A novel meta-heuristic optimization method based on golden ratio in nature

  • Amin Foroughi Nematollahi
  • Abolfazl Rahiminejad
  • Behrooz VahidiEmail author
Methodologies and Application


A novel parameter-free meta-heuristic optimization algorithm known as the golden ratio optimization method (GROM) is proposed. The proposed algorithm is inspired by the golden ratio of plant and animal growth which is formulated by the well-known mathematician Fibonacci. He introduced a series of numbers in which a number (except the first two numbers) is equal to the sum of the two previous numbers. In this series, the ratio of two consecutive numbers is almost the same for all the numbers and is known as golden ratio. This ratio can be extensively found in nature such as snail lacquer part and foliage growth of trees. The proposed approach employed this golden ratio to update the solutions in an optimization algorithm. In the proposed method, the solutions are updated in two different phases to achieve the global best answer. There is no need for any parameter tuning, and the implementation of the proposed method is very simple. In order to evaluate the proposed method, 29 well-known benchmark test functions and also 5 classical engineering optimization problems including 4 mechanical engineering problems and 1 electrical engineering problem are employed. Using several test functions, the performance of the proposed method in solving different problems including discrete, continuous, high dimension, and high constraints problems is testified. The results of the proposed method are compared with those of 11 well-regarded state-of-the-art optimization algorithms. The comparisons are made from different aspects such as the final obtained answer, the speed and behavior of convergence, and CPU time consumption. Superiority of the purposed method from different points of views can be concluded by means of comparisons.


Meta-heuristic Golden ratio optimization method Optimization algorithm Constrained optimization Optimization 


Compliance with ethical standards

Conflict of interest

Author Amin Foroughi Nematollahi declares that he has no conflict of interest. Author Abolfazl Rahiminejad declares that he has no conflict of interest. Author Behrooz Vahidi declares that he has 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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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electrical EngineeringAmirkabir University of TechnologyTehranIran
  2. 2.Department of Electrical and Computer ScienceEsfarayen University of TechnologyEsfarayenIran
  3. 3.Department of Electrical EngineeringAmirkabir University of TechnologyTehranIran

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