The state-of-the-art MEta-heuristics ALgorithms in PYthon (MEALPY)

"Knowledge is power, sharing it is the premise of progress in life. It seems like a burden to someone, but it is the only way to achieve immortality." --- Nguyen Van Thieu

Quick Notification

• New version 1.1.0 is the very different then the previous version ( < 1.0.5) in term of passing hyper-parameters.

• So please careful check your version before using this library.

• If you guys are familiar with writing documentation and would like to join this project. Please send me an email to [email protected]. I am currently working on my master thesis, may not response instantly, so please be patient. Your contribution to this project is greatly appreciated.

• If you guys want me to implement new algorithm, please open an Issues ticket, and better send me an PDF of the original paper so I can read and implement it.

Introduction

• MEALPY is a largest python module for the most of cutting-edge nature-inspired meta-heuristic algorithms (population-based) and is distributed under MIT license.

• But this library for solving single (uni or 1) objective optimization problem only. If you are facing multiple/many objective optimization problems (Finding a Pareto front or reference front) check out my new library "momapy" (A collection of the state-of-the-art Multiple/Many Objective Metaheuristic Algorithms in PYthon). "MOMAPY" will be hosted here: link

• The goals of this framework are:

  • Sharing knowledge of meta-heuristic fields to everyone without a fee
  • Helping other researchers in all field access to optimization algorithms as quickly as possible
  • Implement the classical as well as the state-of-the-art meta-heuristics (The whole history of meta-heuristics, currently including almost 100 algorithms)

• What you can do with this library:

  • Analyse parameters of algorithms.
  • Perform Qualitative Analysis of algorithms.
  • Perform Quantitative Analysis of algorithms.
  • Analyse rate of convergence of algorithms.
  • Test the scalability of algorithms.
  • Analyse the stability of algorithms.
  • Analyse the robustness of algorithms.

• And please giving me some credit if you are using this library. Lots of people just use it without reference.

@software{thieu_nguyen_2020_3711949,
  author       = {Nguyen Van Thieu},
  title        = {A collection of the state-of-the-art MEta-heuristics ALgorithms in PYthon: Mealpy},
  month        = march,
  year         = 2020,
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.3711948},
  url          = {https://doi.org/10.5281/zenodo.3711948}
}

and if you want to cite my paper, take a look at some of my first-author paper here: link

Installation

Dependencies

• Python (>= 3.6)
• Numpy (>= 1.15.1)
• Opfunu (>= 0.8.0)
• Matplotlib (>=3.1.3)
• Scipy (>= 1.4.1)

User installation

Install the current PyPI release:

    pip install mealpy
    pip install --upgrade mealpy 

Or install the development version from GitHub:

    pip install git+https://github.com/thieu1995/mealpy

Example

• Please don't misunderstand between parameters (hyper-parameters) and variables.

• Assumption that you have to find minimum of function F(x) = x1^3 + x2^2 + x3^4 with (-1 <= x1 <= 4), (5 <= x2 <= 10) and (-7 <= x2 <= -4). Then

  • Your solution is x = [x1, x2, x3], x1, x2, x3 here are the variables.
  • The number of dimension (problem size) = 3 (variables)
  • Your fitness value is fx = F(x)
  • lower bound and upper bound: lb = [-1, 5, -7] and ub = [4, 10, -4]
  • parameters (hyper-parameters) is depended on each algorithm.
  • objective function here is F(x) for minimize problem.

# Define an objective function, for example above:
def Fx(solution):
  fx = solution[0] ** 3 + solution[1] ** 2 + solution[2] ** 4
  return fx 

# This is basic example how you can call an optimizer, and its variants. For the version ( MEALPY >= 1.1.0)

from opfunu.cec_basic.cec2014_nobias import *
from mealpy.swarm_based.PSO import BasePSO, PPSO, PSO_W, HPSO_TVA


# Setting parameters
obj_func = F5       # This objective function come from "opfunu" library. You can design your own objective function like above
verbose = False     # Print out the training results
epoch = 500         # Number of iterations / generations / epochs
pop_size = 50       # Populations size (Number of individuals / Number of solutions)

