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{{short description|Competitive algorithm for searching a problem space}}
{{Evolutionary algorithms}}
{{Use dmy dates|date=November 2020}}
[[Image:St 5-xband-antenna.jpg|thumb|The 2006 NASA [[Space Technology 5|ST5]] spacecraft antenna. This complicated shape was found by an evolutionary computer design program to create the best radiation pattern. It is known as an [[evolved antenna]].]]
<!-- Deleted image removed: [[Image:ESA JAXA HUMIES Trajectory.png|thumb|The ESA/JAXA interplanetary Trajectory recipient of the [http://www.genetic-programming.org/combined.php 2013 gold HUMIES ] award. This complex tour of the Jovian Moons was found with the help of an evolutionary technique based on self-adaptation]] -->
In [[computer science]] and [[operations research]], a '''genetic algorithm''' ('''GA''') is a [[metaheuristic]] inspired by the process of [[natural selection]] that belongs to the larger class of [[evolutionary algorithm]]s (EA).<ref>{{Cite book |last1=Pétrowski |first1=Alain |last2=Ben-Hamida |first2=Sana |title=Evolutionary algorithms |publisher=John Wiley & Sons |page=30 |year=2017 |isbn=978-1-119-13638-5 |url=https://books.google.com/books?id=GlGpDgAAQBAJ&dq=genetic+algorithm+evolutionary+algorithms&pg=PP2}}</ref> Genetic algorithms are commonly used to generate high-quality solutions to [[Optimization (mathematics)|optimization]] and [[Search algorithm|search problem]]s via biologically inspired operators such as [[selection (genetic algorithm)|selection]], [[crossover (genetic algorithm)|crossover]], and [[Mutation (genetic algorithm)|mutation]].{{sfn|Mitchell|1996|p=2}} Some examples of GA applications include optimizing [[Decision tree learning|decision trees]] for better performance, solving [[Sudoku solving algorithms|sudoku puzzles]],<ref>{{Cite book|last1=Gerges|first1=Firas|last2=Zouein|first2=Germain|last3=Azar|first3=Danielle|title=Proceedings of the 2018 International Conference on Computing and Artificial Intelligence |chapter=Genetic Algorithms with Local Optima Handling to Solve Sudoku Puzzles |date=2018-03-12|chapter-url=https://doi.org/10.1145/3194452.3194463|series=ICCAI 2018|___location=New York, NY, USA|publisher=Association for Computing Machinery|pages=19–22|doi=10.1145/3194452.3194463|isbn=978-1-4503-6419-5|s2cid=44152535 }}</ref> [[hyperparameter optimization]], and [[causal inference]].<ref>{{cite journal |last1=Burkhart |first1=Michael C. |last2=Ruiz |first2=Gabriel |title=Neuroevolutionary representations for learning heterogeneous treatment effects |journal=Journal of Computational Science |date=2023 |volume=71 |page=102054 |doi=10.1016/j.jocs.2023.102054 |s2cid=258752823 |doi-access=free }}</ref>
== Methodology ==
=== Optimization problems ===
In a genetic algorithm, a [[population]] of [[candidate solution]]s (called individuals, creatures, organisms, or [[phenotype]]s) to an optimization problem is evolved toward better solutions. Each candidate solution has a set of properties (its [[chromosome]]s or [[genotype]]) which can be mutated and altered; traditionally, solutions are represented in binary as strings of 0s and 1s, but other encodings are also possible.{{sfn|Whitley|1994|p=66}}
The evolution usually starts from a population of randomly generated individuals, and is an [[Iteration|iterative process]], with the population in each iteration called a ''generation''. In each generation, the [[fitness (biology)|fitness]] of every individual in the population is evaluated; the fitness is usually the value of the [[objective function]] in the optimization problem being solved. The more fit individuals are [[Stochastics|stochastically]] selected from the current population, and each individual's genome is modified ([[Crossover (genetic algorithm)|recombined]] and possibly randomly mutated) to form a new generation. The new generation of candidate solutions is then used in the next iteration of the [[algorithm]]. Commonly, the algorithm terminates when either a maximum number of generations has been produced, or a satisfactory fitness level has been reached for the population.
A typical genetic algorithm requires:
# a [[genetic representation]] of the solution ___domain,
# a [[fitness function]] to evaluate the solution ___domain.
A standard representation of
Once the genetic representation and the fitness function are defined, a GA proceeds to initialize a population of solutions and then to improve it through repetitive application of the mutation, crossover, inversion and selection operators.
==== Initialization ====
The population size depends on the nature of the problem, but typically contains hundreds or thousands of possible solutions. Often, the initial population is generated randomly, allowing the entire range of possible solutions (the [[Feasible region|search space]]). Occasionally, the solutions may be "seeded" in areas where optimal solutions are likely to be found or the distribution of the sampling probability tuned to focus in those areas of greater interest.<ref>{{cite journal |last1=Luque-Rodriguez |first1=Maria |last2=Molina-Baena |first2=Jose |last3=Jimenez-Vilchez |first3=Alfonso |last4=Arauzo-Azofra |first4=Antonio |title=Initialization of Feature Selection Search for Classification (sec. 3) |journal=Journal of Artificial Intelligence Research |date=2022 |volume=75 |pages=953–983 |doi=10.1613/jair.1.14015 |url=https://www.jair.org/index.php/jair/article/view/14015|doi-access=free }}</ref>
===
{{Main|Selection (genetic algorithm)}}
During each successive generation, a portion of the existing population is [[selection (genetic algorithm)|selected]] to reproduce for a new generation. Individual solutions are selected through a ''fitness-based'' process, where [[Fitness (biology)|fitter]] solutions (as measured by a [[fitness function]]) are typically more likely to be selected. Certain selection methods rate the fitness of each solution and preferentially select the best solutions. Other methods rate only a random sample of the population, as the former process may be very time-consuming.
The fitness function is defined over the genetic representation and measures the ''quality'' of the represented solution. The fitness function is always problem-dependent. For instance, in the [[knapsack problem]] one wants to maximize the total value of objects that can be put in a knapsack of some fixed capacity. A representation of a solution might be an array of bits, where each bit represents a different object, and the value of the bit (0 or 1) represents whether or not the object is in the knapsack. Not every such representation is valid, as the size of objects may exceed the capacity of the knapsack. The ''fitness'' of the solution is the sum of values of all objects in the knapsack if the representation is valid, or 0 otherwise.
In some problems, it is hard or even impossible to define the fitness expression; in these cases, a [[Computer simulation|simulation]] may be used to determine the fitness function value of a [[phenotype]] (e.g. [[computational fluid dynamics]] is used to determine the air resistance of a vehicle whose shape is encoded as the phenotype), or even [[Interactive evolutionary computation|interactive genetic algorithms]] are used.
==== Genetic operators ====
{{Main|Crossover (genetic algorithm)|Mutation (genetic algorithm)}}
The next step is to generate a second generation population of solutions from those selected, through a combination of [[genetic operator]]s: [[crossover (genetic algorithm)|crossover]] (also called recombination), and [[mutation (genetic algorithm)|mutation]].
For each new solution to be produced, a pair of "parent" solutions is selected for breeding from the pool selected previously. By producing a "child" solution using the above methods of crossover and mutation, a new solution is created which typically shares many of the characteristics of its "parents". New parents are selected for each new child, and the process continues until a new population of solutions of appropriate size is generated.
Although reproduction methods that are based on the use of two parents are more "biology inspired", some research<ref>Eiben, A. E. et al (1994). "Genetic algorithms with multi-parent recombination". PPSN III: Proceedings of the International Conference on Evolutionary Computation. The Third Conference on Parallel Problem Solving from Nature: 78–87. {{ISBN|3-540-58484-6}}.</ref><ref>Ting, Chuan-Kang (2005). "On the Mean Convergence Time of Multi-parent Genetic Algorithms Without Selection". Advances in Artificial Life: 403–412. {{ISBN|978-3-540-28848-0}}.</ref> suggests that more than two "parents" generate higher quality chromosomes.
These processes ultimately result in the next generation population of chromosomes that is different from the initial generation. Generally, the average fitness will have increased by this procedure for the population, since only the best organisms from the first generation are selected for breeding, along with a small proportion of less fit solutions. These less fit solutions ensure genetic diversity within the genetic pool of the parents and therefore ensure the genetic diversity of the subsequent generation of children.
