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Evolutionary algorithm

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</style><table class="sidebar nomobile nowraplinks vcard hlist"><tbody><tr><td class="sidebar-pretitle">Part of a series on the</td></tr><tr><th class="sidebar-title-with-pretitle"></th></tr><tr><td class="sidebar-image"></td></tr><tr><td class="sidebar-content hlist">

<ul><li><a href="Chromosome_(evolutionary_algorithm)" title="Chromosome (evolutionary algorithm)">Chromosome</a></li>

<li><a href="Fitness_function" title="Fitness function">Fitness function</a></li>

<li><a href="Genetic_operator" title="Genetic operator">Genetic operator</a>

<ul><li><a href="Crossover_(evolutionary_algorithm)" title="Crossover (evolutionary algorithm)">Crossover</a></li>

<li><a href="Mutation_(evolutionary_algorithm)" title="Mutation (evolutionary algorithm)">Mutation</a></li>

<li><a href="Selection_(evolutionary_algorithm)" title="Selection (evolutionary algorithm)">Selection</a></li></ul></li>

<li><a href="Population_model_(evolutionary_algorithm)" title="Population model (evolutionary algorithm)">Population model</a></li></ul></td>

</tr><tr><th class="sidebar-heading">

<a href="Genetic_algorithm" title="Genetic algorithm">Genetic algorithm</a> (GA)</th></tr><tr><td class="sidebar-content hlist">

<ul><li><a href="Chromosome_(genetic_algorithm)" class="mw-redirect" title="Chromosome (genetic algorithm)">Chromosome</a></li>

<li><a href="Clonal_selection_algorithm" title="Clonal selection algorithm">Clonal selection algorithm</a></li>

<li><a href="Fly_algorithm" title="Fly algorithm">Fly algorithm</a></li>

<li><a href="Genetic_fuzzy_systems" title="Genetic fuzzy systems">Genetic fuzzy systems</a></li>

<li><a href="Genetic_memory_(computer_science)" title="Genetic memory (computer science)">Genetic memory</a></li>

<li><a href="Schema_(genetic_algorithms)" title="Schema (genetic algorithms)">Schema</a></li>

<li><a href="Promoter_based_genetic_algorithm" title="Promoter based genetic algorithm">Promoter based GA</a></li></ul></td>

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<a href="Genetic_programming" title="Genetic programming">Genetic programming</a> (GP)</th></tr><tr><td class="sidebar-content hlist">

<ul><li><a href="Cartesian_genetic_programming" title="Cartesian genetic programming">Cartesian GP</a></li>

<li><a href="Linear_genetic_programming" title="Linear genetic programming">Linear GP</a></li>

<li><a href="Gene_expression_programming" title="Gene expression programming">Gene expression programming</a></li>

<li><a href="Grammatical_evolution" title="Grammatical evolution">Grammatical evolution</a></li>

<li><a href="Multi_expression_programming" title="Multi expression programming">Multi expression programming</a></li></ul></td>

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<a href="Differential_evolution" title="Differential evolution">Differential evolution</a></th></tr><tr><th class="sidebar-heading">

<a href="Evolution_strategy" title="Evolution strategy">Evolution strategy</a></th></tr><tr><th class="sidebar-heading">

<a href="Evolutionary_programming" title="Evolutionary programming">Evolutionary programming</a></th></tr><tr><th class="sidebar-heading">

Related topics</th></tr><tr><td class="sidebar-content hlist">

<ul><li><a href="Cellular_evolutionary_algorithm" title="Cellular evolutionary algorithm">Cellular EA</a></li>

<li><a href="Cultural_algorithm" title="Cultural algorithm">Cultural algorithm</a></li>

<li><a href="Effective_fitness" title="Effective fitness">Effective fitness</a></li>

<li><a href="Evolutionary_computation" title="Evolutionary computation">Evolutionary computation</a></li>

<li><a href="Gaussian_adaptation" title="Gaussian adaptation">Gaussian adaptation</a></li>

<li><a href="Grammar_induction#Grammatical_inference_by_genetic_algorithms" title="Grammar induction">Grammar induction</a></li>

<li><a href="Evolutionary_multimodal_optimization" title="Evolutionary multimodal optimization">Evolutionary multimodal optimization</a></li>

<li><a href="Memetic_algorithm" title="Memetic algorithm">Memetic algorithm</a></li>

<li><a href="Neuroevolution" title="Neuroevolution">Neuroevolution</a></li></ul></td>

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<table class="sidebar sidebar-collapse nomobile nowraplinks hlist"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="Artificial_intelligence" title="Artificial intelligence">Artificial intelligence (AI)</a></th></tr><tr><td class="sidebar-image"></td></tr><tr><td class="sidebar-content">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;color: var(--color-base)"><a href="Artificial_intelligence#Goals" title="Artificial intelligence">Major goals</a></div><div class="sidebar-list-content mw-collapsible-content">