# A - Different way to provide lower bound and upper bound. Here are some examples:

## 1. When you have different lower bound and upper bound for each variables
lb1 = [-3, -5, 1]
ub1 = [5, 10, 100]

md1 = BasePSO(obj_func, lb1, ub1, verbose, epoch, pop_size)
best_pos1, best_fit1, list_loss1 = md1.train()
print(md1.solution[1])

## 2. When you have same lower bound and upper bound for each variables, then you can use:
##      + int or float: then you need to specify your problem size (number of dimensions)
problemSize = 10
lb2 = -5
ub2 = 10
md2 = BasePSO(obj_func, lb2, ub2, verbose, epoch, pop_size, problem_size=problemSize)  # Remember the keyword "problem_size"
best_pos1, best_fit1, list_loss1 = md2.train()
print(md2.solution[1])

##      + array: 2 ways
lb3 = [-5]
ub3 = [10]
md3 = BasePSO(obj_func, lb3, ub3, verbose, epoch, pop_size, problem_size=problemSize)  # Remember the keyword "problem_size"
best_pos1, best_fit1, list_loss1 = md3.train()
print(md3.solution[1])

lb4 = [-5] * problemSize
ub4 = [10] * problemSize
md4 = BasePSO(obj_func, lb4, ub4, verbose, epoch, pop_size)  # No need the keyword "problem_size"
best_pos1, best_fit1, list_loss1 = md4.train()
print(md4.solution[1])

# B - Test with algorithm has batch size idea

## 1. Not using batch size idea

md5 = BasePSO(obj_func, lb4, ub4, verbose, epoch, pop_size)
best_pos1, best_fit1, list_loss1 = md5.train()
print(md1.solution[0])
print(md1.solution[1])
print(md1.loss_train)

## 2. Using batch size idea
batchIdea = True
batchSize = 5

md6 = BasePSO(obj_func, lb4, ub4, verbose, epoch, pop_size, batch_idea=batchIdea, batch_size=batchSize)  # Remember the keywords
best_pos1, best_fit1, list_loss1 = md6.train()
print(md1.solution[0])
print(md1.solution[1])
print(md1.loss_train)


# C - Test with different variants of this algorithm

md1 = PPSO(obj_func, lb4, ub4, verbose, epoch, pop_size)
best_pos1, best_fit1, list_loss1 = md1.train()
print(md1.solution[0])
print(md1.solution[1])
print(md1.loss_train)

md1 = PSO_W(obj_func, lb4, ub4, verbose, epoch, pop_size)
best_pos1, best_fit1, list_loss1 = md1.train()
print(md1.solution[0])
print(md1.solution[1])
print(md1.loss_train)

md1 = HPSO_TVA(obj_func, lb4, ub4, verbose, epoch, pop_size)
best_pos1, best_fit1, list_loss1 = md1.train()
print(md1.solution[0])
print(md1.solution[1])
print(md1.loss_train)

• The batch-size idea is not existed in Meta-heuristics field. I just take an inspiration from training batch-size of neural network field and combine it with metaheuristics. Therefore, some algorithms will have it, some won't. Don't worry, if you don't want to use it, just call the algorithm like usual, you don't need to specify any additional parameters. But if you want to use it, check the example above, you need to specify some additional hyper-parameters.

• And PLEASE read some examples inside folder "examples" before email asking me how to call the optimizer. Lots of simple and complicated examples there. Take your time to learn how to use it.

# Simple example: this is for previous version ( version <= 1.0.5)

from opfunu.cec_basic.cec2014_nobias import *
from mealpy.evolutionary_based.GA import BaseGA

## Setting parameters
obj_func = F1
# lb = [-15, -10, -3, -15, -10, -3, -15, -10, -3, -15, -10, -3, -15, -10, -3]
# ub = [15, 10, 3, 15, 10, 3, 15, 10, 3, 15, 10, 3, 15, 10, 3]
lb = [-100]
ub = [100]
problem_size = 100
batch_size = 25
verbose = True
epoch = 1000
pop_size = 50
pc = 0.95
pm = 0.025

md1 = BaseGA(obj_func, lb, ub, problem_size, batch_size, verbose, epoch, pop_size, 0.85, 0.05)
best_pos1, best_fit1, list_loss1 = md1.train()
print(md1.solution[0])
print(md1.solution[1])
print(md1.loss_train)

# Or run the simple:
python examples/run_simple.py

Changelog

• See the "ChangeLog.md" for a history of notable changes to mealpy.

