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Mutation (genetic Algorithm)
Mutation is a genetic operator used to maintain genetic diversity of the chromosomes of a population of a genetic or, more generally, an evolutionary algorithm (EA). It is analogous to biological mutation. The classic example of a mutation operator of a binary coded genetic algorithm (GA) involves a probability that an arbitrary bit in a genetic sequence will be flipped from its original state. A common method of implementing the mutation operator involves generating a random variable for each bit in a sequence. This random variable tells whether or not a particular bit will be flipped. This mutation procedure, based on the biological point mutation, is called single point mutation. Other types of mutation operators are commonly used for representations other than binary, such as floating-point encodings or representations for combinatorial problems. The purpose of mutation in EAs is to introduce diversity into the sampled population. Mutation operators are used in an attempt to a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Genetic Operator
A genetic operator is an operator used in genetic algorithms to guide the algorithm towards a solution to a given problem. There are three main types of operators (mutation, crossover and 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 chromosomes) into new solutions (crossover) and select between solutions (selection). In his book discussing the use of genetic programming for the optimization of complex problems, computer scientist John Koza has also identified an 'inversion' or 'permutation' operator; however, the effectiveness of this operator has never been conclusively demonstrated and this operator is rarely discussed. Mutation (or mutation-like) operators are said to be '' unary'' operators, as they only operate on one chromosome at a time. In contrast, crossover operators are said to be ''bi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Restriction (mathematics)
In mathematics, the restriction of a function f is a new function, denoted f\vert_A or f , obtained by choosing a smaller domain A for the original function f. The function f is then said to extend f\vert_A. Formal definition Let f : E \to F be a function from a set E to a set F. If a set A is a subset of E, then the restriction of f to A is the function _A : A \to F given by _A(x) = f(x) for x \in A. Informally, the restriction of f to A is the same function as f, but is only defined on A. If the function f is thought of as a relation (x,f(x)) on the Cartesian product E \times F, then the restriction of f to A can be represented by its graph where the pairs (x,f(x)) represent ordered pairs in the graph G. Extensions A function F is said to be an ' of another function f if whenever x is in the domain of f then x is also in the domain of F and f(x) = F(x). That is, if \operatorname f \subseteq \operatorname F and F\big\vert_ = f. A '' '' (respectively, '' '', etc.) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Michigan Press
The University of Michigan Press is part of Michigan Publishing at the University of Michigan Library. It publishes 170 new titles each year in the humanities and social sciences. Titles from the press have earned numerous awards, including Lambda Literary Awards, the PEN/Faulkner Award, the Joe A. Callaway Award, and the Nautilus Book Award. The press has published works by authors who have been awarded the Pulitzer Prize, the National Humanities Medal and the Nobel Prize in Economics. History From 1858 to 1930, the University of Michigan had no organized entity for its scholarly publications, which were generally conference proceedings or department-specific research. The University Press was established in 1930 under the university's Graduate School, and in 1935, Frank E. Robbins, assistant to university president Alexander G. Ruthven, was appointed as the managing editor of the University Press. He would hold this position until 1954, when Fred D. Wieck was appoint ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evolutionary Algorithm
In computational intelligence (CI), an evolutionary algorithm (EA) is a subset of evolutionary computation, a generic population-based metaheuristic optimization algorithm. An EA uses mechanisms inspired by biological evolution, such as reproduction, mutation, recombination, and selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the fitness function determines the quality of the solutions (see also loss function). 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 fitness landscape. Techniques from evolutionary algorithms applied to the modeling of biological evolution are generally limited to explorations of microevolutionary processes and planning models based upon cellular processes. In most real appl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Periodic Boundary Conditions
Periodic boundary conditions (PBCs) are a set of boundary conditions which are often chosen for approximating a large (infinite) system by using a small part called a ''unit cell''. PBCs are often used in computer simulations and mathematical models. The topology of two-dimensional PBC is equal to that of a ''world map'' of some video games; the geometry of the unit cell satisfies perfect two-dimensional tiling, and when an object passes through one side of the unit cell, it re-appears on the opposite side with the same velocity. In topological terms, the space made by two-dimensional PBCs can be thought of as being mapped onto a torus (compactification). The large systems approximated by PBCs consist of an infinite number of unit cells. In computer simulations, one of these is the original simulation box, and others are copies called ''images''. During the simulation, only the properties of the original simulation box need to be recorded and propagated. The ''minimum-image conventi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set (mathematics)