<ul><li><a href="Artificial_general_intelligence" title="Artificial general intelligence">Artificial general intelligence</a></li>

<li><a href="Intelligent_agent" title="Intelligent agent">Intelligent agent</a></li>

<li><a href="Recursive_self-improvement" title="Recursive self-improvement">Recursive self-improvement</a></li>

<li><a href="Automated_planning_and_scheduling" title="Automated planning and scheduling">Planning</a></li>

<li><a href="Computer_vision" title="Computer vision">Computer vision</a></li>

<li><a href="General_game_playing" title="General game playing">General game playing</a></li>

<li><a href="Knowledge_representation_and_reasoning" title="Knowledge representation and reasoning">Knowledge representation</a></li>

<li><a href="Natural_language_processing" title="Natural language processing">Natural language processing</a></li>

<li><a href="Robotics" title="Robotics">Robotics</a></li>

<li><a href="AI_safety" title="AI safety">AI safety</a></li></ul></div></div></td>

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<div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="text-align:center;color: var(--color-base)">Approaches</div><div class="sidebar-list-content mw-collapsible-content">

<ul><li><a href="Machine_learning" title="Machine learning">Machine learning</a></li>

<li><a href="Symbolic_artificial_intelligence" title="Symbolic artificial intelligence">Symbolic</a></li>

<li><a href="Deep_learning" title="Deep learning">Deep learning</a></li>

<li><a href="Bayesian_network" title="Bayesian network">Bayesian networks</a></li>

<li><a href="Hybrid_intelligent_system" title="Hybrid intelligent system">Hybrid intelligent systems</a></li>

<li><a href="Artificial_intelligence_systems_integration" title="Artificial intelligence systems integration">Systems integration</a></li></ul></div></div></td>

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<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;color: var(--color-base)"><a href="Applications_of_artificial_intelligence" title="Applications of artificial intelligence">Applications</a></div><div class="sidebar-list-content mw-collapsible-content">

<ul><li><a href="Machine_learning_in_bioinformatics" title="Machine learning in bioinformatics">Bioinformatics</a></li>

<li><a href="Deepfake" title="Deepfake">Deepfake</a></li>

<li><a href="Machine_learning_in_earth_sciences" title="Machine learning in earth sciences">Earth sciences</a></li>

<li><a href="Applications_of_artificial_intelligence#Finance" title="Applications of artificial intelligence"> Finance </a></li>

<li><a href="Generative_artificial_intelligence" title="Generative artificial intelligence">Generative AI</a>

<li><a href="Generative_audio" title="Generative audio">Audio</a></li>

<li><a href="Music_and_artificial_intelligence" title="Music and artificial intelligence">Music</a></li></ul></li>

<li><a href="Artificial_intelligence_in_government" title="Artificial intelligence in government">Government</a></li>

<li><a href="Artificial_intelligence_in_healthcare" title="Artificial intelligence in healthcare">Healthcare</a>

<ul><li><a href="Artificial_intelligence_in_mental_health" title="Artificial intelligence in mental health">Mental health</a></li></ul></li>

<li><a href="Artificial_intelligence_in_industry" title="Artificial intelligence in industry">Industry</a></li>

<li><a href="AI-assisted_software_development" title="AI-assisted software development">Software development</a></li>

<li><a href="Machine_translation" title="Machine translation">Translation</a></li>

<li><a href="Artificial_intelligence_arms_race" title="Artificial intelligence arms race"> Military </a></li>

<li><a href="Machine_learning_in_physics" title="Machine learning in physics">Physics</a></li>

<li><a href="List_of_artificial_intelligence_projects" title="List of artificial intelligence projects">Projects</a></li></ul></div></div></td>

</tr><tr><td class="sidebar-content">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;color: var(--color-base)"><a href="Philosophy_of_artificial_intelligence" title="Philosophy of artificial intelligence">Philosophy</a></div><div class="sidebar-list-content mw-collapsible-content">

<ul><li><a href="Artificial_consciousness" title="Artificial consciousness">Artificial consciousness</a></li>

<li><a href="Chinese_room" title="Chinese room">Chinese room</a></li>

<li><a href="Friendly_artificial_intelligence" title="Friendly artificial intelligence">Friendly AI</a></li>

<li><a href="AI_control_problem" class="mw-redirect" title="AI control problem">Control problem</a>/<a href="AI_takeover" title="AI takeover">Takeover</a></li>

<li><a href="Ethics_of_artificial_intelligence" title="Ethics of artificial intelligence">Ethics</a></li>

<li><a href="Existential_risk_from_artificial_general_intelligence" class="mw-redirect" title="Existential risk from artificial general intelligence">Existential risk</a></li>

<li><a href="Turing_test" title="Turing test">Turing test</a></li>

<li><a href="Uncanny_valley" title="Uncanny valley">Uncanny valley</a></li></ul></div></div></td>

