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MEALPY: A Framework Of The State-Of-The-Art Meta-Heuristic Algorithms In Python

Project description

MEALPY


GitHub release Wheel PyPI version PyPI - Python Version PyPI - Status PyPI - Downloads Downloads GitHub Release Date Documentation Status Average time to resolve an issue Percentage of issues still open GitHub contributors DOI License: GPL v3

MEALPY is the largest python library for most of the cutting-edge nature-inspired meta-heuristic algorithms (population-based). Population meta-heuristic algorithms (PMA) are the most popular algorithms in the field of approximate optimization.

  • Free software: GNU General Public License (GPL) V3 license
  • Total algorithms: 172 (102 original, 45 official variants, 25 developed variants)
  • Documentation: https://mealpy.readthedocs.io/en/latest/
  • Python versions: 3.7.x, 3.8.x, 3.9.x, 3.10.x
  • Dependencies: numpy, scipy, pandas, matplotlib

Goals

Our goals are to implement all of the classical as well as the state-of-the-art nature-inspired algorithms, create a simple interface that helps researchers access optimization algorithms as quickly as possible, and share knowledge of the optimization field with everyone without a fee. What you can do with mealpy:

  • Analyse parameters of meta-heuristic algorithms.
  • Perform Qualitative and Quantitative Analysis of algorithms.
  • Analyse rate of convergence of algorithms.
  • Test and Analyse the scalability and the robustness of algorithms.
  • Save results in various formats (csv, json, pickle, png, pdf, jpeg)
  • Export and import models

Installation

Install with pip

Install the current PyPI release:

$ pip install mealpy==2.5.1

Install from source

In case you want to install directly from the source code, use:

$ git clone https://github.com/thieu1995/mealpy.git
$ cd mealpy
$ python setup.py install

Usage

After installation, you can import Mealpy as any other Python module:

$ python
>>> import mealpy
>>> mealpy.__version__

Let's go through a basic and advanced example.

Examples

Simple Benchmark Function

from mealpy.bio_based import SMA
import numpy as np

def fitness_function(solution):
    return np.sum(solution**2)

problem = {
    "fit_func": fitness_function,
    "lb": [-100, ] * 30,
    "ub": [100, ] * 30,
    "minmax": "min",
    "log_to": None,
    "save_population": False,
}

## Run the algorithm
model = SMA.BaseSMA(epoch=100, pop_size=50, pr=0.03)
best_position, best_fitness = model.solve(problem)
print(f"Best solution: {best_position}, Best fitness: {best_fitness}")

Constrained Benchmark Function

Multi-objective Benchmark Function

Custom Problem

For our custom problem, we can create a class and inherit from Problem class, named the child class as "Squared". In the initialization method of Squared class we have to set the lb, ub, and minmax of the problem. (lb: is list of lowerbound, ub: is list of upperbound values, minmax is "min" or "max" problem).

Afterwards we have to override the abstract method fit_func() which takes a parameter solution, the solution to be evaluated, and returns the function value. Now we should have something similar as is shown in code snippet bellow. (name is additional parameter we want to add to this class, you can add anything you want).

import numpy as np
from mealpy.bio_based import BBO
from mealpy.utils.problem import Problem

# Our custom problem class
class Squared(Problem):
    def __init__(self, lb=(-5, -5, -5, -5, -5, -5), ub=(5, 5, 5, 5, 5, 5), minmax="min", name="Squared", **kwargs):
        super().__init__(lb, ub, minmax, **kwargs)
        self.name = name

    def fit_func(self, solution):
        return np.sum(solution ** 2)

Now, we define an algorithm, and pass an instance of our Squared class as the problem argument.

problem = Squared(lb=[-10] * 20, ub=[10] * 20, minmax="min")
model = BBO.BaseBBO(epoch=10, pop_size=50)
best_position, best_fitness = model.solve(problem)

print(best_position)
print(best_fitness)
print(model.get_parameters())
print(model.get_name())
print(model.get_attributes()["solution"])
print(model.problem.get_name())
print(model.problem.n_dims)

Tuner class (GridSearchCV/ParameterSearch, Hyper-parameter tuning)

We build a dedicated class, Tuner, that can help you tune your algorithm's parameters.

import numpy as np
from mealpy.bio_based import BBO
from mealpy.tuner import Tuner          # Remember this


def fitness(solution):
    return np.sum(solution**2)

problem = {
    "lb": [-100, ]*50,
    "ub": [100, ]*50,
    "minmax": "min",
    "fit_func": fitness,
    "name": "Squared Problem",
    "log_to": None,
}

paras_bbo_grid = {
    "epoch": [100],
    "pop_size": [50],
    "elites": [2, 3, 4, 5],
    "p_m": [0.01, 0.02, 0.05, 0.1, 0.15, 0.2]
}

if __name__ == "__main__":
    model = BBO.BaseBBO()

    tuner = Tuner(model, paras_bbo_grid)
    tuner.execute(problem=problem, n_trials=10, mode="parallel", n_workers=4)

    print(tuner.best_score)
    print(tuner.best_params)
    print(tuner.best_algorithm)
    print(tuner.best_algorithm.get_name())

    ## Save results to csv file 
    tuner.export_results(save_path="history/tuning", save_as="csv")

    ## Re-solve the best model on your problem 
    best_position, best_fitness = tuner.resolve()

    print(best_position, best_fitness)
    print(tuner.problem.get_name())

Multitask class (Multitask solving)

We also build a dedicated class, Multitask, that can help you run several different scenarios. For example:

  1. Run 1 algorithm with 1 problem, and multiple trials
  2. Run 1 algorithm with multiple problems, and multiple trials
  3. Run multiple algorithms with 1 problem, and multiple trials
  4. Run multiple algorithms with multiple problems, and multiple trials
#### Using multiple algorithm to solve multiple problems with multiple trials

## Import libraries
## For example, we want to solve F5, F10, F29 problem in CEC-2017
from opfunu.cec_based.cec2017 import F52017, F102017, F292017

from mealpy.bio_based import BBO
from mealpy.evolutionary_based import DE
from mealpy.multitask import Multitask          # Remember this


## You can define your own problems

f1 = F52017(30, f_bias=0)
f2 = F102017(30, f_bias=0)
f3 = F292017(30, f_bias=0)

p1 = {
    "lb": f1.lb.tolist(),
    "ub": f1.ub.tolist(),
    "minmax": "min",
    "fit_func": f1.evaluate,
    "name": "F5-CEC2017",
    "log_to": None,
}

p2 = {
    "lb": f2.lb.tolist(),
    "ub": f2.ub.tolist(),
    "minmax": "min",
    "fit_func": f2.evaluate,
    "name": "F10-CEC2017",
    "log_to": None,
}

p3 = {
    "lb": f3.lb.tolist(),
    "ub": f3.ub.tolist(),
    "minmax": "min",
    "fit_func": f3.evaluate,
    "name": "F29-CEC2017",
    "log_to": None,
}

## Define models

model1 = BBO.BaseBBO(epoch=10, pop_size=50)
model2 = BBO.OriginalBBO(epoch=10, pop_size=50)
model3 = DE.BaseDE(epoch=10, pop_size=50)


## Define and run Multitask

if __name__ == "__main__":
    multitask = Multitask(algorithms=(model1, model2, model3), problems=(p1, p2, p3))
    multitask.execute(n_trials=3, mode="parallel", n_workers=6, save_path="history", save_as="csv", save_convergence=True, verbose=True)

    ## Check the directory: history/, you will see list of .csv result files

For more usage examples please look at examples folder.

More advanced examples can also be found in the Mealpy-examples repository.

