Citation Request

If you utilize MEALPY in your academic or professional research, we kindly request that you cite our foundational works to support the project:

@article{van2023mealpy,
    title={MEALPY: An open-source library for latest meta-heuristic algorithms in Python},
    author={Van Thieu, Nguyen and Mirjalili, Seyedali},
    journal={Journal of Systems Architecture},
    year={2023},
    publisher={Elsevier},
    doi={10.1016/j.sysarc.2023.102871}
}

@article{van2023groundwater,
    title={Groundwater level modeling using Augmented Artificial Ecosystem Optimization},
    author={Van Thieu, Nguyen and Barma, Surajit Deb and Van Lam, To and Kisi, Ozgur and Mahesha, Amai},
    journal={Journal of Hydrology},
    volume={617},
    pages={129034},
    year={2023},
    publisher={Elsevier},
    doi={10.1016/j.jhydrol.2022.129034}
}

Note

Contact for Research & Collaboration

If you have an open-ended question, a research inquiry, or are interested in collaboration, feel free to contact the author directly at: nguyenthieu2102@gmail.com

Classification Table

The categorical breakdown below provides a conceptual taxonomy. For the foundational theory behind these classifications, you can refer to this research article. In general, algorithms are categorized according to core computational inspirations:

  • Evolutionary-based: Modeled after Darwinian natural selection and genetic adaptation mechanisms.

  • Swarm-based: Inspired by decentralized collective motion and social interactions found in nature (e.g., flocks, swarms, herds).

  • Physics-based: Derived from fundamental physical laws and universal phenomena (e.g., gravitation, thermal dynamics, multiverse models).

  • Human-based: Simulated from human cognitive activities, societal structures, and behavioral dynamics.

  • Biology-based: Rooted in biological systems, physiological behaviors, or cellular mechanics.

  • System-based: Emulating ecological stability, immune defense responses, or complex network interactions.

  • Math-based: Formulated directly from analytical functions or mathematical operations.

  • Music-based: Inspired by melodic harmonies, composition rules, or instrument tuning dynamics.

  • Sota-based: The state-of-the-art algorithm in CEC competitions.

All Implemented Optimizers

Group

Name

Module

Class

Year

Paras

Difficulty

Kind

Bio-inspired

Artificial Algae Algorithm

AAA

OriginalAAA

2015

5

medium

Original

Bio-inspired

Animated Oat Optimization Algorithm

AOO

OriginalAOO

2025

2

medium

Original

Bio-inspired

Artificial Protozoa Optimizer

APO

OriginalAPO

2024

4

medium

Original

Bio-inspired

Biogeography-Based Optimization

BBO

OriginalBBO

2008

4

easy

Original

Bio-inspired

Biogeography-Based Optimization (Dev)

*

DevBBO

*

4

easy

Developed

Bio-inspired

Brown-Bear Optimization Algorithm

BBOA

OriginalBBOA

2023

2

medium

Original

Bio-inspired

Bacterial Colony Optimization

BCO

OriginalBCO

2012

7

hard

Original

Bio-inspired

Barnacles Mating Optimizer

BMO

OriginalBMO

2020

3

easy

Original

Bio-inspired

Enzyme Action Optimizer

EAO

OriginalEAO

2025

3

easy

Original

Bio-inspired

Earthworm Optimisation Algorithm

EOA

OriginalEOA

2018

8

hard

Original

Bio-inspired

Invasive Weed Optimization

IWO

OriginalIWO

2006

7

medium

Original

Bio-inspired

Satin Bowerbird Optimizer

SBO

OriginalSBO

2017

5

easy

Original

Bio-inspired

Satin Bowerbird Optimizer (Dev)

*

DevSBO

*

5

easy

Developed

Bio-inspired

Secretary Bird Optimization Algorithm

SBOA

OriginalSBOA

2024

2

easy

Original

Bio-inspired

Slime Mould Algorithm

SMA

OriginalSMA

*

3

easy

Original

Bio-inspired

Slime Mould Algorithm (Dev)

*

DevSMA

*

3

easy

Developed

Bio-inspired

Seagull Optimization Algorithm

SOA

OriginalSOA

2019

3

easy

Original

Bio-inspired

Seagull Optimization Algorithm (Dev)

