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An improved nutcracker optimization algorithm for discrete and continuous optimization problems: Design,

Mohamed Abdel-Basset1, Reda Mohamed1, Ibrahim M Hezam2

  • 1Faculty of Computers and Informatics, Zagazig University, Zagazig, Sharqiyah, 44519, Egypt.

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|September 25, 2024
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Summary

A new Improved Nutcracker Optimization Algorithm (INOA) enhances metaheuristic performance for complex problems. INOA offers faster convergence and avoids local minima in discrete and continuous optimization tasks.

Keywords:
Exploitation improvement strategyImage segmentationKapur's entropyNutcracker optimization algorithmPhotovoltaic modelsProton exchange membrane fuel cell

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Area of Science:

  • Computational Intelligence
  • Optimization Algorithms
  • Machine Learning Applications

Background:

  • Traditional optimization methods struggle with complex problems like parameter estimation and image segmentation.
  • Existing metaheuristic algorithms often face slow convergence and local minima issues.
  • Efficient algorithms are needed for parameter estimation in photovoltaic (PV) and proton exchange membrane fuel cell (PEMFC) models, and for multi-thresholding image segmentation.

Purpose of the Study:

  • To introduce and evaluate an Improved Nutcracker Optimization Algorithm (INOA).
  • To address the limitations of existing metaheuristic algorithms in terms of convergence speed and local minima stagnation.
  • To verify INOA's effectiveness in both discrete and continuous search spaces for challenging optimization problems.

Main Methods:

  • The study proposes INOA, an enhanced version of the nutcracker optimization algorithm with a novel convergence improvement strategy.
  • INOA is applied to parameter estimation for single, double, and triple-diode PV models and four PEMFC models.
  • INOA's performance is tested on the multi-thresholding image segmentation problem using various test images.

Main Results:

  • INOA demonstrated superior performance compared to several rival optimizers across discrete and continuous problems.
  • Quantitative improvements ranged from 0.8355% to 3.34% for discrete problems and 4.97% to 99.9% for continuous problems.
  • Validation metrics included convergence curves, standard deviation, average fitness, and Wilcoxon rank-sum tests, confirming INOA's effectiveness, stability, and scalability.

Conclusions:

  • INOA is an effective and robust metaheuristic algorithm for solving complex discrete and continuous optimization problems.
  • The proposed convergence improvement strategy successfully enhances convergence speed and prevents local minima.
  • INOA offers a significant advancement over existing methods for PV and PEMFC parameter estimation and image segmentation.