Get Visualize Figures

  • Tutorials

  • Global best fitness value and Local best fitness value after generations

Light         Dark

  • Global objectives chart and Local objectives chart

Light         Dark

  • Diversity of population chart and Exploration verse Exploitation chart

Light         Dark

  • Running time chart and Trajectory of some first agents chart

Light         Dark

Mealpy Application

Mealpy + Neural Network (Replace the Gradient Descent Optimizer)

  • Time-series Problem:
    • Traditional MLP code: Link
    • Hybrid code (Mealpy + MLP): Link
  • Classification Problem:
    • Traditional MLP code: Link
    • Hybrid code (Mealpy + MLP): Link

Mealpy + Neural Network (Optimize Neural Network Hyper-parameter)

Code: Link

Other Applications

Tutorial Videos

All tutorial videos: Link

All code examples: Link

All visualization examples: Link

Get helps (questions, problems)

Want to have an instant assistant? Join our telegram community at link We share lots of information, questions, and answers there. You will get more support and knowledge there.

Cite Us

If you are using mealpy in your project, we would appreciate citations:

@software{nguyen_van_thieu_2022_6684223,
  author       = {Nguyen Van Thieu and Seyedali Mirjalili},
  title        = {{MEALPY: a Framework of The State-of-The-Art Meta-Heuristic Algorithms in Python}},
  month        = jun,
  year         = 2022,
  publisher    = {Zenodo},
  version      = {v2.4.2},
  doi          = {10.5281/zenodo.6684223},
  url          = {https://doi.org/10.5281/zenodo.6684223}
}

Documents

  • Meta-heuristic Categories: (Based on this article: link)

    • Evolutionary-based: Idea from Darwin's law of natural selection, evolutionary computing
    • Swarm-based: Idea from movement, interaction of birds, organization of social ...
    • Physics-based: Idea from physics law such as Newton's law of universal gravitation, black hole, multiverse
    • Human-based: Idea from human interaction such as queuing search, teaching learning, ...
    • Biology-based: Idea from biology creature (or microorganism),...
    • System-based: Idea from eco-system, immune-system, network-system, ...
    • Math-based: Idea from mathematical form or mathematical law such as sin-cosin
    • Music-based: Idea from music instrument
  • Difficulty - Difficulty Level (Personal Opinion): Objective observation from author. Depend on the number of parameters, number of equations, the original ideas, time spend for coding, source lines of code (SLOC).

    • Easy: A few paras, few equations, SLOC very short
    • Medium: more equations than Easy level, SLOC longer than Easy level
    • Hard: Lots of equations, SLOC longer than Medium level, the paper hard to read.
    • Hard* - Very hard: Lots of equations, SLOC too long, the paper is very hard to read.