*

DevSOA

*

3

easy

Developed

Bio-inspired

Symbiotic Organisms Search

SOS

OriginalSOS

2014

2

easy

Original

Bio-inspired

Starfish Optimization Algorithm

StarfishOA

OriginalStarfishOA

2025

3

medium

Original

Bio-inspired

Tree Physiology Optimization

TPO

DevTPO

2017

5

nightmare

Developed

Bio-inspired

Tunicate Swarm Algorithm

TSA

OriginalTSA

2020

2

medium

Original

Bio-inspired

Tree-Seed Algorithm

TSeedA

OriginalTSeedA

2015

3

medium

Original

Bio-inspired

Virus Colony Search

VCS

OriginalVCS

2016

4

medium

Original

Bio-inspired

Virus Colony Search (Dev)

*

DevVCS

*

4

medium

Developed

Bio-inspired

Wildebeest Herd Optimization

WHO

OriginalWHO

2019

12

nightmare

Original

Evolutionary

Black Widow Optimization Algorithm

BWOA

OriginalBWOA

2020

5

medium

Original

Evolutionary

Coral Reefs Optimization

CRO

OriginalCRO

2014

11

hard

Original

Evolutionary

Opposition-based Coral Reefs Optimization

*

OCRO

2019

12

hard

Variant

Evolutionary

Differential Evolution

DE

OriginalDE

1995

5

easy

Original

Evolutionary

Adaptive Differential Evolution

*

JADE

2009

6

medium

Variant

Evolutionary

Self-Adaptive Differential Evolution

*

SADE

2005

2

medium

Variant

Evolutionary

Self-Adaptive Populations Differential Evolution

*

SAP_DE

2006

3

medium

Variant

Evolutionary

Evolutionary Programming

EP

OriginalEP

1999

3

easy

Original

Evolutionary

*

*

LevyEP

*

3

medium

Developed

Evolutionary

Evolution Strategies

ES

OriginalES

2002

3

easy

Original

Evolutionary

Covariance Matrix Adaptation Evolution Strategy

*

CMA_ES

2003

2

medium

Variant

Evolutionary

*

*

LevyES

*

3

medium

Developed

Evolutionary

Covariance Matrix Adaptation Evolution Strategy (Dev)

*

Simple_CMA_ES

*

2

medium

Developed

Evolutionary

Flower Pollination Algorithm

FPA

OriginalFPA

2012

4

easy

Original

Evolutionary

Genetic Algorithm

GA

BaseGA

1992

4

medium

Original

Evolutionary

Genetic Algorithm

*

OriginalGA

1992

9

medium

Original

Evolutionary

Single Point Mutation Genetic Algorithm (Dev)

*

SingleGA

*

8

medium

Developed

Evolutionary

Elite Single Point Mutation Genetic Algorithm (Dev)

*

EliteSingleGA

*

11

medium

Developed

Evolutionary

Multi Point Mutation Genetic Algorithm (Dev)

*

MultiGA

*

8

medium

Developed

Evolutionary

Elite Multi Point Mutation Genetic Algorithm (Dev)

*

EliteMultiGA

*

11

medium

Developed

Evolutionary

Memetic Algorithm

MA

OriginalMA

1989

7

hard

Original

Evolutionary

Success-History Adaptation Differential Evolution

SHADE

OriginalSHADE

2013

5

medium

Variant

Evolutionary

Success-History Adaptation Differential Evolution (Dev)

*

DevSHADE

2026

4

medium

Variant

Evolutionary

Linear Population Size Reduction Success-History Adaptation Differential Evolution

*

OriginalL_SHADE

2014

7

hard

Variant

Evolutionary

Linear Population Size Reduction Success-History Adaptation Differential Evolution (Dev)

*

DevL_SHADE

2026

4

hard

Variant

Game

Tianji’s Horse Racing Optimization

THRO

OriginalTHRO

2025

2

nightmare

Original

Human

Ali baba and the Forty Thieves

AFT

OriginalAFT

2022

2

easy

Original

Human

Battle Royale Optimization

BRO

OriginalBRO

2021

3

easy

Original

Human

Battle Royale Optimization (Dev)

*

DevBRO

*

3

easy

Developed

Human

Brain Storm Optimization

BSO

OriginalBSO

2011

8

medium

Original

Human

Brain Storm Optimization (Dev)

*

ImprovedBSO

*

7

medium

Developed

Human

Culture Algorithm

CA

OriginalCA

1994

3

easy

Original

Human

Child Drawing Development Optimization

CDDO

OriginalCDDO

2022

4

medium

Original

Human

Coronavirus Herd Immunity Optimization

CHIO

OriginalCHIO

2021

4

medium

Original

Human

Coronavirus Herd Immunity Optimization (Dev)

