Taxonomy of bio-inspired algorithms

Taxonomy of bio-inspired algorithms

Abstract

In recent years, a great variety of nature and bio-inspired algorithms have been published in the literature. These algorithms simulate some natural or biological processes such as natural evolution, to optimize complex problems. Last years, the accumulation of this type of algorithms has achieved a number difficult to manage, so it is needed a good taxonomy that allows researchers to organise existing and future meta-heuristics in well-defined categories. In this work, we have reviewed more than two hundred nature-inspired and bio-inspired algorithms, and proposed two taxonomies that group them in categories ans subcategories, considering two different criteria. The first category consider the source of inspiration, while the second one consider only the behavior of each algorithm. It is shown the proposals in each one of the categories, and the summarise of each category. Later, results of these two taxonomies are compared, and obtained the most similar classic algorithm for each reviewed papers. We have obtained that there is a poor relationship between the natural inspiration of an algorithm and its behavior, and that, their similarities in behavior are greater than expected. Even more, more than half of reviewed proposals are versions of classic algorithms. Although there are many proposals based in different concepts of reality, the majority of them are actually more similar than expected, so authors should focus more on the behaviour. Also, we give several suggestions to continue improving this growing research field.

Keywords –  nature-inspired algorithms, bio-inspired algorithms, taxonomy, classification

1 Introduction

There are many real-world important optimisation problems in which there is not suitable an exact technique to solve it (at least in a reasonable time), due to its complexity, and great number of data to use. Thus, the use of traditional techniques is unsuccessful, and new approaches have to be considered.

Complexity in not unusual, in nature there are a large number of complex systems that perform a surprising performance. The most clear example is the different animal species, what have developed a very specialised systems through an evolutionary process. Evolution has allowed animals to adapt to very inhospitable environments, foraging, very difficult tasks of orientation, and to adapt to radical climatic changes, among other surprising achievements. The animals, organised in independent systems, groups or swarms or colonies (systems quite complex in themselves) have managed to colonise the earth completely, and achieve a global balance that has allowed them to survive for thousands of years.

That success of biological organisms has inspired all kinds of optimization algorithms, called bio-inspired algorithms. These algorithms simulate some biological processes such as natural evolution, where solutions are individuals that mutate and reproduce to generate new candidate ones. When they mimic a collective behavior they are called Swarm Intelligence [296]. These are inspired by different biological animals: movements of birds [79], bats [299] or small insects such as fireflies [298], grasshoppers [232]; mechanisms to locate food exhibited by colony animals such as ants in Artificial Ant Colony (ACO)[72, 71], or bees in Artificial Bee Colony (ABC) algorithms [134]; hunting mechanisms used by different animals, from small ones such as dragonflies [180], to wild wolfs [268] or marine animals such as dolphins [180], or whales [175]; even the reproduction of corals [230], the behavior of very small animals such as krill [118] or the bacteria [162], to name a few. There are also nature-based inspired could also be inspired by natural process like rain [128], electromagnetism [4, 124], astronomy concepts like planets [224] or galaxies [238, 316], music [154], or chemical issues as the temperate [147], gases movement [2], among others. Last years, there have appears also algorithms inspired in human activities, like sports [188, 137], taking decisions [243], or even political systems [242, 15].

Nature and Bio-inspired algorithms have become increasing popular in the last two decades, gaining notoriety since these algorithms can learn and adapt like organisms, obtaining very good results is a wide range of optimisation problems: combinatorial [209], to real-world problems with a increasing number of data as processing images or data mining [296].

Because nature-based and Bio-inspired algorithms are obtained after a process of observing the activities of an natural process or biological organism and converting them into a computational algorithm to optimise, the variety of bio-inspired algorithms easily increases. New discoveries on nature and the fact of the rise of investigation have done researchers to be interested in biological processes. Thanks to that, new bio-inspired meta-heuristics have appeared, obtaining a increasing number of proposals and applications new years, obtaining a real explosion of proposals. Every nature process could be adapted to a meta-heuristic, although not all may reach into an algorithm capable of reaching global optimum values of problems.

Figure 1: Number of Papers with bio-inspired algorithm in the abstract, for years (Scopus database)

In Figure 1, you can see the increasing number of papers/book chapters published in the last years with bio-inspired algorithm in the abstract. In these papers, many of them were proposing new bio-inspired algorithms. It can be observed that with a so huge number of algorithms, it should very convenient be able to organize them into a taxonomy with well-defined characteristics that let researchers to classify both the existing bio-inspired algorithms and new proposals in the future. Unfortunately, authors does not include any type of taxonomy and they only focus on the biological idea of their meta-heuristic.

In this paper, we present two different taxonomies for nature-based algorithms:

  • The first one is a nature-based taxonomy, classifying the algorithms based on its natural or biological inspiration. Our goal is to create a taxonomy in which, given a specific algorithm, we can find its category quickly and without ambiguity.

  • The second one classifies the different reviewed algorithms only based on its behavior, i.e, how they generate new solutions to explore the function to optimise, not by its inspiration source. Our aim is to classify together algorithms with a similar behavior, without considering its nature inspiration.

We believe that this double-taxonomy could be very useful for researchers. The first one could be useful to classify the different proposals by its origin, and the second one specific and useful information about the behavior of the algorithm. These double-classification allows researchers to identify each new proposal in the adequate context.

In order to make a good taxonomy of the meta-heuristics we have focused on the features which make unique each algorithm. Our goal is to create a taxonomy in which, given a specific algorithm, we can find its category quickly and without doubts, in the same category that algorithms with similar features. In order to do that, we have reviewed more than two hundred papers of different types of meta-heuristics to make a proposal of our taxonomies, extracting of each of them their main ideas. We have reviewed that huge quantity of proposals to make our taxonomies as accurate as possible, keeping them, as the same time, simple enough to be useful. There have been in literature previous surveys in this area, as we review in Section 2, but they not only do not do a formal classification of so many algorithms of the literature, as we have done. Also, contrary of those works, we do not limit the classification to their nature-based inspiration, but also we have taken in account the behavior they present.

The classification of our survey is not limited, nevertheless, to the taxonomy. We analyse the relationship between the two different taxonomies to identify if there is a significant correlation between them or not. We also are going to study for each algorithm the most similar algorithms, to identify the most influential meta-heuristics, whose behavior have inspired more nature proposals, including proposals with different inspiration sources. Finally, we do an critical analysis of the results obtained after classifying all the proposals with these two taxonomies, giving suggestions of improvement in this growing research field.

The rest of this paper is organised as follows. In Section 2, we discuss the previous surveys of taxonomy and review of algorithms. In Section 3, we propose our first taxonomy based on the nature inspiration. In Section 4, we propose our second taxonomy, based on the behavior of the algorithm. Moreover, in Section 5 we analyse the differences in both taxonomies, to analyse the relationships among them, and the more influential algorithms in our reviewed papers. In Section 6, an critical analysis is given based on the classification upon these taxonomies. Finally, in Section 7, we summarise our main conclusions.

2 Related works of analysis

The diversity of bio-inspired algorithms and their flexibility to tackle optimisation problems for many research fields have inspired several surveys, the majority for different types of problems [133, 285], including continuous optimisation [185], combinatorial problems [209], or multi-objective problems [305]. For specific real-world problems, sometimes there are so many literature about nature and bio-inspired algorithms, that specific surveys have been developed: For Telecommunications [292], Robotics [25], Data Mining [97], or even specific real-world problems like power systems [69], designing computer networks [73], automatic clustering [131], face recognition [8], or intrusion detection [148].

Many specific bio-inspired algorithms have also produced so many versions that several surveys have appeared specifically for that type of algorithms, from more classic algorithms PSO [16] and DE [197, 60, 63] to more modern ones, like ABC [135, 27], BFOA [62] or BAT [294].

About bio-inspired algorithms, [249] explains how the metaphor and the biological idea is used to create a meta-heuristic and it offers us some examples and characteristics of this process. Books like [30] or [301] show many nature-inspired algorithms, but they are more focused in describing different algorithms than in classify or analyse them.

There are several studied comparing bio-inspired algorithms with a very different behavior, in order to offer a guideline to decide which of them to use for a problem. In [61], the popular PSO and DE versions are compared. This research line is followed by [86] where compared the behavior of different bio-inspired algorithms, in order to give a guideline. More recently, [207] studied several recent bio-inspired algorithms, suggesting by the features of each one in which type of problems each one should be more recommended. More specific is [149], that compare several different algorithms considering its parallel potential using GPU. More recently, there have appeared works [211] that, instead of makes a comparison of individual algorithms, compare groups of algorithms: Swarm Intelligence and Evolutionary Computation, in order to study specific behavior (as their convergence speed). However, its main aim is to compare bio-inspired algorithms, not to classify them. In [83], foraging algorithms (as BFOA) are compared against other evolutionary algorithms. In that paper, algorithms are classified in two big groups, algorithms with cooperation and without cooperation.

In 2013 [95] gives a classification of meta-heuristics attending to their biological inspiration, that start proposing some similar categories: Swarm Intelligence, Physics and Chemistry Based, Bio-inspired algorithms (not SI-based), and a Other algorithms category. However, it is not a hierarchical classification, so it is not an actual taxonomy.

In [18, 221], another classification is proposed, with the categories Evolution Based Method, Physics Based Method, Swarm Based Method, and Human-Based Method. At different of previous one, a new category, Human-Based is proposed, in which there are grouped algorithms inspired in human behavior. The classification is used to catalog more than 40 proposals, obtaining groups similar in size. In this case, there is not a miscellaneous category like in previous one. Similarly to [95], the categories are disjoint groups without subcategories.