** For newbie, we recommend to read the paper of algorithms which difficulty is "easy" or "medium" difficulty level.

Group Name Module Class Year Paras Difficulty
Evolutionary Evolutionary Programming EP OriginalEP 1964 3 easy
Evolutionary - - LevyEP - 3 easy
Evolutionary Evolution Strategies ES OriginalES 1971 3 easy
Evolutionary - - LevyES - 3 easy
Evolutionary Memetic Algorithm MA OriginalMA 1989 7 easy
Evolutionary Genetic Algorithm GA BaseGA 1992 4 easy
Evolutionary - - SingleGA - 7 easy
Evolutionary - - MultiGA - 7 easy
Evolutionary - - EliteSingleGA - 10 easy
Evolutionary - - EliteMultiGA - 10 easy
Evolutionary Differential Evolution DE BaseDE 1997 5 easy
Evolutionary - - JADE 2009 6 medium
Evolutionary - - SADE 2005 2 medium
Evolutionary - - SHADE 2013 4 medium
Evolutionary - - L_SHADE 2014 4 medium
Evolutionary - - SAP_DE 2006 3 medium
Evolutionary Flower Pollination Algorithm FPA OriginalFPA 2014 4 medium
Evolutionary Coral Reefs Optimization CRO OriginalCRO 2014 11 medium
Evolutionary - - OCRO 2019 12 medium
- - - - - - -
Swarm Particle Swarm Optimization PSO OriginalPSO 1995 6 easy
Swarm - - PPSO 2019 2 medium
Swarm - - HPSO_TVAC 2017 4 medium
Swarm - - C_PSO 2015 6 medium
Swarm - - CL_PSO 2006 6 medium
Swarm Bacterial Foraging Optimization BFO OriginalBFO 2002 10 hard
Swarm - - ABFO 2019 8 medium
Swarm Bees Algorithm BeesA OriginalBeesA 2005 8 medium
Swarm - - ProbBeesA 2015 5 medium
Swarm Cat Swarm Optimization CSO OriginalCSO 2006 11 hard
Swarm Artificial Bee Colony ABC OriginalABC 2007 8 medium
Swarm Ant Colony Optimization ACO-R OriginalACOR 2008 5 easy
Swarm Cuckoo Search Algorithm CSA OriginalCSA 2009 3 medium
Swarm Firefly Algorithm FFA OriginalFFA 2009 8 easy
Swarm Fireworks Algorithm FA OriginalFA 2010 7 medium
Swarm Bat Algorithm BA OriginalBA 2010 6 medium
Swarm - - AdaptiveBA - 8 medium
Swarm - - ModifiedBA - 5 medium
Swarm Fruit-fly Optimization Algorithm FOA OriginalFOA 2012 2 easy
Swarm - - BaseFOA - 2 easy
Swarm - - WhaleFOA 2020 2 medium
Swarm Social Spider Optimization SSpiderO OriginalSSpiderO 2018 4 hard*
Swarm Grey Wolf Optimizer GWO OriginalGWO 2014 2 easy
Swarm - - RW_GWO 2019 2 easy
Swarm Social Spider Algorithm SSpiderA OriginalSSpiderA 2015 5 medium
Swarm Ant Lion Optimizer ALO OriginalALO 2015 2 easy
Swarm - - BaseALO - 2 easy
Swarm Moth Flame Optimization MFO OriginalMFO 2015 2 easy
Swarm - - BaseMFO - 2 easy
Swarm Elephant Herding Optimization EHO OriginalEHO 2015 5 easy
Swarm Jaya Algorithm JA OriginalJA 2016 2 easy
Swarm - - BaseJA - 2 easy
Swarm - - LevyJA 2021 2 easy
Swarm Whale Optimization Algorithm WOA OriginalWOA 2016 2 medium
Swarm - - HI_WOA 2019 3 medium
Swarm Dragonfly Optimization DO OriginalDO 2016 2 medium
Swarm Bird Swarm Algorithm BSA OriginalBSA 2016 9 medium
Swarm Spotted Hyena Optimizer SHO OriginalSHO 2017 4 medium
Swarm Salp Swarm Optimization SSO OriginalSSO 2017 2 easy
Swarm Swarm Robotics Search And Rescue SRSR OriginalSRSR 2017 2 hard*
Swarm Grasshopper Optimisation Algorithm GOA OriginalGOA 2017 4 easy
Swarm Coyote Optimization Algorithm COA OriginalCOA 2018 3 medium
Swarm Moth Search Algorithm MSA OriginalMSA 2018 5 easy
Swarm Sea Lion Optimization SLO OriginalSLO 2019 2 medium
Swarm - - ModifiedSLO - 2 medium
Swarm - - ImprovedSLO - 4 medium
Swarm Nake Mole-Rat Algorithm NMRA OriginalNMRA 2019 3 easy
Swarm - - ImprovedNMRA - 4 medium
Swarm Pathfinder Algorithm PFA OriginalPFA 2019 2 medium
Swarm Sailfish Optimizer SFO OriginalSFO 2019 5 easy
Swarm - - ImprovedSFO - 3 medium
Swarm Harris Hawks Optimization HHO OriginalHHO 2019 2 medium
Swarm Manta Ray Foraging Optimization MRFO OriginalMRFO 2020 3 medium
Swarm Bald Eagle Search BES OriginalBES 2020 7 easy
Swarm Sparrow Search Algorithm SSA OriginalSSA 2020 5 medium
Swarm - - BaseSSA - 5 medium
Swarm Hunger Games Search HGS OriginalHGS 2021 4 medium
Swarm Aquila Optimizer AO OriginalAO 2021 2 easy
Swarm Hybrid Grey Wolf - Whale Optimization Algorithm GWO GWO_WOA 2022 2 easy
Swarm Marine Predators Algorithm MPA OriginalMPA 2020 2 medium
Swarm Honey Badger Algorithm HBA OriginalHBA 2022 2 easy
Swarm Sand Cat Swarm Optimization SCSO OriginalSCSO 2022 2 easy
Swarm Tuna Swarm Optimization TSO OriginalTSO 2021 2 medium
Swarm African Vultures Optimization Algorithm AVOA OriginalAVOA 2022 7 medium
Swarm Artificial Gorilla Troops Optimization AGTO OriginalAGTO 2021 5 medium
Swarm Artificial Rabbits Optimization ARO OriginalARO 2022 2 easy
- - - - - - -
Physics Simulated Annealling SA OriginalSA 1987 9 medium
Physics Wind Driven Optimization WDO OriginalWDO 2013 7 easy
Physics Multi-Verse Optimizer MVO OriginalMVO 2016 4 easy
Physics - - BaseMVO - 4 easy
Physics Tug of War Optimization TWO OriginalTWO 2016 2 easy
Physics - - OppoTWO - 2 medium
Physics - - LevyTWO - 2 medium
Physics - - EnhancedTWO 2020 2 medium
Physics Electromagnetic Field Optimization EFO OriginalEFO 2016 6 easy
Physics - - BaseEFO - 6 medium
Physics Nuclear Reaction Optimization NRO OriginalNRO 2019 2 hard*
Physics Henry Gas Solubility Optimization HGSO OriginalHGSO 2019 3 medium
Physics Atom Search Optimization ASO OriginalASO 2019 4 medium
Physics Equilibrium Optimizer EO OriginalEO 2019 2 easy
Physics - - ModifiedEO 2020 2 medium
Physics - - AdaptiveEO 2020 2 medium
Physics Archimedes Optimization Algorithm ArchOA OriginalArchOA 2021 8 medium
- - - - - - -
Human Culture Algorithm CA OriginalCA 1994 3 easy
Human Imperialist Competitive Algorithm ICA OriginalICA 2007 8 hard*
Human Teaching Learning-based Optimization TLO OriginalTLO 2011 2 easy
Human - - BaseTLO 2012 2 easy
Human - - ITLO 2013 3 medium
Human Brain Storm Optimization BSO OriginalBSO 2011 8 medium
Human - - ImprovedBSO 2017 7 medium
Human Queuing Search Algorithm QSA OriginalQSA 2019 2 hard
Human - - BaseQSA - 2 hard
Human - - OppoQSA - 2 hard
Human - - LevyQSA - 2 hard
Human - - ImprovedQSA 2021 2 hard
Human Search And Rescue Optimization SARO OriginalSARO 2019 4 medium
Human - - BaseSARO - 4 medium
Human Life Choice-Based Optimization LCO OriginalLCO 2019 3 easy
Human - - BaseLCO - 3 easy
Human - - ImprovedLCO - 2 easy
Human Social Ski-Driver Optimization SSDO OriginalSSDO 2019 2 easy
Human Gaining Sharing Knowledge-based Algorithm GSKA OriginalGSKA 2019 6 medium
Human - - BaseGSKA - 4 medium
Human Coronavirus Herd Immunity Optimization CHIO OriginalCHIO 2020 4 medium
Human - - BaseCHIO - 4 medium
Human Forensic-Based Investigation Optimization FBIO OriginalFBIO 2020 2 medium
Human - - BaseFBIO - 2 medium
Human Battle Royale Optimization BRO OriginalBRO 2020 3 medium
Human - - BaseBRO - 3 medium
Human Student Psychology Based Optimization SPBO OriginalSPBO 2020 2 medium
Human - - DevSPBO 2 medium
Human Dwarf Mongoose Optimization Algorithm DMOA OriginalDMOA 2022 4 medium
Human - - DevDMOA - 3 medium
- - - - - - -
Bio Invasive Weed Optimization IWO OriginalIWO 2006 7 easy
Bio Biogeography-Based Optimization BBO OriginalBBO 2008 4 easy
Bio - - BaseBBO - 4 easy
Bio Virus Colony Search VCS OriginalVCS 2016 4 hard*
Bio - - BaseVCS - 4 hard*
Bio Satin Bowerbird Optimizer SBO OriginalSBO 2017 5 easy
Bio - - BaseSBO - 5 easy
Bio Earthworm Optimisation Algorithm EOA OriginalEOA 2018 8 medium
Bio Wildebeest Herd Optimization WHO OriginalWHO 2019 12 hard
Bio Slime Mould Algorithm SMA OriginalSMA 2020 3 easy
Bio - - BaseSMA - 3 easy
Bio Barnacles Mating Optimizer BMO OriginalBMO 2018 3 easy
Bio Tunicate Swarm Algorithm TSA OriginalTSA 2020 2 easy
Bio Symbiotic Organisms Search SOS OriginalSOS 2014 2 medium
Bio Seagull Optimization Algorithm SOA OriginalSOA 2019 3 easy
Bio - - DevSOA - 3 easy
- - - - - - -
System Germinal Center Optimization GCO OriginalGCO 2018 4 medium
System - - BaseGCO - 4 medium
System Water Cycle Algorithm WCA OriginalWCA 2012 5 medium
System Artificial Ecosystem-based Optimization AEO OriginalAEO 2019 2 easy
System - - EnhancedAEO 2020 2 medium
System - - ModifiedAEO 2020 2 medium
System - - ImprovedAEO 2021 2 medium
System - - AdaptiveAEO - 2 medium
- - - - - - -
Math Hill Climbing HC OriginalHC 1993 3 easy
Math - - SwarmHC - 3 easy
Math Cross-Entropy Method CEM OriginalCEM 1997 4 easy
Math Sine Cosine Algorithm SCA OriginalSCA 2016 2 easy
Math - - BaseSCA - 2 easy
Math Gradient-Based Optimizer GBO OriginalGBO 2020 5 medium
Math Arithmetic Optimization Algorithm AOA OrginalAOA 2021 6 easy
Math Chaos Game Optimization CGO OriginalCGO 2021 2 easy
Math Pareto-like Sequential Sampling PSS OriginalPSS 2021 4 medium
Math weIghted meaN oF vectOrs INFO OriginalINFO 2022 2 medium
Math RUNge Kutta optimizer RUN OriginalRUN 2021 2 hard
Math Circle Search Algorithm CircleSA OriginalCircleSA 2022 3 easy
- - - - - - -
Music Harmony Search HS OriginalHS 2001 4 easy
Music - - BaseHS - 4 easy

A

  • ABC - Artificial Bee Colony

    • OriginalABC: Karaboga, D. (2005). An idea based on honey bee swarm for numerical optimization (Vol. 200, pp. 1-10). Technical report-tr06, Erciyes university, engineering faculty, computer engineering department.
  • ACOR - Ant Colony Optimization.

