Please check:

Sörensen, K. (2015), Metaheuristics—the metaphor exposed. Intl. Trans. in Op. Res., 22: 3–18. doi:10.1111/itor.12001

You will find there a long lst of metaheuristic approaches as well as very strong arguments about why most of those approaches are simply reformulations of a few core techniques, disguised under some very fancy terminology.

Check this :

https://en.wikipedia.org/wiki/Talk:Metaheuristic/List_of_Metaheuristics

Thanks for your answer !!!

Srta Mahboobeh Parsapoor, I can not find the first reference that you recomended:

1. E. Atashpaz-Gargari and C. Lucas, "Imperialist competitive algorithm: An algorithm for optimization inspired by imperialistic competition," 2007 IEEE Congress on Evolutionary Computation, Singapore, 2007, pp. 4661-4667.

Ok, I have the work mentioned.

Check this also:

https://econ.ubbcluj.ro/~rodica.lung/taco/literatura/Yang_nature_book_part.pdf

 Hi Lemuel,

I recommend you to have a look to the following book published by Springer:

http://link.springer.com/book/10.1007%2F978-1-4419-1665-5

I hope it is useful!

Best regards.

I would modestly include the parameter-free

Problem Dependent Optimization

Journal of Combinatorial Optimization,

ONLINE: 2015, DOI 10.1007/s10878-014-9826-x.

PRINT: Volume 31, Issue 3, April 2016, 1335-1344.

(The final publication is available at link.springer.com, more precisely, at

http://link.springer.com/article/10.1007%2Fs10878-014-9826-x

At Research Gate:

https://www.researchgate.net/publication/270516923_Problem_dependent_optimization_PDO

It does not need adjusting of parameters (although there is a couple of parameters one can play with, if tempted). For those who are going to look into it and try to run an implementation, I have three minor technical remarks/improvements regarding the metaheuristic that virtually eliminate the possibility of worsening the performance even in very long runs:

1) Keep the values of the jump-down function as reals; that is, drop the ceiling function in formula (1)

2) Another suggestion (for very long searches) is to use a default value of 5 for the parameter m. The second parameter, k, does not affect convergence, it only affects how the heuristic runs at the beginning. values k=m=5 are universal; worked equally well in all of (about 7 different) applications we tried.

3) The formula (1) can be rewritten in a slightly more computationally friendly way (avoiding multiplication of large numbers) by adding and subtracting jdc(c(B)) in the numerator, which leaves a smaller fraction after simplification.

Each of these three items could have some feasible effect in very long runs.

You can quickly forget about simulated annealing (and anything else inferior to SA) if you go the distance and write an implementation of PDO:-)

Article Problem dependent optimization (PDO)

Thanks for all the answer !!!

Lemuel:

Estás ignorando el método de Integración de Variables, del cual soy autor. Entre otros, los Algoritmos Genéticos pueden ser considerados una aplicaicón de este método. Te adjunto algunas publicaciones que te pueden ayudar, te pudiera enviar, incluyendo pseudocódigo de algunos algoritmos, etc.. Además, puedes bajar de mi página de Researchgate mi libro Selección de Propuestas, el que expone un método propio que también puede ser considerado como caso particular de Integración de Variables.

Un abrazo,

Arzola

Gracias profesor Arzola.

Cualquier duda le caeré por su local.

Raindrop Method for spatial problems

Bettinger, P., and J. Zhu. 2006. A new heuristic for solving spatially constrained forest planning problems based on mitigation of infeasibilities radiating outward from a forced choice. Silva Fennica. 40: 315-333.

Also,

Threshold Accepting and the Demon Algorithm - which are like simulated annealing

Most of them are the same. You can compress them to a few, they follow the same algorithm but with different presentation. This is my experience. 

Hello,

You may want to check this review paper:

Iztok Fister Jr., Xin-She Yang, Iztok Fister, Janez Brest, Dušan Fister, A Brief Review of Nature-Inspired Algorithms for Optimization. Elektrotehniški vestnik, 80(3), 2013.

