Progress analysis of a multi-recombinative evolution strategy on the highly multimodal Rastrigin function

Area of Science:

• Computational intelligence
• Optimization algorithms
• Evolutionary computation

Background:

• Evolution Strategies (ES) are powerful optimization algorithms.
• Analyzing ES performance on multimodal functions is crucial.
• Understanding convergence dynamics aids algorithm development.

Purpose of the Study:

• To analyze the progress rate of (μ/μI, λ)-ES.
• To develop analytic models for optimization progress.
• To investigate convergence properties on the Rastrigin function.

Main Methods:

• First and second-order progress rate analysis.
• Asymptotic analysis for large dimensionality and population sizes.
• Dynamical systems approach using difference equations.

Main Results:

• Closed-form analytic solutions for progress rates were derived.
• Models accurately predict one-generation progress and local attraction.
• Simulations and real optimization runs show good agreement with models.
• Large mutations enhance global convergence probability at the cost of efficiency.

Conclusions:

• The developed models provide accurate insights into ES optimization dynamics.
• The study enhances understanding of convergence behavior in high-dimensional spaces.
• Findings guide the design of more efficient and effective evolutionary algorithms.