    • OriginalACOR: Socha, K., & Dorigo, M. (2008). Ant colony optimization for continuous domains. European journal of operational research, 185(3), 1155-1173.
  • ALO - Ant Lion Optimizer

    • OriginalALO: Mirjalili S (2015). “The Ant Lion Optimizer.” Advances in Engineering Software, 83, 80-98. doi: 10.1016/j.advengsoft.2015.01.010
    • BaseALO: The developed version
  • AEO - Artificial Ecosystem-based Optimization

    • OriginalAEO: Zhao, W., Wang, L., & Zhang, Z. (2019). Artificial ecosystem-based optimization: a novel nature-inspired meta-heuristic algorithm. Neural Computing and Applications, 1-43.
    • AdaptiveAEO: The adaptive version
    • ImprovedAEO: Rizk-Allah, R. M., & El-Fergany, A. A. (2020). Artificial ecosystem optimizer for parameters identification of proton exchange membrane fuel cells model. International Journal of Hydrogen Energy.
    • EnhancedAEO: Eid, A., Kamel, S., Korashy, A., & Khurshaid, T. (2020). An Enhanced Artificial Ecosystem-Based Optimization for Optimal Allocation of Multiple Distributed Generations. IEEE Access, 8, 178493-178513.
    • ModifiedAEO: Menesy, A. S., Sultan, H. M., Korashy, A., Banakhr, F. A., Ashmawy, M. G., & Kamel, S. (2020). Effective parameter extraction of different polymer electrolyte membrane fuel cell stack models using a modified artificial ecosystem optimization algorithm. IEEE Access, 8, 31892-31909.
  • ASO - Atom Search Optimization

    • OriginalASO: Zhao, W., Wang, L., & Zhang, Z. (2019). Atom search optimization and its application to solve a hydrogeologic parameter estimation problem. Knowledge-Based Systems, 163, 283-304.
  • ArchOA - Archimedes Optimization Algorithm

    • OriginalArchOA: Hashim, F. A., Hussain, K., Houssein, E. H., Mabrouk, M. S., & Al-Atabany, W. (2021). Archimedes optimization algorithm: a new metaheuristic algorithm for solving optimization problems. Applied Intelligence, 51(3), 1531-1551.
  • AOA - Arithmetic Optimization Algorithm

    • OriginalAOA: Abualigah, L., Diabat, A., Mirjalili, S., Abd Elaziz, M., & Gandomi, A. H. (2021). The arithmetic optimization algorithm. Computer methods in applied mechanics and engineering, 376, 113609.
  • AO - Aquila Optimizer

    • OriginalAO: Abualigah, L., Yousri, D., Abd Elaziz, M., Ewees, A. A., Al-qaness, M. A., & Gandomi, A. H. (2021). Aquila Optimizer: A novel meta-heuristic optimization Algorithm. Computers & Industrial Engineering, 157, 107250.
  • AVOA - African Vultures Optimization Algorithm

    • OriginalAVOA: Abdollahzadeh, B., Gharehchopogh, F. S., & Mirjalili, S. (2021). African vultures optimization algorithm: A new nature-inspired metaheuristic algorithm for global optimization problems. Computers & Industrial Engineering, 158, 107408.
  • AGTO - Artificial Gorilla Troops Optimization

    • OriginalAGTO: Abdollahzadeh, B., Soleimanian Gharehchopogh, F., & Mirjalili, S. (2021). Artificial gorilla troops optimizer: a new nature‐inspired metaheuristic algorithm for global optimization problems. International Journal of Intelligent Systems, 36(10), 5887-5958.
  • ARO - Artificial Rabbits Optimization:

    • OriginalARO: Wang, L., Cao, Q., Zhang, Z., Mirjalili, S., & Zhao, W. (2022). Artificial rabbits optimization: A new bio-inspired meta-heuristic algorithm for solving engineering optimization problems. Engineering Applications of Artificial Intelligence, 114, 105082.

B

  • BFO - Bacterial Foraging Optimization

    • OriginalBFO: Passino, K. M. (2002). Biomimicry of bacterial foraging for distributed optimization and control. IEEE control systems magazine, 22(3), 52-67.
    • ABFO: Nguyen, T., Nguyen, B. M., & Nguyen, G. (2019, April). Building resource auto-scaler with functional-link neural network and adaptive bacterial foraging optimization. In International Conference on Theory and Applications of Models of Computation (pp. 501-517). Springer, Cham.
  • BeesA - Bees Algorithm

    • OriginalBeesA: Pham, D. T., Ghanbarzadeh, A., Koc, E., Otri, S., Rahim, S., & Zaidi, M. (2005). The bees algorithm. Technical Note, Manufacturing Engineering Centre, Cardiff University, UK.
    • ProbBeesA: The probabilitic version of: Pham, D. T., Ghanbarzadeh, A., Koç, E., Otri, S., Rahim, S., & Zaidi, M. (2006). The bees algorithm—a novel tool for complex optimisation problems. In Intelligent production machines and systems (pp. 454-459). Elsevier Science Ltd.
  • BBO - Biogeography-Based Optimization

    • OriginalBBO: Simon, D. (2008). Biogeography-based optimization. IEEE transactions on evolutionary computation, 12(6), 702-713.
    • BaseBBO: The developed version
  • BA - Bat Algorithm

    • OriginalBA: Yang, X. S. (2010). A new metaheuristic bat-inspired algorithm. In Nature inspired cooperative strategies for optimization (NICSO 2010) (pp. 65-74). Springer, Berlin, Heidelberg.
    • AdaptiveBA: Wang, X., Wang, W. and Wang, Y., 2013, July. An adaptive bat algorithm. In International Conference on Intelligent Computing(pp. 216-223). Springer, Berlin, Heidelberg.
    • ModifiedBA: Dong, H., Li, T., Ding, R. and Sun, J., 2018. A novel hybrid genetic algorithm with granular information for feature selection and optimization. Applied Soft Computing, 65, pp.33-46.
  • BSO - Brain Storm Optimization

    • OriginalBSO: . Shi, Y. (2011, June). Brain storm optimization algorithm. In International conference in swarm intelligence (pp. 303-309). Springer, Berlin, Heidelberg.
    • ImprovedBSO: El-Abd, M., 2017. Global-best brain storm optimization algorithm. Swarm and evolutionary computation, 37, pp.27-44.
  • BSA - Bird Swarm Algorithm

    • OriginalBSA: Meng, X. B., Gao, X. Z., Lu, L., Liu, Y., & Zhang, H. (2016). A new bio-inspired optimisation algorithm:Bird Swarm Algorithm. Journal of Experimental & Theoretical Artificial Intelligence, 28(4), 673-687.
  • BMO - Barnacles Mating Optimizer:

    • OriginalBMO: Sulaiman, M. H., Mustaffa, Z., Saari, M. M., Daniyal, H., Daud, M. R., Razali, S., & Mohamed, A. I. (2018, June). Barnacles mating optimizer: a bio-inspired algorithm for solving optimization problems. In 2018 19th IEEE/ACIS International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing (SNPD) (pp. 265-270). IEEE.
  • BES - Bald Eagle Search

    • OriginalBES: Alsattar, H. A., Zaidan, A. A., & Zaidan, B. B. (2019). Novel meta-heuristic bald eagle search optimisation algorithm. Artificial Intelligence Review, 1-28.
  • BRO - Battle Royale Optimization

    • OriginalBRO: Rahkar Farshi, T. (2020). Battle royale optimization algorithm. Neural Computing and Applications, 1-19.
    • BaseBRO: The developed version

C

  • CA - Culture Algorithm

    • OriginalCA: Reynolds, R.G., 1994, February. An introduction to cultural algorithms. In Proceedings of the third annual conference on evolutionary programming (Vol. 24, pp. 131-139). River Edge, NJ: World Scientific.
  • CEM - Cross Entropy Method