Online: http://arxiv.org/abs/1307.4186

Too many algorithms you can find given in the book having title:"Innovative

Computational Intelligence: A Rough Guide to 134 " written by Bo Xing Wen-Jing Gao. If you want i can send you this book.

Dear Sr. Drazen Bajer excellent contribution, I appreciate your answer.

Sr. Ibrahim Aydogdu I am interest in the book. Please, do you send me it?

Many researchers argue that most the swarm algorithms you listed are basically the same thing. I personally believe that only few well known metaheuristics brought a real contribution. In particular:

• Local search algorithms
• Variable neighborhood search
• Evolutionary algorithms: Genetic, memetic, and co-evolutionary algorithms
• Particle swarm optimization
• Simulated annealing
• Tabu search
• Ant colony optimization

Greedy randomized adaptive search procedures (GRASP) also can be considered as modern heuristics (metaheuristics).

water cycle algorithm, mine blast algorithm, whale optimization algorithm, dragonfly algorithm, Symbiotic Organisms Search Algorithm, Social Spider Optimiser and many more

Please check:

Sörensen, K. (2015), Metaheuristics—the metaphor exposed. Intl. Trans. in Op. Res., 22: 3–18. doi:10.1111/itor.12001

You will find there a long lst of metaheuristic approaches as well as very strong arguments about why most of those approaches are simply reformulations of a few core techniques, disguised under some very fancy terminology.

Please check this list of metaheuristic algorithms. We keep implementing recent ones in Python. 

https://github.com/7ossam81/EvoloPy/wiki/List-of-optimizers

You can add the following to your list also:

Dragonfly Algorithm (DA)

Biogeography-based optimization (BBO)

Brain Storm Optimization Algorithm (BSO)

Elephant Herd Algorithm (EHO)

Evolutionary Strategy (ES)

Earthworm Optimization Algorithm (EWA)

Flower Pollenation Algorithm (FPA)

Krill Herd algorithm (KH)

Lightning Search Algorithm (LSA)

Monarch Butterfly Optimizatio (MBO)

Moth-Flame Optimization algorithm (MFO)

Population-Based Incremental Learning (PBIL)

Sine Cosine Algorithm (SCA)

Whale Optimization Algorithm (WOA)

I classify "metaheuristic" algorithms by swarm inspired algorithms (agents that follows simple rules for change its position to explore or exploit), and evolutionary computation algorithms.

They need not be evolutionary in nature. Any algorithm which is used to promote/improve/ optimize some other algorithm can be called " meta heuristic"

Classical heuristics work faster compared to the metaheuristics. However, metaheuristics work better in terms of searching for the best optimum. It depends on what problem you are dealing with. Some problems, a faster solution is more important and less accurate solution can be tolerate. Sometime, a precise solution is everything.

water cycle algorithm is also a efficient method in dealing with constrained problems

1. Genetic algorithm —

2. Genetic programming — 

3. Evolutionary strategy — 

4. Evolutionary programming — 

5. Differential evolution —

6. Meme tic algorithm — 

7. Culture algorithm —

8. Tatuchi-Genetic Algorithm — 

9. Co Evolutionary Algorithm —

10. Diploid Evolutionary Algorithm — 

11. Asexual Reproduction Optimization —   

12. Artificial immune system —  

13. Ant colony optimization —  

14. Honeybee hive optimization —

15. Stigmergic society optimization —

16. Artificial bee colony —  

17. Termite colony optimization — 

18. Particle swarm optimization —

19. Imperialist competitive algorithm —

20. Firefly algorithm —

21. Shuffled frog-leaping —

22. Cat swarm optimization —

23. Fruit Fly optimization Al. —

24. Cuckoo optimization Algorithm —

25. Bacterial Foraging optimization Algorithm —  

26. Artificial Fish Swarm Algorithm —   

27. Bat Algorithm — 

28. Lion Pride optimizer — 

29. Group Search optimizer —

30. Krill Herd — 

31. Hunting Search-

32.Grey Wolf Optimizer

Why limiting inspiration to natural phenomena if we can go well beyond? The following paper states well the overall  scientific value of most of the mentioned algorithms:

http://www.oneweirdkerneltrick.com/spectral.pdf

Classical heuristics is much simpler and easier to program. Metaheuristics on contrary need much effort and more coffee to stay at night.

