Equilibrium optimizer: A novel optimization algorithm
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 rand...
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| Veröffentlicht in: | Knowledge-based systems Jg. 191; S. 105190 |
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| Hauptverfasser: | , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Amsterdam
Elsevier B.V
05.03.2020
Elsevier Science Ltd |
| Schlagworte: | |
| ISSN: | 0950-7051, 1872-7409 |
| Online-Zugang: | Volltext |
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| 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.
•Developed a novel optimization algorithm inspired by mass balance models.•Tested EO against well-studied mathematical and engineering benchmarks.•Compared the algorithm to other well-known meta-heuristics.•Demonstrated effectiveness and superiority of the proposed method. |
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| AbstractList | 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.
•Developed a novel optimization algorithm inspired by mass balance models.•Tested EO against well-studied mathematical and engineering benchmarks.•Compared the algorithm to other well-known meta-heuristics.•Demonstrated effectiveness and superiority of the proposed method. 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. |
| ArticleNumber | 105190 |
| Author | Stephens, Brent Faramarzi, Afshin Mirjalili, Seyedali Heidarinejad, Mohammad |
| Author_xml | – sequence: 1 givenname: Afshin surname: Faramarzi fullname: Faramarzi, Afshin email: afaramar@hawk.iit.edu organization: Department of Civil, Architectural, and Environmental Engineering, Illinois Institute of Technology, Chicago, IL, USA – sequence: 2 givenname: Mohammad surname: Heidarinejad fullname: Heidarinejad, Mohammad organization: Department of Civil, Architectural, and Environmental Engineering, Illinois Institute of Technology, Chicago, IL, USA – sequence: 3 givenname: Brent surname: Stephens fullname: Stephens, Brent organization: Department of Civil, Architectural, and Environmental Engineering, Illinois Institute of Technology, Chicago, IL, USA – sequence: 4 givenname: Seyedali surname: Mirjalili fullname: Mirjalili, Seyedali organization: Center for Artificial Intelligence Research and Optimization, Torrens University Australia, Fortitude Valley, Brisbane, QLD 4006, Australia |
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| SubjectTerms | Algorithms Candidates Equilibrium Exploitation Function words Genetic algorithm Genetic algorithms Genetics Heuristic Heuristic methods Mass balance Mathematical functions Metaheuristic Novels Optimization Optimization algorithms Particle Swarm Optimization Physics-based Portfolios Search algorithms Source code |
| Title | Equilibrium optimizer: A novel optimization algorithm |
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