Soft Computing

, Volume 23, Issue 22, pp 12001–12015 | Cite as

A hybrid evolutionary-simplex search method to solve nonlinear constrained optimization problems

  • Alyaa AbdelhalimEmail author
  • Kazuhide Nakata
  • Mahmoud El-Alem
  • Amr Eltawil
Methodologies and Application


This research article presents a novel design of a hybrid evolutionary-simplex search method to solve the class of general nonlinear constrained optimization problems. In this article, the particle swarm optimization (PSO) method and the Nelder–Mead (NM) simplex search algorithm are utilized in a unified way to enhance the overall performance of the proposed solution method. The NM algorithm is used as an integrative step in the PSO method to reinforce the convergence of the PSO method and overcome the global search weakness in the NM algorithm. On the other hand, a penalty function technique is embedded in the proposed method to solve constrained optimization problems. Two levels of numerical experiments were conducted to evaluate the proposed method. First, a comparison is conducted with well-known benchmark problems. Second, the proposed method is tested in solving three engineering design optimization problems. In addition, the results of the proposed method were compared to optimization methods published in the literature in three main criteria: effectiveness, efficiency and robustness. The results show the competitive performance of the proposed method in this article.


Particle swarm optimization Nonlinear optimization Constrained optimization problem Simplex search algorithm 



The Egyptian Ministry of Higher Education (MOHE) grant and the Japanese International Cooperation Agency (JICA) in the scope of the Egypt Japan University of Science and Technology (E-JUST) sponsored this research.

Compliance with ethical standards

Conflict of interest

The Authors listed in this article declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Alyaa Abdelhalim
    • 1
    Email author
  • Kazuhide Nakata
    • 2
  • Mahmoud El-Alem
    • 3
  • Amr Eltawil
    • 4
  1. 1.Production Engineering DepartmentAlexandria UniversityAlexandriaEgypt
  2. 2.Department of Industrial Engineering and EconomicsTokyo Institute of TechnologyTokyoJapan
  3. 3.Department of Mathematics, Faculty of ScienceAlexandria UniversityAlexandriaEgypt
  4. 4.Department of Industrial Engineering and Systems ManagementEgypt Japan University of Science and TechnologyNew Borg Elarab City, AlexandriaEgypt

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