*

DevCHIO

*

4

medium

Developed

Human

Cultural History Optimization Algorithm

CHOA

OriginalCHOA

2025

6

hard

Original

Human

Dream Optimization Algorithm

DOA

OriginalDOA

2025

2

hard

Original

Human

Divine Religions Algorithm

DRA

OriginalDRA

2025

5

hard

Original

Human

Forensic-Based Investigation Optimization

FBIO

OriginalFBIO

2020

2

medium

Original

Human

Forensic-Based Investigation Optimization (Dev)

*

DevFBIO

*

2

medium

Developed

Human

Gaining Sharing Knowledge-based Algorithm

GSKA

OriginalGSKA

2020

6

medium

Original

Human

Gaining Sharing Knowledge-based Algorithm (Dev)

*

DevGSKA

*

4

medium

Developed

Human

Heap-based optimizer

HBO

OriginalHBO

2020

3

hard

Original

Human

Human Conception Optimizer

HCO

OriginalHCO

2022

6

medium

Original

Human

Imperialist Competitive Algorithm

ICA

OriginalICA

2007

8

hard

Original

Human

Incomprehensible but Intelligible-in-time Logics Algorithm

ILA

OriginalILA

2023

7

nightmare

Original

Human

Life Choice-based Optimization

LCO

OriginalLCO

2020

3

easy

Original

Human

Life Choice-based Optimization (Dev)

*

DevLCO

*

3

easy

Developed

Human

Life Choice-based Optimization (Dev)

*

ImprovedLCO

*

2

easy

Developed

Human

Market Game Optimization Algorithm

MGOA

OriginalMGOA

2025

3

easy

Original

Human

Political Optimizer

PO

OriginalPO

2020

3

hard

Original

Human

Queuing Search Algorithm

QSA

OriginalQSA

2018

2

medium

Original

Human

Novel Queuing Search Variant

*

ImprovedQSA

2021

2

medium

Variant

Human

Queuing Search Algorithm (Dev)

*

DevQSA

*

2

medium

Developed

Human

Queuing Search Algorithm (Dev)

*

OppoQSA

*

2

medium

Developed

Human

Queuing Search Algorithm (Dev)

*

LevyQSA

*

2

medium

Developed

Human

Search And Rescue Optimization

SARO

DevSARO

*

4

medium

Original

Human

Search And Rescue Optimization (Dev)

*

OriginalSARO

2019

4

medium

Developed

Human

Student Psychology Based Optimization

SPBO

OriginalSPBO

2020

2

easy

Original

Human

Student Psychology Based Optimization (Dev)

*

DevSPBO

*

2

easy

Developed

Human

Social Ski-Driver Optimization

SSDO

OriginalSSDO

2020

2

medium

Original

Human

Teaching Learning-based Optimization

TLO

OriginalTLO

2011

2

easy

Original

Human

Elitist Teaching Learning-based Optimization

*

ETLBO

2012

3

medium

Variant

Human

Improved Teaching-Learning-based Optimization

*

ImprovedTLO

2013

3

hard

Variant

Human

Teamwork Optimization Algorithm

TOA

OriginalTOA

2021

2

easy

Original

Human

War Strategy Optimization

WarSO

OriginalWarSO

2022

3

easy

Original

Mathematics

Arithmetic Optimization Algorithm

AOA

OriginalAOA

2021

6

medium

Original

Mathematics

Cross-Entropy Method

CEM

OriginalCEM

2005

4

easy

Original

Mathematics

Chaos Game Optimization

CGO

OriginalCGO

2021

2

easy

Original

Mathematics

Circle Search Algorithm

CircleSA

OriginalCircleSA

2022

3

easy

Original

Mathematics

Farthest Better or Nearest Worse Optimizer

FNO

OriginalFNO

2026

2

medium

Original

Mathematics

Gradient-Based Optimizer

GBO

OriginalGBO

2020

5

medium

Original

Mathematics

Geometric Mean Optimizer

GMO

OriginalGMO

2023

2

medium

Original

Mathematics

Hill Climbing

HC

OriginalHC

1993

3

easy

Original

Mathematics

Swarm-based Hill Climbing

*

SwarmHC

*

3

easy

Developed

Mathematics

weIghted meaN oF vectOrs

INFO

OriginalINFO

2022

2

medium

Original

Mathematics

Pareto-like Sequential Sampling

PSS

OriginalPSS

2021

4

medium

Original

Mathematics

Quadratic Interpolation Optimization

QIO

OriginalQIO

2023

2

hard

Original

Mathematics

RUNge Kutta Optimizer

RUN

OriginalRUN

2021

2

medium

Original

Mathematics

Sine Cosine Algorithm

SCA

OriginalSCA

2016

2

easy

Original

Mathematics

QLE Sine Cosine Algorithm

*

QleSCA

2022

4

hard

Variant

Mathematics

Sine Cosine Algorithm (Dev)