</tr><tr><td class="sidebar-content">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;color: var(--color-base)"><a href="History_of_artificial_intelligence" title="History of artificial intelligence">History</a></div><div class="sidebar-list-content mw-collapsible-content">

<ul><li><a href="Timeline_of_artificial_intelligence" title="Timeline of artificial intelligence">Timeline</a></li>

<li><a href="Progress_in_artificial_intelligence" title="Progress in artificial intelligence">Progress</a></li>

<li><a href="AI_winter" title="AI winter">AI winter</a></li>

</tr><tr><td class="sidebar-content">

<div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;color: var(--color-base)">Glossary</div><div class="sidebar-list-content mw-collapsible-content">

<ul><li><a href="Glossary_of_artificial_intelligence" title="Glossary of artificial intelligence">Glossary</a></li></ul></div></div></td>

</tr><tr><td class="sidebar-navbar"></td></tr></tbody></table>

Evolutionary algorithms (EA) reproduce essential elements of biological <a href="Evolution" title="Evolution">evolution</a> in a <a href="Computer_algorithm" class="mw-redirect" title="Computer algorithm">computer algorithm</a> in order to solve "difficult" problems, at least <a href="Approximation" title="Approximation">approximately</a>, for which no exact or satisfactory solution methods are known. They are <a href="Metaheuristics" class="mw-redirect" title="Metaheuristics">metaheuristics</a> and <a href="Bio-inspired_computing#Population-Based_Bio-Inspired_Algorithms" title="Bio-inspired computing">population-based bio-inspired algorithms</a><a href="#cite_note-1">[1]</a> and <a href="Evolutionary_computation" title="Evolutionary computation">evolutionary computation</a>, which itself are part of the field of <a href="Computational_intelligence" title="Computational intelligence">computational intelligence</a>.<a href="#cite_note-EVOALG-2">[2]</a> The mechanisms of biological evolution that an EA mainly imitates are <a href="Reproduction" title="Reproduction">reproduction</a>, <a href="Mutation" title="Mutation">mutation</a>, <a href="Genetic_recombination" title="Genetic recombination">recombination</a> and <a href="Natural_selection" title="Natural selection">selection</a>. <a href="Candidate_solution" class="mw-redirect" title="Candidate solution">Candidate solutions</a> to the <a href="Optimization_problem" title="Optimization problem">optimization problem</a> play the role of individuals in a population, and the <a href="Fitness_function" title="Fitness function">fitness function</a> determines the quality of the solutions (see also <a href="Loss_function" title="Loss function">loss function</a>). Evolution of the population then takes place after the repeated application of the above operators.

Evolutionary algorithms often perform well approximating solutions to all types of problems because they ideally do not make any assumption about the underlying <a href="Fitness_landscape" title="Fitness landscape">fitness landscape</a>. Techniques from evolutionary algorithms applied to the modeling of biological evolution are generally limited to explorations of <a href="Microevolution" title="Microevolution">microevolution</a> (microevolutionary processes) and planning models based upon cellular processes. In most real applications of EAs, computational complexity is a prohibiting factor.<a href="#cite_note-VLSI-3">[3]</a> In fact, this computational complexity is due to fitness function evaluation. <a href="Fitness_approximation" title="Fitness approximation">Fitness approximation</a> is one of the solutions to overcome this difficulty. However, seemingly simple EA can solve often complex problems;<a href="#cite_note-:0-4">[4]</a><a href="#cite_note-:1-5">[5]</a><a href="#cite_note-:2-6">[6]</a> therefore, there may be no direct link between algorithm complexity and problem complexity.

<div class="mw-heading mw-heading2"><h2 id="Generic_definition">Generic definition</h2></div>

The following is an example of a generic evolutionary algorithm:<a href="#cite_note-7">[7]</a><a href="#cite_note-8">[8]</a><a href="#cite_note-9">[9]</a>

<ol><li>Randomly generate the initial <a href="Population_model_(evolutionary_algorithm)" title="Population model (evolutionary algorithm)">population</a> of <a href="Chromosome_(evolutionary_algorithm)" title="Chromosome (evolutionary algorithm)">individuals</a>, the first generation.</li>

<li>Evaluate the <a href="Fitness_function" title="Fitness function">fitness</a> of each individual in the population.</li>

<li>Check, if the goal is reached and the algorithm can be terminated.</li>

<li><a href="Selection_(evolutionary_algorithm)" title="Selection (evolutionary algorithm)">Select</a> individuals as parents, preferably of higher fitness.</li>

<li>Produce offspring with optional <a href="Crossover_(evolutionary_algorithm)" title="Crossover (evolutionary algorithm)">crossover</a> (mimicking <a href="Reproduce" class="mw-redirect" title="Reproduce">reproduction</a>).</li>

<li>Apply <a href="Mutation_(evolutionary_algorithm)" title="Mutation (evolutionary algorithm)">mutation</a> operations on the <a href="Offspring" title="Offspring">offspring</a>.</li>

<li><a href="Selection_(evolutionary_algorithm)" title="Selection (evolutionary algorithm)">Select</a> individuals preferably of lower fitness for replacement with new individuals (mimicking <a href="Natural_selection" title="Natural selection">natural selection</a>).</li>

<li>Return to 2</li></ol>

<div class="mw-heading mw-heading2"><h2 id="Types">Types</h2></div>

Similar techniques differ in <a href="Genetic_representation" title="Genetic representation">genetic representation</a> and other implementation details, and the nature of the particular applied problem.

