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High-dimensional normalized data profiles for testing derivative-free optimization algorithms.

Hassan Musafer1, Emre Tokgoz2, Ausif Mahmood1

  • 1School of Computer Science and Engineering, University of Bridgeport, Bridgeport, CT, United States of America.

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|September 12, 2022
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Summary
This summary is machine-generated.

This study introduces high-dimensional data profiles for evaluating derivative-free optimization algorithms. These new profiles offer a more comprehensive assessment of solver efficiency and robustness compared to traditional methods.

Keywords:
Derivative-Free Optimization AlgorithmsNelder–Mead simplex algorithm (1965)Normalized Data Profiles

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Area of Science:

  • Numerical Analysis
  • Optimization Algorithms
  • Computational Mathematics

Background:

  • Traditional data profiles for optimization algorithms are limited to single dimensions, hindering comprehensive performance evaluation.
  • Assessing the efficiency and robustness of derivative-free optimization algorithms requires multi-dimensional analysis.

Purpose of the Study:

  • To introduce a novel tool using high-dimensional normalized data profiles for evaluating derivative-free optimization algorithms.
  • To demonstrate the necessity of multi-dimensional metrics for analyzing the relative performance of optimization solvers.

Main Methods:

  • Development of high-dimensional normalized data profiles to test multiple performance metrics.
  • Utilization of five sequences of trigonometric simplex designs for feature extraction and global minimum determination.
  • Application of a linear model with proposed data profiles to assess convergence rates of simplex sequences.
  • Comparison of proposed simplexes against the Genetic Nelder-Mead algorithm.

Main Results:

  • The proposed high-dimensional data profiles provide a more comprehensive examination of solver reliability and robustness than existing methods.
  • Experimental results show that the proposed solvers outperform genetic solvers across all accuracy tests.
  • Multi-dimensional analysis is essential for a thorough evaluation of optimization algorithm performance.

Conclusions:

  • High-dimensional data profiles offer a superior method for evaluating derivative-free optimization algorithms.
  • The proposed trigonometric simplex designs demonstrate enhanced performance and robustness.
  • This work advances the field of numerical optimization by providing a more rigorous evaluation framework.