Opinion is divided over the importance of crossover versus mutation. There are many references in [[David B. Fogel|Fogel]] (2006) that support the importance of mutation-based search.
Although crossover and mutation are known as the main genetic operators, it is possible to use other operators such as regrouping, colonization-extinction, or migration in genetic algorithms.{{citation needed|date=November 2019}}
It is worth tuning parameters such as the [[Mutation (genetic algorithm)|mutation]] probability, [[Crossover (genetic algorithm)|crossover]] probability and population size to find reasonable settings for the problem's [[complexity class]] being worked on. A very small mutation rate may lead to [[genetic drift]] (which is non-[[Ergodicity|ergodic]] in nature). A recombination rate that is too high may lead to premature convergence of the genetic algorithm. A mutation rate that is too high may lead to loss of good solutions, unless [[#Elitism|elitist selection]] is employed. An adequate population size ensures sufficient genetic diversity for the problem at hand, but can lead to a waste of computational resources if set to a value larger than required.
==== Heuristics ====
In addition to the main operators above, other [[heuristic]]s may be employed to make the calculation faster or more robust. The ''speciation'' heuristic penalizes crossover between candidate solutions that are too similar; this encourages population diversity and helps prevent premature convergence to a less optimal solution.<ref>{{Cite book|title=Handbook of Evolutionary Computation|last1=Deb|first1=Kalyanmoy|last2=Spears|first2=William M.|s2cid=3547258|publisher=Institute of Physics Publishing|year=1997|chapter=C6.2: Speciation methods}}</ref><ref>{{Cite book|title=Handbook of Natural Computing|last=Shir|first=Ofer M.|date=2012|publisher=Springer Berlin Heidelberg|isbn=9783540929093|editor-last=Rozenberg|editor-first=Grzegorz|pages=1035–1069|language=en|chapter=Niching in Evolutionary Algorithms|doi=10.1007/978-3-540-92910-9_32|editor-last2=Bäck|editor-first2=Thomas|editor-last3=Kok|editor-first3=Joost N.}}</ref>
==== Termination ====
This generational process is repeated until a termination condition has been reached. Common terminating conditions are:
* A solution is found that satisfies minimum criteria
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* The highest ranking solution's fitness is reaching or has reached a plateau such that successive iterations no longer produce better results
* Manual inspection
* Combinations of the above
== The building block hypothesis ==
Genetic algorithms are simple to implement, but their behavior is difficult to understand. In particular, it is difficult to understand why these algorithms frequently succeed at generating solutions of high fitness when applied to practical problems. The building block hypothesis (BBH) consists of:
# A description of a heuristic that performs adaptation by identifying and recombining "building blocks", i.e. low order, low defining-length [[Schema (genetic algorithms)|schemata]] with above average fitness.
# A hypothesis that a genetic algorithm performs adaptation by implicitly and efficiently implementing this heuristic.
Goldberg describes the heuristic as follows:
:"Short, low order, and highly fit schemata are sampled, [[crossover (genetic algorithm)|recombined]] [crossed over], and resampled to form strings of potentially higher fitness. In a way, by working with these particular schemata [the building blocks], we have reduced the complexity of our problem; instead of building high-performance strings by trying every conceivable combination, we construct better and better strings from the best partial solutions of past samplings.
:"Because highly fit schemata of low defining length and low order play such an important role in the action of genetic algorithms, we have already given them a special name: building blocks. Just as a child creates magnificent fortresses through the arrangement of simple blocks of wood, so does a genetic algorithm seek near optimal performance through the juxtaposition of short, low-order, high-performance schemata, or building blocks."{{sfn|Goldberg|1989|p=41}}
Despite the lack of consensus regarding the validity of the building-block hypothesis, it has been consistently evaluated and used as reference throughout the years. Many [[estimation of distribution algorithm]]s, for example, have been proposed in an attempt to provide an environment in which the hypothesis would hold.<ref>{{cite book|last1=Harik|first1=Georges R.|last2=Lobo|first2=Fernando G.|last3=Sastry|first3=Kumara|title=Scalable Optimization via Probabilistic Modeling |chapter=Linkage Learning via Probabilistic Modeling in the Extended Compact Genetic Algorithm (ECGA) |volume=33|date=1 January 2006|pages=39–61|doi=10.1007/978-3-540-34954-9_3|language=en|series=Studies in Computational Intelligence|isbn=978-3-540-34953-2}}</ref><ref>{{cite book|last1=Pelikan|first1=Martin|last2=Goldberg|first2=David E.|last3=Cantú-Paz|first3=Erick|title=BOA: The Bayesian Optimization Algorithm|journal=Proceedings of the 1st Annual Conference on Genetic and Evolutionary Computation - Volume 1|date=1 January 1999|pages=525–532|url=http://dl.acm.org/citation.cfm?id=2933973|isbn=9781558606111|series=Gecco'99}}</ref> Although good results have been reported for some [[List of complexity classes|classes of problem]]s, skepticism concerning the generality and/or practicality of the building-block hypothesis as an explanation for GAs' efficiency still remains. Indeed, there is a reasonable amount of work that attempts to understand its limitations from the perspective of estimation of distribution algorithms.<ref>{{cite book|last1=Coffin|first1=David|last2=Smith|first2=Robert E.|title=Linkage in Evolutionary Computation |chapter=Linkage Learning in Estimation of Distribution Algorithms |volume=157|date=1 January 2008|pages=141–156|doi=10.1007/978-3-540-85068-7_7|language=en|series=Studies in Computational Intelligence|isbn=978-3-540-85067-0}}</ref><ref>{{cite journal|last1=Echegoyen|first1=Carlos|last2=Mendiburu|first2=Alexander|last3=Santana|first3=Roberto|last4=Lozano|first4=Jose A.|title=On the Taxonomy of Optimization Problems Under Estimation of Distribution Algorithms|journal=Evolutionary Computation|date=8 November 2012|volume=21|issue=3|pages=471–495|doi=10.1162/EVCO_a_00095|pmid=23136917|s2cid=26585053|issn=1063-6560}}</ref><ref>{{cite book|last1=Sadowski|first1=Krzysztof L.|last2=Bosman|first2=Peter A.N.|last3=Thierens|first3=Dirk|title=Proceedings of the 15th annual conference on Genetic and evolutionary computation |chapter=On the usefulness of linkage processing for solving MAX-SAT |date=1 January 2013|pages=853–860|doi=10.1145/2463372.2463474|isbn=9781450319638|series=Gecco '13|hdl=1874/290291|s2cid=9986768}}</ref>
== Limitations ==
{{more citations needed section|date=March 2024}}
The practical use of a genetic algorithm has limitations, especially as compared to alternative optimization algorithms:
* Repeated [[fitness function]] evaluation for complex problems is often the most prohibitive and limiting segment of artificial evolutionary algorithms. Finding the optimal solution to complex high-dimensional, multimodal problems often requires very expensive [[fitness function]] evaluations. In real world problems such as structural optimization problems, a single function evaluation may require several hours to several days of complete simulation. Typical optimization methods cannot deal with such types of problem. In this case, it may be necessary to forgo an exact evaluation and use an [[fitness approximation|approximated fitness]] that is computationally efficient. It is apparent that amalgamation of [[fitness approximation|approximate models]] may be one of the most promising approaches to convincingly use GA to solve complex real life problems.{{citation needed|date=March 2024}}
* Genetic algorithms do not scale well with complexity. That is, where the number of elements which are exposed to mutation is large there is often an exponential increase in search space size. This makes it extremely difficult to use the technique on problems such as designing an engine, a house or a plane {{Citation needed|date=December 2020}}. In order to make such problems tractable to evolutionary search, they must be broken down into the simplest representation possible. Hence we typically see evolutionary algorithms encoding designs for fan blades instead of engines, building shapes instead of detailed construction plans, and airfoils instead of whole aircraft designs. The second problem of complexity is the issue of how to protect parts that have evolved to represent good solutions from further destructive mutation, particularly when their fitness assessment requires them to combine well with other parts.{{citation needed|date=March 2024}}
* The "better" solution is only in comparison to other solutions. As a result, the stopping criterion is not clear in every problem.{{citation needed|date=March 2024}}
