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Holland's Schema Theorem
Holland's schema theorem, also called the fundamental theorem of genetic algorithms, is an inequality that results from coarse-graining an equation for evolutionary dynamics. The Schema Theorem says that short, low-order schemata with above-average fitness increase exponentially in frequency in successive generations. The theorem was proposed by John Holland in the 1970s. It was initially widely taken to be the foundation for explanations of the power of genetic algorithms. However, this interpretation of its implications has been criticized in several publications reviewed in, where the Schema Theorem is shown to be a special case of the Price equation with the schema indicator function as the macroscopic measurement. A schema is a template that identifies a subset of strings with similarities at certain string positions. Schemata are a special case of cylinder sets, and hence form a topological space. Description Consider binary strings of length 6. The schema 1*10*1 descri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evolutionary Dynamics
Evolutionary dynamics is the study of the mathematical principles according to which biological organisms as well as cultural ideas evolve and evolved. This is mostly achieved through the mathematical discipline of population genetics, along with evolutionary game theory. Most population genetics considers changes in the frequencies of alleles at a small number of gene loci. When infinitesimal effects at a large number of gene loci are considered, one derives quantitative genetics. Traditional population genetic models deal with alleles and genotypes, and are frequently stochastic. In evolutionary game theory, developed first by John Maynard Smith, evolutionary biology concepts may take a deterministic mathematical form, with selection acting directly on inherited phenotypes. These same models can be applied to studying the evolution of human preferences and ideologies. Many variants on these models have been developed, which incorporate weak selection, mutual population structur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Defining Length
In genetic algorithms and genetic programming defining length L(H) is the maximum distance between two defining symbols (that is symbols that have a fixed value as opposed to symbols that can take any value, commonly denoted as # or *) in schema H. In tree GP schemata, L(H) is the number of links in the minimum tree fragment including all the non-= symbols within a schema H. Example Schemata "00##0", "1###1", "01###", and "##0##" have defining lengths of 4, 4, 1, and 0, respectively. Lengths are computed by determining the last fixed position and subtracting from it the first fixed position. In genetic algorithms as the defining length of a solution increases so does the susceptibility of the solution to disruption due to mutation In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA or viral replication, . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Genetic Drift
Genetic drift, also known as random genetic drift, allelic drift or the Wright effect, is the change in the Allele frequency, frequency of an existing gene variant (allele) in a population due to random chance. Genetic drift may cause gene variants to disappear completely and thereby reduce genetic variation. It can also cause initially rare alleles to become much more frequent and even fixed. When few copies of an allele exist, the effect of genetic drift is more notable, and when many copies exist, the effect is less notable (due to the law of large numbers). In the middle of the 20th century, vigorous debates occurred over the relative importance of natural selection versus neutral processes, including genetic drift. Ronald Fisher, who explained natural selection using Mendelian inheritance, Mendelian genetics, held the view that genetic drift plays at most a minor role in evolution, and this remained the dominant view for several decades. In 1968, population geneticist Mot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multimodal Distribution
In statistics, a multimodal distribution is a probability distribution with more than one mode (i.e., more than one local peak of the distribution). These appear as distinct peaks (local maxima) in the probability density function, as shown in Figures 1 and 2. Categorical, continuous, and discrete data can all form multimodal distributions. Among univariate analyses, multimodal distributions are commonly bimodal. Terminology When the two modes are unequal the larger mode is known as the major mode and the other as the minor mode. The least frequent value between the modes is known as the antimode. The difference between the major and minor modes is known as the amplitude. In time series the major mode is called the acrophase and the antimode the batiphase. Galtung's classification Galtung introduced a classification system (AJUS) for distributions: *A: unimodal distribution – peak in the middle *J: unimodal – peak at either end *U: bimodal – peaks at both ends ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sampling Error
In statistics, sampling errors are incurred when the statistical characteristics of a population are estimated from a subset, or sample, of that population. Since the sample does not include all members of the population, statistics of the sample (often known as estimators), such as means and quartiles, generally differ from the statistics of the entire population (known as parameters). The difference between the sample statistic and population parameter is considered the sampling error.Sarndal, Swenson, and Wretman (1992), Model Assisted Survey Sampling, Springer-Verlag, For example, if one measures the height of a thousand individuals from a population of one million, the average height of the thousand is typically not the same as the average height of all one million people in the country. Since sampling is almost always done to estimate population parameters that are unknown, by definition exact measurement of the sampling errors will not be possible; however they can often ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Genetic Algorithms