Important links

• Official source code repo: https://github.com/thieu1995/mealpy

• Download releases: https://pypi.org/project/mealpy/

• Issue tracker: https://github.com/thieu1995/mealpy/issues

• This project also related to my another projects which are "meta-heuristics" and "neural-network", check it here

  • https://github.com/thieu1995/opfunu
  • https://github.com/thieu1995/metaheuristics
  • https://github.com/chasebk

Contributions

Documents

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

  • Evolutionary: Evolutionary-based
  • Swarm: Swarm-based
  • Physics: Physics-based
  • Human: Human-based
  • Bio: Biology-based
  • System: System-based (eco-system, immune-system, network-system, ...)
  • Math: Math-based
  • Music: Music-based
  • Probabilistic: Probabilistic based algorithm
  • Dummy: Non-sense algorithms and Non-sense papers (code proofs)
    • All algorithms in this library were implemented by me (my code). Including the original version (I read the paper and implement it). Some original papers are very unclear (parameters, equations, algorithm's flow) as I categories it to dummy papers and algorithms (I have already checked carefully the paper, the related papers and searched for Matlab code or any programming code for it).

• Version: Most of the algorithms have the Original version and Base version.

  • original: Taken exactly from the paper
  • changed: Sometimes I changed the flow or how the new solution created/updated (equations) or remove some unnecessary parameters to make algorithm works

• Batch size idea (Personal Choice): Explained in the ChangeLog.md file and above. An algorithm can used it or not.

• Levy: Using levy-flight technique or not

• Type (Personal Opinion): (Based on performance of Base version. The Base version can be Original version)

  • weak: working fine with uni-modal and some multi-modal functions
  • strong: working good with uni-modal, multi-modal, some hybrid and some composite functions
  • best: working well with almost all kind of functions
  • BEST: the best among all algorithms

• Large-scale (Personal Opinion):

  • All algorithm here have been tested with large-scale dimension (2000)
  • Remember in CEC competition:
    • Normal test: 10, 50, 100
    • Large-scale: 100, 500, 1000

• Paras: The number of parameters in the algorithm (Not counting the fixed parameters in the original paper)

  • Almost algorithms have 2 paras (epoch, population_size) and plus some paras depend on each algorithm.
  • Some algorithms belong to "best" or "BEST" type and have only 2 paras meaning the algorithms are outstanding

• 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, I recommend to read the paper of algorithms belong to "best or strong" type, "easy or medium" difficulty level.

A

• ABC - Artificial Bee Colony . 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. Socha, K., & Dorigo, M. (2008). Ant colony optimization for continuous domains. European journal of operational research, 185(3), 1155-1173.

• ALO - Ant Lion Optimizer . Mirjalili S (2015). “The Ant Lion Optimizer.” Advances in Engineering Software, 83, 80-98. doi: 10.1016/j.advengsoft.2015.01.010

• AAA - Artificial Algae Algorithm (SBO) . Uymaz, S. A., Tezel, G., & Yel, E. (2015). Artificial algae algorithm (AAA) for nonlinear global optimization. Applied Soft Computing, 31, 153-171.

• AEO - Artificial Ecosystem-based Optimization . Zhao, W., Wang, L., & Zhang, Z. (2019). Artificial ecosystem-based optimization: a novel nature-inspired meta-heuristic algorithm. Neural Computing and Applications, 1-43.

• ASO - Atom Search Optimization . 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.

B

• BFO - Bacterial Foraging Optimization . Passino, K. M. (2002). Biomimicry of bacterial foraging for distributed optimization and control. IEEE control systems magazine, 22(3), 52-67.

• BeesA - Bees Algorithm . 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.

• BBO - Biogeography-Based Optimization . Simon, D. (2008). Biogeography-based optimization. IEEE transactions on evolutionary computation, 12(6), 702-713.

