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{{Short description|Population models of evolutionary algorithms}}
The '''population model''' of an [[Evolutionary algorithm|evolutionary algorithm]] (EA) describes the structural properties of its population to which its members are subject. A '''population''' is the set of all proposed solutions of an EA considered in one iteration, which are also called ''individuals'' according to the biological role model. The individuals of a population can generate further individuals as offspring with the help of the [[Genetic operator|genetic operator]]s of the procedure.

The simplest and widely used population model in EAs is the ''global'' or ''[[Biology:Panmixia|panmictic]] model'', which corresponds to an unstructured population.<ref name=":3" /><ref name=":6">{{Citation |last1=Gordon |first1=V.S. |title=Serial and Parallel Genetic Algorithms as Function Optimizers |date=1993 |url=https://www.cs.colostate.edu/TechReports/Reports/1993/tr-114.pdf |work=Proceedings of the Fifth International Conference on Genetic Algorithms |pages=177–183 |editor-last=Forrest |editor-first=S. |place=San Mateo, CA |publisher=Morgan Kaufmann |isbn=978-1-55860-299-1 |last2=Whitley |first2=D.}}</ref> It allows each individual to choose any other individual of the population as a partner for the production of offspring by [[Crossover (genetic algorithm)|crossover]], whereby the details of the [[Selection (genetic algorithm)|selection]] are irrelevant as long as the [[Fitness function|fitness]] of the individuals plays a significant role. Due to global mate selection, the genetic information of even slightly better individuals can prevail in a population after a few generations ([[Iteration|iteration]] of an EA), provided that no better other offspring have emerged in this phase. If the solution found in this way is not the [[Mathematical optimization|optimum]] sought, that is called ''[[Biology:Premature convergence|premature convergence]]''.<ref>{{Cite journal |last1=Leung |first1=Yee |last2=Gao |first2=Yong |last3=Xu |first3=Zong-Ben |date=1997 |title=Degree of population diversity - a perspective on premature convergence in genetic algorithms and its Markov chain analysis |url=https://ieeexplore.ieee.org/document/623217 |journal=IEEE Transactions on Neural Networks |volume=8 |issue=5 |pages=1165–1176 |doi=10.1109/72.623217 |issn=1045-9227 |pmid=18255718}}</ref> This effect can be observed more often in panmictic populations.<ref name=":1">{{cite thesis |last=Gorges-Schleuter |first=Martina |date=1990 |title=Genetic Algorithms and Population Structures - A Massively Parallel Algorithm. |type=PhD |publisher=Universität Dortmund, Fakultät für Informatik, Germany }}</ref>

In nature global mating pools are rarely found. What prevails is a certain and limited isolation due to spatial distance. The resulting local neighbourhoods initially evolve independently and [[Biology:Mutant|mutant]]s have a higher chance of persisting over several generations. As a result, [[Biology:Genotype|genotypic]] diversity in the gene pool is preserved longer than in a panmictic population.