    • OriginalCEM: Rubinstein, R. (1999). The cross-entropy method for combinatorial and continuous optimization. Methodology and computing in applied probability, 1(2), 127-190.
  • CSO - Cat Swarm Optimization

    • OriginalCSO: Chu, S. C., Tsai, P. W., & Pan, J. S. (2006, August). Cat swarm optimization. In Pacific Rim international conference on artificial intelligence (pp. 854-858). Springer, Berlin, Heidelberg.
  • CSA - Cuckoo Search Algorithm

    • OriginalCSA: Yang, X. S., & Deb, S. (2009, December). Cuckoo search via Lévy flights. In 2009 World congress on nature & biologically inspired computing (NaBIC) (pp. 210-214). Ieee.
  • CRO - Coral Reefs Optimization

    • OriginalCRO: Salcedo-Sanz, S., Del Ser, J., Landa-Torres, I., Gil-López, S., & Portilla-Figueras, J. A. (2014). The coral reefs optimization algorithm: a novel metaheuristic for efficiently solving optimization problems. The Scientific World Journal, 2014.
    • OCRO: Nguyen, T., Nguyen, T., Nguyen, B. M., & Nguyen, G. (2019). Efficient time-series forecasting using neural network and opposition-based coral reefs optimization. International Journal of Computational Intelligence Systems, 12(2), 1144-1161.
  • COA - Coyote Optimization Algorithm

    • OriginalCOA: Pierezan, J., & Coelho, L. D. S. (2018, July). Coyote optimization algorithm: a new metaheuristic for global optimization problems. In 2018 IEEE congress on evolutionary computation (CEC) (pp. 1-8). IEEE.
  • CHIO - Coronavirus Herd Immunity Optimization

    • OriginalCHIO: Al-Betar, M. A., Alyasseri, Z. A. A., Awadallah, M. A., & Abu Doush, I. (2021). Coronavirus herd immunity optimizer (CHIO). Neural Computing and Applications, 33(10), 5011-5042.
    • BaseCHIO: The developed version
  • CGO - Chaos Game Optimization

    • OriginalCGO: Talatahari, S., & Azizi, M. (2021). Chaos Game Optimization: a novel metaheuristic algorithm. Artificial Intelligence Review, 54(2), 917-1004.
  • CSA - Circle Search Algorithm

    • OriginalCSA: Qais, M. H., Hasanien, H. M., Turky, R. A., Alghuwainem, S., Tostado-Véliz, M., & Jurado, F. (2022). Circle Search Algorithm: A Geometry-Based Metaheuristic Optimization Algorithm. Mathematics, 10(10), 1626.

D

  • DE - Differential Evolution

    • BaseDE: Storn, R., & Price, K. (1997). Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. Journal of global optimization, 11(4), 341-359.
    • JADE: Zhang, J., & Sanderson, A. C. (2009). JADE: adaptive differential evolution with optional external archive. IEEE Transactions on evolutionary computation, 13(5), 945-958.
    • SADE: Qin, A. K., & Suganthan, P. N. (2005, September). Self-adaptive differential evolution algorithm for numerical optimization. In 2005 IEEE congress on evolutionary computation (Vol. 2, pp. 1785-1791). IEEE.
    • SHADE: Tanabe, R., & Fukunaga, A. (2013, June). Success-history based parameter adaptation for differential evolution. In 2013 IEEE congress on evolutionary computation (pp. 71-78). IEEE.
    • L_SHADE: Tanabe, R., & Fukunaga, A. S. (2014, July). Improving the search performance of SHADE using linear population size reduction. In 2014 IEEE congress on evolutionary computation (CEC) (pp. 1658-1665). IEEE.
    • SAP_DE: Teo, J. (2006). Exploring dynamic self-adaptive populations in differential evolution. Soft Computing, 10(8), 673-686.
  • DSA - Differential Search Algorithm (not done)

    • BaseDSA: Civicioglu, P. (2012). Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm. Computers & Geosciences, 46, 229-247.
  • DO - Dragonfly Optimization

    • OriginalDO: Mirjalili, S. (2016). Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Computing and Applications, 27(4), 1053-1073.
  • DMOA - Dwarf Mongoose Optimization Algorithm

    • OriginalDMOA: Agushaka, J. O., Ezugwu, A. E., & Abualigah, L. (2022). Dwarf mongoose optimization algorithm. Computer methods in applied mechanics and engineering, 391, 114570.
    • DevDMOA: The developed version

E

  • ES - Evolution Strategies .

    • OriginalES: Schwefel, H. P. (1984). Evolution strategies: A family of non-linear optimization techniques based on imitating some principles of organic evolution. Annals of Operations Research, 1(2), 165-167.
    • LevyES: Zhang, S., & Salari, E. (2005). Competitive learning vector quantization with evolution strategies for image compression. Optical Engineering, 44(2), 027006.
  • EP - Evolutionary programming .

    • OriginalEP: Fogel, L. J. (1994). Evolutionary programming in perspective: The top-down view. Computational intelligence: Imitating life.
    • LevyEP: Lee, C.Y. and Yao, X., 2001, May. Evolutionary algorithms with adaptive lévy mutations. In Proceedings of the 2001 congress on evolutionary computation (IEEE Cat. No. 01TH8546) (Vol. 1, pp. 568-575). IEEE.
  • EHO - Elephant Herding Optimization .

    • OriginalEHO: Wang, G. G., Deb, S., & Coelho, L. D. S. (2015, December). Elephant herding optimization. In 2015 3rd International Symposium on Computational and Business Intelligence (ISCBI) (pp. 1-5). IEEE.
  • EFO - Electromagnetic Field Optimization .

    • OriginalEFO:Abedinpourshotorban, H., Shamsuddin, S. M., Beheshti, Z., & Jawawi, D. N. (2016). Electromagnetic field optimization: A physics-inspired metaheuristic optimization algorithm. Swarm and Evolutionary Computation, 26, 8-22.
    • BaseEFO: The developed version
  • EOA - Earthworm Optimisation Algorithm .

    • OriginalEOA: Wang, G. G., Deb, S., & dos Santos Coelho, L. (2018). Earthworm optimisation algorithm: a bio-inspired metaheuristic algorithm for global optimisation problems. IJBIC, 12(1), 1-22.
  • EO - Equilibrium Optimizer .

    • OriginalEO: Faramarzi, A., Heidarinejad, M., Stephens, B., & Mirjalili, S. (2019). Equilibrium optimizer: A novel optimization algorithm. Knowledge-Based Systems.
    • ModifiedEO: Gupta, S., Deep, K., & Mirjalili, S. (2020). An efficient equilibrium optimizer with mutation strategy for numerical optimization. Applied Soft Computing, 96, 106542.
    • AdaptiveEO: Wunnava, A., Naik, M. K., Panda, R., Jena, B., & Abraham, A. (2020). A novel interdependence based multilevel thresholding technique using adaptive equilibrium optimizer. Engineering Applications of Artificial Intelligence, 94, 103836.