Recently, [151] offers a review of meta-heuristics from the 1970s until 2015, i.e, from the development of neural networks to novel algorithms like Cuckoo Search, giving a broad view of new proposals, but without proposing a category.

The most recent survey is [44], in which nature-inspired algorithms are classified not by a biological inspiration, but by its behavior. Algorithms are classified based on three different principles. The first one is Learning behavior, how solutions learn from others. It can be individual, local (only inside a neighbourhood), global (between all individuals), and without learning. The second principle is Interaction-collective behavior, if the individuals cooperate or compete between them. The third principle is the diversification-population control, in which they are classified if the population have a converging tendency, a diffuse tendency, or not specific tendency. Then, 22 bio-inspired algorithms are classified by each one of them, and the grouped obtained by each principle are experimentally compared.

3 First Taxonomy: By nature-base inspiration

In this section, we propose a novel taxonomy based on nature-base inspiration of the nature-inspired algorithms in the literature, that allows to classify the great variety in literature.

The proposed taxonomy was developed after spend months reviewing more than 200 papers of different years, starting from more classic proposals in the late 80’s (as Simulated Annealing, [147] or Particle Swarm Optimization, [79]) to more novel techniques proposed until 2018 [34], and 2019 [116]. Thus, it can be considered the more exhaustive review in the area until today, as far as we know.

Taken in account all the reviewed papers, we group the proposals in a category hierarchy. In the hierarchy, not all proposals of a category must fit in one of its subcategories. In our classification the categories of the same level are disjoint sets, that mean that each proposal can be only member of one of these categories, the one considered more suitable considering the nuances of each algorithm that allow us to differentiate it from the others.

Making a classification of the nature inspired algorithms that we can find in literature may be complicated, considering the different sources of inspiration as biological, physical, human-being, … In some papers, author suggest a possible category of more well-established group, but not in all of them. Also, its classification could not be the more adequate when the number of proposals increases. The algorithms of each category were selected by the number of cites, importance in the literature, number of algorithms that were created thanks to the inspiration of that algorithm, …

When establishing a hierarchical classification, it is important to achieve a good trade-off between information and simplicity by the following criterion:

  • When to establish a new division of a category into subcategories: A very demanding criterion can imply categories of little utility, since in that case the same category would group very different algorithms to each other. On the other hand, a very lax criterion can produce a very complex hierarchy and, therefore, with little usefulness. For maintaining simple the taxonomy, we have decided that a category must have at least four algorithms in order to exist. Thus, a category is only decomposed in subcategories if each one of them have both coherence and contains a minimum size of algorithms inside.

  • The number of subcategories into which we divide a category. The criterion followed must be coherent to create subcategories with a meaning useful. In order to maintain reduced that number, we consider that not all algorithms in one category must be member of one of its subcategories. In that way, we avoid to introduce mess categories without cohesion.

{forest}

forked edges, for tree=font=, rounded corners, minimum width=10em, top color=gray!5, bottom color=gray!10, edge+=darkgray, draw=darkgray, align=left, anchor=children,grow=east,s sep=1cm, l sep=1cm, align=left, anchor=west, anchor=base west, before packing=where n children=3calign child=2, calign=child edge, before typesetting nodes=where content=coordinate, [Nature and population-based
Meta-heuristics (278: 100%), blur shadow [Miscelanea
(29: 10.43%)] [Plants Based (8: 2.88%)] [Social Human
Algorithms (33: 11.87%)] [Physics and Chemical
Based (60: 21.58%) [Chemical Based
(12: 4.32%)] [Physical Based
(48: 17.27%)] ] [Swarm Intelligence         
(127: 45.68%) [Others (20: 7.19%)] [Microorganisms
(16: 5.76%)] [Flying animals
(47: 16.91%)] [Terrestrial animals
(29: 10.43%)] [Aquatic animals
(16: 5.76%)] ] [Population Evolution
(21: 7.55%)] ]

Figure 2: Classification of the reviewed papers using the nature-based taxonomy
Figure 3: Ratio of reviewed algorithms by its category, first taxonomy

Figure 2 shows the classification we have reached, indicating, for the 278 reviewed algorithms, the number and ratio of proposals classified in each category and subcategory. It can be observed that the largest group of all is Swarm Intelligence category (near the half of the proposed, 46%), inspired in the Swarm Intelligence concept [30], followed by the physics and chemical category, inspired by different physical behavior or chemical reactions (22% of proposals). Other relevant categories are Social Human Algorithms (12%), inspired by human aspects, and Population Evolution (7%), inspired by the evolution theory over a population of individuals, that includes very classic algorithms like genetic algorithms. There is a new category, Plants Based, not included in other taxonomies. Nearly 10% of proposals are so different between them that they cannot be grouped in new categories. The percentage of classification of each category is visually displayed in Figure 3.

In next subsections we are going to give a brief global view of different categories. For each category we are going to describe the main characteristics of each of them, an example, and a table with the algorithms belonging to that category.

3.1 Population Evolution

This category is composed of population-based algorithms inspired in the nature evolution. Each individual represents a solution of the problem and has an associated fitness value (the value of the problem for that solution). These algorithms, through a process of breeding and survival the population of solutions evolves optimising the problem. Thus, this category is characterised by the fact of being inspired by the concept of population evolution (without considering activities of individuals other than reproduction).

More in detail, in these algorithms we have a population with individuals that have the ability to breed. Therefore, from the parents we get children and these new individuals introduce some variety regard their parents. These characteristics allow them to adapt to the environment. Thanks to that mechanism we have a population that evolves through the generations, results are improved and that characteristic is what it makes the difference with other categories.

Population Evolution
Algorithm Name Acronym Year Reference
Artificial Infections Disease Optimization AIDO 2016 [122]
Asexual Reproduction Optimization ARO 2010 [91]
Biogeography Based Optimization BBO 2008 [247]
Bird Mating Optimization BMO 2014 [14]
Bean Optimization Algorithm BOA 2011 [311]
Coral Reefs Optimization CRO 2014 [230]
Differential Evolution DE 1997 [213]
Ecogeography-Based Optimization EBO 2014 [314]
Eco-Inspired Evolutionary Algorithm EEA 2011 [206]
Evolution Strategies ES 2002 [26]
Genetic Algorithms GA 1989 [167]
Gene Expression GE 2001 [94]
Immune-Inspired Computational Intelligence ICI 2008 [52]
Weed Colonization Optimization IWO 2006 [169]
Marriage In Honey Bees Optimization MHBO 2001 [1]
Queen-Bee Evolution QBE 2003 [255]
SuperBug Algorithm SuA 2012 [10]
Stem Cells Algorithm SCA 2011 [257]
Sheep Flock Heredity Model SFHM 2001 [196]
Self-Organizing Migrating Algorithm SOMA 2004 [306]
Variable Mesh Optimization VMO 2012 [215]
Table 1: Meta-heuristics of the category Population Evolution

In Table 1 there are shown algorithms in this category. It can observed well-known and classic well-known algorithms as Genetic Algorithms, GA, and Differential Evolution, DE, and other algorithms based in reproduction of different biological organisms.

3.2 Swarm Intelligence

Swarm Intelligence, SI, is already a consolidated term in the literature, introduced by Gerardo Beni and Jing Wang in 1989 [25]. It can be defined as the collective behavior of decentralised, self-organised systems, natural or artificial. The expression was proposed in the context of robotic systems, but now is generalised as the collective emergent intelligence of a group of simple agents. Thus, meta-heuristics based in Swarm Intelligence are the ones whose inspiration is based on the collective behavior of animal societies, such as an insects colony or a flock of birds. The first one of this category was Particle Swarm Optimization, PSO [79], and Ant Colony Optimization, ACO [79], later appears more algorithms like the well-known Artificial Bee Colonies [134], and more recent algorithms as Firefly Algorithm [298], or Grasshopper Optimisation Algorithm [232].

Swarm Intelligence algorithms are shown in Tables 2, 3, 4, and 5. This is the most numerous category of all, and we can find some categories with regard to the type of animals that have inspired the algorithms: flying animals, algorithms inspired in the flying movement of birds and flying animals like insects; terrestrial animals, inspired in the foraging and hunter mechanisms of land animals; aquatic animals, inspired in movement of fish or other aquatic animals, like dolphins, with particular detection of school of fish; and microorganisms, inspired in microorganisms like virus, bacteria and algae.

Inside each subcategory, we have also distinguished whether they are inspired by the foraging action of the inspired living creature, Foraging-inspired is another popular term related to this type of inspiration [32], or by it movement in general. When the behavior of the algorithm is inspired both in the movement and the foraging, it is catalogued as foraging.

