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A Fast kNN Algorithm Using Multiple Space-Filling Curves.

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Acceleration of Global Optimization Algorithm by Detecting Local Extrema Based on Machine Learning.

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This study introduces a novel deterministic algorithm for global optimization, enhanced by machine learning to identify local minima regions. This approach accelerates convergence by reducing search trials for computationally expensive problems.

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Area of Science:

  • Computational Mathematics
  • Numerical Analysis
  • Machine Learning

Background:

  • Global optimization problems are computationally intensive due to multi-extremal, nondifferentiable, and "black box" objective functions.
  • Existing methods like multistart and nature-inspired algorithms have limitations in efficiency and applicability.

Purpose of the Study:

  • To develop and evaluate a deterministic global optimization algorithm.
  • To integrate machine learning for identifying regions of attraction of local minima.
  • To accelerate the convergence of global search algorithms.

Main Methods:

  • A deterministic algorithm for global extremum finding, distinct from multistart or nature-inspired approaches.
  • A nested optimization scheme for multidimensional problem-solving.
  • Application of machine learning techniques to identify basins of attraction for local minima.

Main Results:

  • The proposed algorithm and machine learning integration significantly accelerate convergence in global optimization.
  • Computational experiments on numerous problems confirm reduced search trials for achieving desired accuracy.
  • The method effectively handles multi-extremal and nondifferentiable "black box" functions.

Conclusions:

  • The combined deterministic and machine learning approach offers a more efficient solution for complex global optimization tasks.
  • This method provides a practical strategy for reducing computational cost in scientific and engineering applications.
  • The findings suggest a promising direction for future research in advanced optimization techniques.