

Keywords:
Parameter controlblack-box complexity.evolutionary computationruntime analysis

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Area of Science:

  • Computer Science
  • Artificial Intelligence
  • Optimization Algorithms

Background:

  • Elitist unary unbiased search algorithms often assume maximizing expected progress is optimal for problems like OneMax.
  • Previous work suggested this drift maximization approach is nearly optimal for such algorithms.

Purpose of the Study:

  • To investigate whether drift maximization is indeed the optimal strategy for evolutionary algorithms.
  • To determine if alternative mutation strategies offer superior performance.

Main Methods:

  • Analysis of the OneMax problem using elitist unary unbiased search algorithms.
  • Comparison of drift-maximizing mutation strengths with optimal mutation strengths across various fitness levels.
  • Mathematical proofs to demonstrate deviations from drift maximization.

Main Results:

  • Drift maximization is not optimal for the OneMax problem.
  • Optimal mutation strengths exceed drift-maximizing ones for fitness levels between n/2 and 2n/3.
  • The optimal (1+1) Evolutionary Algorithm (EA) and its variants may require higher mutation rates than previously assumed.

Conclusions:

  • The assumption of drift maximization as the sole optimal strategy is challenged.
  • Evolutionary algorithms may benefit from more 'risk-affine' approaches, employing higher mutation rates.
  • Findings have implications for designing more effective optimization algorithms.