It is therefore obvious to divide the previously global population by substructures. Two basic models were introduced for this purpose, the ''island models'', which are based on a division of the population into fixed subpopulations that exchange individuals from time to time,<ref name=":3" /><ref name=":0">{{cite thesis |last=Cantú-Paz |first=Erik |date=1999 |title=Efficient and Accurate Parallel Genetic Algorithms |series=Genetic Algorithms and Evolutionary Computation |volume=1 |type=PhD thesis, University of Illinois, Urbana-Champaign, USA |publisher=Springer, New York, NY |url=https://link.springer.com/book/10.1007/978-1-4615-4369-5 |doi=10.1007/978-1-4615-4369-5 |isbn=978-1-4613-6964-6 |language=en}}</ref> and the ''neighbourhood models'', which assign individuals to overlapping neighbourhoods,<ref name=":1" /><ref name=":8">{{Citation |last=Gorges-Schleuter |first=Martina |title=Explicit parallelism of genetic algorithms through population structures |date=1991 |url=http://link.springer.com/10.1007/BFb0029746 |work=Parallel Problem Solving from Nature |volume=496 |pages=150–159 |editor-last=Schwefel |editor-first=Hans-Paul |series=Lecture Notes in Computer Science |place=Berlin/Heidelberg |publisher=Springer-Verlag |language=en |doi=10.1007/bfb0029746 |isbn=978-3-540-54148-6 |access-date=2022-12-15 |editor2-last=Männer |editor2-first=Reinhard}}</ref> also known as ''cellular genetic'' or ''evolutionary algorithms'' (cGA or cEA).<ref name=":2">{{Cite book |last1=Gordon |first1=V. Scott |last2=Mathias |first2=Keith |last3=Whitley |first3=Darrell |title=Proceedings of the 1994 ACM symposium on Applied computing - SAC '94 |chapter=Cellular genetic algorithms as function optimizers |date=1994 |chapter-url=http://portal.acm.org/citation.cfm?doid=326619.326732 |language=en |location=Phoenix, Arizona, United States |publisher=ACM Press |pages=237–241 |doi=10.1145/326619.326732 |isbn=978-0-89791-647-9|s2cid=6418773 }}</ref><ref name=":5">{{Cite journal |last1=Giacobini |first1=M. |last2=Tomassini |first2=M. |last3=Tettamanzi |first3=A.G.B. |last4=Alba |first4=E. |date=October 2005 |title=Selection Intensity in Cellular Evolutionary Algorithms for Regular Lattices |url=https://www.researchgate.net/publication/3418844 |journal=IEEE Transactions on Evolutionary Computation |language=en |volume=9 |issue=5 |pages=489–505 |doi=10.1109/TEVC.2005.850298 |s2cid=3184685 |issn=1089-778X}}</ref> The associated division of the population also suggests a corresponding parallelization of the procedure. For this reason, the topic of population models is also frequently discussed in the literature in connection with the parallelization of EAs.<ref name=":3">{{Cite journal |last=Cantú-Paz |first=Erik |date=1998 |title=A survey of parallel genetic algorithms |url=https://neo.lcc.uma.es/cEA-web/documents/cant98.pdf |journal=Calculateurs Paralleles |volume=10 |issue=2 |pages=141–171}}</ref><ref name=":6" /><ref name=":1" /><ref name=":0" /><ref name=":7">{{Cite book |last1=Khalloof |first1=Hatem |last2=Mohammad |first2=Mohammad |last3=Shahoud |first3=Shadi |last4=Duepmeier |first4=Clemens |last5=Hagenmeyer |first5=Veit |title=Proceedings of the 12th International Conference on Management of Digital EcoSystems |chapter=A Generic Flexible and Scalable Framework for Hierarchical Parallelization of Population-Based Metaheuristics |date=2020-11-02 |chapter-url=https://dl.acm.org/doi/10.1145/3415958.3433041 |language=en |location=Virtual Event United Arab Emirates |publisher=ACM |pages=124–131 |doi=10.1145/3415958.3433041 |isbn=978-1-4503-8115-4|s2cid=227179748 }}</ref><ref name=":11">{{Citation |last=Sudholt |first=Dirk |title=Parallel Evolutionary Algorithms |date=2015 |url=http://staffwww.dcs.shef.ac.uk/people/d.sudholt/parallel-eas.pdf |work=Springer Handbook of Computational Intelligence |pages=929–959 |editor-last=Kacprzyk |editor-first=Janusz |place=Berlin, Heidelberg |publisher=Springer |language=en |doi=10.1007/978-3-662-43505-2_46 |isbn=978-3-662-43504-5 |access-date=2023-02-13 |editor2-last=Pedrycz |editor2-first=Witold}}</ref>

