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Progress Rate Analysis of Evolution Strategies on the Rastrigin Function: First Results.

Amir Omeradzic1, Hans-Georg Beyer1

  • 1Research Center Business Informatics, Vorarlberg University of Applied Sciences, Hochschulstraße 1, 6850 Dornbirn, Austria.

Parallel Problem Solving From Nature : ... PPSN ... Proceedings. International Conference on Parallel Problem Solving From Nature
|March 27, 2024
PubMed
Summary
This summary is machine-generated.

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This study derives a first-order progress rate for multi-recombinative Evolution Strategies (ES) on the Rastrigin function. The derived rate helps understand optimization performance and convergence properties.

Area of Science:

  • * Evolutionary Computation
  • * Optimization Theory
  • * Applied Mathematics

Background:

  • * The Rastrigin function is a highly multimodal benchmark for global optimization.
  • * Evolution Strategies (ES) are stochastic optimization algorithms.
  • * Analyzing the progress rate of ES is crucial for understanding their efficiency.

Purpose of the Study:

  • * To derive a first-order progress rate for intermediate multi-recombinative Evolution Strategy (μ/μ, λ)-ES.
  • * To analyze the performance of this rate on the Rastrigin test function.
  • * To investigate the influence of mutation strength and distance to the optimizer on progress.

Main Methods:

  • * Linearized model using noisy order statistics.
  • * Determination of mutation-induced variance for the Rastrigin function.
Keywords:
Evolution StrategiesGlobal optimizationProgress rate analysisRastrigin function

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  • * Iteration of progress using dynamical systems approach and comparison with simulations.

    • Main Results:

    • * A first-order progress rate approximation was derived and validated against simulations.
    • * Strengths and limitations of the approximation were identified based on mutation strength and optimizer distance.
    • * The property of global convergence was discussed within the derived approximation.

    Conclusions:

    • * The derived first-order progress rate provides insights into ES performance on multimodal functions.
    • * The study highlights the need for improved progress rate models and extensions to higher orders.
    • * Future work includes incorporating positional fluctuations for a more comprehensive analysis.