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A convergence analysis of unconstrained and bound constrained evolutionary pattern search.

W E Hart1

  • 1Sandia National Laboratories, Optimization/Uncertainty Estimation Department, P.O. Box 5800, MS 1110, Albuquerque, NM 87185-1110, USA. wehart@sandia.gov

Evolutionary Computation
|April 6, 2001
PubMed
Summary

We introduce evolutionary pattern search algorithms (EPSAs) that adapt step sizes for better optimization. These algorithms offer a proven, exact convergence theory for optimization problems.

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Area of Science:

  • Optimization algorithms
  • Evolutionary computation
  • Numerical analysis

Background:

  • Evolutionary algorithms (EAs) are widely used for complex optimization.
  • Existing EAs often lack precise convergence guarantees.
  • Pattern search methods offer robust optimization frameworks.

Purpose of the Study:

  • To introduce and analyze a novel class of evolutionary algorithms: evolutionary pattern search algorithms (EPSAs).
  • To establish a rigorous convergence theory for EPSAs in unconstrained and bound-constrained optimization.
  • To demonstrate the adaptive capabilities of EPSAs in modifying mutation step sizes.

Main Methods:

  • EPSAs adaptively adjust mutation step size based on optimization success.
  • EPSAs are analyzed as stochastic pattern search methods.

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  • A probabilistic, weak stationary point convergence theory is developed without approximating the stochastic process.

    • Main Results:

    • EPSAs demonstrate adaptive step-size modification.
    • The study establishes a probabilistic, weak stationary point convergence theory for EPSAs.
    • The convergence analysis precisely characterizes EPSA behavior without approximation.

    Conclusions:

    • EPSAs represent a novel class of evolutionary algorithms with adaptive step-size control.
    • The developed convergence theory provides exact characterization of EPSA behavior.
    • EPSAs offer a theoretically sound approach to unconstrained and bound-constrained optimization.