*

DevSCA

*

2

easy

Developed

Mathematics

Success History Intelligent Optimizer

SHIO

OriginalSHIO

2022

2

easy

Original

Mathematics

Tabu Search

TS

OriginalTS

2004

5

medium

Original

Music

Harmony Search

HS

OriginalHS

2001

4

easy

Original

Music

Harmony Search (Dev)

*

DevHS

*

4

easy

Developed

Physics

Archimedes Optimization Algorithm

ArchOA

OriginalArchOA

2021

8

medium

Original

Physics

Atom Search Optimization

ASO

OriginalASO

2019

4

hard

Original

Physics

Chernobyl Disaster Optimizer

CDO

OriginalCDO

2023

2

medium

Original

Physics

Cosmic Evolution Optimization

CEO

OriginalCEO

2025

5

hard

Original

Physics

Electromagnetic Field Optimization

EFO

DevEFO

*

6

medium

Original

Physics

Electromagnetic Field Optimization

*

OriginalEFO

2016

6

medium

Original

Physics

Equilibrium Optimizer

EO

OriginalEO

2020

2

medium

Original

Physics

Modified Equilibrium Optimizer

*

ModifiedEO

2020

2

medium

Variant

Physics

Adaptive Equilibrium Optimization

*

AdaptiveEO

2020

2

medium

Variant

Physics

Electrical Storm Optimization

ESO

OriginalESO

2025

2

hard

Original

Physics

Energy Valley Optimizer

EVO

OriginalEVO

2023

2

medium

Original

Physics

Flow Direction Algorithm

FDA

OriginalFDA

2021

3

medium

Original

Physics

Fick’s Law Algorithm

FLA

OriginalFLA

2023

8

nightmare

Original

Physics

General Relativity Search Algorithm

GRSA

OriginalGRSA

2015

7

hard

Original

Physics

Henry Gas Solubility Optimization

HGSO

OriginalHGSO

2019

3

hard

Original

Physics

Kirchhoff’s Law Algorithm

KLA

OriginalKLA

2025

2

medium

Original

Physics

Kepler Optimization Algorithm

KOA

OriginalKOA

2023

5

hard

Original

Physics

Light Spectrum Optimizer

LSO

OriginalLSO

2022

6

nightmare

Original

Physics

Light Spectrum Optimizer (Dev)

*

DevLSO

*

5

nightmare

Developed

Physics

Mirage Search Optimization

MSO

OriginalMSO

2025

2

medium

Original

Physics

Multi-Verse Optimizer

MVO

OriginalMVO

2016

4

medium

Original

Physics

Multi-Verse Optimizer (Dev)

*

DevMVO

2016

4

medium

Developed

Physics

Nuclear Reaction Optimization

NRO

OriginalNRO

2019

2

nightmare

Original

Physics

physical phenomenon of RIME-ice

RIME

OriginalRIME

2023

3

easy

Original

Physics

Simulated Annealing

SA

OriginalSA

1983

4

easy

Original

Physics

Simulated Annealing (Dev)

*

GaussianSA

*

5

easy

Developed

Physics

Simulated Annealing (Dev)

*

SwarmSA

*

9

easy

Developed

Physics

Stellar Oscillation Optimizer

SOO

OriginalSOO

2025

2

medium

Original

Physics

Schrodinger Optimizer

SRA

OriginalSRA

2025

2

medium

Original

Physics

Tug of War Optimization

TWO

OriginalTWO

2017

2

medium

Original

Physics

Enhanced Tug of War Optimization

*

EnhancedTWO

2020

2

medium

Variant

Physics

Tug of War Optimization (Dev)

*

OppoTWO

*

2

medium

Developed

Physics

Tug of War Optimization (Dev)

*

LevyTWO

*

2

medium

Developed

Physics

Wind Driven Optimization

WDO

OriginalWDO

2013

7

medium

Original

SOTA

Improved Multi-operator Differential Evolution Algorithm

IMODE

OriginalIMODE

2020

4

nightmare

SOTA

SOTA

Ensemble sinusoidal differential covariance matrix adaptation with Euclidean neighborhood