At https://aisearch.github.io/#/ we present a list of all the algorithms we found published. The list can be easily filter by name, author and year of publication. We also provide the publication article link to each algorithm. 

My friend:

Do you already studied the Integratiion of Variables method? Yesterday I uploaded to my researchgate profile a presentation devoted to the most successful  developed in the frame o this method algorithms.   It is true that  is not worse wedge that  from the same wood?

José Arzola

Currently, a List of metaheuristics algorithms is about 40 (or maybe else more). But I would be interested to see a List of Lower Bound algorithms too, at least Five such algorithms. Please, if you know anything about such algorithms, send any links to view. I want to repeat my point of view again: Developing a heuristic or metaheuristic algorithm is not any science, it is only CRAFT and no more.

More detailed interpretation can be seen on the links

https://www.researchgate.net/post/Why_are_so_many_people_interested_in_multiple_objectives_in_general_and_metaheuristics_in_particular

https://www.researchgate.net/post/Computing_bounds_for_a_minimization_problem

I think meta heuristics algorithms name is a despective one. I prefer to categorize these paradigmes as algorithms derived from evolutionary computation, swarm intelligence and finally consider the rest of the algorithms as nature inspired.

Bacterial Memetic Algorithm

1. Random forest search

2. River formation

3. Stochastic diffusion search

you can see

Intelligent water drops algorithm (Shah-Hosseini 2007)

You can find them:

https://github.com/fcampelo/EC-Bestiary

You can also add,

Quantum particle swarm method

Cross entropy method etc

Quantum inspired algorithms

I do not recommend to attempt to list out metaheuristics according to specific names and terminologies, as most methods promoted nowadays rely on artistic/fancy terminologies and natural analogies but boil down to a few core optimization concepts known for a long time. I recommend to read this first instead:

Article Metaheuristics -- the metaphor exposed

As well as recent surveys that analyse the core success factors of recent metaheuristics:

Article Metaheuristics in Combinatorial Optimization: Overview and C...

Article Heuristics for Multi-Attribute Vehicle Routing Problems : A ...

Salp Optimization algorithm, Dec. 2017.

Article Salp Swarm Algorithm: A bio-inspired optimizer for engineeri...

Grasshopper Optimisation Algorithm

Hydrological Cycle Algorithm

Mass and Energy Balances Algorithm

Rain Water Algorithm

Football Game Algorithm

Team game algorithm

List of metaheuristics algorithms:

Ant colony optimization

Ant lion optimizer

Artificial bee colony algorithm

Bat algorithm

Biogeography-based optimization

Brain Storm Optimization Algorithm

Cat swarm optimization

Crow search algorithm

Cuckoo optimization algorithm

Cuckoo search algorithm

Differential evolution

Dragonfly Algorithm

Earthworm Optimization Algorithm

ELephant Herd Algorithm

Evolutionary Strategy

Firefly algorithm

Flower Pollenation Algorithm

Football Game Algorithm

Genetic algorithm

Glowworm swarm optimization

Gravitational search algorithm

Grasshopper Optimization algorithm

Grey wolf optimizer

Harmony search

Hydrological Cycle Algorithm

Krill Herd algorithm

Lightning Search Algorithm

Mass and Energy Balances Algorithm

Multi-verse optimizer

Monarch Butterfly Optimizatio

Moth-Flame Optimization algorithm

Particle swarm optimization

Population-Based Incremental Learning

Quantum inspired algorithm

Rain Water Algorithm

Salp Swarm Algorithm

Shuffled complex evolution

Simulated annealing

Sine Cosine Algorithm

Tabu search

Teaching-learning-based optimization

Team game algorithm

Whale Optimization Algorithm

The following paper presents a comprehensive survey of the field of metaheuristics. It lists a large number of metaheuristic algorithms.