F

  • FFA - Firefly Algorithm

    • OriginalFFA: Łukasik, S., & Żak, S. (2009, October). Firefly algorithm for continuous constrained optimization tasks. In International conference on computational collective intelligence (pp. 97-106). Springer, Berlin, Heidelberg.
  • FA - Fireworks algorithm

    • OriginalFA: Tan, Y., & Zhu, Y. (2010, June). Fireworks algorithm for optimization. In International conference in swarm intelligence (pp. 355-364). Springer, Berlin, Heidelberg.
  • FPA - Flower Pollination Algorithm

    • OriginalFPA: Yang, X. S. (2012, September). Flower pollination algorithm for global optimization. In International conference on unconventional computing and natural computation (pp. 240-249). Springer, Berlin, Heidelberg.
  • FOA - Fruit-fly Optimization Algorithm

    • OriginalFOA: Pan, W. T. (2012). A new fruit fly optimization algorithm: taking the financial distress model as an example. Knowledge-Based Systems, 26, 69-74.
    • BaseFOA: The developed version
    • WhaleFOA: Fan, Y., Wang, P., Heidari, A. A., Wang, M., Zhao, X., Chen, H., & Li, C. (2020). Boosted hunting-based fruit fly optimization and advances in real-world problems. Expert Systems with Applications, 159, 113502.
  • FBIO - Forensic-Based Investigation Optimization

    • OriginalFBIO: Chou, J.S. and Nguyen, N.M., 2020. FBI inspired meta-optimization. Applied Soft Computing, p.106339.
    • BaseFBIO: Fathy, A., Rezk, H. and Alanazi, T.M., 2021. Recent approach of forensic-based investigation algorithm for optimizing fractional order PID-based MPPT with proton exchange membrane fuel cell.IEEE Access,9, pp.18974-18992.
  • FHO - Fire Hawk Optimization

    • OriginalFHO: Azizi, M., Talatahari, S., & Gandomi, A. H. (2022). Fire Hawk Optimizer: a novel metaheuristic algorithm. Artificial Intelligence Review, 1-77.

G

  • GA - Genetic Algorithm

    • BaseGA: Holland, J. H. (1992). Genetic algorithms. Scientific american, 267(1), 66-73.
    • SingleGA: De Falco, I., Della Cioppa, A. and Tarantino, E., 2002. Mutation-based genetic algorithm: performance evaluation. Applied Soft Computing, 1(4), pp.285-299.
    • MultiGA: De Jong, K.A. and Spears, W.M., 1992. A formal analysis of the role of multi-point crossover in genetic algorithms. Annals of mathematics and Artificial intelligence, 5(1), pp.1-26.
    • EliteSingleGA: Elite version of Single-point mutation GA
    • EliteMultiGA: Elite version of Multiple-point mutation GA
  • GWO - Grey Wolf Optimizer

    • OriginalGWO: Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014). Grey wolf optimizer. Advances in engineering software, 69, 46-61.
    • RW_GWO: Gupta, S., & Deep, K. (2019). A novel random walk grey wolf optimizer. Swarm and evolutionary computation, 44, 101-112.
    • GWO_WOA: Obadina, O. O., Thaha, M. A., Althoefer, K., & Shaheed, M. H. (2022). Dynamic characterization of a master–slave robotic manipulator using a hybrid grey wolf–whale optimization algorithm. Journal of Vibration and Control, 28(15-16), 1992-2003.
  • GOA - Grasshopper Optimisation Algorithm

    • OriginalGOA: Saremi, S., Mirjalili, S., & Lewis, A. (2017). Grasshopper optimisation algorithm: theory and application. Advances in Engineering Software, 105, 30-47.
  • GCO - Germinal Center Optimization

    • OriginalGCO: Villaseñor, C., Arana-Daniel, N., Alanis, A. Y., López-Franco, C., & Hernandez-Vargas, E. A. (2018). Germinal center optimization algorithm. International Journal of Computational Intelligence Systems, 12(1), 13-27.
    • BaseGCO: The developed version
  • GSKA - Gaining Sharing Knowledge-based Algorithm

    • OriginalGSKA: Mohamed, A. W., Hadi, A. A., & Mohamed, A. K. (2019). Gaining-sharing knowledge based algorithm for solving optimization problems: a novel nature-inspired algorithm. International Journal of Machine Learning and Cybernetics, 1-29.
    • BaseGSKA: Mohamed, A.W., Hadi, A.A., Mohamed, A.K. and Awad, N.H., 2020, July. Evaluating the performance of adaptive GainingSharing knowledge based algorithm on CEC 2020 benchmark problems. In 2020 IEEE Congress on Evolutionary Computation (CEC) (pp. 1-8). IEEE.
  • GBO - Gradient-Based Optimizer

    • OriginalGBO: Ahmadianfar, I., Bozorg-Haddad, O., & Chu, X. (2020). Gradient-based optimizer: A new metaheuristic optimization algorithm. Information Sciences, 540, 131-159.

H

  • HC - Hill Climbing .

    • OriginalHC: Talbi, E. G., & Muntean, T. (1993, January). Hill-climbing, simulated annealing and genetic algorithms: a comparative study and application to the mapping problem. In [1993] Proceedings of the Twenty-sixth Hawaii International Conference on System Sciences (Vol. 2, pp. 565-573). IEEE.
    • SwarmHC: The developed version based on swarm-based idea (Original is single-solution based method)
  • HS - Harmony Search .

    • OriginalHS: Geem, Z. W., Kim, J. H., & Loganathan, G. V. (2001). A new heuristic optimization algorithm:harmony search. simulation, 76(2), 60-68.
    • BaseHS: The developed version
  • HHO - Harris Hawks Optimization .

    • OriginalHHO: Heidari, A. A., Mirjalili, S., Faris, H., Aljarah, I., Mafarja, M., & Chen, H. (2019). Harris hawks optimization: Algorithm and applications. Future Generation Computer Systems, 97, 849-872.
  • HGSO - Henry Gas Solubility Optimization .

    • OriginalHGSO: Hashim, F. A., Houssein, E. H., Mabrouk, M. S., Al-Atabany, W., & Mirjalili, S. (2019). Henry gas solubility optimization: A novel physics-based algorithm. Future Generation Computer Systems, 101, 646-667.
  • HGS - Hunger Games Search .

    • OriginalHGS: Yang, Y., Chen, H., Heidari, A. A., & Gandomi, A. H. (2021). Hunger games search:Visions, conception, implementation, deep analysis, perspectives, and towards performance shifts. Expert Systems with Applications, 177, 114864.
  • HHOA - Horse Herd Optimization Algorithm (not done) .

    • BaseHHOA: MiarNaeimi, F., Azizyan, G., & Rashki, M. (2021). Horse herd optimization algorithm: A nature-inspired algorithm for high-dimensional optimization problems. Knowledge-Based Systems, 213, 106711.
  • HBA - Honey Badger Algorithm:

    • OriginalHBA: Hashim, F. A., Houssein, E. H., Hussain, K., Mabrouk, M. S., & Al-Atabany, W. (2022). Honey Badger Algorithm: New metaheuristic algorithm for solving optimization problems. Mathematics and Computers in Simulation, 192, 84-110.

I

  • IWO - Invasive Weed Optimization .

    • OriginalIWO: Mehrabian, A. R., & Lucas, C. (2006). A novel numerical optimization algorithm inspired from weed colonization. Ecological informatics, 1(4), 355-366.
  • ICA - Imperialist Competitive Algorithm

    • OriginalICA: Atashpaz-Gargari, E., & Lucas, C. (2007, September). Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. In 2007 IEEE congress on evolutionary computation (pp. 4661-4667). Ieee.
  • INFO - weIghted meaN oF vectOrs:

    • OriginalINFO: Ahmadianfar, I., Heidari, A. A., Gandomi, A. H., Chu, X., & Chen, H. (2021). RUN beyond the metaphor: An efficient optimization algorithm based on Runge Kutta method. Expert Systems with Applications, 181, 115079.

J

  • JA - Jaya Algorithm
    • OriginalJA: Rao, R. (2016). Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems. International Journal of Industrial Engineering Computations, 7(1), 19-34.
    • BaseJA: The developed version
    • LevyJA: Iacca, G., dos Santos Junior, V. C., & de Melo, V. V. (2021). An improved Jaya optimization algorithm with Levy flight. Expert Systems with Applications, 165, 113902.

