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Benchmarking parameter-free AMaLGaM on functions with and without noise.

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The adapted maximum-likelihood Gaussian model iterated density-estimation evolutionary algorithm (AMaLGaM) is a parameter-free optimization tool that performs well on many problems, showing robustness to noise and efficient scalability.

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Area of Science:

  • Numerical Optimization
  • Evolutionary Algorithms
  • Machine Learning

Background:

  • Estimation-of-Distribution Algorithms (EDAs) are crucial for numerical optimization.
  • Existing EDAs often require parameter tuning, limiting their applicability.
  • The 2009 Black Box Optimization Benchmarking (BBOB) framework provides a standard for evaluating optimization algorithms.

Purpose of the Study:

  • To introduce and evaluate a parameter-free EDA, AMaLGaM, for numerical optimization.
  • To compare AMaLGaM against a variant (iAMaLGaM) and assess the impact of covariance matrix factorization.
  • To investigate the performance of AMaLGaM on noisy optimization problems and evaluate noise-averaging strategies.

Main Methods:

  • Development of AMaLGaM, a parameter-free EDA based on a Gaussian model.
  • Benchmarking AMaLGaM and iAMaLGaM on the 2009 BBOB framework, including noisy variants.
  • Systematic study of covariance matrix factorization's effect on performance.
  • Assessment of noise-averaging techniques with multiple evaluations per solution.

Main Results:

  • AMaLGaM demonstrated efficient performance and perceived polynomial scalability on various problems, including multimodal ones.
  • It achieved top-tier results on functions like step-ellipsoid and Katsuuras but struggled with higher-dimensional, rotated problems.
  • AMaLGaM exhibited greater robustness to noise than iAMaLGaM, attributed to its larger population size.
  • Factorizing the covariance matrix negatively impacted performance on rotated search spaces.
  • Noise averaging was less efficient than direct EDA application unless noise was uniformly distributed.

Conclusions:

  • Parameter-free AMaLGaM is a highly competitive and robust algorithm for numerical optimization, particularly effective on a wide range of BBOB functions.
  • The algorithm's performance is sensitive to search space characteristics like rotation, and its robustness to noise is a key advantage.
  • AMaLGaM represents a significant advancement in EDAs, offering strong performance without the need for parameter tuning.