Hussain, K., Salleh, M. N. M., Cheng, S., & Shi, Y. (2018). Metaheuristic research: a comprehensive survey. Artificial Intelligence Review, 1-43.

The following link includes a survey article that contains the categories of the Metaheuristic algorithms.

Article A survey on applications and variants of the cuckoo search algorithm

All the best for all.

Evolutionary Computation Bestiary

https://github.com/fcampelo/EC-Bestiary

(frequently updated)

Hi

this is my Algorithm. it is a new New Metaheuristic

Farmland Fertility: A New Metaheuristic Algorithm for Solving Continuous Optimization Problems

Gray wolves optimization(GWO)

Sine cosine algorithm(SCA)

Particul swarem(PSO) ,salps swarem algorithm(SSA),sine cosine algorithm(SCA)

There are 2 books by Dr.Bozorg-Haddad in which several evolutionary and meta-heuristic algorithms have been introduced, for example TLBO.

Pity Beetle Algorithm (PBA)

Chapter Metaheuristic Algorithms: A Comprehensive Review

This can also be added into the list:

Tree physiology Optimization (TPO)

Some References:

1)Tree Physiology Optimization in Benchmark Function and Traveling Salesman Problem

https://doi.org/10.1515/jisys-2017-0156

2)Tree physiology optimization on SISO and MIMO PID control tuning

https://doi.org/10.1007/s00521-018-3588-9

Team Game Algorithm (TGA) could be added to your list.

Book: Metaheuristics Algorithms in Power Systems, Springer 2019

Spider Monkey Optimization (SMO)

wind driven optimization (WDO) algorithm

Salp swarm

Invasive Weed Optimization

TLBO

Kindly see the following link for classification of meta-heuristic algorithms:

Article Generalized Ant Colony Optimizer: swarm-based meta-heuristic...

1-Sperm Swarm Optimization Algorithm (SSO).

2- Multi-Objective Optimization Algorithms Based on sperm Fertilization Procedure (MOSFP)

https://dl.acm.org/citation.cfm?id=3193100

This algorithm can also be added to your list:

Harris hawks optimization (HHO) published in 2019

This algorithm can also be added to your list:

Stellar-Mass Black Hole Optimization

All the answers are great

Galactic swarm optimization algorithm

Stellar Mass Black hole optimization algorithm

The list is long andgrows every week

I am a little worried. There are too many answers without a reference. Of course I can find it and I might even know it, but this is not the point. Please provide a proper reference or do not bring it in. I was also worried about not really diving into matheuristics, i.e., metaheuristics hybridisations with mathematical programming.

There are, just to name a few (sorry for using those references that I know most):

POPMUSIC (do not blame me for the name; it is actually nice and it was already "invented" 1999):

E. Taillard and S. Voß. Popmusic - Partial optimization metaheuristic with special intensification conditions. In C. Ribeiro and P. Hansen, editors, Essays and Surveys in Metaheuristics, pages 613- 629. Kluwer, Boston, 2002. [DOI 10.1007/978-1-4615-1507-4_27]

The corridor method:

M. Sniedovich and S. Voß. The corridor method: A dynamic programming inspired metaheuristic. Control and Cybernetics 35 (2006), 551 - 578. [ http://matwbn.icm.edu.pl/ksiazki/cc/cc35/cc3534.pdf ]

Generalized local branching:

A. Hill and S. Voß. Generalized local branching heuristics and the capacitated ring tree problem. Discrete Applied Mathematics 242 (2018), 34 - 52. [DOI 10.1016/j.dam.2017.09.010] For another type of entry into the topic see: https://en.wikipedia.org/wiki/Matheuristics

Of course it is different from all the above.