== Island models ==
[[File:Island population model of an evolutionary algorithm.png|thumb|Example of an island model consisting of eight islands and two neighbourhood structures: a simple unidirectional ring (black arrows) and a more complex structure (green and black arrows)]]
In the island model, also called the ''migration model'' or ''coarse grained model'', evolution takes place in strictly divided subpopulations. These can be organised panmictically, but do not have to be. From time to time an exchange of individuals takes place, which is called ''migration''.<ref name=":6" /><ref name=":0" /> The time between an exchange is called an ''epoch'' and its end can be triggered by various criteria: E.g. after a given time or given number of completed generations, or after the occurrence of stagnation. Stagnation can be detected, for example, by the fact that no fitness improvement has occurred in the island for a given number of generations. Island models introduce a variety of new strategy parameters:<ref name=":4">{{Citation |last=Cantú-Paz |first=Erick |title=Topologies, Migration Rates, and Multi-Population Parallel Genetic Algorithms |date=1999 |url=https://dl.acm.org/doi/pdf/10.5555/2933923.2933933 |work=Proc. of the 1st Annual Conf. on Genetic and Evolutionary Computation (GECCO) |pages=91–98 |publication-date=1999 |language=en}}</ref><ref>{{Cite journal |last1=Belkadi |first1=K. |last2=Gourgand |first2=M. |last3=Benyettou |first3=M. |date=2006-11-08 |title=Parallel genetic algorithms with migration for the hybrid flow shop scheduling problem |journal=Journal of Applied Mathematics and Decision Sciences |language=en |volume=2006 |pages=1–17 |doi=10.1155/JAMDS/2006/65746 |issn=1173-9126|doi-access=free }}</ref><ref>{{Cite journal |last1=Abdelhafez |first1=Amr |last2=Alba |first2=Enrique |last3=Luque |first3=Gabriel |date=September 2019 |title=Performance analysis of synchronous and asynchronous distributed genetic algorithms on multiprocessors |url=https://www.researchgate.net/publication/333839442 |journal=Swarm and Evolutionary Computation |language=en |volume=49 |pages=147–157 |doi=10.1016/j.swevo.2019.06.003|s2cid=196193164 }}</ref><ref name=":12">{{Cite journal |last1=Adar |first1=N. |last2=Kuvat |first2=G. |date=2016 |title=Parallel Genetic Algorithms with Dynamic Topology using Cluster Computing |url=http://www.aece.ro/abstractplus.php?year=2016&number=3&article=11 |journal=Advances in Electrical and Computer Engineering |language=en |volume=16 |issue=3 |pages=73–80 |doi=10.4316/AECE.2016.03011 |issn=1582-7445|doi-access=free }}</ref>
* Number of subpopulations
* Size of the subpopulations
* Neighbourhood relations between islands: they determine which islands are considered neighbouring and can thus exchange individuals, see picture of a simple unidirectional ring (black arrows) and its extension by additional bidirectional neighbourhood relations (additional green arrows)
*Criteria for the termination of an epoch, synchronous or asynchronous migration
* Migration rate: number or proportion of individuals involved in migration.
* Migrant selection: There are many alternatives for this. E.g. the best individuals can replace the worst or randomly selected ones. Depending on the migration rate, this can affect one or more individuals at a time.

With these parameters, the selection pressure can be influenced to a considerable extent. For example, it increases with the interconnectedness of the islands and decreases with the number of subpopulations or the epoch length.

