Equilibrium optimizer: A novel optimization algorithm

By Afshin Faramarzi, Mohammad Heidarinejad, Brent E. Stephens, Seyed Mohammad Mirjalili. Knowledge-Based Systems, 2020

1,916 citations recorded by the source corpus.

Abstract 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 .

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/65b178fcf2fa537755a40db47bb2a5652b4d1e2f

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Citations in the corpus

Puma optimizer (PO): a novel metaheuristic optimization algorithm and its application in machine learning (2024, neutral): “Additionally, Faramarzi et al. [22] introduced a new Equilibrium Optimizer (EO) inspired by control volume mass balance models and uses each solution as a search agent with its position to achieve the equilibrium state.”
Archimedes optimization algorithm: a new metaheuristic algorithm for solving optimization problems (2020, background): “…search algorithm (LSA) [30] is inspired by the lightening phenomena in nature, atom search optimization (ASO) [31], equilibrium optimization (EO) [32], magnetic optimization algorithm (MOA) [33] borrows idea from Bict-Savart law of electromagnetism, electromagnetic field optimization (EFO) [34]…”
Tuna Swarm Optimization: A Novel Swarm-Based Metaheuristic Algorithm for Global Optimization (2021, methodology): “ese algorithms include particle swarm optimization (PSO) [28], grey wolf optimizer (GWO) [30], whale optimization algorithm (WOA) [44], and Salp swarm algorithm (SSA) [45], which are the more frequently used algorithms in the optimization field, and Harris Hawks optimization (HHO) [46], equilibrium ”
Hippopotamus optimization algorithm: a novel nature-inspired optimization algorithm (2024, background): “…Optimization (TEO) 100 , Turbulent Flow of Water-based Optimization (TFWO) 101 , Water Cycle Algorithm (WCA) 102 , Equilibrium Optimizer (EO) 103 , Lévy Flight Distribution (LFD) 104 , and Crystal Structure Algorithm (CryStAl) 105 which takes inspiration from the symmetric arrangement of…”
The Arithmetic Optimization Algorithm (2021, neutral): “Excellent performance of an algorithm requires a proper balance between these two strategies [10–12].”
Political Optimizer: A novel socio-inspired meta-heuristic for global optimization (2020, neutral): “…(BB-BC) optimization algorithm [36], Water Cycle Algorithm (WCA) [37], Artiﬁcial Electric Field Algorithm (AEFA) [38], Equilibrium Optimizer (EO) [39], Newton particle optimizer (NwPO) [40], Quantum Approximate Optimization Algorithm (QAOA) [41], Physarum-Energy Optimization algorithm (PEO)…”