And too bad that you missed the talks by Marco Caserta (in Denver) and myself (in Geneva) on two conferences in 2018:

https://www.euro-online.org/websites/eume/event/eume-2018-geneva/

https://www.abstractsonline.com/pp8/#!/4594/presentation/695

Here are a few more references:

M. Fischetti, A. Lodi, and D. Salvagnin. Just MIP it! In V. Maniezzo, T. Stützle, and S. Voß, editors, Matheuristics: Hybridizing Metaheuristics and Mathematical Programming, pages 39-70. Springer US, 2010.

M. Fischetti, C. Polo, and M. Scantamburlo. A local branching heuristic mixed-integer programs with 2-level variables, with an application to a telecommunication network design problem. Networks, 44(2):61-72, 2004.

E. Danna, E. Rothberg, and C. Le Pape. Exploring relaxation induced neighborhoods to improve MIP solutions. Mathematical Programming, 102(1):71-90, 2005.

M. Caserta and S. Voß. Metaheuristics: Intelligent problem solving. In V. Maniezzo, T. Stützle, and S. Voß, editors, Matheuristics: Hybridizing Metaheuristics and Mathematical Programming, pages 1-38. Springer US, 2010.

May be we should write a survey to find the most influential matheuristics papers. The above should be included.

And there is much much more;

kindly explore.

BTW: Do you remember quite old approaches like vocabulary building, chunking, consistent chains etc. ?

We have rejuvenated that as fixed set search:

R. Jovanovic, M. Tuba and S. Voß. Fixed set search applied to the traveling salesman problem. Lecture Notes in Computer Science 11299 (2019), 63 - 77. Chapter Fixed Set Search Applied to the Traveling Salesman Problem: ...

R. Jovanovic and S. Voß. Fixed set search applied to the minimum weighted vertex cover problem. Lecture Notes in Computer Science, accepted.

References to the older ideas are included in the above references.

Try it especially on top of GRASP.

@Metaheuristics Algorithms

• Animal Migration Optimization
• Ant Colony Optimization
• Ant Lion Optimization Algorithm
• Artificial Algae Algorithm
• Artificial Bee Colony Algorithm
• Artificial Chemical Process Algorithm
• Artificial Ecosystem Algorithm
• Artificial Fish Swarm Optimization
• Artificial Immune Systems
• Bacterial Evolutionary Algorithm
• Bat Algorithm
• Bird Mating Optimizer
• Bull Optimisation Algorithm
• Bumble Bees Mating Optimization
• Cellular Automata
• Central Force Optimization
• Chaos Optimization Algorithm
• Chemical Reaction Algorithm
• Chicken Swarm Optimization
• Collective Animal Behavior
• Construct, Merge, Solve & Adapt
• Coral Reefs Optimization
• Cuckoo Search
• Cultural Algorithms
• Cuttlefish Algorithm
• Differential Evolution
• Dragonfly Algorithm
• Earthworm Optimization
• Elephant Herd Algorithm
• Emperor Penguins Colony
• Evolutionary Computation and Metaheuristics
• Firefly Algorithm
• Forest Optimization Algorithm
• Fuzzy-metaheuristic Methods
• Genetic Programming
• Grasshopper Optimization Algorithm
• Gravitational Search Algorithm
• Greedy Randomized Adaptive Search
• Grey Wolf Optimizer
• Group Search Optimizer
• Guided Local Search & Fast Local Search
• Harmony Search
• Honey-Bees Mating Optimization
• Hunting Search Algorithm
• Krill Herd Algorithm
• Intelligent Water Drops Algorithm
• Iterated Local Search
• Locust Search Algorithm
• Memetic Algorithms
• Meta-Heuristic Algorithms for Deep Learning
• Mine Blast Algorithm
• Monarch Butterfly Optimization
• Moth-Flame Optimization Algorithm
• Multi-objective Optimisation
• Multiple Operator Metaheuristics
• Neighborhood Search Metaheuristics
• Parliamentary Optimization Algorithm
• Particle Swarm Optimization
• Photosynthetic and Enzyme Algorithm
• Physarum Polycephalum Algorithm
• Population Based Metaheuristics
• Rainfall Optimization Algorithm
• River Formation Dynamics
• Roach Infestation Optimization
• Salp Swarm Algorithm
• Scatter Search
• Seed-Based Plant Propagation Algorithm
• Sheep Flocks Heredity Model Algorithm
• Shuffled Frog Leaping Algorithm
• Simulated Annealing
• Social Cognitive Optimization
• Social Spider Optimization
• Sperm Swarm Optimization Algorithm
• Spiral Optimization Algorithm
• Stellar-Mass Black Hole Optimization
• Stochastic Search
• Strawberry Algorithm
• Tabu Search
• Teaching-Learning-Based Optimization
• Team Game Algorithm
• The States of Matter Search
• Tree Physiology Optimization
• Variable Neighbourhood Search
• Water Wave Optimization
• Whale Optimization Algorithm
• Wind-Driven Optimization