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 algorithms (EA). Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems via biologically inspired operators such as selection, crossover, and mutation. Some examples of GA applications include optimizing decision trees for better performance, solving sudoku puzzles, hyperparameter optimization, and causal inference. Methodology Optimization problems In a genetic algorithm, a population of candidate solutions (called individuals, creatures, organisms, or phenotypes) to an optimization problem is evolved toward better solutions. Each candidate solution has a set of properties (its chromosomes or genotype) which can be mutated and altered; traditionally, solutions are represented in binary as strings of 0s and 1s, but other encodi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Genetic Operator
A genetic operator is an Operator (programming), operator used in evolutionary algorithms (EA) to guide the algorithm towards a solution to a given problem. There are three main types of operators (Mutation (evolutionary algorithm) , mutation, Crossover (evolutionary algorithm), crossover and selection (evolutionary algorithm), selection), which must work in conjunction with one another in order for the algorithm to be successful. Genetic operators are used to create and maintain genetic diversity (mutation operator), combine existing solutions (also known as chromosome (evolutionary algorithm), chromosomes) into new solutions (crossover) and select between solutions (selection). The classic representatives of evolutionary algorithms include Genetic algorithm, genetic algorithms, Evolution strategy, evolution strategies, genetic programming and evolutionary programming. In his book discussing the use of genetic programming for the optimization of complex problems, computer scienti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wildcard Character
In software, a wildcard character is a kind of placeholder represented by a single character (computing), character, such as an asterisk (), which can be interpreted as a number of literal characters or an empty string. It is often used in file searches so the full name need not be typed. Telecommunication In telecommunications, a wildcard is a character that may be substituted for any of a defined subset of all possible characters. * In high-frequency (HF) radio automatic link establishment, the wildcard character may be substituted for any one of the 36 upper-case alphanumeric characters. * Whether the wildcard character represents a single character or a String (computer science), string of characters must be specified. Computing In computer (software) technology, a wildcard is a symbol used to replace or represent zero or more characters. Matching wildcards, Algorithms for matching wildcards have been developed in a number of recursion, recursive and non-recursive varietie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Henry Holland
John Henry Holland (February 2, 1929 – August 9, 2015) was an American scientist and professor of electrical engineering and computer science at the University of Michigan. He was a pioneer in what became known as genetic algorithms. Biography John Henry Holland was born on February 2, 1929 in Fort Wayne, Indiana, the elder child of son of Gustave A. Holland (b. July 24, 1896, Russian Poland) and Mildred P. Gfroerer (b. July 1, 1901, Columbus Grove, Ohio). He had one younger sister, Shirley Ann "Hollie" Holland (born c. 1931). Holland studied physics at the Massachusetts Institute of Technology and received a B.S. degree in 1950. He then studied Mathematics at the University of Michigan, receiving an M.S. in 1954. In 1959, he received the first computer science Ph.D. from the University of Michigan. He was a Professor of psychology and Professor of electrical engineering and computer science at the University of Michigan, Ann Arbor. He held visiting positions at the Rowla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Space
In mathematics, a topological space is, roughly speaking, a Geometry, geometrical space in which Closeness (mathematics), closeness is defined but cannot necessarily be measured by a numeric Distance (mathematics), distance. More specifically, a topological space is a Set (mathematics), set whose elements are called Point (geometry), points, along with an additional structure called a topology, which can be defined as a set of Neighbourhood (mathematics), neighbourhoods for each point that satisfy some Axiom#Non-logical axioms, axioms formalizing the concept of closeness. There are several equivalent definitions of a topology, the most commonly used of which is the definition through open sets, which is easier than the others to manipulate. A topological space is the most general type of a space (mathematics), mathematical space that allows for the definition of Limit (mathematics), limits, Continuous function (topology), continuity, and Connected space, connectedness. Common types ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cylinder Set
In mathematics, the cylinder sets form a basis of the product topology on a product of sets; they are also a generating family of the cylinder σ-algebra. General definition Given a collection S of sets, consider the Cartesian product X = \prod_ Y of all sets in the collection. The canonical projection corresponding to some Y\in S is the function p_ : X \to Y that maps every element of the product to its Y component. A cylinder set is a preimage of a canonical projection or finite intersection of such preimages. Explicitly, it is a set of the form, \bigcap_^n p_^ \left(A_i\right) = \left\ for any choice of n, finite sequence of sets Y_1,...Y_n\in S and subsets A_ \subseteq Y_i for 1 \leq i \leq n. Then, when all sets in S are topological spaces, the product topology is generated by cylinder sets corresponding to the components' open sets. That is cylinders of the form \bigcap_^n p_^ \left(U_i\right) where for each i, U_i is open in Y_i. In the same manner, in case of measura ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