• BA - Bat Algorithm . 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.

• BSO - Brain Storm Optimization . Shi, Y. (2011, June). Brain storm optimization algorithm. In International conference in swarm intelligence (pp. 303-309). Springer, Berlin, Heidelberg.

• BSA - Bird Swarm Algorithm . 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.

• BES - Bald Eagle Search . 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. Rahkar Farshi, T. (2020). Battle royale optimization algorithm. Neural Computing and Applications, 1-19.

C

• CA - Culture Algorithm . 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 . 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 . 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.

• CRO - Coral Reefs Optimization . 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.

D

• DE - Differential Evolution . 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.

• DSA - Differential Search Algorithm . Civicioglu, P. (2012). Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm. Computers & Geosciences, 46, 229-247.

• DO - Dragonfly Optimization . 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.

E

• ES - Evolution Strategies . 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.

• EP - Evolutionary programming . Fogel, L. J. (1994). Evolutionary programming in perspective: The top-down view. Computational intelligence: Imitating life.

• EHO - Elephant Herding Optimization . 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 . 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.

• EOA - Earthworm Optimisation Algorithm . 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 . Faramarzi, A., Heidarinejad, M., Stephens, B., & Mirjalili, S. (2019). Equilibrium optimizer: A novel optimization algorithm. Knowledge-Based Systems.

F

• FireflyA - Firefly Algorithm . 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 . 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 . 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.

• FBIO - Forensic-Based Investigation Optimization . Chou, J.S. and Nguyen, N.M., 2020. FBI inspired meta-optimization. Applied Soft Computing, p.106339.

• FOA - Fruit-fly Optimization Algorithm. Pan, W. T. (2012). A new fruit fly optimization algorithm: taking the financial distress model as an example. Knowledge-Based Systems, 26, 69-74.

G

• GA - Genetic Algorithm . Holland, J. H. (1992). Genetic algorithms. Scientific american, 267(1), 66-73.

• GWO - Grey Wolf Optimizer . Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014). Grey wolf optimizer. Advances in engineering software, 69, 46-61.

• GOA - Grasshopper Optimisation Algorithm . Saremi, S., Mirjalili, S., & Lewis, A. (2017). Grasshopper optimisation algorithm: theory and application. Advances in Engineering Software, 105, 30-47.

• GCO - Germinal Center Optimization . 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.

• GSKA - Gaining Sharing Knowledge-based Algorithm . 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.

H

• HC - Hill Climbing . 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.

• HS - Harmony Search . Geem, Z. W., Kim, J. H., & Loganathan, G. V. (2001). A new heuristic optimization algorithm: harmony search. simulation, 76(2), 60-68.

• HHO - Harris Hawks Optimization . 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 . 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.

I

• IWO - Invasive Weed Optimization . 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 .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.

J

• JA - Jaya Algorithm. 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.

K

L

• LCBO - Life Choice-Based Optimization . Khatri, A., Gaba, A., Rana, K. P. S., & Kumar, V. (2019). A novel life choice-based optimizer. Soft Computing, 1-21.

M

• MA - Memetic Algorithm . 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 . Mirjalili, S. (2015). Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowledge-based systems, 89, 228-249.

• MVO - Multi-Verse Optimizer . 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.

• MSA - Moth Search Algorithm . Wang, G. G. (2018). Moth search algorithm: a bio-inspired metaheuristic algorithm for global optimization problems. Memetic Computing, 10(2), 151-164.

• NMRA - Nake Mole-rat Algorithm . Salgotra, R., & Singh, U. (2019). The naked mole-rat algorithm. Neural Computing and Applications, 31(12), 8837-8857.

• MRFO - Manta Ray Foraging Optimization . 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.

N

• NRO - Nuclear Reaction Optimization . 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.

O

P

• PSO - Particle Swarm Optimization . 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.

• PFA - Pathfinder Algorithm . Yapici, H., & Cetinkaya, N. (2019). A new meta-heuristic optimizer: Pathfinder algorithm. Applied Soft Computing, 78, 545-568.

Q

• QSA - Queuing Search Algorithm . 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.