LSHADEcnEpSin

OriginalLSHADEcnEpSin

2017

9

nightmare

SOTA

Swarm

Artificial Bee Colony

ABC

OriginalABC

2007

3

medium

Original

Swarm

Ant Colony Optimization Continuous

ACOR

OriginalACOR

2008

5

medium

Original

Swarm

Artificial Gorilla Troops Optimization

AGTO

OriginalAGTO

2021

5

medium

Original

Swarm

Modified Gorilla Troops Optimization

*

MGTO

2023

3

medium

Variant

Swarm

Artificial Hummingbird Algorithm

AHA

OriginalAHA

2022

2

medium

Original

Swarm

Archerfish Hunting Optimizer

AHO

OriginalAHO

2022

4

hard

Original

Swarm

Ant Lion Optimizer

ALO

OriginalALO

2015

2

medium

Original

Swarm

Ant Lion Optimizer (Dev)

*

DevALO

*

2

medium

Developed

Swarm

Aquila Optimization

AO

OriginalAO

2021

2

easy

Original

Swarm

Adaptive Aquila Optimizer

*

AAO

2024

4

medium

Developed

Swarm

Artificial Rabbits Optimization

ARO

OriginalARO

2022

2

easy

Original

Swarm

Levy flight Artificial Rabbit Algorithm

*

LARO

2022

2

medium

Variant

Swarm

Improved Artificial Rabbits Optimization (Dev)

*

IARO

*

2

medium

Developed

Swarm

African Vultures Optimization Algorithm

AVOA

OriginalAVOA

2021

7

medium

Original

Swarm

Bat-inspired Algorithm

BA

OriginalBA

2010

6

medium

Original

Swarm

Adaptive Bat-inspired Algorithm (Dev)

*

AdaptiveBA

*

8

medium

Developed

Swarm

Bat-inspired Algorithm (Dev)

*

DevBA

*

5

medium

Developed

Swarm

Bees Algorithm

BeesA

OriginalBeesA

2006

8

medium

Original

Swarm

Probabilistic Bees Algorithm

*

ProbBeesA

2015

5

medium

Variant

Swarm

Bees Algorithm (Dev)

*

CleverBookBeesA

*

8

medium

Developed

Swarm

Bald Eagle Search

BES

OriginalBES

2020

7

hard

Original

Swarm

Bacterial Foraging Optimization

BFO

OriginalBFO

2002

10

hard

Original

Swarm

Adaptive Bacterial Foraging Optimization

*

ABFO

2019

8

hard

Variant

Swarm

Bird Swarm Algorithm

BSA

OriginalBSA

2016

9

hard

Original

Swarm

Beluga Whale Optimization

BWO

OriginalBWO

2022

2

hard

Original

Swarm

Cuckoo Catfish Optimizer

CCO

OriginalCCO

2025

4

hard

Original

Swarm

Catch Fish Optimization Algorithm

CFOA

OriginalCFOA

2024

2

medium

Original

Swarm

Chameleon Swarm Algorithm

ChameleonSA

OriginalChameleonSA

2021

10

medium

Original

Swarm

Improved Chameleon Swarm Algorithm

*

IChameleonSA

2024

6

hard

Variant

Swarm

Chimp Optimization Algorithm

ChOA

OriginalChOA

2020

2

medium

Original

Swarm

Cheetah Optimizer

CO

OriginalCO

2022

3

medium

Original

Swarm

Coyote Optimization Algorithm

COA

OriginalCOA

2018

3

medium

Original

Swarm

Coati Optimization Algorithm

CoatiOA

OriginalCoatiOA

2023

2

easy

Original

Swarm

Competitive Swarm Optimizer

CompSO

OriginalCompSO

2015

3

easy

Original

Swarm

Crayfish Optimization Algorithm

CrayfishOA

OriginalCrayfishOA

2023

2

easy

Original

Swarm

Cuckoo Search Algorithm

CSA

OriginalCSA

2009

3

easy

Original

Swarm

Cat Swarm Optimization

CSO

OriginalCSO

2006

11

hard

Original

Swarm

Dandelion Optimizer

DandelionO

OriginalDandelionO

2022

2

medium

Original

Swarm

Dandelion Optimizer (Dev)

*

DevDandelionO

*

2

medium

Developed

Swarm

Dung Beetle Optimizer

DBO

OriginalDBO

2022

5

medium

Original

Swarm

Dwarf Mongoose Optimization Algorithm

DMOA

OriginalDMOA

2022

4

medium

Original

Swarm

Dwarf Mongoose Optimization Algorithm (Dev)