== Neighbourhood models or cellular evolutionary algorithms ==
[[File:Two-dimensional neighborhood model of the population of an evolutionary algorithm.png|thumb|244x244px|Torus structure (right) with two exemplary two-dimensional neighbourhood figures (left). The block-shaped demes of individuals A and B have the two common neighbours shown in yellow.]]
The neighbourhood model, also called ''diffusion model'' or ''fine grained model'', defines a topological neighbouhood relation between the individuals of a population that is independent of their [[Biology:Phenotype|phenotypic]] properties. The fundamental idea of this model is to provide the EA population with a special structure defined as a connected graph, in which each vertex is an individual that communicates with its nearest neighbours.<ref name=":6" /><ref name=":8" /> Particularly, individuals are conceptually set in a toroidal mesh, and are only allowed to [[Crossover (genetic algorithm)|recombine]] with close individuals. This leads to a kind of locality known as ''isolation by distance''.<ref name=":8" /><ref name=":2" /> The set of potential mates of an individual is called its neighbourhood or ''deme''. The adjacent figure illustrates that by showing two slightly overlapping neighbourhoods of two individuals marked yellow, through which genetic information can spread between the two demes. It is known that in this kind of algorithm, similar individuals tend to cluster and create ''[[Biology:Ecological niche|niches]]'' that are independent of the deme boundaries and, in particular, can be larger than a deme.<ref name=":8" /><ref name=":2" /> There is no clear borderline between adjacent groups, and close niches could be easily colonized by competitive ones and maybe merge solution contents during this process. Simultaneously, farther niches can be affected more slowly.<ref name=":8" /><ref name=":2" /> EAs with this type of population are also well known as ''cellular EAs'' (cEA)<ref name=":5" /><ref name=":9">{{Citation |last1=Alba |first1=Enrique |title=Cellular Evolutionary Algorithms: Evaluating the Influence of Ratio |date=2000 |url=http://link.springer.com/10.1007/3-540-45356-3_3 |work=Parallel Problem Solving from Nature PPSN VI |volume=1917 |pages=29–38 |editor-last=Schoenauer |editor-first=Marc |place=Berlin, Heidelberg |publisher=Springer |doi=10.1007/3-540-45356-3_3 |isbn=978-3-540-41056-0 |access-date=2023-02-11 |last2=Troya |first2=José Ma |editor2-last=Deb |editor2-first=Kalyanmoy |editor3-last=Rudolph |editor3-first=Günther |editor4-last=Yao |editor4-first=Xin}}</ref> or ''cellular [[Genetic algorithm|genetic algorithm]]s'' (cGA).<ref name=":2" /><ref>{{Cite book |last1=Folino |first1=G. |last2=Pizzuti |first2=C. |last3=Spezzano |first3=G. |title=Proceedings Tenth IEEE International Conference on Tools with Artificial Intelligence (Cat. No.98CH36294) |chapter=Combining cellular genetic algorithms and local search for solving satisfiability problems |date=1998 |chapter-url=https://ieeexplore.ieee.org/document/744842 |location=Taipei, Taiwan |publisher=IEEE |pages=192–198 |doi=10.1109/TAI.1998.744842 |isbn=978-0-7803-5214-8|s2cid=8048158 }}</ref>

[[File:cEA neighborhood types.png|212x212px|thumb|Examples of neighbouhoods, also called demes, in two-dimensional cellular EAs: linear, compact, diamond and... any other.|left]]
[[File:One-dimensional neighborhood model of the population of an evolutionary algorithm.png|thumb|275x275px|Two examples overlapping neighbourhoods (demes) of the one-dimensional ring-shaped neighbourhood model of an EA. The two demes of  individuals X and Y overlap minimally, while those of A and B show a maximum overlap.|right]]
A commonly used structure for arranging the individuals of a population is a 2D toroidal grid,<ref name=":3" /><ref name=":6" /><ref name=":9" /> although the number of dimensions can be easily extended (to 3D) or reduced (to 1D, e.g. a ring,<ref name=":8" /><ref name=":9" /> see the figure on the right). The neighbourhood of a particular individual in the grid is defined in terms of the ''[[Taxicab geometry|Manhattan distance]]'' from it to others in the population. In the basic algorithm, all the neighbourhoods have the same size and identical shapes. The two most commonly used neighbourhoods for two dimesional cEAs are L5 and C9, see the figure on the left. Here, ''L'' stands for ''Linear'' while ''C'' stands for ''Compact''.  Each deme represents a panmictic subpopulation within which mate selection and the acceptance of offspring takes place by replacing the parent. The rules for the acceptance of offspring are local in nature and based on the neighbourhood: for example, it can be specified that the best offspring must be better than the parent being replaced or, less strictly, only better than the worst individual in the deme.<ref name=":6" /><ref name=":8" /> The first rule is ''elitist'' and creates a higher selective pressure than the second non-elitist rule. In ''elitist EAs'', the best individual of a population always survives. In this respect, they deviate from the biological model.