* In many problems, GAs have a tendency to converge towards [[local optimum|local optima]] or even arbitrary points rather than the [[global optimum]] of the problem. This means that it does not "know how" to sacrifice short-term fitness to gain longer-term fitness. The likelihood of this occurring depends on the shape of the [[fitness landscape]]: certain problems may provide an easy ascent towards a global optimum, others may make it easier for the function to find the local optima. This problem may be alleviated by using a different fitness function, increasing the rate of mutation, or by using selection techniques that maintain a diverse population of solutions,<ref>{{cite journal|last1=Taherdangkoo|first1=Mohammad|last2=Paziresh |first2=Mahsa |last3=Yazdi |first3=Mehran |last4= Bagheri |first4=Mohammad Hadi |title=An efficient algorithm for function optimization: modified stem cells algorithm|journal=Central European Journal of Engineering|date=19 November 2012|volume=3|issue=1|pages=36–50|doi=10.2478/s13531-012-0047-8|doi-access=free}}</ref> although the [[No free lunch in search and optimization|No Free Lunch theorem]]<ref>Wolpert, D.H., Macready, W.G., 1995. No Free Lunch Theorems for Optimisation. Santa Fe Institute, SFI-TR-05-010, Santa Fe.</ref> proves that there is no general solution to this problem. A common technique to maintain diversity is to impose a "niche penalty", wherein, any group of individuals of sufficient similarity (niche radius) have a penalty added, which will reduce the representation of that group in subsequent generations, permitting other (less similar) individuals to be maintained in the population. This trick, however, may not be effective, depending on the landscape of the problem. Another possible technique would be to simply replace part of the population with randomly generated individuals, when most of the population is too similar to each other. Diversity is important in genetic algorithms (and [[genetic programming]]) because crossing over a homogeneous population does not yield new solutions. In [[Evolution strategy|evolution strategies]] and [[evolutionary programming]], diversity is not essential because of a greater reliance on mutation.{{citation needed|date=March 2024}}
* Operating on dynamic data sets is difficult, as genomes begin to converge early on towards solutions which may no longer be valid for later data. Several methods have been proposed to remedy this by increasing genetic diversity somehow and preventing early convergence, either by increasing the probability of mutation when the solution quality drops (called ''triggered hypermutation''), or by occasionally introducing entirely new, randomly generated elements into the gene pool (called ''random immigrants''). Again, [[Evolution strategy|evolution strategies]] and [[evolutionary programming]] can be implemented with a so-called "comma strategy" in which parents are not maintained and new parents are selected only from offspring. This can be more effective on dynamic problems.{{citation needed|date=March 2024}}
* GAs cannot effectively solve problems in which the only fitness measure is a binary pass/fail outcome (like [[decision problem]]s), as there is no way to converge on the solution (no hill to climb). In these cases, a random search may find a solution as quickly as a GA. However, if the situation allows the success/failure trial to be repeated giving (possibly) different results, then the ratio of successes to failures provides a suitable fitness measure.{{citation needed|date=March 2024}}
* For specific optimization problems and problem instances, other optimization algorithms may be more efficient than genetic algorithms in terms of speed of convergence. Alternative and complementary algorithms include [[Evolution strategy|evolution strategies]], [[evolutionary programming]], [[simulated annealing]], [[Gaussian adaptation]], [[hill climbing]], and [[swarm intelligence]] (e.g.: [[ant colony optimization]], [[particle swarm optimization]]) and methods based on [[integer linear programming]]. The suitability of genetic algorithms is dependent on the amount of knowledge of the problem; well known problems often have better, more specialized approaches.{{citation needed|date=March 2024}}
== Variants ==
=== Chromosome representation ===
{{main | genetic representation }}
The simplest algorithm represents each chromosome as a [[Bit array|bit string]]. Typically, numeric parameters can be represented by [[integer]]s, though it is possible to use [[floating point]] representations. The floating point representation is natural to [[Evolution strategy|evolution strategies]] and [[evolutionary programming]]. The notion of real-valued genetic algorithms has been offered but is really a misnomer because it does not really represent the building block theory that was proposed by [[John Henry Holland]] in the 1970s. This theory is not without support though, based on theoretical and experimental results (see below). The basic algorithm performs crossover and mutation at the bit level. Other variants treat the chromosome as a list of numbers which are indexes into an instruction table, nodes in a [[linked list]], [[associative array|hashes]], [[object (computer science)|objects]], or any other imaginable [[data structure]]. Crossover and mutation are performed so as to respect data element boundaries. For most data types, specific variation operators can be designed. Different chromosomal data types seem to work better or worse for different specific problem domains.
When bit-string representations of integers are used, [[Gray coding]] is often employed. In this way, small changes in the integer can be readily affected through mutations or crossovers. This has been found to help prevent premature convergence at so-called ''Hamming walls'', in which too many simultaneous mutations (or crossover events) must occur in order to change the chromosome to a better solution.
Other approaches involve using arrays of real-valued numbers instead of bit strings to represent chromosomes. Results from the theory of schemata suggest that in general the smaller the alphabet, the better the performance, but it was initially surprising to researchers that good results were obtained from using real-valued chromosomes. This was explained as the set of real values in a finite population of chromosomes as forming a ''virtual alphabet'' (when selection and recombination are dominant) with a much lower cardinality than would be expected from a floating point representation.<ref name=Goldberg1991>{{cite book|last=Goldberg|first=David E.|title=Parallel Problem Solving from Nature|chapter=The theory of virtual alphabets|journal=Parallel Problem Solving from Nature, Lecture Notes in Computer Science|year=1991|volume=496|pages=13–22|doi=10.1007/BFb0029726|series=Lecture Notes in Computer Science|isbn=978-3-540-54148-6}}</ref><ref name=Janikow1991>{{cite journal|last1=Janikow|first1=C. Z.|first2=Z. |last2=Michalewicz |title=An Experimental Comparison of Binary and Floating Point Representations in Genetic Algorithms|journal=Proceedings of the Fourth International Conference on Genetic Algorithms|year=1991|pages=31–36|url=http://www.cs.umsl.edu/~janikow/publications/1991/GAbin/text.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.cs.umsl.edu/~janikow/publications/1991/GAbin/text.pdf |archive-date=2022-10-09 |url-status=live|access-date=2 July 2013}}</ref>
An expansion of the Genetic Algorithm accessible problem ___domain can be obtained through more complex encoding of the solution pools by concatenating several types of heterogenously encoded genes into one chromosome.<ref name=Patrascu2014>{{cite journal|last1=Patrascu|first1=M.|last2=Stancu|first2=A.F.|last3=Pop|first3=F.|title=HELGA: a heterogeneous encoding lifelike genetic algorithm for population evolution modeling and simulation|journal=Soft Computing|year=2014|volume=18|issue=12|pages=2565–2576|doi=10.1007/s00500-014-1401-y|s2cid=29821873}}</ref> This particular approach allows for solving optimization problems that require vastly disparate definition domains for the problem parameters. For instance, in problems of cascaded controller tuning, the internal loop controller structure can belong to a conventional regulator of three parameters, whereas the external loop could implement a linguistic controller (such as a fuzzy system) which has an inherently different description. This particular form of encoding requires a specialized crossover mechanism that recombines the chromosome by section, and it is a useful tool for the modelling and simulation of complex adaptive systems, especially evolution processes.
Another important expansion of the Genetic Algorithm (GA) accessible solution space was driven by the need to make representations amenable to variable levels of knowledge about the solution states. Variable-length representations were inspired by the observation that, in nature, evolution tends to progress from simpler organisms to more complex ones—suggesting an underlying rationale for embracing flexible structures.<ref>Goldberg, D.E., Korb, B., & Deb, K. (1989). Messy Genetic Algorithms: Motivation, Analysis, and First Results. Complex Systems, 3(5), 493–530. ISSN 0891-2513.</ref> A second, more pragmatic motivation was that most real-world engineering and knowledge-based problems do not naturally conform to rigid knowledge structures.<ref>Davidor, Y. (1991). Genetic Algorithms and Robotics: A Heuristic Strategy for Optimization. World Scientific Series in Robotics and Intelligent Systems: Volume 1.</ref>
These early innovations in variable-length representations laid essential groundwork for the development of [[Genetic programming]], which further extended the classical GA paradigm. Such representations required enhancements to the simplistic genetic operators used for fixed-length chromosomes, enabling the emergence of more sophisticated and adaptive GA models.