K

L

  • LCO - Life Choice-based Optimization
    • OriginalLCO: Khatri, A., Gaba, A., Rana, K. P. S., & Kumar, V. (2019). A novel life choice-based optimizer. Soft Computing, 1-21.
    • BaseLCO: The developed version
    • ImprovedLCO: The improved version using Gaussian distribution and Mutation Mechanism

M

  • MA - Memetic Algorithm

    • OriginalMA: Moscato, P. (1989). On evolution, search, optimization, genetic algorithms and martial arts: Towards memetic algorithms. Caltech concurrent computation program, C3P Report, 826, 1989.
  • MFO - Moth Flame Optimization

    • OriginalMFO: Mirjalili, S. (2015). Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowledge-based systems, 89, 228-249.
    • BaseMFO: The developed version
  • MVO - Multi-Verse Optimizer

    • OriginalMVO: Mirjalili, S., Mirjalili, S. M., & Hatamlou, A. (2016). Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Computing and Applications, 27(2), 495-513.
    • BaseMVO: The developed version
  • MSA - Moth Search Algorithm

    • OriginalMSA: Wang, G. G. (2018). Moth search algorithm: a bio-inspired metaheuristic algorithm for global optimization problems. Memetic Computing, 10(2), 151-164.
  • MRFO - Manta Ray Foraging Optimization

    • OriginalMRFO: Zhao, W., Zhang, Z., & Wang, L. (2020). Manta ray foraging optimization: An effective bio-inspired optimizer for engineering applications. Engineering Applications of Artificial Intelligence, 87, 103300.
  • MPA - Marine Predators Algorithm:

    • OriginalMPA: Faramarzi, A., Heidarinejad, M., Mirjalili, S., & Gandomi, A. H. (2020). Marine Predators Algorithm: A nature-inspired metaheuristic. Expert systems with applications, 152, 113377.

N

  • NRO - Nuclear Reaction Optimization

    • OriginalNRO: Wei, Z., Huang, C., Wang, X., Han, T., & Li, Y. (2019). Nuclear Reaction Optimization: A novel and powerful physics-based algorithm for global optimization. IEEE Access.
  • NMRA - Nake Mole-Rat Algorithm

    • OriginalNMRA: Salgotra, R., & Singh, U. (2019). The naked mole-rat algorithm. Neural Computing and Applications, 31(12), 8837-8857.
    • ImprovedNMRA: Singh, P., Mittal, N., Singh, U. and Salgotra, R., 2021. Naked mole-rat algorithm with improved exploration and exploitation capabilities to determine 2D and 3D coordinates of sensor nodes in WSNs. Arabian Journal for Science and Engineering, 46(2), pp.1155-1178.

O

P

  • PSO - Particle Swarm Optimization

    • OriginalPSO: Eberhart, R., & Kennedy, J. (1995, October). A new optimizer using particle swarm theory. In MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science (pp. 39-43). Ieee.
    • PPSO: Ghasemi, M., Akbari, E., Rahimnejad, A., Razavi, S. E., Ghavidel, S., & Li, L. (2019). Phasor particle swarm optimization: a simple and efficient variant of PSO. Soft Computing, 23(19), 9701-9718.
    • HPSO_TVAC: Ghasemi, M., Aghaei, J., & Hadipour, M. (2017). New self-organising hierarchical PSO with jumping time-varying acceleration coefficients. Electronics Letters, 53(20), 1360-1362.
    • C_PSO: Liu, B., Wang, L., Jin, Y. H., Tang, F., & Huang, D. X. (2005). Improved particle swarm optimization combined with chaos. Chaos, Solitons & Fractals, 25(5), 1261-1271.
    • CL_PSO: Liang, J. J., Qin, A. K., Suganthan, P. N., & Baskar, S. (2006). Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE transactions on evolutionary computation, 10(3), 281-295.
  • PFA - Pathfinder Algorithm

    • OriginalPFA: Yapici, H., & Cetinkaya, N. (2019). A new meta-heuristic optimizer: Pathfinder algorithm. Applied Soft Computing, 78, 545-568.
  • PSS - Pareto-like Sequential Sampling

    • OriginalPSS: Shaqfa, M., & Beyer, K. (2021). Pareto-like sequential sampling heuristic for global optimisation. Soft Computing, 25(14), 9077-9096.

Q

  • QSA - Queuing Search Algorithm
    • OriginalQSA: Zhang, J., Xiao, M., Gao, L., & Pan, Q. (2018). Queuing search algorithm: A novel metaheuristic algorithm for solving engineering optimization problems. Applied Mathematical Modelling, 63, 464-490.
    • BaseQSA: The developed version
    • OppoQSA: Zheng, X. and Nguyen, H., 2022. A novel artificial intelligent model for predicting water treatment efficiency of various biochar systems based on artificial neural network and queuing search algorithm. Chemosphere, 287, p.132251.
    • LevyQSA: Abderazek, H., Hamza, F., Yildiz, A.R., Gao, L. and Sait, S.M., 2021. A comparative analysis of the queuing search algorithm, the sine-cosine algorithm, the ant lion algorithm to determine the optimal weight design problem of a spur gear drive system. Materials Testing, 63(5), pp.442-447.
    • ImprovedQSA: Nguyen, B.M., Hoang, B., Nguyen, T. and Nguyen, G., 2021. nQSV-Net: a novel queuing search variant for global space search and workload modeling. Journal of Ambient Intelligence and Humanized Computing, 12(1), pp.27-46.

R

  • RUN - RUNge Kutta optimizer:
    • OriginalRUN: Ahmadianfar, I., Heidari, A. A., Gandomi, A. H., Chu, X., & Chen, H. (2021). RUN beyond the metaphor: An efficient optimization algorithm based on Runge Kutta method. Expert Systems with Applications, 181, 115079.

S

  • SA - Simulated Annealling

    • OriginalSA: . Van Laarhoven, P. J., & Aarts, E. H. (1987). Simulated annealing. In Simulated annealing: Theory and applications (pp. 7-15). Springer, Dordrecht.
  • SSpiderO - Social Spider Optimization

    • OriginalSSpiderO: Cuevas, E., Cienfuegos, M., ZaldíVar, D., & Pérez-Cisneros, M. (2013). A swarm optimization algorithm inspired in the behavior of the social-spider. Expert Systems with Applications, 40(16), 6374-6384.
  • SOS - Symbiotic Organisms Search:

    • OriginalSOS: Cheng, M. Y., & Prayogo, D. (2014). Symbiotic organisms search: a new metaheuristic optimization algorithm. Computers & Structures, 139, 98-112.
  • SSpiderA - Social Spider Algorithm

    • OriginalSSpiderA: James, J. Q., & Li, V. O. (2015). A social spider algorithm for global optimization. Applied Soft Computing, 30, 614-627.
  • SCA - Sine Cosine Algorithm

    • OriginalSCA: Mirjalili, S. (2016). SCA: a sine cosine algorithm for solving optimization problems. Knowledge-Based Systems, 96, 120-133.
    • BaseSCA: Attia, A.F., El Sehiemy, R.A. and Hasanien, H.M., 2018. Optimal power flow solution in power systems using a novel Sine-Cosine algorithm. International Journal of Electrical Power & Energy Systems, 99, pp.331-343.
  • SRSR - Swarm Robotics Search And Rescue

    • OriginalSRSR: Bakhshipour, M., Ghadi, M. J., & Namdari, F. (2017). Swarm robotics search & rescue: A novel artificial intelligence-inspired optimization approach. Applied Soft Computing, 57, 708-726.
  • SBO - Satin Bowerbird Optimizer