The overlap of the neighbourhoods causes a mostly slow spread of genetic information across the neighbourhood boundaries, hence the name ''diffusion model''. A better offspring now needs more generations than in panmixy to spread in the population. This promotes the emergence of local niches and their local evolution, thus preserving genotypic diversity over a longer period of time. The result is a better and dynamic balance between [[Breadth-first search|breadth]] and [[Depth-first search|depth search]] adapted to the search space during a run. Depth search takes place in the niches and breadth search in the niche boundaries and through the evolution of the different niches of the whole population.<ref>{{Cite book |last1=Alba |first1=Enrique |url=https://www.springer.com/business/operations+research/book/978-0-387-77609-5 |title=Cellular genetic algorithms |last2=Dorronsoro |first2=Bernabé |date=2008 |publisher=Springer |isbn=978-0-387-77610-1 |location=New York |pages=12 |oclc=370728730}}</ref> For the same neighbourhood size, the spread of genetic information is larger for elongated figures like L9 than for a block like C9, and again significantly larger than for a ring.<ref name=":10">{{Citation |last=Gorges-Schleuter |first=Martina |title=A comparative study of global and local selection in evolution strategies |date=1998 |url=http://link.springer.com/10.1007/BFb0056879 |work=Parallel Problem Solving from Nature — PPSN V |series=Lecture Notes in Computer Science |volume=1498 |pages=367–377 |editor-last=Eiben |editor-first=Agoston E. |place=Berlin, Heidelberg |publisher=Springer |doi=10.1007/bfb0056879 |isbn=978-3-540-65078-2 |access-date=2023-02-11 |editor2-last=Bäck |editor2-first=Thomas |editor3-last=Schoenauer |editor3-first=Marc |editor4-last=Schwefel |editor4-first=Hans-Paul}}</ref> This means that ring neighbourhoods are well suited for achieving high quality results, even if this requires comparatively long run times. On the other hand, if one is primarily interested in fast and good, but possibly suboptimal results, 2D topologies are more suitable.

== Comparison ==
When applying both population models to genetic algorithms,<ref name=":0" /><ref name=":8" /> evolutionary strategy<ref name=":10" /><ref>{{Citation |last=Sprave |first=Joachim |title=Linear neighborhood evolution strategy |date=1994 |url=http://ls11-www.cs.tu-dortmund.de/~joe/papers/ep94.pdf |work=Proceedings of the 3rd Annual Conference on Evolutionary Programming |pages=42–51 |place=Singapore |publisher=World Scientific |language=en |access-date=2022-11-05 }}</ref> and other EAs,<ref>{{Cite journal |last=Jakob |first=Wilfried |date=2010-09-01 |title=A general cost-benefit-based adaptation framework for multimeme algorithms |url=https://doi.org/10.1007/s12293-010-0040-9 |journal=Memetic Computing |language=en |publisher=p. 207 |volume=2 |issue=3 |pages=201–218 |doi=10.1007/s12293-010-0040-9 |s2cid=167807 |issn=1865-9292}}</ref><ref>{{cite journal|last1=Alba |first1=Enrique |last2=Dorronsoro |first2=Bernabé |last3=Alfonso |first3=Hugo |title=Cellular Memetic Algorithms |journal=Journal of Computer Science and Technology |date=2005 |volume=5 |issue=4 |pages=257–263 |url=https://journal.info.unlp.edu.ar/JCST/article/view/845 |access-date=2022-11-04 }}</ref> the splitting of a total population into subpopulations usually reduces the risk of premature convergence and leads to better results overall more reliably and faster than would be expected with panmictic EAs.

