Equilibrium optimizer: A novel optimization algorithm

Afshin Faramarzi, Mohammad Heidarinejad, Brent Stephens, Seyedali Mirjalili

Research output: Contribution to journalArticlepeer-review

645 Citations (Scopus)


This paper presents a novel, optimization algorithm called Equilibrium Optimizer (EO), inspired by control volume mass balance models used to estimate both dynamic and equilibrium states. In EO, each particle (solution) with its concentration (position) acts as a search agent. The search agents randomly update their concentration with respect to best-so-far solutions, namely equilibrium candidates, to finally reach to the equilibrium state (optimal result). A well-defined “generation rate” term is proved to invigorate EO's ability in exploration, exploitation, and local minima avoidance. The proposed algorithm is benchmarked with 58 unimodal, multimodal, and composition functions and three engineering application problems. Results of EO are compared to three categories of existing optimization methods, including: (i) the most well-known meta-heuristics, including Genetic Algorithm (GA), Particle Swarm Optimization (PSO); (ii) recently developed algorithms, including Grey Wolf Optimizer (GWO), Gravitational Search Algorithm (GSA), and Salp Swarm Algorithm (SSA); and (iii) high performance optimizers, including CMA-ES, SHADE, and LSHADE-SPACMA. Using average rank of Friedman test, for all 58 mathematical functions EO is able to outperform PSO, GWO, GA, GSA, SSA, and CMA-ES by 60%, 69%, 94%, 96%, 77%, and 64%, respectively, while it is outperformed by SHADE and LSHADE-SPACMA by 24% and 27%, respectively. The Bonferroni–Dunnand Holm's tests for all functions showed that EO is significantly a better algorithm than PSO, GWO, GA, GSA, SSA and CMA-ES while its performance is statistically similar to SHADE and LSHADE-SPACMA. The source code of EO is publicly availabe at https://github.com/afshinfaramarzi/Equilibrium-Optimizer, http://built-envi.com/portfolio/equilibrium-optimizer/ and http://www.alimirjalili.com/SourceCodes/EOcode.zip.

Original languageEnglish
Article number105190
JournalKnowledge-Based Systems
Publication statusPublished - 1 Jan 2019


  • Genetic algorithm
  • Metaheuristic
  • Optimization
  • Particle Swarm Optimization
  • Physics-based


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