*

DevDMOA

*

3

medium

Developed

Swarm

Dragonfly Optimization

DO

OriginalDO

2016

2

medium

Original

Swarm

Dove Swarm Optimization

DSO

OriginalDSO

2022

4

easy

Original

Swarm

Electric Eel Foraging Optimization

EEFO

OriginalEEFO

2024

2

medium

Original

Swarm

Eel and Grouper Optimizer

EGO

OriginalEGO

2024

2

medium

Original

Swarm

Elephant Herding Optimization

EHO

OriginalEHO

2015

5

easy

Original

Swarm

Emperor Penguins Colony

EPC

DevEPC

2019

6

hard

Original

Swarm

Egret Swarm Optimization Algorithm

ESOA

OriginalESOA

2022

2

hard

Original

Swarm

Fireworks Algorithm

FA

OriginalFA

2010

7

easy

Original

Swarm

Fitness Dependent Optimizer

FDO

OriginalFDO

2019

3

medium

Original

Swarm

Firefly Algorithm

FFA

OriginalFFA

2009

8

easy

Original

Swarm

Multiple Learning FA based on Gender Difference

*

MLFA_GD

2025

7

medium

Variant

Swarm

Fennec Fox Optimization

FFO

OriginalFFO

2022

2

easy

Original

Swarm

Fire Hawk Optimization

FHO

OriginalFHO

2022

2

medium

Original

Swarm

Fruit-fly Optimization Algorithm

FOA

OriginalFOA

2012

2

easy

Original

Swarm

Fruit-fly Optimization Algorithm (Dev)

*

DevFOA

*

2

easy

Developed

Swarm

Whale Fruit-fly Optimization Algorithm

*

WhaleFOA

2020

2

easy

Developed

Swarm

Fox Optimizer

FOX

OriginalFOX

2023

4

easy

Original

Swarm

Fox Optimizer (Dev)

*

DevFOX

*

5

easy

Original

Swarm

Gekko Japonicus Algorithm

GJA

OriginalGJA

2025

5

medium

Original

Swarm

Golden jackal optimization

GJO

OriginalGJO

2022

2

easy

Original

Swarm

Grasshopper Optimization Algorithm

GOA

OriginalGOA

2017

4

easy

Original

Swarm

Glider Snake Optimizer

GSO

OriginalGSO

2026

3

easy

Original

Swarm

Giant Trevally Optimizer

GTO

OriginalGTO

2022

4

medium

Original

Swarm

Giant Trevally Optimizer

*

Matlab102GTO

*

2

medium

Variant

Swarm

Giant Trevally Optimizer

*

Matlab101GTO

*

2

medium

Variant

Swarm

Grey Wolf Optimizer

GWO

OriginalGWO

2014

2

easy

Original

Swarm

Random Walk Grey Wolf Optimizer

*

RW_GWO

2019

2

easy

Variant

Swarm

Improved Grey Wolf Optimization

*

IGWO

2018

4

easy

Variant

Swarm

Chaotic-based Grey Wolf Optimizer

*

ChaoticGWO

2018

4

medium

Variant

Swarm

Fuzzy Hierarchical Operator - Grey Wolf Optimizer

*

FuzzyGWO

2017

3

easy

Variant

Swarm

Incremental model-based Grey Wolf Optimizer

*

IncrementalGWO

2021

3

easy

Variant

Swarm

Expanded Grey Wolf Optimizer

*

ExGWO

2021

2

easy

Variant

Swarm

Diversity enhanced Strategy based Grey Wolf Optimizer

*

DS_GWO

2022

4

medium

Variant

Swarm

Improved Opposite-based Learning Grey Wolf Optimizer

*

IOBL_GWO

2021

2

medium

Variant

Swarm

Opposition-based learning Grey Wolf Optimizer

*

OGWO

2021

4

medium

Variant

Swarm

Efficient and Robust Grey Wolf Optimizer

*

ER_GWO

2020

5

medium

Variant

Swarm

Cauchy‑Gaussian mutation and improved search strategy GWO

*

CG_GWO

2022

2

medium

Variant

Swarm

Hybrid Grey Wolf - Whale Optimization Algorithm

*

GWO_WOA

2022

2

easy

Hybrid

Swarm

Grey Wolf Optimizer (Dev)