R

S

• SA - Simulated Annealling . Van Laarhoven, P. J., & Aarts, E. H. (1987). Simulated annealing. In Simulated annealing: Theory and applications (pp. 7-15). Springer, Dordrecht.

• SSO - Social Spider Optimization . 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.

• SSA - Social Spider Algorithm . James, J. Q., & Li, V. O. (2015). A social spider algorithm for global optimization. Applied Soft Computing, 30, 614-627.

• SCA - Sine Cosine Algorithm . Mirjalili, S. (2016). SCA: a sine cosine algorithm for solving optimization problems. Knowledge-Based Systems, 96, 120-133.

• SRSR - Swarm Robotics Search And Rescue . 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 . 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.

• SalpSO - Salp Swarm Optimization . 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 . 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.

• SARO - Search And Rescue Optimization . 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.

• SSDO - Social Ski-Driver Optimization . 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.

• SMA - Slime Mould Algorithm. 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.

• SpaSA - Sparrow Search Algorithm . 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

T

• TLO - Teaching Learning Optimization . 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.

• TWO - Tug of War Optimization . Kaveh, A., & Zolghadr, A. (2016). A novel meta-heuristic algorithm: tug of war optimization. Iran University of Science & Technology, 6(4), 469-492.

U

V

• VCS - Virus Colony Search . 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.

W

• WCA - Water Cycle Algorithm . 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 . Mirjalili, S., & Lewis, A. (2016). The whale optimization algorithm. Advances in engineering software, 95, 51-67.

• WHO - Wildebeest Herd Optimization . 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 . 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

Y

Z

Dummy Algorithms

• AAA - Artificial Algae Algorithm . Uymaz, S. A., Tezel, G., & Yel, E. (2015). Artificial algae algorithm (AAA) for nonlinear global optimization. Applied Soft Computing, 31, 153-171.

• BWO - Black Widow Optimization . Hayyolalam, V., & Kazem, A. A. P. (2020). Black Widow Optimization Algorithm: A novel meta-heuristic approach for solving engineering optimization problems. Engineering Applications of Artificial Intelligence, 87, 103249.

• BOA - Butterfly Optimization Algorithm. Arora, S., & Singh, S. (2019). Butterfly optimization algorithm: a novel approach for global optimization. Soft Computing, 23(3), 715-734.

• BMO - Blue Monkey Optimization . Blue Monkey Optimization: (2019) The Blue Monkey: A New Nature Inspired Metaheuristic Optimization Algorithm. DOI: http://dx.doi.org/10.21533/pen.v7i3.621

• EPO - Emperor Penguin Optimizer . Dhiman, G., & Kumar, V. (2018). Emperor penguin optimizer: A bio-inspired algorithm for engineering problems. Knowledge-Based Systems, 159, 20-50.

• PIO - Pigeon-Inspired Optimization . Duan, H., & Qiao, P. (2014). Pigeon-inspired optimization: a new swarm intelligence optimizer for air robot path planning. International journal of intelligent computing and cybernetics.

• RHO - Rhino Herd Optimization . Wang, G. G., Gao, X. Z., Zenger, K., & Coelho, L. D. S. (2018, December). A novel metaheuristic algorithm inspired by rhino herd behavior. In Proceedings of The 9th EUROSIM Congress on Modelling and Simulation, EUROSIM 2016, The 57th SIMS Conference on Simulation and Modelling SIMS 2016 (No. 142, pp. 1026-1033). Linköping University Electronic Press.

• SLO - Sea Lion Optimization . Masadeh, R., Mahafzah, B. A., & Sharieh, A. (2019). Sea Lion Optimization Algorithm. Sea, 10(5).

• SOA - Sandpiper Optimization Algorithm . Kaur, A., Jain, S., & Goel, S. (2020). Sandpiper optimization algorithm: a novel approach for solving real-life engineering problems. Applied Intelligence, 50(2), 582-619.

• STOA - Sooty Tern Optimization Algorithm. Sooty Tern Optimization Algorithm: Dhiman, G., & Kaur, A. (2019). STOA: A bio-inspired based optimization algorithm for industrial engineering problems. Engineering Applications of Artificial Intelligence, 82, 148-174.