Swarm Intelligence (I)
Algorithm Name Acronym Subcategory Type Year Reference
Artificial Algae Algorithm AAA Micro Movement 2015 [272]
Artificial Beehive Algorithm ABA Flying Foraging 2009 [192]
Artificial Bee Colony ABC Flying Foraging 2007 [134]
African Buffalo Optimization ABO Terrestrial Foraging 2016 [24]
Ant Colony Optimization ACO Terrestrial Foraging 1996 [72]
Ant Lion Optimizer ALO Terrestrial Foraging 2015 [179]
Artificial Searching Swarm Algorithm ASSA Other Movement 2009 [39]
Artificial Tribe Algorithm ATA Other Movement 2009 [41]
African Wild Dog Algorithm AWDA Terrestrial Foraging 2013 [253]
Bald Eagle Search BES Flying Foraging 2019 [9]
Bees Algorithm BA Flying Foraging 2006 [208]
Bumblebees BB Flying Foraging 2009 [50]
Bee Colony-Inspired Algorithm BCIA Flying Foraging 2009 [106]
Bee Colony Optimization BCO Flying Foraging 2005 [265]
Bacterial Colony Optimization BCO.1 Micro Foraging 2012 [200]
Bacterial Chemotaxis Optimization BCO.2 Micro Foraging 2002 [58]
Biomimicry Of Social Foraging Bacteria for Distributed Optimization BFOA Micro Foraging 2002 [162]
Bacterial Foraging Optimization BFOA.1 Micro Foraging 2009 [62]
Bacterial-GA Foraging BGAF Micro Foraging 2007 [40]
BeeHive Algorithm BHA Flying Foraging 2004 [279]
Bees Life Algorithm BLA Flying Foraging 2018 [28]
Bat Intelligence BI Flying Foraging 2012 [166]
Bat Inspired Algorithm BIA Flying Foraging 2010 [299]
Blind, Naked Mole-Rats Algorithm BNMR Terrestrial Foraging 2013 [258]
Butterfly Optimizer BO Flying Movement 2015 [150]
Bee System BS Flying Foraging 1997 [233]
Bee System BS.1 Flying Foraging 2002 [161]
Bird Swarm Algorithm BSA Flying Movement 2016 [171]
Bee Swarm Optimization BSO Flying Foraging 2010 [6]
Bioluminiscent Swarm Optimization Algorithm BSO.1 Flying Foraging 2011 [66]
Bees Swarm Optimization Algorithm BSOA Flying Foraging 2005 [74]
Table 2: Meta-heuristics of the category Swarm Intelligence (I)
Swarm Intelligence (II)
Algorithm Name Acronym Subcategory Type Year Reference
Collective Animal Behavior CAB Other Foraging 2012 [53]
Catfish Optimization Algorithm CAO Aquatic Movement 2011 [245]
Cricket Behavior-Based Algorithm CBBE Terrestrial Movement 2016 [33]
Chaotic Dragonfly Algorithm CDA Flying Foraging 2018 [235]
Cuttlefish Algorithm CFA Aquatic Movement 2013 [81]
Consultant Guide Search CGS Other Movement 2010 [125]
Cuckoo Optimization Algorithm COA Flying Foraging 2011 [219]
Camel Traveling Behavior COA.1 Terrestrial Movement 2016 [123]
Cuckoo Search CS Flying Foraging 2009 [291]
Cat Swarm Optimization CSO Terrestrial Movement 2006 [43]
Chicken Swarm Optimization CSO.1 Terrestrial Movement 2014 [172]
Dragonfly Algorithm DA Flying Foraging 2016 [180]
Dolphin Echolocation DE.1 Aquatic Foraging 2013 [140]
Dolphin Partner Optimization DPO Aquatic Movement 2009 [244]
Elephant Herding Optimization EHO Terrestrial Movement 2016 [275]
Eagle Strategy ES.1 Flying Foraging 2010 [293]
Elephant Search Algorithm ESA Terrestrial Foraging 2015 [67]
Egyptian Vulture Optimization Algorithm EV Flying Foraging 2013 [256]
Firefly Algorithm FA Flying Foraging 2009 [298]
Flocking Base Algorithms FBA Flying Movement 2006 [56]
Fast Bacterial Swarming Algorithm FBSA Micro Foraging 2008 [45]
Frog Call Inspired Algorithm FCA Terrestrial Movement 2009 [194]
Flock by Leader FL Flying Movement 2012 [23]
Fruit Fly Optimization Algorithm FOA Flying Foraging 2012 [205]
Fish Swarm Algorithm FSA Aquatic Foraging 2011 [271]
Fish School Search FSS Aquatic Foraging 2008 [19]
Group Escape Behavior GEB Aquatic Movement 2011 [174]
Good Lattice Swarm Optimization GLSO Other Movement 2007 [251]
Grasshopper Optimisation Algorithm GOA Terrestrial Foraging 2017 [232]
Glowworm Swarm Optimization GSO Micro Movement 2013 [316]
Group Search Optimizer GSO.1 Other Movement 2009 [114]
Goose Team Optimization GTO Flying Movement 2008 [277]
Grey Wolf Optimizer GWO Terrestrial Foraging 2014 [177]
Table 3: Meta-heuristics of the category Swarm Intelligence (II)
Swarm Intelligence (III)
Algorithm Name Acronym Subcategory Type Year Reference
Harry’s Hawk Optimization Algorithm HHO Flying Foraging 2019 [116]
Hoopoe Heuristic Optimization HHO.1 Flying Foraging 2012 [85]
Hunting Search HuS Other Foraging 2010 [203]
Honeybee Social Foraging HSF Flying Foraging 2007 [216]
Hierarchical Swarm Model HSM Other Movement 2010 [37]
Invasive Tumor Optimization Algorithm ITGO Micro Movement 2015 [262]
Jaguar Algorithm JA Terrestrial Foraging 2015 [36]
Krill Herd KH Aquatic Foraging 2012 [118]
Lion Algorithm LA Terrestrial Foraging 2012 [220]
Seven-Spot Labybird Optimization LBO Flying Foraging 2013 [278]
Lion Optimization Algorithm LOA Terrestrial Foraging 2016 [302]
Locust Swarms Optimization LSO Aquatic Foraging 2009 [38]
Magnetotactic Bacteria Optimization Algorithm MBO Micro Movement 2013 [182]
Monarch Butterfly Optimization MBO.1 Flying Movement 2017 [276]
Migrating Birds Optimization MBO.2 Flying Movement 2012 [77]
Modified Cuckoo Search MCS Flying Foraging 2009 [274]
Modified Cockroach Swarm Optimization MCSO Terrestrial Foraging 2011 [202]
Moth Flame Optimization Algorithm MFO Flying Movement 2015 [178]
Monkey Search MS Terrestrial Foraging 2007 [191]
Natural Aggregation Algorithm NAA Other Movement 2016 [164]
OptBees OB Flying Foraging 2012 [165]
Optimal Foraging Algorithm OFA Other Foraging 2017 [318]
Population Migration Algorithm PMA Other Movement 2009 [309]
Prey Predator Algorithm PPA Other Foraging 2015 [163]
Particle Swarm Optimization PSO Flying Movement 1995 [79]
Penguins Search Optimization Algorithm PSOA Aquatic Foraging 2013 [103]
Roach Infestation Problem RIO Terrestrial Foraging 2008 [113]
Reincarnation Concept Optimization Algorithm ROA Other Movement 2010 [241]
Shark Search Algorithm SA Aquatic Foraging 1998 [117]
Simulated Bee Colony SBC Flying Foraging 2009 [168]
Satin Bowerbird Optimizer SBO Flying Movement 2017 [109]
Table 4: Meta-heuristics of the category Swarm Intelligence (III)
Swarm Intelligence (IV)
Algorithm Name Acronym Subcategory Type Year Reference
Sine Cosine Algorithm SCA.2 Other Movement 2016 [181]
Snap-Drift Cuckoo Search SDCS Flying Foraging 2016 [222]
Shuffled Frog-Leaping Algorithm SFLA Terrestrial Movement 2006 [89]
Swarm Inspired Projection Algorithm SIP Flying Foraging 2009 [250]
Slime Mould Algorithm SMA Micro Foraging 2008 [186]
Spider Monkey Optimization SMO Terrestrial Foraging 2014 [35]
Seeker Optimization Algorithm SOA Other Movement 2007 [59]
Symbiosis Organisms Search SOS Other Movement 2014 [42]
Social Spider Algorithm SSA Terrestrial Foraging 2015 [303]
Shark Smell Optimization SSO Aquatic Foraging 2016 [3]
Swallow Swarm Optimization SSO.1 Flying Foraging 2013 [198]
Social Spider Optimization SSO.2 Terrestrial Foraging 2013 [54]
See-See Partidge Chicks Optimization SSPCO Flying Movement 2015 [204]
Surface-Simplex Swarm Evolution Algorithm SSSE Other Movement 2017 [107]
Sperm Whale Algorithm SWA Aquatic Movement 2016 [80]
Termite Hill Algorithm TA Terrestrial Foraging 2012 [319]
Termite Colony Optimization TCO Terrestrial Foraging 2010 [115]
The Great Salmon Run Algorithm TGSR Aquatic Movement 2013 [190]
Virtual Ants Algorithm VAA Flying Foraging 2006 [295]
Virtual Bees Algorithm VBA Flying Foraging 2005 [297]
Virus Colony Search VCS Micro Movement 2016 [157]
Virus Optimization Algorithm VOA Micro Movement 2009 [132]
Viral Systems Optimization VSO Micro Movement 2008 [51]
Wasp Colonies Algorithm WCA Flying Foraging 1991 [268]
Wolf Colony Algorithm WCA.1 Terrestrial Foraging 2011 [160]
Worm Optimization WO Micro Foraging 2014 [12]
Whale Optimization Algorithm WOA Aquatic Foraging 2016 [175]
Wolf Pack Search WPS Terrestrial Foraging 2007 [289]
Weightless Swarm Algorithm WSA Other Movement 2012 [269]
Wolf Search Algorithm WSA.1 Terrestrial Foraging 2012 [263]
Wasp Swarm Optimization WSO Flying Foraging 2005 [210]
Zombie Survival Optimization ZSO Other Foraging 2012 [267]
Table 5: Meta-heuristics of the category Swarm Intelligence (IV)

Subcategories of SI algorithms by the environment

The global SI category can been divided in functions on the type of animals. Between the possible categories, we have grouped them according to its more characteristic environment (aquatic, terrestrial or aerial). This criterion not only is very intuitive, since it inherits a criterion already applied in animal taxonomies, but it also relies on the fact that these environments condition the movement and hunting mode of the different species.

