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Landscape Analysis for Surrogate Models in the Evolutionary Black-Box Context.

Zbyněk Pitra1, Jan Koza2, Jiří Tumpach3

  • 1Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University Břehová 7, 115 19 Prague, Czech Republic z.pitra@gmail.com.

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This study explores how surrogate model accuracy relates to black-box function landscapes during optimization. Findings aim to guide automated selection and tuning of surrogate models for better performance.

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Area of Science:

  • Optimization
  • Machine Learning
  • Computational Science

Background:

  • Surrogate modeling is crucial for expensive black-box optimization.
  • Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is a leading optimizer for such tasks.
  • Understanding surrogate model behavior within optimization is key to improving efficiency.

Purpose of the Study:

  • To investigate the link between surrogate model predictive accuracy, their configurations, and black-box function landscape features.
  • To lay the groundwork for automated surrogate model selection and tuning strategies.
  • To analyze model error dependencies on landscape characteristics during optimization.

Main Methods:

  • Feature analysis identified 14 relevant landscape features from an initial 384.
  • Explored error dependencies of four surrogate models across 39 settings.
  • Utilized three input data selection methods within surrogate-assisted CMA-ES.
  • Conducted experiments on noiseless benchmarks using the Comparing Continuous Optimizers (COCO) framework.

Main Results:

  • Significant non-robust features were identified and similar landscape features were clustered.
  • Specific relationships between landscape features and surrogate model errors were uncovered.
  • Model error dependencies varied based on settings and input data selection methods.

Conclusions:

  • The study provides insights into surrogate model behavior within evolutionary optimization.
  • Results can inform the development of adaptive strategies for selecting and tuning surrogate models.
  • Understanding landscape-model interactions is vital for optimizing expensive black-box problems.