On a Population Sizing Model for Evolution Strategies Optimizing the Highly Multimodal Rastrigin Function

Area of Science:

• Optimization algorithms
• Computational intelligence
• Machine learning

Background:

• Evolution Strategies (ES) are stochastic optimization algorithms.
• The Rastrigin function is a common benchmark for evaluating global optimization performance.
• Determining appropriate population sizes for ES is crucial for reliable convergence.

Purpose of the Study:

• To develop a predictive model for the convergence success probability of a vanilla Evolution Strategy on the Rastrigin function.
• To derive a population size scaling formula for ensuring high convergence security.
• To analyze the impact of search space dimensionality on ES performance.

Main Methods:

• A mathematical model was developed to analyze the convergence probability of Evolution Strategies.
• The model specifically targets the Rastrigin test function.
• Population size scaling was investigated in relation to search space dimensionality.

Main Results:

• A method for calculating the success probability of ES convergence to the Rastrigin global optimum was established.
• A population size scaling formula was derived.
• The formula enables estimation of required population sizes for guaranteed convergence security.

Conclusions:

• The presented model provides a theoretical basis for understanding ES convergence on challenging multimodal functions.
• The derived population size formula is a practical tool for practitioners to set appropriate population sizes.
• This work contributes to the reliable application of Evolution Strategies in high-dimensional optimization problems.