<ul><li><a href="Genetic_algorithm" title="Genetic algorithm">Genetic algorithm</a> – This is the most popular type of EA. One seeks the solution of a problem in the form of strings of numbers (traditionally binary, although the best representations are usually those that reflect something about the problem being solved),<a href="#cite_note-VLSI-3">[3]</a> by applying operators such as recombination and mutation (sometimes one, sometimes both). This type of EA is often used in <a href="Optimization_(mathematics)" class="mw-redirect" title="Optimization (mathematics)">optimization</a> problems.</li>

<li><a href="Genetic_programming" title="Genetic programming">Genetic programming</a> – Here the solutions are in the form of computer programs, and their fitness is determined by their ability to solve a computational problem. There are many variants of Genetic Programming:

<ul><li><a href="Cartesian_genetic_programming" title="Cartesian genetic programming">Cartesian genetic programming</a></li>

<li><a href="Gene_expression_programming" title="Gene expression programming">Gene expression programming</a></li>

<li><a href="Grammatical_evolution" title="Grammatical evolution">Grammatical evolution</a></li>

<li><a href="Linear_genetic_programming" title="Linear genetic programming">Linear genetic programming</a></li>

<li><a href="Multi_expression_programming" title="Multi expression programming">Multi expression programming</a></li></ul></li>

<li><a href="Evolutionary_programming" title="Evolutionary programming">Evolutionary programming</a> – Similar to evolution strategy, but with a deterministic selection of all parents.</li>

<li><a href="Evolution_strategy" title="Evolution strategy">Evolution strategy</a> (ES) – Works with vectors of real numbers as representations of solutions, and typically uses self-adaptive mutation rates. The method is mainly used for numerical optimization, although there are also variants for combinatorial tasks.<a href="#cite_note-10">[10]</a><a href="#cite_note-11">[11]</a><a href="#cite_note-eaoverview-12">[12]</a>

<li><a href="Natural_evolution_strategy" title="Natural evolution strategy">Natural evolution strategy</a></li></ul></li>

<li><a href="Differential_evolution" title="Differential evolution">Differential evolution</a> – Based on vector differences and is therefore primarily suited for <a href="Numerical_optimization" class="mw-redirect" title="Numerical optimization">numerical optimization</a> problems.</li>

<li>Coevolutionary algorithm – Similar to genetic algorithms and evolution strategies, but the created solutions are compared on the basis of their outcomes from interactions with other solutions. Solutions can either compete or cooperate during the search process. Coevolutionary algorithms are often used in scenarios where the fitness landscape is dynamic, complex, or involves competitive interactions.<a href="#cite_note-13">[13]</a><a href="#cite_note-14">[14]</a></li>

<li><a href="Neuroevolution" title="Neuroevolution">Neuroevolution</a> – Similar to genetic programming but the genomes represent artificial neural networks by describing structure and connection weights. The genome encoding can be direct or indirect.</li>

<li><a href="Learning_classifier_system" title="Learning classifier system">Learning classifier system</a> – Here the solution is a set of classifiers (rules or conditions). A Michigan-LCS evolves at the level of individual classifiers whereas a Pittsburgh-LCS uses populations of classifier-sets. Initially, classifiers were only binary, but now include real, neural net, or <a href="S-expression" title="S-expression">S-expression</a> types. Fitness is typically determined with either a strength or accuracy based <a href="Reinforcement_learning" title="Reinforcement learning">reinforcement learning</a> or <a href="Supervised_learning" title="Supervised learning">supervised learning</a> approach.</li>

<li>Quality–Diversity algorithms – QD algorithms simultaneously aim for high-quality and diverse solutions. Unlike traditional optimization algorithms that solely focus on finding the best solution to a problem, QD algorithms explore a wide variety of solutions across a problem space and keep those that are not just high performing, but also diverse and unique.<a href="#cite_note-15">[15]</a><a href="#cite_note-16">[16]</a><a href="#cite_note-17">[17]</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="Theoretical_background">Theoretical background</h2></div>

The following theoretical principles apply to all or almost all EAs.