Flying Animals This category is composed of meta-heuristics based on the concept of Swarm Intelligence in which the trajectory of agents is inspired by flying movements, like birds, bats, or other flying insects. The most well-known algorithm in this subcategory are PSO [79] and ABC [134].

Terrestrial Animals Meta-heuristics in this category are inspired by foraging or movements in terrestrial animals. The most well-known algorithm of this category is classic meta-heuristic, ACO [72], inspired in the mechanism used by ants to locate and transport its food. This category also includes other popular algorithms like GWO [177], inspired in the wild wolf hunting strategy, LOA [302], inspired in the lions and their hunting methods, or the more recent GOA [232], inspired in the grasshoppers and its jumping motion.

Aquatic animals This type of meta-heuristics are inspired in aquatic animals. Their aquatic nature have inspired different exploration mechanisms. It contains popular algorithms as KH, inspired in krill [118], WOA [175], inspired in whales, and algorithms inspired in echolocation of dolphins to detect fish like DPO [244] and Dolphin Echolocation [140].

Microorganisms Meta-heuristics based on microorganisms are related with food search by bacteria. A bacteria colony performs a movement to search for food and once they have found and taken it, they split to search again in the environment. Other types of meta-heuristics that can be part of this category are the ones related with virus, they usually replicate the infection process of the virus to the cells. The most known algorithm of this category is BFOA [162].

Types of SI algorithms by the inspirational behavior

Another criterion to group algorithms is the specific behavior of the animal that captured the attention of researchers and inspired the algorithm. In previous Tables 2-5 for each algorithm the type is indicated, considering the following behavior:

Movement We have consider that an algorithm belongs to this type, Movement inspiration if the biological inspiration is mainly the animal movement. The relevant of the movement could be by the own movement (inspired in the flying movement of birds as PSO [79], inspired in jumping animals like frogs as SFLA [89], or aquatic movements as DPO [244]), or by the movement of the population (inspired by swarms movements like BSA [171], migration of populations like PMA [309], or migration of particular animals like salmon [190], among others).

Foraging Sometimes the inspiration, more than the movement strategy, is the mechanism used to obtain their food. It can the mechanisms to surround the animals (like GWO [177] and LA [220], inspired in greys and lions hunting techniques, respectively), particular mechanisms to find the food (like ACO [72], inspired in ants), or other strategies to explore the are looking for the food (like the echolocation in dolphins [140] or the light mechanisms in the fireflies [298]). Sometimes, the movement of the animal is very oriented for getting the food, in that case we have considered into the foraging inspiration type, and not in the movement inspiration type. Nowadays, foraging-inspired is a term that is becoming more and more consolidated, appearing in the name of several bio-inspired algorithms.

3.3 Physics/Quimics based algorithms

These algorithms are characterised and that they try to imitate the behavior of phenomena of both subjects, such as gravity, electromagnetism, electric charges and water movement, in relation with Physics, and chemical reactions and gases particles movement if we talk about Chemistry.

The complete list of algorithms in this category is in Table 6 and 7 for the Physics based algorithms, and Table 8 for the Chemical based algorithms.

In this category we can find some well-known algorithms of last century like Simulated Annealing [147] or one of the most important algorithms of Physics, Gravitational Search Algorithm, GSA [224], that have produce a inspired a variety of space-based algorithms as BH or GBSA. Also, there are well-known algorithms like Harmony Search, HS [154], that although inspired in the music, a human invention, it has more in common with other physical algorithms in its usage of sound waves, that with Social Human algorithm, the following category.

Physics based (I)
Algorithm Name Acronym Year Reference
Artificial Electric Field Algorithm AEFA 2019 [287]
Artificial Physics Optimization APO 2009 [284]
Big Bang Big Crunch BBBC 2006 [87]
Black Hole Optimization BH 2013 [111]
Colliding Bodies Optimization CBO 2014 [142]
Crystal Energy Optimization Algorithm CEO 2016 [93]
Central Force Optimization CFO 2008 [98]
Charged Systems Search CSS 2010 [146]
Electromagnetic Field Optimization EFO 2016 [4]
Electromagnetism Mechanism Optimization EMO 2003 [124]
Galaxy Based Search Algoritm GBSA 2011 [238]
Gravitational Clustering Algorithm GCA 1999 [152]
Gravitational Emulation Local Search GELS 2009 [17]
Gravitational Field Algorithm GFA 2010 [313]
Gravitational Interactions Algorithm GIO 2011 [96]
General Relativity Search Algorithm GRSA 2015 [22]
Gravitational Search Algorithm GSA 2009 [224]
Galactic Swarm Optimization GSO.2 2016 [195]
Harmony Elements Algorithm HEA 2009 [57]
Hysteresis for Optimization HO 2002 [304]
Hurricane Based Optimization Algorithm HO.2 2014 [227]
Harmony Search HS 2005 [154]
Intelligence Water Drops Algorithm IWD 2009 [237]
Light Ray Optimization LRO 2010 [129]
Lightning Search Algorithm LSA 2015 [240]
Magnetic Optimization Algorithm MFO.1 2008 [264]
Method of Musical Composition MMC 2014 [189]
Melody Search MS.1 2011 [13]
Multi-Verse Optimizer MVO 2016 [176]
Optics Inspired Optimization OIO 2015 [138]
Particle Collision Algorithm PCA 2007 [228]
PopMusic Algorithm PopMusic 2002 [259]
River Formation Dynamics RFD 2007 [217]
Radial Movement Optimization RMO 2014 [218]
Ray Optimization RO 2012 [141]
Space Gravitational Algorithm SGA 2005 [119]
Table 6: Meta-heuristics of the category Physics Based (I)
Physics based (II)
Algorithm Name Acronym Year Reference
States Matter Optimization Algorithm SMS 2014 [55]
Spiral Dynamics Optimization SO 2011 [260]
Spiral Optimization Algorithm SPOA 2010 [130]
Self-Driven Particles SPP 1995 [273]
Vibrating Particle Systems Algorithm VPO 2017 [144]
Vortex Search Algorithm VS 2015 [70]
Water Cycle Algorithm WCA.2 2012 [88]
Water Evaporation Optimization WEO 2016 [145]
Water Flow-Like Algorithms WFA 2007 [290]
Water Flow Algorithm WFA.1 2007 [20]
Water-Flow Algorithm Optimization WFO 2011 [270]
Water Wave Optimization Algorithm WWA 2015 [315]
Table 7: Meta-heuristics of the category Physics Based (II)
Chemistry based
Algorithm Name Acronym Year Reference
Artificial Chemical Process ACP 2005 [126]
Artificial Chemical Reaction Optimization Algorithm ACROA 2011 [7]
Artificial Reaction Algorithm ARA 2013 [170]
Chemical Reaction Optimization Algorithm CRO.1 2010 [153]
Gases Brownian Motion Optimization GBMO 2013 [2]
Ions Motion Optimization Algoirthm IMO 2015 [127]
Integrated Radiation Optimization IRO 2007 [46]
Kinetic Gas Molecules Optimization KGMO 2014 [183]
Photosynthetic Algorithm PA 1999 [193]
Simulated Annealing SA.1 1989 [147]
Synergistic Fibroblast Optimization SFO 2017 [252]
Thermal Exchange Optimization TEO 2017 [139]
Table 8: Meta-heuristics of the category Chemical Based

3.4 Social Human Algorithms

Algorithms of this category are inspired by human social concepts, such as decision making and ideas related to the expansion/competition of ideologies inside the society as ideology, inspiration of IA [121], or political concepts, as ICA [15]. Also, it includes algorithms inspired in sport competitions like SLC [188]. There are several important algorithms in this category along the literature as Imperialist Competitive Algorithm and Ideology Algorithm. Brainstorming algorithms had also a huge impact with several algorithms like BSO [243] and GBSO [84].

The complete list of algorithms in this category is in Table 9.

Social Human Behavior
Algorithm Name Acronym Year Reference
Anarchic Society Optimization ASO 2012 [242]
Brain Storm Optimization Algorithm BSO.2 2011 [243]
Collective Decision Optimization Algorithm CDOA 2017 [308]
Cognitive Behavior Optimization Algorithm COA.2 2016 [158]
Competitive Optimization Algorithm COOA 2016 [239]
Cultural Algorithms CA 1999 [283]
Football Game Inspired Algorithms FCA.1 2009 [90]
FIFA World Cup Competitions FIFAAO 2016 [226]
Global-Best Brain Storm Optimization Algorithm GBSO 2017 [84]
Group Counseling Optimization GCO 2010 [82]
Group Leaders Optimization Algorithm GLOA 2011 [64]
Greedy Politics Optimization Algorithm GPO 2014 [155]
Human Evolutionary Model HEM 2007 [187]
Human Group Formation HGF 2010 [266]
Human-Inspired Algorithms HIA 2009 [307]
Ideology Algorithm IA 2016 [121]
Imperialist Competitive Algorithm ICA 2007 [15]
League Championship Algorithm LCA 2014 [137]
Leaders and Followers Algorithm LFA 2015 [105]
Old Bachelor Acceptance OBA 1995 [120]
Oriented Search Algorithm OSA 2008 [310]
Parliamentary Optimization Algorithm POA 2008 [31]
Social Behavior Optimization Algorithm SBO.1 2003 [225]
Social Cognitive Optimization Algorithm SCOA 2010 [280]
Social Emotional Optimization Algorithm SEA 2010 [286]
Stochastic Focusing Search SFS 2008 [281]
Soccer Game Optimization SGO 2012 [78]
Soccer League Competition SLC 2014 [188]
Teaching-Learning Based Optimization Algorithm TLBO 2011 [223]
Tug Of War Optimization TWO 2016 [143]
Unconscious Search US 2012 [11]
Volleyball Premier League Algorithm VPL 2017 [184]
Wisdom of Artificial Crowds WAC 2011 [288]
Table 9: Metaheuristics of the category Social Human Behavior
Plants-Based
Algorithm Name Acronym Year Reference
Artificial Plants Optimization Algorithm APO.1 2013 [312]
Forest Optimization Algorithm FOA.1 2014 [102]
Flower Pollination Algorithm FPA 2012 [300]
Plant Propagation Algorithm PPA.1 2009 [254]
Paddy Field Algorithm PFA 2009 [212]
Runner Root Algorithm RRA 2015 [173]
Saplings Growing Up Algorithm SGA.1 2007 [136]
Self-Defense Mechanism Of The Plants Algorithm SDMA 2018 [34]
Table 10: Meta-heuristics of the category Plants-Based

3.5 Plants Based

In this category, there are included algorithms inspired by plants. In this case, there is not communication between the agents, at different of Swarm Intelligence category. One of the most well-known is Forest Optimization Algorithms [102], inspired by the process of plant reproduction. In Table 10 there is the complete list of algorithms in this category.

