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A hybrid cuckoo search algorithm with Nelder Mead method for solving global optimization problems.

Ahmed F Ali1, Mohamed A Tawhid2

  • 1Department of Computer Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt ; Department of Mathematics and Statistics, Faculty of Science, Thompson Rivers University, 900 McGill Road, Kamloop, BC V2C 0C8 Canada.

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Summary
This summary is machine-generated.

A new hybrid cuckoo search and Nelder-Mead (HCSNM) algorithm efficiently solves integer and minimax optimization problems. This novel approach combines global exploration with deep exploitation for improved performance.

Keywords:
Cuckoo search algorithmInteger programming problems minimax problemsNelder–Mead method

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Area of Science:

  • Optimization algorithms
  • Computational intelligence
  • Mathematical programming

Background:

  • Metaheuristic population-based methods, like the cuckoo search algorithm, are widely applied to real-world problems.
  • Standard cuckoo search can suffer from slow convergence, particularly in complex optimization tasks.
  • Integer and minimax optimization problems present unique challenges requiring robust solution methodologies.

Purpose of the Study:

  • To introduce a novel hybrid algorithm, HCSNM, integrating cuckoo search and Nelder-Mead methods.
  • To enhance the efficiency and convergence speed of cuckoo search for optimization.
  • To address the complexities of integer and minimax optimization problems.

Main Methods:

  • The hybrid cuckoo search and Nelder-Mead method (HCSNM) was developed.
  • HCSNM employs standard cuckoo search for initial exploration.
  • The best solution from cuckoo search is then refined by the Nelder-Mead method for intensification.

Main Results:

  • HCSNM demonstrated superior efficiency in solving tested integer programming and minimax problems.
  • The algorithm effectively balanced global exploration and local exploitation.
  • Performance was validated against eight and seven established algorithms for integer and minimax problems, respectively.

Conclusions:

  • The proposed HCSNM algorithm is an effective approach for solving integer and minimax optimization problems.
  • HCSNM offers a significant improvement over standard cuckoo search by accelerating convergence.
  • The hybrid strategy provides a robust and efficient optimization tool for complex problems.