*

DevGWO

2026

2

easy

Developed

Swarm

Honey Badger Algorithm

HBA

OriginalHBA

2022

2

easy

Original

Swarm

Hunger Games Search

HGS

OriginalHGS

2021

4

medium

Original

Swarm

Harris Hawks Optimization

HHO

OriginalHHO

2019

2

easy

Original

Swarm

Hippopotamus Optimization Algorithm

HO

OriginalHO

2024

2

medium

Original

Swarm

Jaya Algorithm

JA

OriginalJA

2016

2

easy

Original

Swarm

Levy-flight Jaya Algorithm

*

LevyJA

2021

2

easy

Variant

Swarm

Jaya Algorithm (Dev)

*

DevJA

*

2

easy

Developed

Swarm

Moth-Flame Optimization

MFO

OriginalMFO

2015

2

easy

Original

Swarm

Mountain Gazelle Optimizer

MGO

OriginalMGO

2022

2

medium

Original

Swarm

Musk Ox Optimizer

MO

OriginalMO

2026

2

medium

Original

Swarm

Marine Predators Algorithm

MPA

OriginalMPA

2020

2

medium

Original

Swarm

Manta Ray Foraging Optimization

MRFO

OriginalMRFO

2020

3

medium

Original

Swarm

Wavelet Mutation and Quadratic Interpolation MRFO

*

WMQIMRFO

2022

4

hard

Variant

Swarm

Moth Search Algorithm

MSA

OriginalMSA

2018

5

medium

Original

Swarm

Mantis Shrimp Optimization Algorithm

MShOA

OriginalMShOA

2025

2

nightmare

Original

Swarm

Mantis Shrimp Optimization Algorithm (Dev)

*

DevMShOA

2025

3

nightmare

Developed

Swarm

Northern Goshawk Optimization

NGO

OriginalNGO

2021

2

easy

Original

Swarm

Naked Mole-Rat Algorithm

NMRA

OriginalNMRA

2019

3

easy

Original

Swarm

Naked Mole-Rat Algorithm (Dev)

*

ImprovedNMRA

*

4

easy

Developed

Swarm

Narwhal Optimization Algorithm

NWOA

OriginalNWOA

2025

5

hard

Original

Swarm

Narwhal Optimization

*

OriginalNO

2024

4

easy

Original

Swarm

Osprey Optimization Algorithm

OOA

OriginalOOA

2022

2

easy

Original

Swarm

Orca Optimization Algorithm

ORCA

OriginalOrcaOA

2020

4

easy

Original

Swarm

Orca Predation Algorithm

*

OriginalOrcaPA

2020

5

medium

Original

Swarm

Owl Search Algorithm

OSA

OriginalOSA

2018

4

easy

Original

Swarm

Pathfinder Algorithm

PFA

OriginalPFA

2019

2

easy

Original

Swarm

Pelican Optimization Algorithm

POA

OriginalPOA

2022

2

easy

Original

Swarm

Particle Swarm Optimization

PSO

OriginalPSO

1995

5

easy

Original

Swarm

Adaptive Inertia Weight Particle Swarm Optimization

*

AIW_PSO

2006

5

medium

Variant

Swarm

Linearly Decreasing inertia Weight Particle Swarm Optimization

*

LDW_PSO

1995

6

medium

Variant

Swarm

Phasor Particle Swarm Optimization

*

P_PSO

2019

2

medium

Variant

Swarm

Hierarchical PSO Time-Varying Acceleration

*

HPSO_TVAC

2017

4

easy

Variant

Swarm

Chaos Particle Swarm Optimization

*

C_PSO

2005

6

medium

Variant

Swarm

Comprehensive Learning Particle Swarm Optimization

*

CL_PSO

2006

6

medium

Variant

Swarm

Quantum Delta-Potential-Well-Based Particle Swarm Optimization

*

QDPSO

2004

3

easy

Variant

Swarm

Red Fox Optimization

RFO

OriginalRFO

2021

4

medium

Original

Swarm

Reptile Search Algorithm

RSA

OriginalRSA

2022

4

medium

Original

Swarm

Sand Cat Swarm Optimization

SCSO

OriginalSCSO

2022

2

easy

Original

Swarm

Sea-Horse Optimization

SeaHO

OriginalSeaHO

2022

2

medium

Original

Swarm

Serval Optimization Algorithm

ServalOA

OriginalServalOA

2022

2

easy

Original

Swarm

SailFish Optimizer

SFO

OriginalSFO

2019

5

medium

Original

Swarm

Improved Sailfish Optimizer (Dev)

