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