Island models have the disadvantage compared to neighbourhood models that they introduce a large number of new strategy parameters. Despite the existing studies on this topic in the literature,<ref name=":4" /><ref>{{Cite book |last1=Wen-Yang Lin |last2=Tzung-Pei Hong |last3=Shu-Min Liu |title=2004 IEEE International Conference on Systems, Man and Cybernetics (IEEE Cat. No.04CH37583) |chapter=On adapting migration parameters for multi-population genetic algorithms |date=2004 |chapter-url=https://ieeexplore.ieee.org/document/1401108 |location=The Hague, Netherlands |publisher=IEEE |volume=6 |pages=5731–5735 |doi=10.1109/ICSMC.2004.1401108 |isbn=978-0-7803-8567-2|s2cid=31844333 }}</ref><ref>{{Cite journal |last1=Hong |first1=Tzung-Pei |last2=Lin |first2=Wen-Yang |last3=Liu |first3=Shu-Min |last4=Lin |first4=Jiann-Horng |date=2007-04-20 |title=Dynamically Adjusting Migration Rates for Multi-Population Genetic Algorithms |url=https://www.fujipress.jp/jaciii/jc/jacii001100040410 |journal=Journal of Advanced Computational Intelligence and Intelligent Informatics |language=en |volume=11 |issue=4 |pages=410–415 |doi=10.20965/jaciii.2007.p0410 |issn=1883-8014|doi-access=free }}</ref> a certain risk of unfavourable settings remains for the user. With neighbourhood models, on the other hand, only the size of the neighbourhood has to be specified and, in the case of the two-dimensional model, the choice of the neighbourhood figure is added.

== Parallelism ==
Since both population models imply population partitioning, they are well suited as a basis for parallelizing an EA.<ref name=":0" /><ref name=":11" /><ref>{{Cite book |last1=Luque |first1=Gabriel |url=http://link.springer.com/10.1007/978-3-642-22084-5 |title=Parallel Genetic Algorithms |last2=Alba |first2=Enrique |date=2011 |publisher=Springer |isbn=978-3-642-22083-8 |series=Studies in Computational Intelligence |volume=367 |location=Berlin, Heidelberg |doi=10.1007/978-3-642-22084-5}}</ref> This applies even more to cellular EAs, since they rely only on locally available information about the members of their respective demes. Thus, in the extreme case, an independent execution thread can be assigned to each individual, so that the entire cEA can run on a parallel hardware platform.<ref name=":8" /><ref>{{Cite book |last1=Luque |first1=Gabriel |last2=Alba |first2=Enrique |last3=Dorronsoro |first3=Bernabé |title=Proceedings of the 11th Annual conference on Genetic and evolutionary computation |chapter=An asynchronous parallel implementation of a cellular genetic algorithm for combinatorial optimization |date=July 2009 |chapter-url=https://dl.acm.org/doi/10.1145/1569901.1570088 |language=en |location=Montreal Québec Canada |publisher=ACM |pages=1395–1402 |doi=10.1145/1569901.1570088 |isbn=978-1-60558-325-9|s2cid=14113702 }}</ref><ref>{{Cite book |last1=Zhongwen Luo |last2=Hongzhi Liu |title=2006 IEEE International Conference on Evolutionary Computation |chapter=Cellular Genetic Algorithms and Local Search for 3-SAT problem on Graphic Hardware |date=2006 |chapter-url=https://ieeexplore.ieee.org/document/1688685 |location=Vancouver, BC, Canada |publisher=IEEE |pages=2988–2992 |doi=10.1109/CEC.2006.1688685 |isbn=978-0-7803-9487-2|s2cid=8142372 }}</ref> The island model also supports parallelization, e.g. by assigning a processor to each island. If the subpopulations of the islands are organized panmictically, all evaluations of the descendants of a generation can be parallelized additionally.<ref name=":7" /><ref name=":12" /><ref>{{Cite journal |last1=Cahon |first1=S. |last2=Melab |first2=N. |last3=Talbi |first3=E.-G. |date=May 2004 |title=ParadisEO: A Framework for the Reusable Design of Parallel and Distributed Metaheuristics |url=http://link.springer.com/10.1023/B:HEUR.0000026900.92269.ec |journal=Journal of Heuristics |language=en |volume=10 |issue=3 |pages=357–380 |doi=10.1023/B:HEUR.0000026900.92269.ec |s2cid=14972999 |issn=1381-1231}}</ref> In real-world applications the evaluations are usually by far the most time-consuming part. Of course, it is also possible to design the island sub-populations as cEAs, so that the statements made before about parallelizing cEAs apply. In this way, hierarchical population structures with the appropriate parallelizations can be created.<ref name=":7" /> Not only comparatively expensive computer clusters but also inexpensive graphics cards ([[Graphics processing unit|GPUs]]) can be used for parallelization.<ref>{{Cite book |last=Jähne |first=Paul |url=https://subs.emis.de/LNI/Proceedings/Proceedings259/2163.pdf |title=Overview of the current state of research on parallelisation of evolutionary algorithms on graphic cards |date=2016 |work=Informatik 2016 Tagung vom 26. - 30. September 2016 |publisher=Gesellschaft für Informatik, FRG |isbn=978-3-88579-653-4 |editor-last=Mayr |editor-first=Heinrich Christian |location=Bonn |language=en |oclc=962381748 |editor-last2=Pinzger |editor-first2=Martin}}</ref><ref>{{Cite journal |last1=García-Calvo |first1=Raúl |last2=Guisado |first2=Jl |last3=Diaz-del-Rio |first3=Fernando |last4=Córdoba |first4=Antonio |last5=Jiménez-Morales |first5=Francisco |date=January 2018 |title=Graphics Processing Unit–Enhanced Genetic Algorithms for Solving the Temporal Dynamics of Gene Regulatory Networks |journal=Evolutionary Bioinformatics |language=en |volume=14 |doi=10.1177/1176934318767889 |issn=1176-9343 |pmid=29662297 |pmc=5898668 }}</ref>