*

ImprovedSFO

*

3

medium

Developed

Swarm

Superb Fairy-wren Optimization Algorithm

SFOA

OriginalSFOA

2025

4

easy

Original

Swarm

Spotted Hyena Optimizer

SHO

OriginalSHO

2017

4

medium

Original

Swarm

Sea Lion Optimization Algorithm

SLO

OriginalSLO

2019

2

easy

Original

Swarm

Improved Sea Lion Optimization

*

ImprovedSLO

2022

4

medium

Variant

Swarm

Modified Sea Lion Optimization (Dev)

*

ModifiedSLO

*

2

medium

Developed

Swarm

Spider Monkey Optimization

SMO

DevSMO

2014

4

nightmare

Original

Swarm

Squirrel Search Algorithm

SquirrelSA

OriginalSquirrelSA

2019

7

nightmare

Original

Swarm

Swarm Robotics Search And Rescue

SRSR

OriginalSRSR

2017

2

nightmare

Original

Swarm

Sparrow Search Algorithm

SSA

OriginalSSA

2020

5

medium

Original

Swarm

Sparrow Search Algorithm (Dev)

*

DevSSA

*

5

medium

Developed

Swarm

Salp Swarm Optimization

SSO

OriginalSSO

2017

2

easy

Original

Swarm

Social Spider Algorithm (Dev)

SSpiderA

DevSSpiderA

2015

5

hard

Developed

Swarm

Social Spider Optimization

SSpiderO

OriginalSSpiderO

2018

4

nightmare

Original

Swarm

Siberian Tiger Optimization

STO

OriginalSTO

2022

2

easy

Original

Swarm

Tasmanian Devil Optimization

TDO

OriginalTDO

2022

2

easy

Original

Swarm

Tuna Swarm Optimization

TSO

OriginalTSO

2021

2

hard

Original

Swarm

Walrus Optimization Algorithm

WaOA

OriginalWaOA

2022

2

easy

Original

Swarm

Whale Optimization Algorithm

WOA

OriginalWOA

2016

2

easy

Original

Swarm

Hybrid Improved Whale Optimization Algorithm

*

HI_WOA

2019

3

medium

Variant

Swarm

Whale Optimization Algorithm with Modified Mutualism

*

OriginalWOAmM

2021

6

hard

Variant

Swarm

Whale Optimization Algorithm (Dev)

*

DevWOA

*

2

easy

Developed

Swarm

Whale Optimization Algorithm with Modified Mutualism (Dev)

*

DevWOAmM

*

6

hard

Developed

Swarm

White Shark Optimizer

WSO

OriginalWSO

2022

10

nightmare

Original

Swarm

Zebra Optimization Algorithm

ZOA

OriginalZOA

2022

2

easy

Original

System

Artificial Ecosystem-based Optimization

AEO

OriginalAEO

2020

2

medium

Original

System

Improved Artificial Ecosystem-based Optimization

*

ImprovedAEO

2021

2

medium

Variant

System

Enhanced Artificial Ecosystem-Based Optimization

*

EnhancedAEO

2020

2

medium

Variant

System

Modified Artificial Ecosystem-Based Optimization

*

ModifiedAEO

2020

2

medium

Variant

System

Augmented Artificial Ecosystem Optimization

*

AugmentedAEO

2022

2

medium

Variant

System

Germinal Center Optimization

GCO

OriginalGCO

2018

4

easy

Original

System

Germinal Center Optimization (Dev)

*

DevGCO

*

4

easy

Developed

System

Water Cycle Algorithm

WCA

OriginalWCA

2012

5

medium

Original

Difficulty Levels

Author’s subjective metric evaluating parameter configurations, mathematical equation density, conceptual complexity, and source lines of code (SLOC):

  • Easy: Minimal tunable parameters, straightforward mathematical models, concise code footprint.

  • Medium: Moderate equation volume and standard implementation scale.

  • Hard: Heavy mathematical formulations, extensive SLOC, and high cognitive overhead in literature comprehension.

  • Nightmare: Advanced theoretical depth, extensive equations, and highly complex codebase architecture.

Hint

Advice for Beginners

If you are new to the field of meta-heuristics, we strongly recommend starting your learning journey by reading papers and exploring source codes for algorithms categorized under the “Easy” or “Medium” difficulty levels.

Algorithm References

For the complete and regularly updated list of references for all implemented algorithms, please consult the References Section on our GitHub README.

License

MEALPY is open-source software and is officially released under the MIT License.