==
A practical variant of the general process of constructing a new population is to allow the best organism(s) from the current generation to carry over to the next, unaltered. This strategy is known as ''elitist selection'' and guarantees that the solution quality obtained by the GA will not decrease from one generation to the next.<ref>{{cite conference |last1=Baluja |first1=Shumeet |first2=Rich |last2=Caruana |title=Removing the genetics from the standard genetic algorithm |conference=[[International Conference on Machine Learning|ICML]] |year=1995 |url=http://www.ri.cmu.edu/pub_files/pub2/baluja_shumeet_1995_1/baluja_shumeet_1995_1.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.ri.cmu.edu/pub_files/pub2/baluja_shumeet_1995_1/baluja_shumeet_1995_1.pdf |archive-date=2022-10-09 |url-status=live}}</ref>
=== Parallel implementations ===
[[parallel algorithm|Parallel]] implementations of genetic algorithms come in two flavors. Coarse-grained parallel genetic algorithms assume a population on each of the computer nodes and migration of individuals among the nodes. Fine-grained parallel genetic algorithms assume an individual on each processor node which acts with neighboring individuals for selection and reproduction.
Other variants, like genetic algorithms for [[online optimization]] problems, introduce time-dependence or noise in the fitness function.
=== Adaptive GAs ===
Genetic algorithms with adaptive parameters (adaptive genetic algorithms, AGAs) is another significant and promising variant of genetic algorithms. The probabilities of crossover (pc) and mutation (pm) greatly determine the degree of solution accuracy and the convergence speed that genetic algorithms can obtain. Researchers have analyzed GA convergence analytically.<ref>{{Cite journal |last1=Stannat |first1=W. |title=On the convergence of genetic algorithms – a variational approach |journal=Probab. Theory Relat. Fields |volume=129 |pages=113–132 |year=2004 |doi=10.1007/s00440-003-0330-y|s2cid=121086772 |doi-access=free }}</ref><ref>{{Cite journal |last1=Sharapov |first1=R.R. |last2=Lapshin |first2=A.V. |title=Convergence of genetic algorithms |journal=Pattern Recognit. Image Anal. |volume=16 |pages=392–397 |year=2006 |issue=3 |doi=10.1134/S1054661806030084|s2cid=22890010 }}</ref>
Instead of using fixed values of ''pc'' and ''pm'', AGAs utilize the population information in each generation and adaptively adjust the ''pc'' and ''pm'' in order to maintain the population diversity as well as to sustain the convergence capacity. In AGA (adaptive genetic algorithm),<ref>{{Cite journal |last1=Srinivas |first1=M. |last2=Patnaik |first2=L. |title=Adaptive probabilities of crossover and mutation in genetic algorithms |journal=IEEE Transactions on Systems, Man, and Cybernetics |volume=24 |issue=4 |pages=656–667 |year=1994 |doi=10.1109/21.286385 |url=http://eprints.iisc.ac.in/6971/2/adaptive.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://eprints.iisc.ac.in/6971/2/adaptive.pdf |archive-date=2022-10-09 |url-status=live }}</ref> the adjustment of ''pc'' and ''pm'' depends on the fitness values of the solutions. There are more examples of AGA variants: Successive zooming method is an early example of improving convergence.<ref>{{Cite journal |last1=Kwon |first1=Y.D. |last2=Kwon |first2=S.B. |last3=Jin |first3=S.B. |last4=Kim |first4=J.Y. |title=Convergence enhanced genetic algorithm with successive zooming method for solving continuous optimization problems |journal=Computers & Structures |volume=81 |issue=17 |pages=1715–1725 |year=2003 |doi=10.1016/S0045-7949(03)00183-4}}</ref> In ''CAGA'' (clustering-based adaptive genetic algorithm),<ref>{{cite journal |last1=Zhang |first1=J. |last2=Chung |first2=H. |last3=Lo, W. L. |title=Clustering-Based Adaptive Crossover and Mutation Probabilities for Genetic Algorithms |journal=IEEE Transactions on Evolutionary Computation |volume=11 |issue=3 |pages=326–335 |year=2007 |doi=10.1109/TEVC.2006.880727 |s2cid=2625150 }}</ref> through the use of clustering analysis to judge the optimization states of the population, the adjustment of ''pc'' and ''pm'' depends on these optimization states. Recent approaches use more abstract variables for deciding ''pc'' and ''pm''. Examples are dominance & co-dominance principles<ref>{{Cite journal |last1=Pavai |first1=G. |last2=Geetha |first2=T.V. |title= New crossover operators using dominance and co-dominance principles for faster convergence of genetic algorithms|journal=Soft Comput |volume=23 |pages=3661–3686 |year=2019 |issue=11 |doi=10.1007/s00500-018-3016-1|s2cid=254028984 }}</ref> and LIGA (levelized interpolative genetic algorithm), which combines a flexible GA with modified A* search to tackle search space anisotropicity.<ref>{{Cite journal |last1=Li |first1=J.C.F. |last2=Zimmerle |first2=D. |last3=Young |first3=P. |title=Flexible networked rural electrification using levelized interpolative genetic algorithm |journal=Energy & AI |volume=10 |pages=100186 |year=2022 |doi=10.1016/j.egyai.2022.100186|s2cid=250972466 |doi-access=free |bibcode=2022EneAI..1000186L }}</ref>
It can be quite effective to combine GA with other optimization methods. A GA tends to be quite good at finding generally good global solutions, but quite inefficient at finding the last few mutations to find the absolute optimum. Other techniques (such as [[Hill climbing|simple hill climbing]]) are quite efficient at finding absolute optimum in a limited region. Alternating GA and hill climbing can improve the efficiency of GA {{Citation needed|date=July 2016}} while overcoming the lack of robustness of hill climbing.
This means that the rules of genetic variation may have a different meaning in the natural case. For instance – provided that steps are stored in consecutive order – crossing over may sum a number of steps from maternal DNA adding a number of steps from paternal DNA and so on. This is like adding vectors that more probably may follow a ridge in the phenotypic landscape. Thus, the efficiency of the process may be increased by many orders of magnitude. Moreover, the [[Chromosomal inversion|inversion operator]] has the opportunity to place steps in consecutive order or any other suitable order in favour of survival or efficiency.<ref>See for instance [http://www.thisurlisfalse.com/evolution-in-a-nutshell/ Evolution-in-a-nutshell] {{Webarchive|url=https://web.archive.org/web/20160415193505/http://www.thisurlisfalse.com/evolution-in-a-nutshell/ |date=15 April 2016 }} or example in [[travelling salesman problem]], in particular the use of an [[edge recombination operator]].</ref>
A variation, where the population as a whole is evolved rather than its individual members, is known as gene pool recombination.
A number of variations have been developed to attempt to improve performance of GAs on problems with a high degree of fitness epistasis, i.e. where the fitness of a solution consists of interacting subsets of its variables. Such algorithms aim to learn (before exploiting) these beneficial phenotypic interactions. As such, they are aligned with the Building Block Hypothesis in adaptively reducing disruptive recombination. Prominent examples of this approach include the mGA,<ref>{{cite journal |url=http://www.complex-systems.com/issues/03-5.html |first1=D. E. |last1=Goldberg |first2=B. |last2=Korb |first3=K. |last3=Deb |title=Messy Genetic Algorithms : Motivation Analysis, and First Results |journal=Complex Systems |volume=5 |issue=3 |pages=493–530 |year=1989 }}</ref> GEMGA<ref>[https://www.osti.gov/servlets/purl/524858 Gene expression: The missing link in evolutionary computation]</ref> and LLGA.<ref>{{cite thesis |last=Harik |first=G. |date=1997 |title=Learning linkage to efficiently solve problems of bounded difficulty using genetic algorithms |type=PhD |publisher=Dept. Computer Science, University of Michigan, Ann Arbour |url=http://portal.acm.org/citation.cfm?id=269517 }}</ref>
== Problem domains ==
Problems which appear to be particularly appropriate for solution by genetic algorithms include [[Genetic algorithm scheduling|timetabling and scheduling problems]], and many scheduling software packages are based on GAs{{Citation needed|date=December 2011}}. GAs have also been applied to [[engineering]].<ref>Tomoiagă B, Chindriş M, Sumper A, Sudria-Andreu A, Villafafila-Robles R. [http://www.mdpi.com/1996-1073/6/3/1439/pdf Pareto Optimal Reconfiguration of Power Distribution Systems Using a Genetic Algorithm Based on NSGA-II. ] Energies. 2013; 6(3):1439-1455.</ref> Genetic algorithms are often applied as an approach to solve [[global optimization]] problems.
