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Edge Recombination Operator
The edge recombination operator (ERO) is an operator that creates a path that is similar to a set of existing paths (parents) by looking at the edges rather than the vertices. The main application of this is for crossover in genetic algorithms when a genotype with non-repeating gene sequences is needed such as for the travelling salesman problem. It was described by Darrell Whitley and others in 1989. Algorithm ERO is based on an adjacency matrix, which lists the neighbors of each node in any parent. For example, in a travelling salesman problem such as the one depicted, the node map for the parents CABDEF and ABCEFD (see illustration) is generated by taking the first parent, say, 'ABCEFD' and recording its immediate neighbors, including those that roll around the end of the string. Therefore; ... -> <- ... ...is converted into the following |
Path (graph Theory)
In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges). A directed path (sometimes called dipathGraph Structure Theory: Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Graph Minors, Held June 22 to July 5, 1991p.205/ref>) in a directed graph is a finite or infinite sequence of edges which joins a sequence of distinct vertices, but with the added restriction that the edges be all directed in the same direction. Paths are fundamental concepts of graph theory, described in the introductory sections of most graph theory texts. See e.g. Bondy and Murty (1976), Gibbons (1985), or Diestel (2005). Korte et al. (1990) cover more advanced algorithmic topics concerning paths in graphs. Definitions Walk, trail, and path * A walk is a finite or infinite sequence of edges which joins a sequence of vertices. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crossover (genetic Algorithm)
In genetic algorithms and evolutionary computation, crossover, also called recombination, is a genetic operator used to combine the genetic information of two parents to generate new offspring. It is one way to stochastically generate new solutions from an existing population, and is analogous to the crossover that happens during sexual reproduction in biology. Solutions can also be generated by cloning an existing solution, which is analogous to asexual reproduction. Newly generated solutions are typically mutated before being added to the population. Different algorithms in evolutionary computation may use different data structures to store genetic information, and each genetic representation can be recombined with different crossover operators. Typical data structures that can be recombined with crossover are bit arrays, vectors of real numbers, or trees. Examples Traditional genetic algorithms store genetic information in a chromosome represented by a bit array. Crossover m ... [...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 by relying on biologically inspired operators such as mutation, crossover and selection. Some examples of GA applications include optimizing decision trees for better performance, solving sudoku puzzles, hyperparameter optimization, etc. 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 encodings are also possible. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Travelling Salesman Problem
The travelling salesman problem (also called the travelling salesperson problem or TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research. The travelling purchaser problem and the vehicle routing problem are both generalizations of TSP. In the theory of computational complexity, the decision version of the TSP (where given a length ''L'', the task is to decide whether the graph has a tour of at most ''L'') belongs to the class of NP-complete problems. Thus, it is possible that the worst-case running time for any algorithm for the TSP increases superpolynomially (but no more than exponentially) with the number of cities. The problem was first formulated in 1930 and is one of the most intensively studied p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Darrell Whitley
Darrell is a given name derived from an English surname, which was derived from Norman-French , originally denoting one who came from Airelle in France. There are no longer any towns in France called Airelle, but is the French word for huckleberry. Darrell may refer to: Sports * Darrell Allums (born 1958), American basketball player * Darrell Armstrong, NBA basketball player * Darrell Campbell, American football defensive tackle on the practice squad of the Chicago Bears * Darrell Clarke, manager of Bristol Rovers football club * Darrell Daniels, American football player * Darrell Evans, former third baseman and first baseman in Major League Baseball * Darrell Green, cornerback for the Washington Redskins from 1983 to 2002 * Darrell Griffith, former NBA basketball player who spent his entire career with the Utah Jazz * Darrell Jackson, American football wide receiver currently playing for the Seattle Seahawks of the National Football League * Darrell Johnson, Major League ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adjacency Matrix
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal. If the graph is undirected (i.e. all of its edges are bidirectional), the adjacency matrix is symmetric. The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory. The adjacency matrix of a graph should be distinguished from its incidence matrix, a different matrix representation whose elements indicate whether vertex–edge pairs are incident or not, and its degree matrix, which contains information about the degree of each vertex. Definition For a simple graph with vertex set , the adjacency matrix is a square matrix such that its element is one when there is an edge from vertex to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Genetic Ero Crossover
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Genetic may refer to: * Genetics, in biology, the science of genes, heredity, and the variation of organisms **Genetic, used as an adjective, refers to genes *** Genetic disorder, any disorder caused by a genetic mutation, whether inherited or de novo ***Genetic mutation, a change in a gene ****Heredity, genes and their mutations being passed from parents to offspring **Genetic recombination, refers to the recombining of alleles resulting in a new molecule of DNA *Genetic relationship (linguistics), in linguistics, a relationship between two languages with a common ancestor language *Genetic algorithm, in computer science, a kind of search technique modeled on evolutionary biology See also *Genetic memory (other) Genetic memory may refer to: *Genetic memory (psychology) In psychology, genetic memory is a theorized phenomenon in which certain kinds of memories could be inherited, being present at birth in the absence of any associated sensory experience, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Union (set Theory)
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations through which sets can be combined and related to each other. A refers to a union of zero (0) sets and it is by definition equal to the empty set. For explanation of the symbols used in this article, refer to the table of mathematical symbols. Union of two sets The union of two sets ''A'' and ''B'' is the set of elements which are in ''A'', in ''B'', or in both ''A'' and ''B''. In set-builder notation, :A \cup B = \. For example, if ''A'' = and ''B'' = then ''A'' ∪ ''B'' = . A more elaborate example (involving two infinite sets) is: : ''A'' = : ''B'' = : A \cup B = \ As another example, the number 9 is ''not'' contained in the union of the set of prime numbers and the set of even numbers , because 9 is neither prime nor even. Sets cannot have duplicate elements, so the union of the sets and is . Multip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of The Basque Country
The University of the Basque Country ( eu, Euskal Herriko Unibertsitatea, ''EHU''; es, Universidad del País Vasco, ''UPV''; UPV/EHU) is a Spanish public university of the Basque Autonomous Community. Heir of the University of Bilbao, initially it was made up of the Faculty of Economic and Business Sciences of Sarriko (1955), Medicine (1968) and Sciences (1968). Following the General Law of Education (1970), the Nautical School (1784), the School of Business Studies of Bilbao (1818) and the Technical Schools of Engineers (1897) joined in, until it grew into the complex of thirty centers that compose it presently. It has campuses over the three provinces of the autonomous community: Biscay Campus (in Leioa, Bilbao, Portugalete and Barakaldo), Gipuzkoa Campus (in San Sebastián and Eibar), and Álava Campus in Vitoria-Gasteiz. It stands out as the main research institution in the Basque Country, carrying out 90% of the basic research carried out in that territory and benefiting fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cycle Crossover
Cycle, cycles, or cyclic may refer to: Anthropology and social sciences * Cyclic history, a theory of history * Cyclical theory, a theory of American political history associated with Arthur Schlesinger, Sr. * Social cycle, various cycles in social sciences ** Business cycle, the downward and upward movement of gross domestic product (GDP) around its ostensible, long-term growth trend Arts, entertainment, and media Films * ''Cycle'' (2008 film), a Malayalam film * ''Cycle'' (2017 film), a Marathi film Literature * ''Cycle'' (magazine), an American motorcycling enthusiast magazine * Literary cycle, a group of stories focused on common figures Music Musical terminology * Cycle (music), a set of musical pieces that belong together ** Cyclic form, a technique of construction involving multiple sections or movements ** Interval cycle, a collection of pitch classes generated from a sequence of the same interval class ** Song cycle, individually complete songs designed to be p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