how to do optimization PID using list metaheuristic algorithm?

Please read my paper "The social engineering optimizer (SEO)" EAAI. You can find a complete list of metaheuristics.

If you want to see the most "strange" names, please check

the Evolutionary Computation Bestiary

https://github.com/fcampelo/EC-Bestiary

I would probably not recommend trying any of these.....

#The Frog jumping optimization .

metaheuristic methods include the Tabu search, ant colony optimization, particle swarm optimization, and simulated annealing.

Folllowing paper has some popular meta-heuristic algorithms:

Kumar, A. & Bawa, S. Soft Comput (2019). https://doi.org/10.1007/s00500-019-04155-4

HHO

See the literature review in this paper: Article The Social Engineering Optimizer (SEO)

HGSO

Social spider optimization

Clonal selection algorithm

Artificial Immune Network Optimization

WCA or Water Cycle Algorithm

There's no end to it. Many new metaheuristic algorithms are being proposed every day. For example:

Atom Search Optimization

Salp Swarm Algorithm

Tree Growth Optimization

Vortex Search Algorithm

to name a few.

Sea lion optimization algorithm

There is tow new meta-heuristics algorithms proposed for any kind of problem.

1. Hybrid Improved Dolphin Echolocation and Ant Colony Optimization

For discrete domain

Article Hybrid Improved Dolphin Echolocation and Ant Colony Optimiza...

2. An enhanced time evolutionary optimization

For continuous domain

Article An enhanced time evolutionary optimization for solving engin...

Lightning attachment procedure optimization (LAPO)

https://www.hindawi.com/journals/cin/2019/1589303/

algorithm of the innovative gunner (AIG)

https://www.tandfonline.com/doi/abs/10.1080/0305215X.2019.1565282?journalCode=geno20

Please find our recent work on simulating the optimization algorithm's behavior using the deep learning models:

Preprint From feature selection to continuous optimization

please check the below article. it's a novel metaheuristic algorithm and has a new optimization style.

Article Donkey and Smuggler Optimization Algorithm: A Collaborative ...

The latest one is: Nomadic People Optimizer (9/2019)

Article A new algorithm for normal and large-scale optimization prob...

I also have a question related to the topic.

What is the fast algorithm that can be used for optimizing the deep learning model parameters instead of gradient-descent optimization? Specifically with large dimension-features.

Mohammed Al-Andoli when it comes to optimizing parameters, you can have a look at adam - references are given e.g. in the scikit package (Python). Also hyperparameter optimization is a highly interesting topic where we can employ metaheuristics. One procedure often used in deep learning is e.g. https://github.com/hyperopt/hyperopt .

You can find a comprehensive list of Nature Inspired algorithms (to-date) in my Report Technical Report An application-based taxonomy of Nature Inspired Intelligent...

which is available at: http://mde-lab.aegean.gr/images/stories/docs/reportnii2019.pdf

I will keep this list updated with new techniques.