As a general rule of thumb genetic algorithms might be useful in problem domains that have a complex [[fitness landscape]] as mixing, i.e., [[Mutation (genetic algorithm)|mutation]] in combination with [[Crossover (genetic algorithm)|crossover]], is designed to move the population away from [[local optima]] that a traditional [[hill climbing]] algorithm might get stuck in. Observe that commonly used crossover operators cannot change any uniform population. Mutation alone can provide [[ergodicity]] of the overall genetic algorithm process (seen as a [[Markov chain]]).
Examples of problems solved by genetic algorithms include: mirrors designed to funnel sunlight to a solar collector,<ref>{{cite web|last=Gross|first=Bill|title=A solar energy system that tracks the sun|url=https://www.ted.com/talks/bill_gross_a_solar_energy_system_that_tracks_the_sun|work=TED|date=2 February 2009 |access-date=20 November 2013}}</ref> antennae designed to pick up radio signals in space,<ref>{{citation |first1=G. S. |last1=Hornby |first2=D. S. |last2=Linden |first3=J. D. |last3=Lohn |url=http://ti.arc.nasa.gov/m/pub-archive/1244h/1244%20(Hornby).pdf |title=Automated Antenna Design with Evolutionary Algorithms}}</ref> walking methods for computer figures,<ref>{{Cite web | url=http://goatstream.com/research/papers/SA2013/index.html | title=Flexible Muscle-Based Locomotion for Bipedal Creatures}}</ref> optimal design of aerodynamic bodies in complex flowfields<ref>{{Cite journal|last1=Evans|first1=B.|last2=Walton|first2=S.P.|date=December 2017|title=Aerodynamic optimisation of a hypersonic reentry vehicle based on solution of the Boltzmann–BGK equation and evolutionary optimisation|journal=Applied Mathematical Modelling|volume=52|pages=215–240|doi=10.1016/j.apm.2017.07.024|issn=0307-904X|url=https://cronfa.swan.ac.uk/Record/cronfa34688|doi-access=free}}</ref>
In his ''Algorithm Design Manual'', [[Steven Skiena|Skiena]] advises against genetic algorithms for any task:
{{blockquote|[I]t is quite unnatural to model applications in terms of genetic operators like mutation and crossover on bit strings. The pseudobiology adds another level of complexity between you and your problem. Second, genetic algorithms take a very long time on nontrivial problems. [...] [T]he analogy with evolution—where significant progress require [sic] millions of years—can be quite appropriate.
[...]
I have never encountered any problem where genetic algorithms seemed to me the right way to attack it. Further, I have never seen any computational results reported using genetic algorithms that have favorably impressed me. Stick to [[simulated annealing]] for your heuristic search voodoo needs.|Steven Skiena<ref>{{cite book |last=Skiena |first=Steven |author-link=Steven Skiena |title = The Algorithm Design Manual |publisher=[[Springer Science+Business Media]] |edition=2nd |year = 2010 |isbn=978-1-849-96720-4}}</ref>{{rp|267}}}}
== History ==
In 1950, [[Alan Turing]] proposed a "learning machine" which would parallel the principles of evolution.<ref name="mind.oxfordjournals.org">{{cite journal|last1=Turing|first1=Alan M.|title=Computing machinery and intelligence|journal=Mind|volume=LIX|issue=238|pages=433–460|doi=10.1093/mind/LIX.236.433|date=October 1950}}</ref> Computer simulation of evolution started as early as in 1954 with the work of [[Nils Aall Barricelli]], who was using the computer at the [[Institute for Advanced Study]] in [[Princeton, New Jersey]].<ref name="Barricelli 1954 45–68">{{cite journal|last=Barricelli|first=Nils Aall|year=1954|author-link=Nils Aall Barricelli|title=Esempi numerici di processi di evoluzione|journal=Methodos|pages=45–68}}</ref><ref name="Barricelli 1957 143–182">{{cite journal|last=Barricelli|first=Nils Aall|year=1957|author-link=Nils Aall Barricelli|title=Symbiogenetic evolution processes realized by artificial methods|journal=Methodos|pages=143–182}}</ref> His 1954 publication was not widely noticed. Starting in 1957,<ref name="Fraser 1957 484–491">{{cite journal|last=Fraser|first=Alex|author-link=Alex Fraser (scientist)|year=1957|title=Simulation of genetic systems by automatic digital computers. I. Introduction|journal=Aust. J. Biol. Sci.|volume=10|issue=4|pages=484–491|doi=10.1071/BI9570484|doi-access=free}}</ref> the Australian quantitative geneticist [[Alex Fraser (scientist)|Alex Fraser]] published a series of papers on simulation of [[artificial selection]] of organisms with multiple loci controlling a measurable trait. From these beginnings, computer simulation of evolution by biologists became more common in the early 1960s, and the methods were described in books by Fraser and Burnell (1970)<ref name="Fraser 1970">{{cite book|last1=Fraser|first1=Alex|author-link=Alex Fraser (scientist)|first2=Donald |last2=Burnell|year=1970|title=Computer Models in Genetics|publisher=McGraw-Hill|___location=New York|isbn=978-0-07-021904-5}}</ref> and Crosby (1973).<ref name="Crosby 1973">{{cite book|last=Crosby|first=Jack L.|year=1973|title=Computer Simulation in Genetics|publisher=John Wiley & Sons|___location=London|isbn=978-0-471-18880-3}}</ref> Fraser's simulations included all of the essential elements of modern genetic algorithms. In addition, [[Hans-Joachim Bremermann]] published a series of papers in the 1960s that also adopted a population of solution to optimization problems, undergoing recombination, mutation, and selection. Bremermann's research also included the elements of modern genetic algorithms.<ref>[http://berkeley.edu/news/media/releases/96legacy/releases.96/14319.html 02.27.96 - UC Berkeley's Hans Bremermann, professor emeritus and pioneer in mathematical biology, has died at 69]</ref> Other noteworthy early pioneers include Richard Friedberg, George Friedman, and Michael Conrad. Many early papers are reprinted by [[David B. Fogel|Fogel]] (1998).<ref>{{cite book|editor-last=Fogel|editor-first=David B. |year=1998|title=Evolutionary Computation: The Fossil Record|publisher=IEEE Press|___location=New York|isbn=978-0-7803-3481-6}}</ref>
Although Barricelli, in work he reported in 1963, had simulated the evolution of ability to play a simple game,<ref>{{cite journal|last=Barricelli|first=Nils Aall|year=1963|title=Numerical testing of evolution theories. Part II. Preliminary tests of performance, symbiogenesis and terrestrial life|journal=Acta Biotheoretica|volume=16|issue=3–4|pages=99–126|doi=10.1007/BF01556602|s2cid=86717105}}</ref> [[artificial evolution]] only became a widely recognized optimization method as a result of the work of [[Ingo Rechenberg]] and [[Hans-Paul Schwefel]] in the 1960s and early 1970s – Rechenberg's group was able to solve complex engineering problems through [[Evolution strategy|evolution strategies]].<ref>{{cite book|last=Rechenberg|first=Ingo|year=1973|title=Evolutionsstrategie|place=Stuttgart|publisher=Holzmann-Froboog|isbn=978-3-7728-0373-4}}</ref><ref>{{cite book|last=Schwefel|first=Hans-Paul|year=1974|title=Numerische Optimierung von Computer-Modellen (PhD thesis)}}</ref><ref>{{cite book|last=Schwefel|first=Hans-Paul|year=1977|title=Numerische Optimierung von Computor-Modellen mittels der Evolutionsstrategie : mit einer vergleichenden Einführung in die Hill-Climbing- und Zufallsstrategie|place=Basel; Stuttgart | publisher=Birkhäuser| isbn=978-3-7643-0876-6}}</ref><ref>{{cite book|last=Schwefel|first=Hans-Paul|year=1981|title=Numerical optimization of computer models (Translation of 1977 Numerische Optimierung von Computor-Modellen mittels der Evolutionsstrategie|place=Chichester; New York|publisher=Wiley|isbn=978-0-471-09988-8}}</ref> Another approach was the evolutionary programming technique of [[Lawrence J. Fogel]], which was proposed for generating artificial intelligence. [[Evolutionary programming]] originally used finite state machines for predicting environments, and used variation and selection to optimize the predictive logics. Genetic algorithms in particular became popular through the work of [[John Henry Holland|John Holland]] in the early 1970s, and particularly his book ''Adaptation in Natural and Artificial Systems'' (1975). His work originated with studies of [[cellular automata]], conducted by [[John Henry Holland|Holland]] and his students at the [[University of Michigan]]. Holland introduced a formalized framework for predicting the quality of the next generation, known as [[Holland's Schema Theorem]]. Research in GAs remained largely theoretical until the mid-1980s, when The First International Conference on Genetic Algorithms was held in [[Pittsburgh, Pennsylvania]].