Miscelanea
Algorithm Name Acronym Year Reference
Atmosphere Clouds Model ACM 2013 [100]
Artificial Cooperative Search ACS 2012 [47]
Across Neighbourhood Search ANS 2016 [282]
Bar Systems BS.2 2008 [68]
Backtracking Search Optimization BSO.3 2012 [48]
Cloud Model-Based Algorithm CMBDE 2012 [317]
Chaos Optimization Algorithm COA.3 1998 [156]
Clonal Selection Algorithm CSA 2000 [201]
Differential Search Algorithm DSA 2012 [49]
Exchange Market Algorithm EMA 2014 [104]
Extremal Optimization EO 2000 [29]
Fireworks Algorithm Optimization FAO 2010 [261]
Grenade Explosion Method GEM 2010 [5]
Heart Optimization HO.1 2014 [112]
Interior Search Algorithm ISA 2014 [99]
Keshtel Algorithm KA 2014 [108]
Kaizen Programming KP 2014 [65]
Membrane Algorithms MA 2005 [199]
Mine Blast Algorithm MBA 2013 [229]
Passing Vehicle Search PVS 2016 [234]
Artificial Raindrop Algorithm RDA 2014 [128]
Scientifics Algoritmhs SA.2 2014 [92]
Stochastic Fractal Search SFS.1 2015 [231]
Search Group Algorithm SGA.2 2015 [246]
Simple Optimization SOPT 2012 [110]
Small World Optimization SWO 2006 [75]
The Great Deluge Algorithm TGD 1993 [76]
Wind Driven Optimization WDO 2010 [21]
Ying-Yang Pair Optimization YYOP 2016 [214]
Table 11: Meta-heuristics of the category Miscelanea

3.6 Miscelanea

In this category there are include the algorithms that do not fit in any of the previous categories, i.e., we can find algorithms of diverse characteristics or abilities like Ying-Yang Pair Optimization, YYOP [214].

Although the category defined does not present an uniform behavior, we have decided to created to show algorithms with a very different inspiration. The idea is that, in a future, when they arise more algorithms inspired in similar concepts that existing in this category, then they can form a new category by their own, reducing the Miscelanea category size. If we let these algorithms in the global category, that logical step in the evolution of the taxonomy will be more difficult.

The complete list of algorithms in this category is in Table 11.

4 Second Taxonomy: By behavior

In this second taxonomy, we are going to catalog the different proposals by its behavior, without considering their inspirational nature. In order to do that, we need a clear criterion but that, at the same time, could summarize as much as possible the behavior of the algorithm. The criterion followed is the mechanism used to create new solutions, or change existing solutions, because is one of the main features of each algorithm.

First, we have divided the proposals in two categories:

Diffferential-Vector movement

in which the new solutions are produced by a shift or a mutation of a previous solution. The new one could compete against previous one, or another one of the population to get into the population. This type of generation implies a solution as reference that is changed to produce the search. Maybe the most representative of this category would be the PSO [79], in which each solution evolves with a velocity vector to explore the domain search. Other popular algorithm is DE [63], in which new solutions are produced by differential vectors over existing solutions. One a solution is selected as reference one, the second part is decided the movement, influenced by other solutions. The decision as to which solutions are influential in the movement is a decision that has an enormous influence on behavior. We divide this category considering that decision. The search can be guided considering all the population, only the significant solutions (like the best and/or the worst ones), or using a small group, that could be the neighbourhood around each solution, or, in algorithms with subpopulations, only the subpopulation in which each solution belongs.

Solution creation

in which the new solutions are not generated by mutation/movement of a single solution, but by combination of several ones (so there is not a only one main parent solution), or other mechanism. The are usually two approaches to create new solutions. The first one is by combination, or crossover of several solutions, the classic GA [167] is a clear example of this type. Another approach is by stigmergy, in which there is an indirect coordination between the different solutions or agents, usually using an intermediate structure, to generate better ones. The classic example of this is the Ant Colony Optimization, ACO [71], in which new solutions are generated by the trace of pheromones left by different agents.

{forest}

forked edges, for tree=font=, rounded corners, top color=gray!5, bottom color=gray!10, edge+=darkgray, line width=1pt, draw=darkgray, align=left, anchor=children, s sep=1cm, l sep=1cm, align=left, anchor=west, anchor=base west, before packing=where n children=3calign child=2, calign=child edge, before typesetting nodes=where content=coordinate, [Nature and population-based
Meta-heuristics (278: 100%), blur shadow [Solution Creation
Based (90: 32.37%) [Combination
(82: 29.50%)] [Stimergy
(8: 2.88%)] ] [Differential-Vector
Movement (188: 67.63%) [All Population
(13: 4.68%)] [Groups Based
(24: 8.63%) [Subpopulation
(20 : 7.19%)] [Neighbourhood
(4 : 1.44%)] ] [Representative
Based (151: 54.32%)] ] ]

Figure 4: Classification of the reviewed papers using the behavior taxonomy

Figure 4 shows the classification we have reached, indicating, for the 278 reviewed algorithms, the number and ratio of proposals classified in each category and subcategory. It can be observed that the most natural-inspired proposals the new solutions are generated by differential-vector movement of existing ones (67% vs 32%), and, among them, the search is mainly guided (54% in global, 80% from this category) by representative solutions, mainly the current best solution (in a scheme very similar to PSO). Thus, this process, to create new solutions by movement vectors orient to the best solution, is the search mechanism chosen by more than half (54%) of all the 278 proposals.

In next subsections we are going to give a brief global view of different categories. For each category we are going to describe the main characteristics of each of them, an example, and a table with the algorithms belonging to that category.

4.1 Solution Creation

This category is composed of algorithms that explore the domain search generating new solutions, not moving existing ones. This group is a significant ratio (32%) of all proposals. In particular, this category includes many classic algorithms, like GA [167]. These methods have the main advantage to be able to adapt the generation method to the particular problem, allowing different possible representations and, therefore, be applied to a wider range of problems.

In the following, we describe the different categories.

Creation by Combination

The most common option to generate new solution is to combine existing ones. In these algorithms, different solutions are selected, and combined using a crossover or combining method to create new solutions. The underlying idea is that combining good solutions can be generate good, even better, solutions. The combining method can be specific for the problem to optimise or more general. It is one mechanism that can be adapted to many different representation. The more popular algorithm in this category is genetic algorithm [167], but there are many bio-inspired algorithm with a similar behavior from different nature-inspiration, like Cultural Optimization CA [283] (Social Human category), Lion Algorithm LA [302] (Swarm Intelligence), Particle Collision Algorithm PCA [228] (Chemical), Light Ray Optimization LRO [129] (Physics), ….

Tables 12, 13, and 14 show the algorithms in this category.