However, it is important to stress that cEAs, or EAs with a population distributed across islands, represent a search model that differs in many ways from traditional EAs. Moreover, they can run on both sequential and parallel platforms, which highlights the fact that model and implementation are two different concepts.

== Bibliography ==
* Erick Cantú-Paz (2001): ''Efficient and Accurate Parallel Genetic Algorithms'' (PhD thesis, University of Illinois, Urbana-Champaign, USA). Springer, New York, NY. {{ISBN|978-1-4613-6964-6}} {{doi|10.1007/978-1-4615-4369-5}} 
* Martina Gorges-Schleuter (1990): ''Genetic Algorithms and Population Structures - A Massively Parallel Algorithm.'' PhD thesis, Universität Dortmund, Fakultät für Informatik, Germany. 
* Enrique Alba, Bernabé Dorronsoro (2008): ''[https://www.springer.com/business/operations+research/book/978-0-387-77609-5 Cellular Genetic Algorithms]''. Springer, New York, NY. {{ISBN|978-0-387-77609-5}}  {{doi|10.1007/978-0-387-77610-1}}
* Dirk Sudholt (2015): ''[http://staffwww.dcs.shef.ac.uk/people/d.sudholt/parallel-eas.pdf Parallel Evolutionary Algorithms]''. In Janusz Kacprzyk, Witold Pedrycz (eds.): Parallel Evolutionary Algorithms. Springer, Berlin, Heidelberg, pp.&nbsp;929–959 {{ISBN|978-3-662-43504-5}} {{doi|10.1007/978-3-662-43505-2 46}}
* Gabriel Luque, Enrique Alba (2011): ''[https://link.springer.com/book/10.1007/978-3-642-22084-5 Parallel Genetic Algorithms]''. Springer, Berlin Heidelberg. {{ISBN|978-3-642-22083-8}} {{doi|10.1007/978-3-642-22084-5}}

== See also ==
* [[Cellular automaton]]
* [[Dual-phase evolution]]
* [[Evolutionary algorithm]]
* [[Metaheuristic]]

== References ==
<references />

[[Category:Evolutionary algorithms]]

{{Sourceattribution|Population model (evolutionary algorithm)}}