Taxonomy of bioinspired algorithms
Abstract
In recent years, a great variety of nature and bioinspired 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 metaheuristics in welldefined categories. In this work, we have reviewed more than two hundred natureinspired and bioinspired 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 – natureinspired algorithms, bioinspired algorithms, taxonomy, classification
1 Introduction
There are many realworld 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 bioinspired 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 naturebased 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 Bioinspired 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 realworld problems with a increasing number of data as processing images or data mining [296].
Because naturebased and Bioinspired 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 bioinspired 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 bioinspired metaheuristics 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 metaheuristic, although not all may reach into an algorithm capable of reaching global optimum values of problems.
In Figure 1, you can see the increasing number of papers/book chapters published in the last years with bioinspired algorithm in the abstract. In these papers, many of them were proposing new bioinspired 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 welldefined characteristics that let researchers to classify both the existing bioinspired 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 metaheuristic.
In this paper, we present two different taxonomies for naturebased algorithms:

The first one is a naturebased 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 doubletaxonomy 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 doubleclassification allows researchers to identify each new proposal in the adequate context.
In order to make a good taxonomy of the metaheuristics 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 metaheuristics 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 naturebased 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 metaheuristics, 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 bioinspired 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 multiobjective problems [305]. For specific realworld problems, sometimes there are so many literature about nature and bioinspired algorithms, that specific surveys have been developed: For Telecommunications [292], Robotics [25], Data Mining [97], or even specific realworld problems like power systems [69], designing computer networks [73], automatic clustering [131], face recognition [8], or intrusion detection [148].
Many specific bioinspired 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 bioinspired algorithms, [249] explains how the metaphor and the biological idea is used to create a metaheuristic and it offers us some examples and characteristics of this process. Books like [30] or [301] show many natureinspired algorithms, but they are more focused in describing different algorithms than in classify or analyse them.
There are several studied comparing bioinspired 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 bioinspired algorithms, in order to give a guideline. More recently, [207] studied several recent bioinspired 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 bioinspired 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 metaheuristics attending to their biological inspiration, that start proposing some similar categories: Swarm Intelligence, Physics and Chemistry Based, Bioinspired algorithms (not SIbased), 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 HumanBased Method. At different of previous one, a new category, HumanBased 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 metaheuristics 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 natureinspired 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 Interactioncollective behavior, if the individuals cooperate or compete between them. The third principle is the diversificationpopulation control, in which they are classified if the population have a converging tendency, a diffuse tendency, or not specific tendency. Then, 22 bioinspired algorithms are classified by each one of them, and the grouped obtained by each principle are experimentally compared.
3 First Taxonomy: By naturebase inspiration
In this section, we propose a novel taxonomy based on naturebase inspiration of the natureinspired 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, humanbeing, … In some papers, author suggest a possible category of more wellestablished 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 tradeoff 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.
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 populationbased 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] 
EcogeographyBased Optimization  EBO  2014  [314] 
EcoInspired Evolutionary Algorithm  EEA  2011  [206] 
Evolution Strategies  ES  2002  [26] 
Genetic Algorithms  GA  1989  [167] 
Gene Expression  GE  2001  [94] 
ImmuneInspired Computational Intelligence  ICI  2008  [52] 
Weed Colonization Optimization  IWO  2006  [169] 
Marriage In Honey Bees Optimization  MHBO  2001  [1] 
QueenBee Evolution  QBE  2003  [255] 
SuperBug Algorithm  SuA  2012  [10] 
Stem Cells Algorithm  SCA  2011  [257] 
Sheep Flock Heredity Model  SFHM  2001  [196] 
SelfOrganizing Migrating Algorithm  SOMA  2004  [306] 
Variable Mesh Optimization  VMO  2012  [215] 
In Table 1 there are shown algorithms in this category. It can observed wellknown and classic wellknown 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, selforganised 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, metaheuristics 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 wellknown 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, Foraginginspired 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 ColonyInspired 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] 
BacterialGA 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 MoleRats 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] 
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 BehaviorBased 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] 
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] 
SevenSpot 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] 
Swarm Intelligence (IV)  