<div class="mw-heading mw-heading3"><h3 id="No_free_lunch_theorem">No free lunch theorem</h3></div>

The <a href="No_free_lunch_theorem" title="No free lunch theorem">no free lunch theorem</a> of optimization states that all optimization strategies are equally effective when the set of all optimization problems is considered. Under the same condition, no evolutionary algorithm is fundamentally better than another. This can only be the case if the set of all problems is restricted. This is exactly what is inevitably done in practice. Therefore, to improve an EA, it must exploit problem knowledge in some form (e.g. by choosing a certain mutation strength or a <a href="Genetic_representation" title="Genetic representation">problem-adapted coding</a>). Thus, if two EAs are compared, this constraint is implied. In addition, an EA can use problem specific knowledge by, for example, not randomly generating the entire start population, but creating some individuals through <a href="Heuristic_(computer_science)" title="Heuristic (computer science)">heuristics</a> or other procedures.<a href="#cite_note-Davis91-18">[18]</a><a href="#cite_note-19">[19]</a> Another possibility to tailor an EA to a given problem domain is to involve suitable heuristics, <a href="Local_search_(optimization)" title="Local search (optimization)">local search procedures</a> or other problem-related procedures in the process of generating the offspring. This form of extension of an EA is also known as a <a href="Memetic_algorithm" title="Memetic algorithm">memetic algorithm</a>. Both extensions play a major role in practical applications, as they can speed up the search process and make it more robust.<a href="#cite_note-Davis91-18">[18]</a><a href="#cite_note-20">[20]</a>

<div class="mw-heading mw-heading3"><h3 id="Convergence">Convergence</h3></div>

For EAs in which, in addition to the offspring, at least the best individual of the parent generation is used to form the subsequent generation (so-called elitist EAs), there is a general proof of <a href="Convergence_(logic)" title="Convergence (logic)">convergence</a> under the condition that an <a href="Optimum" class="mw-redirect" title="Optimum">optimum</a> exists. <a href="Without_loss_of_generality" title="Without loss of generality">Without loss of generality</a>, a maximum search is assumed for the proof:

From the property of elitist offspring acceptance and the existence of the optimum it follows that per generation <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle k}</annotation>

</semantics>

</math><img src="./c3c9a2c7b599b37105512c5d570edc034056dd40.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}" loading="lazy"> an improvement of the fitness <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle F}</annotation>

</semantics>

</math><img src="./545fd099af8541605f7ee55f08225526be88ce57.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}" loading="lazy"> of the respective best individual <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x'}">

<msup>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle x'}</annotation>

</semantics>

</math><img src="./0ac74959896052e160a5953102e4bc3850fe93b2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.014ex; height:2.509ex;" alt="{\displaystyle x'}" loading="lazy"> will occur with a probability <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P>0}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P>0}</annotation>

</semantics>

</math><img src="./bd713165b8911d1e29aabe51e8ed093fa4b349ae.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.006ex; height:2.176ex;" alt="{\displaystyle P>0}" loading="lazy">. Thus:

</mrow>

</msubsup>

</mrow>

</msubsup>

</mrow>

</msubsup>

</mrow>

</msubsup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle F(x'_{1})\leq F(x'_{2})\leq F(x'_{3})\leq \cdots \leq F(x'_{k})\leq \cdots }</annotation>

</semantics>

</math><img src="./4d70687f45f0950405bb95440e4f000fce484cba.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:44.709ex; height:3.009ex;" alt="{\displaystyle F(x'_{1})\leq F(x'_{2})\leq F(x'_{3})\leq \cdots \leq F(x'_{k})\leq \cdots }" loading="lazy"></dd></dl>

I.e., the fitness values represent a <a href="Monotonic_function" title="Monotonic function">monotonically</a> non-decreasing <a href="Sequence" title="Sequence">sequence</a>, which is <a href="Bounded_set" title="Bounded set">bounded</a> due to the existence of the optimum. From this follows the convergence of the sequence against the optimum.

Since the proof makes no statement about the speed of convergence, it is of little help in practical applications of EAs. But it does justify the recommendation to use elitist EAs. However, when using the usual <a href="Panmixia" title="Panmixia">panmictic</a> <a href="Population_model_(evolutionary_algorithm)" title="Population model (evolutionary algorithm)">population model</a>, elitist EAs tend to <a href="Premature_convergence" title="Premature convergence">converge prematurely</a> more than non-elitist ones.<a href="#cite_note-21">[21]</a> In a panmictic population model, mate selection (see step 4 of the <a class="mw-selflink-fragment" href="#Generic_definition">generic definition</a>) is such that every individual in the entire population is eligible as a mate. In <a href="Population_model_(evolutionary_algorithm)" title="Population model (evolutionary algorithm)">non-panmictic populations</a>, selection is suitably restricted, so that the dispersal speed of better individuals is reduced compared to panmictic ones. Thus, the general risk of premature convergence of elitist EAs can be significantly reduced by suitable population models that restrict mate selection.<a href="#cite_note-22">[22]</a><a href="#cite_note-23">[23]</a>

<div class="mw-heading mw-heading3"><h3 id="Virtual_alphabets">Virtual alphabets</h3></div>