===Commercial products===
In the late 1980s, General Electric started selling the world's first genetic algorithm product, a mainframe-based toolkit designed for industrial processes.<ref>{{Cite book|url=https://books.google.com/books?id=-MszVdu_PAMC&q=general+electric+genetic+algorithm+mainframe|title=An Approach to Designing an Unmanned Helicopter Autopilot Using Genetic Algorithms and Simulated Annealing|last=Aldawoodi|first=Namir|year=2008|isbn=978-0549773498|pages=99|via=Google Books}}</ref>{{Circular reference|date=January 2021}}
In 1989, Axcelis, Inc. released [[Evolver (software)|Evolver]], the world's first commercial GA product for desktop computers. [[The New York Times]] technology writer [[John Markoff]] wrote<ref>{{cite news|last=Markoff|first=John|title=What's the Best Answer? It's Survival of the Fittest|newspaper=New York Times|url=https://www.nytimes.com/1990/08/29/business/business-technology-what-s-the-best-answer-it-s-survival-of-the-fittest.html|access-date=2016-07-13|date=29 August 1990}}</ref> about Evolver in 1990, and it remained the only interactive commercial genetic algorithm until 1995.<ref>Ruggiero, Murray A.. (1 August 2009) [http://www.futuresmag.com/2009/08/01/fifteen-years-and-counting?t=technology&page=2 Fifteen years and counting] {{Webarchive|url=https://web.archive.org/web/20160130054823/http://www.futuresmag.com/2009/08/01/fifteen-years-and-counting?t=technology&page=2 |date=30 January 2016 }}. Futuresmag.com. Retrieved on 2013-08-07.</ref> Evolver was sold to Palisade in 1997, translated into several languages, and is currently in its 6th version.<ref>[http://www.palisade.com/evolver/ Evolver: Sophisticated Optimization for Spreadsheets]. Palisade. Retrieved on 2013-08-07.</ref> Since the 1990s, [[MATLAB]] has built in three [[derivative-free optimization]] heuristic algorithms (simulated annealing, particle swarm optimization, genetic algorithm) and two direct search algorithms (simplex search, pattern search).<ref>{{cite journal | doi=10.1109/ACCESS.2019.2923092 | title=Benchmarks for Evaluating Optimization Algorithms and Benchmarking MATLAB Derivative-Free Optimizers for Practitioners' Rapid Access | year=2019 | last1=Li | first1=Lin | last2=Saldivar | first2=Alfredo Alan Flores | last3=Bai | first3=Yun | last4=Chen | first4=Yi | last5=Liu | first5=Qunfeng | last6=Li | first6=Yun | journal=IEEE Access | volume=7 | pages=79657–79670 | s2cid=195774435 | doi-access=free | bibcode=2019IEEEA...779657L }}</ref>
== Related techniques ==
{{See also|List of genetic algorithm applications}}
===Parent fields===
Genetic algorithms are a sub-field:
*[[Evolutionary algorithms]]
*[[Evolutionary computing]]
*[[Metaheuristic]]s
*[[Stochastic optimization]]
*[[Optimization (mathematics)|Optimization]]
===Related fields===
====Evolutionary algorithms====
{{More citations needed section|date=May 2011}}
{{main|Evolutionary algorithm}}
Evolutionary algorithms is a sub-field of [[Evolutionary Computation|evolutionary computing]].
* [[Evolution strategy|Evolution strategies]] (ES, see Rechenberg, 1994) evolve individuals by means of mutation and intermediate or discrete recombination. ES algorithms are designed particularly to solve problems in the real-value ___domain.<ref>{{cite book|last=Cohoon|first=J|display-authors=etal|title=Evolutionary algorithms for the physical design of VLSI circuits|url= https://www.ifte.de/mitarbeiter/lienig/cohoon.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.ifte.de/mitarbeiter/lienig/cohoon.pdf |archive-date=2022-10-09 |url-status=live|journal=Advances in Evolutionary Computing: Theory and Applications|publisher= Springer, pp. 683-712, 2003|isbn=978-3-540-43330-9|year=2002}}</ref> They use self-adaptation to adjust control parameters of the search. De-randomization of self-adaptation has led to the contemporary Covariance Matrix Adaptation Evolution Strategy ([[CMA-ES]]).
* [[Evolutionary programming]] (EP) involves populations of solutions with primarily mutation and selection and arbitrary representations. They use self-adaptation to adjust parameters, and can include other variation operations such as combining information from multiple parents.
* [[Estimation of Distribution Algorithm]] (EDA) substitutes traditional reproduction operators by model-guided operators. Such models are learned from the population by employing machine learning techniques and represented as Probabilistic Graphical Models, from which new solutions can be sampled<ref>{{cite book|last1=Pelikan|first1=Martin|last2=Goldberg|first2=David E.|last3=Cantú-Paz|first3=Erick|title=BOA: The Bayesian Optimization Algorithm|journal=Proceedings of the 1st Annual Conference on Genetic and Evolutionary Computation - Volume 1|date=1 January 1999|pages=525–532|url=http://dl.acm.org/citation.cfm?id=2933973|isbn=9781558606111|series=Gecco'99}}</ref><ref>{{cite book|last1=Pelikan|first1=Martin|title=Hierarchical Bayesian optimization algorithm : toward a new generation of evolutionary algorithms|date=2005|publisher=Springer|___location=Berlin [u.a.]|isbn=978-3-540-23774-7|edition=1st}}</ref> or generated from guided-crossover.<ref>{{cite book|last1=Thierens|first1=Dirk|title=Parallel Problem Solving from Nature, PPSN XI |chapter=The Linkage Tree Genetic Algorithm|date=11 September 2010|pages=264–273|doi=10.1007/978-3-642-15844-5_27|language=en|isbn=978-3-642-15843-8}}</ref>
* [[Genetic programming]] (GP) is a related technique popularized by [[John Koza]] in which computer programs, rather than function parameters, are optimized. Genetic programming often uses [[Tree (data structure)|tree-based]] internal [[data structure]]s to represent the computer programs for adaptation instead of the [[List (computing)|list]] structures typical of genetic algorithms. There are many variants of Genetic Programming, including [[Cartesian genetic programming]], [[Gene expression programming]],<ref>{{cite journal|last=Ferreira|first=C|title=Gene Expression Programming: A New Adaptive Algorithm for Solving Problems|url= http://www.gene-expression-programming.com/webpapers/GEP.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.gene-expression-programming.com/webpapers/GEP.pdf |archive-date=2022-10-09 |url-status=live|journal=Complex Systems |year=2001|volume=13 |issue=2 |pages=87–129|arxiv=cs/0102027|bibcode=2001cs........2027F}}</ref> [[grammatical evolution]], [[Linear genetic programming]], [[Multi expression programming]] etc.