Solution Creation - Combination (I)
Algorithm Name Acronym Year Reference
Artificial Beehive Algorithm ABA 2009 [192]
Artificial Chemical Reaction Optimization Algorithm ACROA 2011 [7]
Artificial Infections Disease Optimization AIDO 2016 [122]
Artificial Reaction Algorithm ARA 2013 [170]
Asexual Reproduction Optimization ARO 2010 [91]
Bacterial-GA Foraging BGAF 2007 [40]
Bumblebees BB 2009 [50]
Biogeography Based Optimization BBO 2008 [247]
Bee Colony Optimization BCO 2005 [265]
BeeHive Algorithm BHA 2004 [279]
Bees Life Algorithm BLA 2018 [28]
Bird Mating Optimization BMO 2014 [14]
Bean Optimization Algorithm BOA 2011 [311]
Bee System BS 1997 [233]
Bar Systems BS.2 2008 [68]
Backtracking Search Optimization BSO.3 2012 [48]
Bees Swarm Optimization Algorithm BSOA 2005 [74]
Cultural Algorithms CA 1999 [283]
Crystal Energy Optimization Algorithm CEO 2016 [93]
Consultant Guide Search CGS 2010 [125]
Coral Reefs Optimization CRO 2014 [230]
Chemical Reaction Optimization Algorithm CRO.1 2010 [153]
Cuckoo Search CS 2009 [291]
Clonal Selection Algorithm CSA 2000 [201]
Dolphin Echolocation DE.1 2013 [140]
Ecogeography-Based Optimization EBO 2014 [314]
Eco-Inspired Evolutionary Algorithm EEA 2011 [206]
Electromagnetic Field Optimization EFO 2016 [4]
Extremal Optimization EO 2000 [29]
Evolution Strategies ES 2002 [26]
Egyptian Vulture Optimization Algorithm EV 2013 [256]
Frog Call Inspired Algorithm FCA 2009 [194]
Forest Optimization Algorithm FOA.1 2014 [102]
Table 12: Algorithms of the category Solution Creation-Combination (I)
Solution Creation - Combination (II)
Algorithm Name Acronym Year Reference
Genetic Algorithms GA 1989 [167]
Galaxy Based Search Algoritm GBSA 2011 [238]
Gene Expression GE 2001 [94]
Group Leaders Optimization Algorithm GLOA 2011 [64]
Harmony Search HS 2005 [154]
Harmony Elements Algorithm HEA 2009 [57]
Human Evolutionary Model HEM 2007 [187]
Human-Inspired Algorithms HIA 2009 [307]
Hysteresis for Optimization HO 2002 [304]
Immune-Inspired Computational Intelligence ICI 2008 [52]
Invasive Tumor Optimization Algorithm ITGO 2015 [262]
Weed Colonization Optimization IWO 2006 [169]
Keshtel Algorithm KA 2014 [108]
Kaizen Programming KP 2014 [65]
Lion Algorithm LA 2012 [220]
Light Ray Optimization LRO 2010 [129]
Migrating Birds Optimization MBO.2 2012 [77]
Marriage In Honey Bees Optimization MHBO 2001 [1]
Method of Musical Composition MMC 2014 [189]
Melody Search MS.1 2011 [13]
Natural Aggregation Algorithm NAA 2016 [164]
Old Bachelor Acceptance OBA 1995 [120]
Photosynthetic Algorithm PA 1999 [193]
Particle Collision Algorithm PCA 2007 [228]
PopMusic Algorithm PopMusic 2002 [259]
Queen-Bee Evolution QBE 2003 [255]
Reincarnation Concept Optimization Algorithm ROA 2010 [241]
Shark Search Algorithm SA 1998 [117]
Simulated Annealing SA.1 1989 [147]
Scientifics Algoritmhs SA.2 2014 [92]
SuperBug Algorithm SuA 2012 [10]
Simulated Bee Colony SBC 2009 [168]
Snap-Drift Cuckoo Search SDCS 2016 [222]
Self-Defense Mechanism Of The Plants Algorithm SDMA 2018 [34]
Sheep Flock Heredity Model SFHM 2001 [196]
Table 13: Algorithms of the category Solution Creation-Combination (II)
Solution Creation - Combination (III)
Algorithm Name Acronym Year Reference
Shuffled Frog-Leaping Algorithm SFLA 2006 [89]
Saplings Growing Up Algorithm SGA.1 2007 [136]
Search Group Algorithm SGA.2 2015 [246]
Self-Organizing Migrating Algorithm SOMA 2004 [306]
Simple Optimization SOPT 2012 [110]
The Great Deluge Algorithm TGD 1993 [76]
Small World Optimization SWO 2006 [75]
Virus Optimization Algorithm VOA 2009 [132]
Viral Systems Optimization VSO 2008 [51]
Wasp Colonies Algorithm WCA 1991 [268]
Water Flow-Like Algorithms WFA 2007 [290]
Water Flow Algorithm WFA.1 2007 [20]
Wasp Swarm Optimization WSO 2005 [210]
Ying-Yang Pair Optimization YYOP 2016 [214]
Table 14: Algorithms of the category Solution Creation-Combination (III)

Creation by stigmergy

Another popular option of creating new solutions, is the stigmergy. In this model, there is an indirect coordination between the different solutions or agents, used to create new solutions. This communication is usually done using an intermediate structure, with information obtained from the different solutions, used to generate new solutions oriented to more promising areas.

An example of this algorithm is the Ant Colony Optimization, ACO [71]. In this algorithm, inspired by the foraging mechanism of ants, each solution produces a trace of pheromones in function on its fitness. Later, new solutions are generated, dimension by dimension, considering the pheromones, enforcing the search around most promising values for each dimension.

In Table 15 there are listed the algorithms in this category. This is a reduced list, with the majority of them inspired, similarly to ACO, to swarm intelligence algorithms (and in particular, based on insects), but there are also several algorithms inspired in physics, like algorithms inspired in water flow [270] and river formation [217].

Solution Creation - Stimergy
Algorithm Name Acronym Year Reference
Ant Colony Optimization ACO 1996 [72]
Bee System BS.1 2002 [161]
Intelligence Water Drops Algorithm IWD 2009 [237]
River Formation Dynamics RFD 2007 [217]
Termite Hill Algorithm TA 2012 [319]
Virtual Ants Algorithm VAA 2006 [295]
Virtual Bees Algorithm VBA 2005 [297]
Water-Flow Algorithm Optimization WFO 2011 [270]
Table 15: Algorithms of the category Solution Creation-Stimergy

4.2 Differential-Vector Movement

In this popular category (it contains 67% of the analysed algorithms) the new solutions are obtained by the movement of existing ones. Using a solution as reference, it is moved using a differential vector to create a new one (that could replace the previous one or it competes to be included into the population).

The crucial decision is how that differential vector is calculated. This differential vector could be calculated toward another solution (usually a better one), or through lineal combination of different differential vector, allowing the combination of attraction vectors (toward best solutions) with repulsion vectors (away from worse ones, or from other solutions, to enforce diversity).

The mathematical nature of this operation usually restricts the domain of the representation to a numerical representation, usually real parameters.

This category is divided in function of which solutions are considered to create the movement vector. In the following, we are going to describe each case.

All Population

One possible criterion is used all the individuals in the population to generate the movement of each solution. In these algorithms, all individuals have a influence over the movement of the other ones. Because there are not always guided by the best ones, the influence is usually weighted according to fitness difference and/or distance between solutions. A significant example is Firefly [298], in which a solution suffers a force toward better solutions, in function on the distance (more nearly have a stronger influence than far away solutions). There are algorithms based on different categories in previous taxonomy.

Influenced by All Population
Algorithm Name Acronym Year Reference
Artificial Electric Field Algorithm AEFA 2019 [287]
Artificial Plants Optimization Algorithm APO.1 2013 [312]
Chaotic Dragonfly Algorithm CDA 2018 [235]
Central Force Optimization CFO 2008 [98]
Charged Systems Search CSS 2010 [146]
Electromagnetism Mechanism Optimization EMO 2003 [124]
Firefly Algorithm FA 2009 [298]
Gravitational Clustering Algorithm GCA 1999 [152]
Group Counseling Optimization GCO 2010 [82]
Gravitational Search Algorithm GSA 2009 [224]
Human Group Formation HGF 2010 [266]
Hoopoe Heuristic Optimization HHO.1 2012 [85]
Integrated Radiation Optimization IRO 2007 [46]
Table 16: Algorithms of the subcategory Influenced by All Population

Representative solutions

In this group, the most numerous, the different movement of each solution is only influenced by a small group of representative solutions. Mainly these representative are the best solutions, being able to be guided only by the current best individual of the population.

The classic example is PSO [79], in which each solution or particle is guided by the global current best solution and best solution obtained by that particle during the search. Another classic algorithm in this category is the majority of DEs [63], in which sometimes the influence of best one (or better ones) is combined with a differential vector toward random individuals (for more diversity). However, in this category there are many algorithms with other differences as considering nearly better solutions (as Bat Inspired Algorithm [299], Brain Storm Optimization Algorithm [243]), or the worse ones (to avoid less promising regions), as Grasshopper algorithm [232]. The majority of all proposals are into this category (more than half of all considered algorithms), specially the Swarm-Intelligence category, possible because many of them have a behavior inspiration by PSO or DE (we will see than in Section 5).

Tables 17, 18, 19, 20, and 21 show the different algorithms in this category.

