GMO: geometric mean optimizer for solving engineering problems

Farshad Rezaei, Hamid R. Safavi, Mohamed Abd Elaziz, Seyedali Mirjalili

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


This paper introduces a new meta-heuristic technique, named geometric mean optimizer (GMO) that emulates the unique properties of the geometric mean operator in mathematics. This operator can simultaneously evaluate the fitness and diversity of the search agents in the search space. In GMO, the geometric mean of the scaled objective values of a certain agent’s opposites is assigned to that agent as its weight representing its overall eligibility to guide the other agents in the search process when solving an optimization problem. Furthermore, the GMO has no parameter to tune, contributing its results to be highly reliable. The competence of the GMO in solving optimization problems is verified via implementation on 52 standard benchmark test problems including 23 classical test functions, 29 CEC2017 test functions as well as nine constrained engineering problems. The results presented by the GMO are then compared with those offered by several newly proposed and popular meta-heuristic algorithms. The results demonstrate that the GMO significantly outperforms its competitors on a vast range of the problems. Source codes of GMO are publicly available at

Original languageEnglish
JournalSoft Computing
Publication statusPublished - 2023


  • Fuzzy logic
  • Geometric mean optimizer
  • Global optimization
  • Meta-heuristic technique


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