With the theory of virtual alphabets, <a href="David_E._Goldberg" title="David E. Goldberg">David E. Goldberg</a> showed in 1990 that by using a representation with real numbers, an EA that uses classical <a href="Crossover_(genetic_algorithm)" class="mw-redirect" title="Crossover (genetic algorithm)">recombination operators</a> (e.g. uniform or n-point crossover) cannot reach certain areas of the search space, in contrast to a coding with binary numbers.<a href="#cite_note-24">[24]</a> This results in the recommendation for EAs with real representation to use arithmetic operators for recombination (e.g. arithmetic mean or intermediate recombination). With suitable operators, real-valued representations are more effective than binary ones, contrary to earlier opinion.<a href="#cite_note-25">[25]</a><a href="#cite_note-26">[26]</a>

<div class="mw-heading mw-heading2"><h2 id="Comparison_to_other_concepts">Comparison to other concepts</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Biological_processes">Biological processes</h3></div>

A possible limitation of many evolutionary algorithms is their lack of a clear <a href="Genotype%E2%80%93phenotype_distinction" title="Genotype–phenotype distinction">genotype–phenotype distinction</a>. In nature, the fertilized egg cell undergoes a complex process known as <a href="Embryogenesis" class="mw-redirect" title="Embryogenesis">embryogenesis</a> to become a mature <a href="Phenotype" title="Phenotype">phenotype</a>. This indirect <a href="Encoding" class="mw-redirect" title="Encoding">encoding</a> is believed to make the genetic search more robust (i.e. reduce the probability of fatal mutations), and also may improve the <a href="Evolvability" title="Evolvability">evolvability</a> of the organism.<a href="#cite_note-27">[27]</a><a href="#cite_note-28">[28]</a> Such indirect (also known as generative or developmental) encodings also enable evolution to exploit the regularity in the environment.<a href="#cite_note-29">[29]</a> Recent work in the field of <a href="Artificial_development" title="Artificial development">artificial embryogeny</a>, or artificial developmental systems, seeks to address these concerns. And <a href="Gene_expression_programming" title="Gene expression programming">gene expression programming</a> successfully explores a genotype–phenotype system, where the genotype consists of linear multigenic chromosomes of fixed length and the phenotype consists of multiple expression trees or computer programs of different sizes and shapes.<a href="#cite_note-30">[30]</a>

<div class="mw-heading mw-heading3"><h3 id="Monte-Carlo_methods">Monte-Carlo methods</h3></div>

Both method classes have in common that their individual search steps are determined by chance. The main difference, however, is that EAs, like many other metaheuristics, learn from past search steps and incorporate this experience into the execution of the next search steps in a method-specific form. With EAs, this is done firstly through the fitness-based selection operators for partner choice and the formation of the next generation. And secondly, in the type of search steps: In EA, they start from a current solution and change it or they mix the information of two solutions. In contrast, when dicing out new solutions in <a href="Monte_Carlo_method" title="Monte Carlo method">Monte-Carlo methods</a>, there is usually no connection to existing solutions.<a href="#cite_note-31">[31]</a><a href="#cite_note-32">[32]</a>

If, on the other hand, the search space of a task is such that there is nothing to learn, Monte-Carlo methods are an appropriate tool, as they do not contain any algorithmic overhead that attempts to draw suitable conclusions from the previous search. An example of such tasks is the proverbial search for a needle in a haystack, e.g. in the form of a flat (hyper)plane with a single narrow peak.

<div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2></div>

The areas in which evolutionary algorithms are practically used are almost unlimited<a href="#cite_note-:2-6">[6]</a> and range from industry,<a href="#cite_note-33">[33]</a><a href="#cite_note-34">[34]</a> engineering,<a href="#cite_note-VLSI-3">[3]</a><a href="#cite_note-:0-4">[4]</a><a href="#cite_note-35">[35]</a> complex scheduling,<a href="#cite_note-:1-5">[5]</a><a href="#cite_note-36">[36]</a><a href="#cite_note-37">[37]</a> agriculture,<a href="#cite_note-38">[38]</a> robot movement planning<a href="#cite_note-39">[39]</a> and finance<a href="#cite_note-40">[40]</a><a href="#cite_note-41">[41]</a> to research<a href="#cite_note-42">[42]</a><a href="#cite_note-43">[43]</a> and <a href="Evolutionary_art" title="Evolutionary art">art</a>. The application of an evolutionary algorithm requires some rethinking from the inexperienced user, as the approach to a task using an EA is different from conventional exact methods and this is usually not part of the curriculum of engineers or other disciplines. For example, the fitness calculation must not only formulate the goal but also support the evolutionary search process towards it, e.g. by rewarding improvements that do not yet lead to a better evaluation of the original quality criteria. For example, if peak utilisation of resources such as personnel deployment or energy consumption is to be avoided in a scheduling task, it is not sufficient to assess the maximum utilisation. Rather, the number and duration of exceedances of a still acceptable level should also be recorded in order to reward reductions below the actual maximum peak value.<a href="#cite_note-:3-44">[44]</a> There are therefore some publications that are aimed at the beginner and want to help avoiding beginner's mistakes as well as leading an application project to success.<a href="#cite_note-:3-44">[44]</a><a href="#cite_note-45">[45]</a><a href="#cite_note-46">[46]</a> This includes clarifying the fundamental question of when an EA should be used to solve a problem and when it is better not to.