Influenced by Representative Solutions
Algorithm Name Acronym Year Reference
Artificial Algae Algorithm AAA 2015 [272]
Artificial Bee Colony ABC 2007 [134]
African Buffalo Optimization ABO 2016 [24]
Atmosphere Clouds Model ACM 2013 [100]
Ant Lion Optimizer ALO 2015 [179]
Across Neighbourhood Search ANS 2016 [282]
Anarchic Society Optimization ASO 2012 [242]
Artificial Searching Swarm Algorithm ASSA 2009 [39]
Artificial Tribe Algorithm ATA 2009 [41]
African Wild Dog Algorithm AWDA 2013 [253]
Big Bang Big Crunch BBBC 2006 [87]
Bacterial Chemotaxis Optimization BCO.2 2002 [58]
Bacterial Colony Optimization BCO.1 2012 [200]
Bald Eagle Search Optimization BES 2019 [9]
Black Hole Optimization BH 2013 [111]
Bat Intelligence BI 2012 [166]
Bat Inspired Algorithm BIA 2010 [299]
Blind, Naked Mole-Rats Algorithm BNMR 2013 [258]
Butterfly Optimizer BO 2015 [150]
Bird Swarm Algorithm BSA 2016 [171]
Bee Swarm Optimization BSO 2010 [6]
Bioluminiscent Swarm Optimization Algorithm BSO.1 2011 [66]
Brain Storm Optimization Algorithm BSO.2 2011 [243]
Collective Animal Behavior CAB 2012 [53]
Catfish Optimization Algorithm CAO 2011 [245]
Cricket Behavior-Based Algorithm CBBE 2016 [33]
Collective Decision Optimization Algorithm CDOA 2017 [308]
Cloud Model-Based Algorithm CMBDE 2012 [317]
Camel Traveling Behavior COA.1 2016 [123]
Cognitive Behavior Optimization Algorithm COA.2 2016 [158]
Chaos Optimization Algorithm COA.3 1998 [156]
Competitive Optimization Algorithm COOA 2016 [239]
Cat Swarm Optimization CSO 2006 [43]
Table 17: Algorithms of the subcategory Influenced by Representative Solutions (I)
Influenced by Representative Solutions (II)
Algorithm Name Acronym Year Reference
Dragonfly Algorithm DA 2016 [180]
Differential Evolution DE 1997 [213]
Dolphin Partner Optimization DPO 2009 [244]
Differential Search Algorithm DSA 2012 [49]
Elephant Herding Optimization EHO 2016 [275]
Elephant Search Algorithm ESA 2015 [67]
Eagle Strategy ES.1 2010 [293]
Fireworks Algorithm Optimization FAO 2010 [261]
Flocking Base Algorithms FBA 2006 [56]
Fast Bacterial Swarming Algorithm FBSA 2008 [45]
Football Game Inspired Algorithms FCA.1 2009 [90]
FIFA World Cup Competitions FIFAAO 2016 [226]
Flock by Leader FL 2012 [23]
Fruit Fly Optimization Algorithm FOA 2012 [205]
Flower Pollination Algorithm FPA 2012 [300]
Fish Swarm Algorithm FSA 2011 [271]
Fish School Search FSS 2008 [19]
Gases Brownian Motion Optimization GBMO 2013 [2]
Global-Best Brain Storm Optimization Algorithm GBSO 2017 [84]
Group Escape Behavior GEB 2011 [174]
Grenade Explosion Method GEM 2010 [5]
Gravitational Field Algorithm GFA 2010 [313]
Gravitational Interactions Algorithm GIO 2011 [96]
Good Lattice Swarm Optimization GLSO 2007 [251]
Grasshopper Optimisation Algorithm GOA 2017 [232]
General Relativity Search Algorithm GRSA 2015 [22]
Glowworm Swarm Optimization GSO 2013 [316]
Galactic Swarm Optimization GSO.2 2016 [195]
Goose Team Optimization GTO 2008 [277]
Grey Wolf Optimizer GWO 2014 [177]
Harry’s Hawk Optimization Algorithm HHO 2019 [116]
Heart Optimization HO.1 2014 [112]
Hurricane Based Optimization Algorithm HO.2 2014 [227]
Hunting Search HuS 2010 [203]
Table 18: Algorithms of the category Influenced by Representative Solutions (II)
Influenced by Representative Solutions (III)
Algorithm Name Acronym Year Reference
Honeybee Social Foraging HSF 2007 [216]
Ideology Algorithm IA 2016 [121]
Imperialist Competitive Algorithm ICA 2007 [15]
Interior Search Algorithm ISA 2014 [99]
Jaguar Algorithm JA 2015 [36]
Kinetic Gas Molecules Optimization KGMO 2014 [183]
Krill Herd KH 2012 [118]
Seven-Spot Ladybird Optimization LBO 2013 [278]
League Championship Algorithm LCA 2014 [137]
Leaders and Followers Algorithm LFA 2015 [105]
Lightning Search Algorithm LSA 2015 [240]
Locust Swarms Optimization LSO 2009 [38]
Membrane Algorithms MA 2005 [199]
Mine Blast Algorithm MBA 2013 [229]
Magnetotactic Bacteria Optimization Algorithm MBO 2013 [182]
Modified Cuckoo Search MCS 2009 [274]
Modified Cockroach Swarm Optimization MCSO 2011 [202]
Moth Flame Optimization Algorithm MFO 2015 [178]
Magnetic Optimization Algorithm MFO.1 2008 [264]
Monkey Search MS 2007 [191]
Multi-Verse Optimizer MVO 2016 [176]
OptBees OB 2012 [165]
Optimal Foraging Algorithm OFA 2017 [318]
Optics Inspired Optimization OIO 2015 [138]
Oriented Search Algorithm OSA 2008 [310]
Paddy Field Algorithm PFA 2009 [212]
Population Migration Algorithm PMA 2009 [309]
Parliamentary Optimization Algorithm POA 2008 [31]
Prey Predator Algorithm PPA 2015 [163]
Plant Propagation Algorithm PPA.1 2009 [254]
Particle Swarm Optimization PSO 1995 [79]
Penguins Search Optimization Algorithm PSOA 2013 [103]
Table 19: Algorithms of the subcategory Influenced by Representative Solutions (III)
Influenced by Representative Solutions (IV)
Algorithm Name Acronym Year Reference
Passing Vehicle Search PVS 2016 [234]
Artificial Raindrop Algorithm RDA 2014 [128]
Roach Infestation Problem RIO 2008 [113]
Radial Movement Optimization RMO 2014 [218]
Ray Optimization RO 2012 [141]
Runner Root Algorithm RRA 2015 [173]
Satin Bowerbird Optimizer SBO 2017 [109]
Stem Cells Algorithm SCA 2011 [257]
Sine Cosine Algorithm SCA.2 2016 [181]
Social Cognitive Optimization Algorithm SCOA 2010 [280]
Social Emotional Optimization Algorithm SEA 2010 [286]
Synergistic Fibroblast Optimization SFO 2017 [252]
Stochastic Focusing Search SFS 2008 [281]
Stochastic Fractal Search SFS.1 2015 [231]
Space Gravitational Algorithm SGA 2005 [119]
Soccer Game Optimization SGO 2012 [78]
Swarm Inspired Projection Algorithm SIP 2009 [250]
Soccer League Competition SLC 2014 [188]
Slime Mould Algorithm SMA 2008 [186]
Spider Monkey Optimization SMO 2014 [35]
States Matter Optimization Algorithm SMS 2014 [55]
Spiral Dynamics Optimization SO 2011 [260]
Spiral Optimization Algorithm SPOA 2010 [130]
Self-Driven Particles SPP 1995 [273]
Seeker Optimization Algorithm SOA 2007 [59]
Symbiosis Organisms Search SOS 2014 [42]
Social Spider Algorithm SSA 2015 [303]
Shark Smell Optimization SSO 2016 [3]
Swallow Swarm Optimization SSO.1 2013 [198]
Social Spider Optimization SSO.2 2013 [54]
See-See Partidge Chicks Optimization SSPCO 2015 [204]
Surface-Simplex Swarm Evolution Algorithm SSSE 2017 [107]
Table 20: Algorithms of the category Influenced by Representative Solutions (IV)
Influenced by Representative Solutions (V)
Algorithm Name Acronym Year Reference
Termite Colony Optimization TCO 2010 [115]
The Great Salmon Run Algorithm TGSR 2013 [190]
Teaching-Leaning Based Optimization Algorithm TLBO 2011 [223]
Tug Of War Optimization TWO 2016 [143]
Unconscious Search US 2012 [11]
Virus Colony Search VCS 2016 [157]
Variable Mesh Optimization VMO 2012 [215]
Volleyball Premier League Algorithm VPL 2017 [184]
Vibrating Particle Systems Algorithm VPO 2017 [144]
Vortex Search Algorithm VS 2015 [70]
Wolf Colony Algorithm WCA.1 2011 [160]
Water Cycle Algorithm WCA.2 2012 [88]
Wind Driven Optimization WDO 2010 [21]
Water Evaporation Optimization WEO 2016 [145]
Whale Optimization Algorithm WOA 2016 [175]
Wolf Pack Search WPS 2007 [289]
Weightless Swarm Algorithm WSA 2012 [269]
Wolf Search Algorithm WSA.1 2012 [263]
Water Wave Optimization Algorithm WWA 2015 [315]
Zombie Survival Optimization ZSO 2012 [267]
Table 21: Algorithms of the category Influenced by Representative Solutions (V)

Group Based

In this category, there are the algorithms that uses not representative solutions of all population (like the current best solution), but it only consider solutions of a group of the population. When the deplacement movement consider both a group and a representative of all the population, it is in previous category, because usually the global representative has the stronger influence over the search.

There are two different subcategories:

Subpopulation based In this subcategory, there is not a only population, but there are several subpopulations, and each solution is only affected by the other solutions in the same subpopulation. Table 22 shows the algorithms in that category. Examples of algorithms in these categories are the Lion Algorithm [220], or the Monarch Butterfly Optimization, MBO [276].

Subpopulation Based
Algorithm Name Acronym Year Reference
Artificial Chemical Process ACP 2005 [126]
Artificial Cooperative Search ACS 2012 [47]
Artificial Physics Optimization APO 2009 [284]
Bee Colony-Inspired Algorithm BCIA 2009 [106]
Colliding Bodies Optimization CBO 2014 [142]
Cuttlefish Algorithm CFA 2013 [81]
Cuckoo Optimization Algorithm COA 2011 [219]
Chicken Swarm Optimization CSO.1 2014 [172]
Exchange Market Algorithm EMA 2014 [104]
Greedy Politics Optimization Algorithm GPO 2014 [155]
Group Search Optimizer GSO.1 2009 [114]
Hierarchical Swarm Model HSM 2010 [37]
Ions Motion Optimization Algorithm IMO 2015 [127]
Lion Optimization Algorithm LOA 2016 [302]
Monarch Butterfly Optimization MBO.1 2017 [276]
Social Behavior Optimization Algorithm SBO.1 2003 [225]
Sperm Whale Algorithm SWA 2016 [80]
Thermal Exchange Optimization TEO 2017 [139]
Wisdom of Artificial Crowds WAC 2011 [288]
Worm Optimization WO 2014 [12]
Table 22: Algorithms of the category Solution Subpopulation Based

Neighbourhood based In this subcategory, each solution is affected only by solutions in its local neighbourhood. Table 23 shows the algorithms in that category. Examples of algorithms in these categories are the Bacterial Foraging Optimization [162], in which all the solutions in the neighbourhood affect, in a attractive way (if the other solution has better fitness) or in a repulsive way (when the other solution is worse).