A set is the mathematical model for a collection of different things; a set contains ''elements'' or ''members'', which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics. Indeed, set theory, more specifically Zermelo–Fraenkel set theory, has been the standard way to provide rigorous foundations for all branches of mathematics since the first half of the 20th century. History The concept of a set emerged in mathematics at the end of the 19th century. The German word for set, ''Menge'', was coined by Bernard Bolzano in his work '' Paradoxes of the Infinite''. Georg Cantor, one of the founders of set theory, gave the following ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation
In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set. Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set , namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set. Anagrams of words whose letters are different are also permutations: the letters are already ordered in the original word, and the anagram is a reordering of the letters. The study of permutations of finite sets is an important topic in the fields of combinatorics and group theory. Permutations are used in almost every branch of mathematics, and in many other fields of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Without Loss Of Generality
''Without loss of generality'' (often abbreviated to WOLOG, WLOG or w.l.o.g.; less commonly stated as ''without any loss of generality'' or ''with no loss of generality'') is a frequently used expression in mathematics. The term is used to indicate the assumption that follows is chosen arbitrarily, narrowing the premise to a particular case, but does not affect the validity of the proof in general. The other cases are sufficiently similar to the one presented that proving them follows by essentially the same logic. As a result, once a proof is given for the particular case, it is trivial to adapt it to prove the conclusion in all other cases. In many scenarios, the use of "without loss of generality" is made possible by the presence of symmetry. For example, if some property ''P''(''x'',''y'') of real numbers is known to be symmetric in ''x'' and ''y'', namely that ''P''(''x'',''y'') is equivalent to ''P''(''y'',''x''), then in proving that ''P''(''x'',''y'') holds for every ''x' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chromosome (genetic Algorithm)
In genetic algorithms, a chromosome (also sometimes called a genotype) is a set of parameters which define a proposed solution to the problem that the genetic algorithm is trying to solve. The set of all solutions is known as the ''population''. The chromosome is often represented as a binary string, although a wide variety of other data structures are also used. Chromosome design The design of the chromosome and its parameters is by necessity specific to the problem to be solved. Traditionally, chromosomes are represented in binary as strings of 0s and 1s, however other encodings are also possible; almost any representation which allows the solution to be represented as a finite-length string can be used. Finding a suitable representation of the problem domain for a chromosome is an important consideration, as a good representation will make the search easier by limiting the search space; similarly, a poorer representation will allow a larger search space. The mutation operator an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Distribution
In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is : f(x) = \frac e^ The parameter \mu is the mean or expectation of the distribution (and also its median and mode), while the parameter \sigma is its standard deviation. The variance of the distribution is \sigma^2. A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution converges to a normal dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Deviation Diagram (decimal Comma)
Standard may refer to: Symbols * Colours, standards and guidons, kinds of military signs * Standard (emblem), a type of a large symbol or emblem used for identification Norms, conventions or requirements * Standard (metrology), an object that bears a defined relationship to a unit of measure used for calibration of measuring devices * Standard (timber unit), an obsolete measure of timber used in trade * Breed standard (also called bench standard), in animal fancy and animal husbandry * BioCompute Standard, a standard for next generation sequencing * ''De facto'' standard, product or system with market dominance * Gold standard, a monetary system based on gold; also used metaphorically for the best of several options, against which the others are measured * Internet Standard, a specification ratified as an open standard by the Internet Engineering Task Force * Learning standards, standards applied to education content * Standard displacement, a naval term describing the weig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