* [[Grouping genetic algorithm]] (GGA) is an evolution of the GA where the focus is shifted from individual items, like in classical GAs, to groups or subset of items.<ref name="Falkenauer">{{cite book|last=Falkenauer|first=Emanuel|author-link=Emanuel Falkenauer|year=1997|title=Genetic Algorithms and Grouping Problems|publisher=John Wiley & Sons Ltd|___location=Chichester, England|isbn=978-0-471-97150-4}}</ref> The idea behind this GA evolution proposed by [[Emanuel Falkenauer]] is that solving some complex problems, a.k.a. ''clustering'' or ''partitioning'' problems where a set of items must be split into disjoint group of items in an optimal way, would better be achieved by making characteristics of the groups of items equivalent to genes. These kind of problems include [[bin packing problem|bin packing]], line balancing, [[cluster analysis|clustering]] with respect to a distance measure, equal piles, etc., on which classic GAs proved to perform poorly. Making genes equivalent to groups implies chromosomes that are in general of variable length, and special genetic operators that manipulate whole groups of items. For bin packing in particular, a GGA hybridized with the Dominance Criterion of Martello and Toth, is arguably the best technique to date.
* [[Interactive evolutionary algorithm]]s are evolutionary algorithms that use human evaluation. They are usually applied to domains where it is hard to design a computational fitness function, for example, evolving images, music, artistic designs and forms to fit users' aesthetic preference.
====Swarm intelligence====
{{main|Swarm intelligence}}
Swarm intelligence is a sub-field of [[Evolutionary Computation|evolutionary computing]].
* [[Ant colony optimization]] ('''ACO''') uses many ants (or agents) equipped with a pheromone model to traverse the solution space and find locally productive areas.
*Although considered an [[Estimation of distribution algorithm]],<ref>{{cite journal|last1=Zlochin|first1=Mark|last2=Birattari|first2=Mauro|last3=Meuleau|first3=Nicolas|last4=Dorigo|first4=Marco|title=Model-Based Search for Combinatorial Optimization: A Critical Survey|journal=Annals of Operations Research|date=1 October 2004|volume=131|issue=1–4|pages=373–395|doi=10.1023/B:ANOR.0000039526.52305.af|language=en|issn=0254-5330|citeseerx=10.1.1.3.427|s2cid=63137}}</ref> [[Particle swarm optimization]] (PSO) is a computational method for multi-parameter optimization which also uses population-based approach. A population (swarm) of candidate solutions (particles) moves in the search space, and the movement of the particles is influenced both by their own best known position and swarm's global best known position. Like genetic algorithms, the PSO method depends on information sharing among population members. In some problems the PSO is often more computationally efficient than the GAs, especially in unconstrained problems with continuous variables.<ref>Rania Hassan, Babak Cohanim, Olivier de Weck, Gerhard Vente
r (2005) [https://www.mit.edu/~deweck/PDF_archive/3%20Refereed%20Conference/3_50_AIAA-2005-1897.pdf A comparison of particle swarm optimization and the genetic algorithm]</ref>
====Other evolutionary computing algorithms====
Evolutionary computation is a sub-field of the [[metaheuristic]] methods.
* [[Memetic algorithm]] (MA), often called ''hybrid genetic algorithm'' among others, is a population-based method in which solutions are also subject to local improvement phases. The idea of memetic algorithms comes from [[meme]]s, which unlike genes, can adapt themselves. In some problem areas they are shown to be more efficient than traditional evolutionary algorithms.
* [[Bacteriologic algorithm]]s (BA) inspired by [[evolutionary ecology]] and, more particularly, bacteriologic adaptation. Evolutionary ecology is the study of living organisms in the context of their environment, with the aim of discovering how they adapt. Its basic concept is that in a heterogeneous environment, there is not one individual that fits the whole environment. So, one needs to reason at the population level. It is also believed BAs could be successfully applied to complex positioning problems (antennas for cell phones, urban planning, and so on) or data mining.<ref>{{cite journal|url=http://www.irisa.fr/triskell/publis/2005/Baudry05d.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.irisa.fr/triskell/publis/2005/Baudry05d.pdf |archive-date=2022-10-09 |url-status=live|first=Benoit|last=Baudry |author2=Franck Fleurey |author3-link=Jean-Marc Jézéquel|author3=Jean-Marc Jézéquel |author4=Yves Le Traon|title=Automatic Test Case Optimization: A Bacteriologic Algorithm|date=March–April 2005|pages=76–82|journal=IEEE Software|issue=2|doi=10.1109/MS.2005.30|volume=22|s2cid=3559602|access-date=9 August 2009}}</ref>
* [[Cultural algorithm]] (CA) consists of the population component almost identical to that of the genetic algorithm and, in addition, a knowledge component called the belief space.
* [[Differential evolution]] (DE) inspired by migration of superorganisms.<ref>{{cite journal|last=Civicioglu|first=P.|title=Transforming Geocentric Cartesian Coordinates to Geodetic Coordinates by Using Differential Search Algorithm|journal=Computers &Geosciences|year=2012|volume=46|pages=229–247|doi=10.1016/j.cageo.2011.12.011|bibcode=2012CG.....46..229C}}</ref>
* [[Gaussian adaptation]] (normal or natural adaptation, abbreviated NA to avoid confusion with GA) is intended for the maximisation of manufacturing yield of signal processing systems. It may also be used for ordinary parametric optimisation. It relies on a certain theorem valid for all regions of acceptability and all Gaussian distributions. The efficiency of NA relies on information theory and a certain theorem of efficiency. Its efficiency is defined as information divided by the work needed to get the information.<ref>{{cite journal|last=Kjellström|first=G.|title= On the Efficiency of Gaussian Adaptation|journal=Journal of Optimization Theory and Applications|volume=71|issue=3|pages=589–597|date=December 1991|doi= 10.1007/BF00941405|s2cid=116847975}}</ref> Because NA maximises mean fitness rather than the fitness of the individual, the landscape is smoothed such that valleys between peaks may disappear. Therefore it has a certain "ambition" to avoid local peaks in the fitness landscape. NA is also good at climbing sharp crests by adaptation of the moment matrix, because NA may maximise the disorder ([[average information]]) of the Gaussian simultaneously keeping the [[mean fitness]] constant.
====Other metaheuristic methods====
Metaheuristic methods broadly fall within [[Stochastic optimization|stochastic]] optimisation methods.
* [[Simulated annealing]] (SA) is a related global optimization technique that traverses the search space by testing random mutations on an individual solution. A mutation that increases fitness is always accepted. A mutation that lowers fitness is accepted probabilistically based on the difference in fitness and a decreasing temperature parameter. In SA parlance, one speaks of seeking the lowest energy instead of the maximum fitness. SA can also be used within a standard GA algorithm by starting with a relatively high rate of mutation and decreasing it over time along a given schedule.
* [[Tabu search]] (TS) is similar to simulated annealing in that both traverse the solution space by testing mutations of an individual solution. While simulated annealing generates only one mutated solution, tabu search generates many mutated solutions and moves to the solution with the lowest energy of those generated. In order to prevent cycling and encourage greater movement through the solution space, a tabu list is maintained of partial or complete solutions. It is forbidden to move to a solution that contains elements of the tabu list, which is updated as the solution traverses the solution space.
* [[Extremal optimization]] (EO) Unlike GAs, which work with a population of candidate solutions, EO evolves a single solution and makes [[local search (optimization)|local]] modifications to the worst components. This requires that a suitable representation be selected which permits individual solution components to be assigned a quality measure ("fitness"). The governing principle behind this algorithm is that of ''emergent'' improvement through selectively removing low-quality components and replacing them with a randomly selected component. This is decidedly at odds with a GA that selects good solutions in an attempt to make better solutions.
====Other stochastic optimisation methods====
* The [[Cross-entropy method|cross-entropy (CE) method]] generates candidate solutions via a parameterized probability distribution. The parameters are updated via cross-entropy minimization, so as to generate better samples in the next iteration.
* Reactive search optimization (RSO) advocates the integration of sub-symbolic machine learning techniques into search heuristics for solving complex optimization problems. The word reactive hints at a ready response to events during the search through an internal online feedback loop for the self-tuning of critical parameters. Methodologies of interest for Reactive Search include machine learning and statistics, in particular [[reinforcement learning]], [[Active learning (machine learning)|active or query learning]], [[Artificial neural network|neural networks]], and [[metaheuristics]].