Neighbourhood Based
Algorithm Name Acronym Year Reference
Bees Algorithm BA 2006 [208]
Biomimicry Of Social Foraging Bacteria for Distributed Optimization BFOA 2002 [162]
Bacterial Foraging Optimization BFOA.1 2009 [62]
Gravitational Emulation Local Search GELS 2009 [17]
Table 23: Algorithms of the category Solution Movement-Groups-Neighbourhood

5 Difference between the taxonomies and more influential algorithms

In this section we are going to analyse the results obtained by the different taxonomies.

From our survey, comparing the different taxonomies, it can be observed that there is a strong correlation between them, observing that features characterizing one algorithm are rarely associated with its inspirational model. For instance, algorithms inspired in concepts as differences as the gravitational forces, like GFA [313], and in animal evolution, like african buffalos, ABO [24], have a lot of similarity between them and with PSO [79]. In can be observed that, in the second taxonomy, each category have algorithms of many different nature-inspiration sources. The contrary is also very common, proposals with very similar bio-inspiration, and so they are in the same category, but with completely resultant algorithms. A good example is the Delphi Echolocation algorithm (DE [140]) and the Dolphin Partner Optimization [244], both are inspired in the same animal (dolphin) and its mechanism to detect fishes (echolocation), but obtaining very different algorithms: First one create new solutions by combination, while second one is very similar to PSO, guided mainly by the best solution.

Even more, not only the largest subcategory of second taxonomy (Differential-Vector Movements guided by the representative) there more than half of proposals (54%), but also it contains algorithms from all the different categories in first taxonomy: Social Human (as Anarchic Society Optimization, ASO, [242]), microorganisms (Bacterial Colony Optimization [200]), Physics/Chemistry category (as Fireworks Algorithm Optimization, FAO [261]), Evolutionary Population (as Variable Mesh Optimization, VMO [215]), even Plants-Based (as Flower Pollination Algorithm, FPA [300]). Also, it is not only for that subcategory, others, like Creation solutions, also includes algorithms for so many nature inspirations.

Considering the previous examples, it is clear that the real behavior of the proposed algorithm is a lot more informative that their nature or biological inspiration. Even more, in our classification, with a so wide nature inspiration algorithms, in all reviewed proposals (more than two hundreds) we have observed that the huge diversity in the inspiration does not guarantee diversity in the behavior of the algorithms. Another previous works in the literature have proposed doubts about if the novelty in the nature inspiration actually means different algorithms that could produce competitive results [248, 101].

From previous section, we have observed that the majority of proposals (more than half, 54%) generates new solutions based on differential-vector forces over existing ones, like in PSO or DE. Next, we are going to observe which of the classic algorithms are more similar to new ones.

From our study of the total of papers (211), until 125 contained off them (59% of the total), were so mainly influenced by previous classic algorithms (PSO, DE, GA, ACO, ABC or SA), that without the bio-inspiration, they could be considered as small versions of them. Only 86 papers (41%) have enough differences to be considered a new proposal by itself instead of a version of a existing algorithm.

Reference algorithms Papers Percentage
PSO 48 22.75%
DE 39 18.48%
GA 21 9.95%
ACO 6 2.84%
ABC 8 3.79%
SA 3 1.42%
Total strongly based
on classic algorithms 125 59.24%
Table 24: Ratio of similar algorithms in the survey of meta-heuristics
Figure 5: Classification of proposals by its original algorithm
Figure 6: Ratio of similar algorithms in the survey of meta-heuristics

Then, in order to know of which are the most influential reference algorithms used to construct bio-inspired algorithms, we have grouped the proposals which could be considered versions of the same reference algorithm. Figure 5 shows the classification of each algorithm based on its behavior, and the number of proposals in each classification are summarized in Table 24, and visually shown in Figure 6.

From Table 24, it can be observed that the most influential algorithm was PSO, appearing in a 22% of proposals (and the 38% of proposals clearly based on a previous algorithm). Not only it is a very well-known bio-inspired algorithm (one of the more visible ones in the Swarm Intelligence category), but also it is the reference of many bio-inspired algorithms. As we can see, PSO is the biggest representative of its category. The simplicity of this algorithm and its ability to reach an optimum quickly have inspired many authors to create new metaheuristics base in it. Thus, many algorithms that try to simulate the behavior of biological systems finally carry out the optimization through a movement mechanism strongly influenced by PSO (in some cases, without any significant difference).

The second more influential algorithm is DE, a well-know algorithm that did not come from a strong nature inspiration, only the evolution of a population. This algorithm, is with GA, the most representative algorithms in the Evolutionary Computation category. Its technique of creating new solutions with a lineal combination of existing ones, is mainly used by the 18% of all proposals, maybe by its good behavior in many optimization problems [185].

The third one is GA, a very classic algorithm whose mechanisms have been used by around 10% of all reviewed nature-inspired algorithms.

From a point of view of categories of algorithms, the categories whose algorithms are more used to create new nature-based algorithms, are two. For one hand, Swarm Intelligence, almost 30% of all studied nature inspired algorithms are variations of SW algorithms (PSO, ACO, and ABC) Evolutionary Algorithms category is also used another 28% of cases. It is also remarkable that more classic algorithms, GA and SA, are used by only the 11% of proposals, showing that its influence is declining, compared to other algorithms, such as DE and PSO.

To summarize, although in the last years there have been proposed many nature-inspired algorithms (we have reviewed more than two hundreds of proposals, and the number of nature-inspired proposed rise every year), more than half are small versions of only three very classical algorithms (PSO, DE, and GA), confirming that a huge number of nature sources does not mean significant different algorithms.

6 Improving the state of bio-inspired algorithms

After reviewing the proposals, we have extracted several issues that we consider are challenges that nature-inspired have to deal with, in not particular order.

  • First, as it was shown in Section 5, although there are nowadays a huge number of nature inspired algorithms (and the number increases each year) the diversity in the algorithms themselves is much more limited. There are algorithms of different categories with different inspiration sources that are very closed in terms of behavior. Thus, researchers should be more focus on designing algorithms by its good behavior (good performance, simplicity, ability to run it in parallel, suitability to a specific type of problems, …) than in its new nature inspiration source, because there is already an excessive stack of proposals without innovation or improvement over previous ones.

  • Several papers are difficult to understand due to the extended usage of the vocabulary related to the natural inspiration. It is logical to use the semantic of the domain, but it would be desirable that the description of the algorithm could be defined also using the terms more related with the optimization process, like optimum/a and individuals or solutions. An excessive usage of the specific terminology (without indicate the correspondences) could make difficult to follow the details of the algorithm for researchers not so accustomed to such terminology.

  • The lack of good comparisons is another important drawback of many proposals. When these new algorithms are proposed, unfortunately many of them are only mainly compared with very basic and classic algorithms (like GA or PSO). However, these algorithms have been widely surpassed by more advanced versions over the years, so obtaining better performance than classic algorithm like those is relatively easy, and does not demonstrate competitive performance [101]. Sometimes there are also compared with similarly inspired algorithms, but still not with competitive algorithms outside that semantic niche [101, 159]. This is a very seriously barrier for their application in real-world problems: until they do not prove to be competitive, there will not actually be used, or known outside the original authors.

  • Finally, we would also like to note that the metaheuristics with the best results in many competitions [185], are far from being bio-inspired algorithms, although some of them retain their nature-inspired roots, mainly the DE algorithms. It was expected, because the lack of good comparisons do not encourages researchers to use them as reference algorithms to design better proposals. The current tendency of so many proposals can be counterproductive, it could be better to have a more reduced number of proposals but with better ideas that could improve performance.

To summarize, the wide and growing number of nature-inspired proposals not only make difficult to keep up, but it does not provide, in terms of performance and behavioral differences, what is expected. Bio-inspired algorithms are a very active and promising field [236], but in order to improve its evolution, better comparisons must be used in the proposals, that could produce a evolution of new versions that could give better competitive results and/or other significant advantages.

7 Conclusions

Nature and biological organisms have been a source of inspiration of many algorithms. During last years, many nature and bio-inspired algorithms have been proposed, achieving a number difficult to manage. A good taxonomy would be very desirable, because it allow researchers to organize them with well-defined characteristics that let researchers to classify both the existing algorithms and new proposals in the future. Unfortunately, there is not a clear taxonomy, developed considering the different proposals through the years.

In this work, we have reviewed more than two hundred nature and bio-inspired algorithms and we have proposed both taxonomies that group the different proposals in categories and subcategories. The first one considering its source of inspiration, and the second one considering its behavior. It is shown the proposals in each one of the categories, and the summarize of each category.

Then, the different taxonomies have been compared, and identified for each one of them the more similar classic algorithm. We have observed that there is a poor relationship between the natural inspiration of an algorithm and its behavior, and that, although many algorithms have very different biological and nature sources, their similarities are greater than expected. Even more, more of 50% of all proposals follow a very similar behavior (exploring moving using a differential-vector toward the current best solution), so the suppose innovation obtained by so many proposals is not such. Even more, more of 50% of proposals are versions of algorithms like PSO, DE, or GA. Specially PSO, more than 20% of proposed nature and bio-inspired algorithms in last years was actually versions of PSO. Also, 18% of the studied proposals were versions of the DE model. Thus, although there are many proposals based in different concepts of reality, the majority of them are actually more similar than expected.

Finally, after remarking several future challenges for these algorithms, we give several suggestions to continue improving the field.

Acknowledgments

This work was supported by grants from the Spanish Ministry of Science and the European Fund (FEDER) under projects (TIN2017-89517-P, …).

Compliance with Ethical Standards

Ethical approval: This article does not contain any studies with human participants or animals performed by any of the authors.

Funding: This work was supported by grants from the Spanish Ministry of Science and the European Fund (FEDER) under projects (TIN2017-89517-P, …).

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