<div class="mw-heading mw-heading2"><h2 id="Related_techniques_and_other_global_search_methods">Related techniques and other global search methods</h2></div>

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There are some other proven and widely used methods of nature inspired global search techniques such as

<ul><li><a href="Memetic_algorithm" title="Memetic algorithm">Memetic algorithm</a> – A hybrid method, inspired by <a href="Richard_Dawkins" title="Richard Dawkins">Richard Dawkins</a>'s notion of a meme. It commonly takes the form of a population-based algorithm (frequently an EA) coupled with individual learning procedures capable of performing local refinements. Emphasizes the exploitation of problem-specific knowledge and tries to orchestrate local and global search in a synergistic way.</li>

<li>A <a href="Population_model_(evolutionary_algorithm)#Neighbourhood_models_or_cellular_evolutionary_algorithms" title="Population model (evolutionary algorithm)">cellular evolutionary or memetic algorithm</a> uses a topological neighborhood relation between the individuals of a population for restricting the mate selection and by that reducing the propagation speed of above-average individuals. The idea is to maintain genotypic diversity in the population over a longer period of time to reduce the risk of premature convergence.</li>

<li><a href="Ant_colony_optimization" class="mw-redirect" title="Ant colony optimization">Ant colony optimization</a> is based on the ideas of ant foraging by pheromone communication to form paths. Primarily suited for <a href="Combinatorial_optimization" title="Combinatorial optimization">combinatorial optimization</a> and <a href="Graph_theory" title="Graph theory">graph</a> problems.</li>

<li><a href="Particle_swarm_optimization" title="Particle swarm optimization">Particle swarm optimization</a> is based on the ideas of animal flocking behaviour. Also primarily suited for <a href="Numerical_optimization" class="mw-redirect" title="Numerical optimization">numerical optimization</a> problems.</li>

<li><a href="Gaussian_adaptation" title="Gaussian adaptation">Gaussian adaptation</a> – Based on information theory. Used for maximization of manufacturing yield, <a href="Mean_fitness" class="mw-redirect" title="Mean fitness">mean fitness</a> or <a href="Average_information" class="mw-redirect" title="Average information">average information</a>. See for instance <a href="Entropy_in_thermodynamics_and_information_theory" title="Entropy in thermodynamics and information theory">Entropy in thermodynamics and information theory</a>.</li></ul>

In addition, many new nature-inspired or metaphor-guided algorithms have been proposed since the beginning of this century. For criticism of most publications on these, see the remarks at the end of the introduction to the article on <a href="Metaheuristic" title="Metaheuristic">metaheuristics</a>.

<div class="mw-heading mw-heading2"><h2 id="Examples">Examples</h2></div>

In 2020, <a href="Google" title="Google">Google</a> stated that their AutoML-Zero can successfully rediscover classic algorithms such as the concept of neural networks.<a href="#cite_note-47">[47]</a>

The computer simulations <a href="Tierra_(computer_simulation)" title="Tierra (computer simulation)">Tierra</a> and <a href="Avida_(software)" title="Avida (software)">Avida</a> attempt to model <a href="Macroevolution" title="Macroevolution">macroevolutionary</a> dynamics.

<div class="mw-heading mw-heading2"><h2 id="Gallery">Gallery</h2></div>

<div class="gallerytext">A two-population EA search over a constrained <a href="Rosenbrock_function" title="Rosenbrock function">Rosenbrock function</a> with bounded global optimum</div>

</li>

<div class="gallerytext">A two-population EA search over a constrained <a href="Rosenbrock_function" title="Rosenbrock function">Rosenbrock function</a>. Global optimum is not bounded.</div>

</li>

<div class="gallerytext"><a href="Estimation_of_distribution_algorithm" title="Estimation of distribution algorithm">Estimation of distribution algorithm</a> over <a href="Keane's_bump_function" class="mw-redirect" title="Keane's bump function">Keane's bump function</a></div>

</li>

<div class="gallerytext">A two-population EA search of a bounded optima of <a href="Test_functions_for_optimization#Test_functions_for_constrained_optimization" title="Test functions for optimization">Simionescu's function</a></div>

</li>

</ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li><a rel="nofollow" class="external text" href="https://www.staracle.com/general/evolutionaryAlgorithms.php">An Overview of the History and Flavors of Evolutionary Algorithms</a></li></ul>