    • OriginalSBO: Moosavi, S. H. S., & Bardsiri, V. K. (2017). Satin bowerbird optimizer: a new optimization algorithm to optimize ANFIS for software development effort estimation. Engineering Applications of Artificial Intelligence, 60, 1-15.
    • BaseSBO: The developed version
  • SHO - Spotted Hyena Optimizer

    • OriginalSHO: Dhiman, G., & Kumar, V. (2017). Spotted hyena optimizer: a novel bio-inspired based metaheuristic technique for engineering applications. Advances in Engineering Software, 114, 48-70.
  • SSO - Salp Swarm Optimization

    • OriginalSSO: Mirjalili, S., Gandomi, A. H., Mirjalili, S. Z., Saremi, S., Faris, H., & Mirjalili, S. M. (2017). Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems. Advances in Engineering Software, 114, 163-191.
  • SFO - Sailfish Optimizer

    • OriginalSFO: Shadravan, S., Naji, H. R., & Bardsiri, V. K. (2019). The Sailfish Optimizer: A novel nature-inspired metaheuristic algorithm for solving constrained engineering optimization problems. Engineering Applications of Artificial Intelligence, 80, 20-34.
    • ImprovedSFO: Li, L.L., Shen, Q., Tseng, M.L. and Luo, S., 2021. Power system hybrid dynamic economic emission dispatch with wind energy based on improved sailfish algorithm. Journal of Cleaner Production, 316, p.128318.
  • SARO - Search And Rescue Optimization

    • OriginalSARO: Shabani, A., Asgarian, B., Gharebaghi, S. A., Salido, M. A., & Giret, A. (2019). A New Optimization Algorithm Based on Search and Rescue Operations. Mathematical Problems in Engineering, 2019.
    • BaseSARO: The developed version using Levy-flight
  • SSDO - Social Ski-Driver Optimization

    • OriginalSSDO: Tharwat, A., & Gabel, T. (2019). Parameters optimization of support vector machines for imbalanced data using social ski driver algorithm. Neural Computing and Applications, 1-14.
  • SLO - Sea Lion Optimization

    • OriginalSLO: Masadeh, R., Mahafzah, B. A., & Sharieh, A. (2019). Sea Lion Optimization Algorithm. Sea, 10(5).
    • ImprovedSLO: The developed version
    • ModifiedSLO: Masadeh, R., Alsharman, N., Sharieh, A., Mahafzah, B.A. and Abdulrahman, A., 2021. Task scheduling on cloud computing based on sea lion optimization algorithm. International Journal of Web Information Systems.
  • Seagull Optimization Algorithm

    • OriginalSOA: Dhiman, G., & Kumar, V. (2019). Seagull optimization algorithm: Theory and its applications for large-scale industrial engineering problems. Knowledge-based systems, 165, 169-196.
    • DevSOA: The developed version
  • SMA - Slime Mould Algorithm

    • OriginalSMA: Li, S., Chen, H., Wang, M., Heidari, A. A., & Mirjalili, S. (2020). Slime mould algorithm: A new method for stochastic optimization. Future Generation Computer Systems.
    • BaseSMA: The developed version
  • SSA - Sparrow Search Algorithm

    • OriginalSSA: Jiankai Xue & Bo Shen (2020) A novel swarm intelligence optimization approach: sparrow search algorithm, Systems Science & Control Engineering, 8:1, 22-34, DOI: 10.1080/21642583.2019.1708830
    • BaseSSA: The developed version
  • SPBO - Student Psychology Based Optimization

    • OriginalSPBO: Das, B., Mukherjee, V., & Das, D. (2020). Student psychology based optimization algorithm: A new population based optimization algorithm for solving optimization problems. Advances in Engineering software, 146, 102804.
    • DevSPBO: The developed version
  • SCSO - Sand Cat Swarm Optimization

    • OriginalSCSO: Seyyedabbasi, A., & Kiani, F. (2022). Sand Cat swarm optimization: a nature-inspired algorithm to solve global optimization problems. Engineering with Computers, 1-25.

T

  • TLO - Teaching Learning Optimization

    • OriginalTLO: Rao, R. V., Savsani, V. J., & Vakharia, D. P. (2011). Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Computer-Aided Design, 43(3), 303-315.
    • BaseTLO: Rao, R., & Patel, V. (2012). An elitist teaching-learning-based optimization algorithm for solving complex constrained optimization problems. International Journal of Industrial Engineering Computations, 3(4), 535-560.
    • ImprovedTLO: Rao, R. V., & Patel, V. (2013). An improved teaching-learning-based optimization algorithm for solving unconstrained optimization problems. Scientia Iranica, 20(3), 710-720.
  • TWO - Tug of War Optimization

    • OriginalTWO: Kaveh, A., & Zolghadr, A. (2016). A novel meta-heuristic algorithm: tug of war optimization. Iran University of Science & Technology, 6(4), 469-492.
    • OppoTWO: Kaveh, A., Almasi, P. and Khodagholi, A., 2022. Optimum Design of Castellated Beams Using Four Recently Developed Meta-heuristic Algorithms. Iranian Journal of Science and Technology, Transactions of Civil Engineering, pp.1-13.
    • LevyTWO: The developed version using Levy-flight
    • ImprovedTWO: Nguyen, T., Hoang, B., Nguyen, G., & Nguyen, B. M. (2020). A new workload prediction model using extreme learning machine and enhanced tug of war optimization. Procedia Computer Science, 170, 362-369.
  • TSA - Tunicate Swarm Algorithm

    • OriginalTSA: Kaur, S., Awasthi, L. K., Sangal, A. L., & Dhiman, G. (2020). Tunicate Swarm Algorithm: A new bio-inspired based metaheuristic paradigm for global optimization. Engineering Applications of Artificial Intelligence, 90, 103541.
  • TSO - Tuna Swarm Optimization

    • OriginalTSO: Xie, L., Han, T., Zhou, H., Zhang, Z. R., Han, B., & Tang, A. (2021). Tuna swarm optimization: a novel swarm-based metaheuristic algorithm for global optimization. Computational intelligence and Neuroscience, 2021.

U

V

  • VCS - Virus Colony Search
    • OriginalVCS: Li, M. D., Zhao, H., Weng, X. W., & Han, T. (2016). A novel nature-inspired algorithm for optimization: Virus colony search. Advances in Engineering Software, 92, 65-88.
    • BaseVCS: The developed version

W

  • WCA - Water Cycle Algorithm

    • OriginalWCA: Eskandar, H., Sadollah, A., Bahreininejad, A., & Hamdi, M. (2012). Water cycle algorithm–A novel metaheuristic optimization method for solving constrained engineering optimization problems. Computers & Structures, 110, 151-166.
  • WOA - Whale Optimization Algorithm

    • OriginalWOA: Mirjalili, S., & Lewis, A. (2016). The whale optimization algorithm. Advances in engineering software, 95, 51-67.
    • HI_WOA: Tang, C., Sun, W., Wu, W., & Xue, M. (2019, July). A hybrid improved whale optimization algorithm. In 2019 IEEE 15th International Conference on Control and Automation (ICCA) (pp. 362-367). IEEE.
  • WHO - Wildebeest Herd Optimization

    • OriginalWHO: Amali, D., & Dinakaran, M. (2019). Wildebeest herd optimization: A new global optimization algorithm inspired by wildebeest herding behaviour. Journal of Intelligent & Fuzzy Systems, (Preprint), 1-14.
  • WDO - Wind Driven Optimization

    • OriginalWDO: Bayraktar, Z., Komurcu, M., & Werner, D. H. (2010, July). Wind Driven Optimization (WDO): A novel nature-inspired optimization algorithm and its application to electromagnetics. In 2010 IEEE antennas and propagation society international symposium (pp. 1-4). IEEE.

X

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