==See also==
* [[Genetic programming]]
* [[List of genetic algorithm applications]]
* [[particle filter|Genetic algorithms in signal processing (a.k.a. particle filters)]]
* [[Propagation of schema]]
* [[Universal Darwinism]]
* [[Metaheuristics]]
* [[Learning classifier system]]
* [[Rule-based machine learning]]
== References ==
{{Reflist|30em}}
== Bibliography ==
{{Refbegin}}
* {{Cite book | title=Genetic Programming – An Introduction | last1=Banzhaf | first1=Wolfgang | last2=Nordin | first2=Peter | last3=Keller | first3=Robert | last4=Francone | first4=Frank | year=1998 | isbn=978-1558605107 | publisher=Morgan Kaufmann | ___location=San Francisco, CA | url-access=registration | url=https://archive.org/details/geneticprogrammi00wolf }}
* {{Cite journal|last1=Bies|first1=Robert R. |last2=Muldoon |first2=Matthew F. |last3=Pollock |first3=Bruce G. |last4=Manuck |first4=Steven |last5=Smith |first5=Gwenn |last6=Sale |first6=Mark E. |year=2006|title=A Genetic Algorithm-Based, Hybrid Machine Learning Approach to Model Selection|journal=Journal of Pharmacokinetics and Pharmacodynamics|volume=33 |issue=2 |pages=196–221 |pmid=16565924 |doi=10.1007/s10928-006-9004-6 |s2cid=39571129 }}
* {{Cite journal|last1=Cha|first1=Sung-Hyuk|last2=Tappert |first2=Charles C. |year=2009|title=A Genetic Algorithm for Constructing Compact Binary Decision Trees|journal=Journal of Pattern Recognition Research |volume=4|issue=1|pages=1–13|doi=10.13176/11.44|citeseerx=10.1.1.154.8314 }}
* {{Cite book | last1=Eiben | first1=Agoston | last2=Smith | first2=James | year=2003 | title=Introduction to Evolutionary Computing | publisher=Springer | isbn=978-3540401841 }}
* {{Cite journal|last=Fraser|first=Alex S.|year=1957|title=Simulation of Genetic Systems by Automatic Digital Computers. I. Introduction|journal=Australian Journal of Biological Sciences|volume=10|issue=4|pages=484–491|doi=10.1071/BI9570484 |doi-access=free}}
* {{Cite book| last=Goldberg | first=David | year=1989 | title=Genetic Algorithms in Search, Optimization and Machine Learning | isbn=978-0201157673 | publisher=Addison-Wesley Professional | ___location=Reading, MA }}
* {{Cite book| last=Goldberg | first=David | year=2002 | title=The Design of Innovation: Lessons from and for Competent Genetic Algorithms | publisher=Kluwer Academic Publishers | ___location=Norwell, MA | isbn=978-1402070983 }}
* {{Cite book| last=Fogel | first=David | title=Evolutionary Computation: Toward a New Philosophy of Machine Intelligence | publisher=IEEE Press | ___location=Piscataway, NJ | edition=3rd | isbn=978-0471669517 | year=2006 }}
* {{Cite book | last1=Hingston | first1=Philip | last2=Barone | first2=Luigi | last3=Michalewicz | first3=Zbigniew | title=Design by Evolution: Advances in Evolutionary Design | year=2008 | publisher=Springer | isbn=978-3540741091 }}
* {{Cite book | last=Holland | first=John | title=Adaptation in Natural and Artificial Systems | publisher=MIT Press | ___location=Cambridge, MA | year=1992 | isbn=978-0262581110 | url-access=registration | url=https://archive.org/details/adaptationinnatu00holl }}
* {{Cite book | last=Koza | first=John | title=Genetic Programming: On the Programming of Computers by Means of Natural Selection | year = 1992 | publisher=MIT Press | ___location=Cambridge, MA | isbn=978-0262111706 }}
* {{Cite book | last=Michalewicz | first=Zbigniew | year=1996 | title=Genetic Algorithms + Data Structures = Evolution Programs | publisher=Springer-Verlag | isbn=978-3540606765 }}
* {{Cite book | last=Mitchell | first=Melanie | title=An Introduction to Genetic Algorithms | year=1996 | publisher=MIT Press | ___location=Cambridge, MA | isbn = 9780585030944 }}
* {{Cite book |last1=Poli |first1=R. |last2=Langdon |first2=W. B. |last3=McPhee |first3=N. F. |year=2008 |title=A Field Guide to Genetic Programming | publisher=Lulu.com, freely available from the internet | isbn = 978-1-4092-0073-4 }}{{self-published inline|date=February 2020}}
* Rechenberg, Ingo (1994): Evolutionsstrategie '94, Stuttgart: Fromman-Holzboog.
* {{cite journal |last1=Schmitt |first1=Lothar M. |last2=Nehaniv |first2=Chrystopher L. |last3=Fujii |first3=Robert H. |date=1998 |url=https://www.sciencedirect.com/science/article/pii/S0304397598000048/pdf?md5=28a658a4dc5aef635bbf3c8560129925&pid=1-s2.0-S0304397598000048-main.pdf&_valck=1 |title=Linear analysis of genetic algorithms |journal=Theoretical Computer Science |volume=208 |pages=111–148 }}
* {{cite journal |last1=Schmitt |first1=Lothar M. |date=2001 |title=Theory of Genetic Algorithms |journal=Theoretical Computer Science |volume=259 |issue=1–2 |pages=1–61 |doi=10.1016/S0304-3975(00)00406-0 |doi-access=free }}
* {{cite journal |last1=Schmitt |first1=Lothar M. |date=2004 |title=Theory of Genetic Algorithms II: models for genetic operators over the string-tensor representation of populations and convergence to global optima for arbitrary fitness function under scaling |journal=Theoretical Computer Science |volume=310 |issue=1–3 |pages=181–231 |doi=10.1016/S0304-3975(03)00393-1 |doi-access=free }}
* Schwefel, Hans-Paul (1974): Numerische Optimierung von Computer-Modellen (PhD thesis). Reprinted by Birkhäuser (1977).
* {{Cite book | last=Vose
* {{Cite journal | last=Whitley | first=Darrell | title=A genetic algorithm tutorial | journal=Statistics and Computing | doi=10.1007/BF00175354 | volume=4 | issue=2 | pages=65–85 | year=1994 | url=http://cobweb.cs.uga.edu/~potter/CompIntell/ga_tutorial.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://cobweb.cs.uga.edu/~potter/CompIntell/ga_tutorial.pdf |archive-date=2022-10-09 |url-status=live | citeseerx=10.1.1.184.3999 | s2cid=3447126 }}<!--| access-date=5 January 2013-->
{{
== External links ==
=== Resources ===
* [https://web.archive.org/web/20160303215222/http://www.geneticprogramming.com/ga/index.htm] Provides a list of resources in the genetic algorithms field
* [https://www.staracle.com/general/evolutionaryAlgorithms.php An Overview of the History and Flavors of Evolutionary Algorithms]
=== Tutorials ===
* [https://www2.econ.iastate.edu/tesfatsi/holland.gaintro.htm Genetic Algorithms - Computer programs that "evolve" in ways that resemble natural selection can solve complex problems even their creators do not fully understand] An excellent introduction to GA by John Holland and with an application to the Prisoner's Dilemma
* [http://www.i4ai.org/EA-demo/ An online interactive Genetic Algorithm tutorial for a reader to practise or learn how a GA works]: Learn step by step or watch global convergence in batch, change the population size, crossover rates/bounds, mutation rates/bounds and selection mechanisms, and add constraints.
* [https://web.archive.org/web/20130615042000/http://samizdat.mines.edu/ga_tutorial/ga_tutorial.ps A Genetic Algorithm Tutorial by Darrell Whitley Computer Science Department Colorado State University] An excellent tutorial with much theory
* [http://cs.gmu.edu/~sean/book/metaheuristics/ "Essentials of Metaheuristics"], 2009 (225 p). Free open text by Sean Luke.
* [http://www.it-weise.de/projects/book.pdf Global Optimization Algorithms – Theory and Application] {{Webarchive|url=https://web.archive.org/web/20080911075107/http://www.it-weise.de/projects/book.pdf |date=11 September 2008 }}
* [https://mpatacchiola.github.io/blog/2017/03/14/dissecting-reinforcement-learning-5.html Genetic Algorithms in Python] Tutorial with the intuition behind GAs and Python implementation.
* [http://www-personal.umich.edu/~axe/research/Evolving.pdf Genetic Algorithms evolves to solve the prisoner's dilemma.] Written by Robert Axelrod.
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