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</style></div><div role="navigation" class="navbox" aria-labelledby="Evolutionary_computation153" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Evolutionary_computation153" style="font-size:114%;margin:0 4em"><a href="Evolutionary_computation" title="Evolutionary computation">Evolutionary computation</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Main Topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul>

<li><a href="Evolutionary_data_mining" title="Evolutionary data mining">Evolutionary data mining</a></li>

<li><a href="Evolutionary_multimodal_optimization" title="Evolutionary multimodal optimization">Evolutionary multimodal optimization</a></li>

<li><a href="Human-based_evolutionary_computation" title="Human-based evolutionary computation">Human-based evolutionary computation</a></li>

<li><a href="Interactive_evolutionary_computation" title="Interactive evolutionary computation">Interactive evolutionary computation</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Algorithm" title="Algorithm">Algorithms</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Cellular_evolutionary_algorithm" title="Cellular evolutionary algorithm">Cellular evolutionary algorithm</a></li>

<li><a href="CMA-ES" title="CMA-ES">Covariance Matrix Adaptation Evolution Strategy (CMA-ES)</a></li>

<li><a href="Cultural_algorithm" title="Cultural algorithm">Cultural algorithm</a></li>

<li><a href="Differential_evolution" title="Differential evolution">Differential evolution</a></li>

<li><a href="Evolutionary_programming" title="Evolutionary programming">Evolutionary programming</a></li>

<li><a href="Genetic_algorithm" title="Genetic algorithm">Genetic algorithm</a></li>

<li><a href="Genetic_programming" title="Genetic programming">Genetic programming</a></li>

<li><a href="Gene_expression_programming" title="Gene expression programming">Gene expression programming</a></li>

<li><a href="Evolution_strategy" title="Evolution strategy">Evolution strategy</a></li>

<li><a href="Natural_evolution_strategy" title="Natural evolution strategy">Natural evolution strategy</a></li>

<li><a href="Neuroevolution" title="Neuroevolution">Neuroevolution</a></li>

<li><a href="Learning_classifier_system" title="Learning classifier system">Learning classifier system</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related techniques</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Swarm_intelligence" title="Swarm intelligence">Swarm intelligence</a></li>

<li><a href="Ant_colony_optimization" class="mw-redirect" title="Ant colony optimization">Ant colony optimization</a></li>

<li><a href="Bees_algorithm" title="Bees algorithm">Bees algorithm</a></li>

<li><a href="Cuckoo_search" title="Cuckoo search">Cuckoo search</a></li>

<li><a href="Particle_swarm_optimization" title="Particle swarm optimization">Particle swarm optimization</a></li>

<li><a href="Bacterial_Colony_Optimization" class="mw-redirect" title="Bacterial Colony Optimization">Bacterial Colony Optimization</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Metaheuristic" title="Metaheuristic">Metaheuristic methods</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Firefly_algorithm" title="Firefly algorithm">Firefly algorithm</a></li>

<li><a href="Harmony_search" class="mw-redirect" title="Harmony search">Harmony search</a></li>

<li><a href="Gaussian_adaptation" title="Gaussian adaptation">Gaussian adaptation</a></li>

<li><a href="Memetic_algorithm" title="Memetic algorithm">Memetic algorithm</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Artificial_development" title="Artificial development">Artificial development</a></li>

<li><a href="Artificial_intelligence" title="Artificial intelligence">Artificial intelligence</a></li>

<li><a href="Artificial_life" title="Artificial life">Artificial life</a></li>

<li><a href="Digital_organism" title="Digital organism">Digital organism</a></li>

<li><a href="Evolutionary_robotics" title="Evolutionary robotics">Evolutionary robotics</a></li>

<li><a href="Fitness_function" title="Fitness function">Fitness function</a></li>

<li><a href="Fitness_landscape" title="Fitness landscape">Fitness landscape</a></li>

<li><a href="Fitness_approximation" title="Fitness approximation">Fitness approximation</a></li>

<li><a href="Genetic_operators" class="mw-redirect" title="Genetic operators">Genetic operators</a></li>

<li><a href="Interactive_evolutionary_computation" title="Interactive evolutionary computation">Interactive evolutionary computation</a></li>

<li><a href="No_free_lunch_in_search_and_optimization" title="No free lunch in search and optimization">No free lunch in search and optimization</a></li>

<li><a href="Machine_learning" title="Machine learning">Machine learning</a></li>

<li><a href="Mating_pool" title="Mating pool">Mating pool</a></li>

<li><a href="Premature_convergence" title="Premature convergence">Premature convergence</a></li>

<li><a href="Program_synthesis" title="Program synthesis">Program synthesis</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Academic_journal" title="Academic journal">Journals</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Evolutionary_Computation_(journal)" title="Evolutionary Computation (journal)">Evolutionary Computation (journal)</a></li></ul>

</div></td></tr></tbody></table></div></div><div><div class="zim-footer">

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