Algorithm Name  Acronym  Subcategory  Type  Year  Reference 
Sine Cosine Algorithm  SCA.2  Other  Movement  2016  [181] 
SnapDrift Cuckoo Search  SDCS  Flying  Foraging  2016  [222] 
Shuffled FrogLeaping 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] 
SeeSee Partidge Chicks Optimization  SSPCO  Flying  Movement  2015  [204] 
SurfaceSimplex 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] 
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.
Terrestrial Animals Metaheuristics in this category are inspired by foraging or movements in terrestrial animals. The most wellknown algorithm of this category is classic metaheuristic, 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 metaheuristics 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 Metaheuristics 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 metaheuristics 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 25 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, foraginginspired is a term that is becoming more and more consolidated, appearing in the name of several bioinspired 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 wellknown 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 spacebased algorithms as BH or GBSA. Also, there are wellknown 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] 
MultiVerse 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] 
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] 
SelfDriven 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 FlowLike Algorithms  WFA  2007  [290] 
Water Flow Algorithm  WFA.1  2007  [20] 
WaterFlow Algorithm Optimization  WFO  2011  [270] 
Water Wave Optimization Algorithm  WWA  2015  [315] 
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] 
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] 
GlobalBest 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] 
HumanInspired 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] 
TeachingLearning 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] 
PlantsBased  

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] 
SelfDefense Mechanism Of The Plants Algorithm  SDMA  2018  [34] 
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 wellknown 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 ModelBased 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] 
YingYang Pair Optimization  YYOP  2016  [214] 
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 YingYang 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:
 DiffferentialVector 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.
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 naturalinspired proposals the new solutions are generated by differentialvector 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 bioinspired algorithm with a similar behavior from different natureinspiration, 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), ….
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] 
BacterialGA 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] 
EcogeographyBased Optimization  EBO  2014  [314] 
EcoInspired 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] 
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] 
HumanInspired Algorithms  HIA  2009  [307] 
Hysteresis for Optimization  HO  2002  [304] 
ImmuneInspired 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] 
QueenBee 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] 
SnapDrift Cuckoo Search  SDCS  2016  [222] 
SelfDefense Mechanism Of The Plants Algorithm  SDMA  2018  [34] 
Sheep Flock Heredity Model  SFHM  2001  [196] 
Solution Creation  Combination (III)  

Algorithm Name  Acronym  Year  Reference 
Shuffled FrogLeaping Algorithm  SFLA  2006  [89] 
Saplings Growing Up Algorithm  SGA.1  2007  [136] 
Search Group Algorithm  SGA.2  2015  [246] 
SelfOrganizing 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 FlowLike Algorithms  WFA  2007  [290] 
Water Flow Algorithm  WFA.1  2007  [20] 
Wasp Swarm Optimization  WSO  2005  [210] 
YingYang Pair Optimization  YYOP  2016  [214] 
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] 
WaterFlow Algorithm Optimization  WFO  2011  [270] 
4.2 DifferentialVector 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] 
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 SwarmIntelligence category, possible because many of them have a behavior inspiration by PSO or DE (we will see than in Section 5).
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 MoleRats 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 BehaviorBased Algorithm  CBBE  2016  [33] 
Collective Decision Optimization Algorithm  CDOA  2017  [308] 
Cloud ModelBased 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] 
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] 
GlobalBest 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] 
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] 
SevenSpot 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] 
MultiVerse 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] 
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] 
SelfDriven 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] 
SeeSee Partidge Chicks Optimization  SSPCO  2015  [204] 
SurfaceSimplex Swarm Evolution Algorithm  SSSE  2017  [107] 
Influenced by Representative Solutions (V)  

Algorithm Name  Acronym  Year  Reference 
Termite Colony Optimization  TCO  2010  [115] 
The Great Salmon Run Algorithm  TGSR  2013  [190] 
TeachingLeaning 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] 
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 ColonyInspired 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] 
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] 
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 natureinspiration sources. The contrary is also very common, proposals with very similar bioinspiration, 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 (DifferentialVector 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 PlantsBased (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 differentialvector 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 bioinspiration, 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% 
Then, in order to know of which are the most influential reference algorithms used to construct bioinspired 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 wellknown bioinspired algorithm (one of the more visible ones in the Swarm Intelligence category), but also it is the reference of many bioinspired 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 wellknow 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 natureinspired algorithms.
From a point of view of categories of algorithms, the categories whose algorithms are more used to create new naturebased 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 natureinspired algorithms (we have reviewed more than two hundreds of proposals, and the number of natureinspired 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 bioinspired algorithms
After reviewing the proposals, we have extracted several issues that we consider are challenges that natureinspired 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 realworld 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 bioinspired algorithms, although some of them retain their natureinspired 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 natureinspired proposals not only make difficult to keep up, but it does not provide, in terms of performance and behavioral differences, what is expected. Bioinspired 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 bioinspired 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 welldefined 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 bioinspired 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 differentialvector 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 bioinspired 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 (TIN201789517P, …).
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 (TIN201789517P, …).
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