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Fitness (genetic Algorithm)
A fitness function is a particular type of objective or cost function that is used to summarize, as a single figure of merit, how close a given candidate solution is to achieving the set aims. It is an important component of evolutionary algorithms (EA), such as genetic programming, evolution strategies or genetic algorithms. An EA is a metaheuristic that reproduces the basic principles of biological evolution as a computer algorithm in order to solve challenging optimization or planning tasks, at least approximately. For this purpose, many candidate solutions are generated, which are evaluated using a fitness function in order to guide the evolutionary development towards the desired goal. Similar quality functions are also used in other metaheuristics, such as ant colony optimization or particle swarm optimization. In the field of EAs, each candidate solution, also called an ''individual'', is commonly represented as a string of numbers (referred to as a chromosome). After ea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Objective Function
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its opposite (in specific domains, variously called a reward function, a profit function, a utility function, a fitness function, etc.), in which case it is to be maximized. The loss function could include terms from several levels of the hierarchy. In statistics, typically a loss function is used for parameter estimation, and the event in question is some function of the difference between estimated and true values for an instance of data. The concept, as old as Laplace, was reintroduced in statistics by Abraham Wald in the middle of the 20th century. In the context of economics, for example, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Co-evolution
In biology, coevolution occurs when two or more species reciprocally affect each other's evolution through the process of natural selection. The term sometimes is used for two traits in the same species affecting each other's evolution, as well as gene-culture coevolution. Charles Darwin mentioned evolutionary interactions between flowering plants and insects in ''On the Origin of Species'' (1859). Although he did not use the word coevolution, he suggested how plants and insects could evolve through reciprocal evolutionary changes. Naturalists in the late 1800s studied other examples of how interactions among species could result in reciprocal evolutionary change. Beginning in the 1940s, plant pathologists developed breeding programs that were examples of human-induced coevolution. Development of new crop plant varieties that were resistant to some diseases favored rapid evolution in pathogen populations to overcome those plant defenses. That, in turn, required the development of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Fitness Function
A fitness function is a particular type of objective or cost function that is used to summarize, as a single figure of merit, how close a given candidate solution is to achieving the set aims. It is an important component of evolutionary algorithms (EA), such as genetic programming, evolution strategies or genetic algorithms. An EA is a metaheuristic that reproduces the basic principles of biological evolution as a computer algorithm in order to solve challenging optimization or planning tasks, at least approximately. For this purpose, many candidate solutions are generated, which are evaluated using a fitness function in order to guide the evolutionary development towards the desired goal. Similar quality functions are also used in other metaheuristics, such as ant colony optimization or particle swarm optimization. In the field of EAs, each candidate solution, also called an ''individual'', is commonly represented as a string of numbers (referred to as a chromosome). A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Penalty Method
In mathematical optimization, penalty methods are a certain class of algorithms for solving constrained optimization problems. A penalty method replaces a constrained optimization problem by a series of unconstrained problems whose solutions ideally converge to the solution of the original constrained problem. The unconstrained problems are formed by adding a term, called a penalty function, to the objective function that consists of a ''penalty parameter'' multiplied by a measure of violation of the constraints. The measure of violation is nonzero when the constraints are violated and is zero in the region where constraints are not violated. Description Let us say we are solving the following constrained problem: : \min_x f(\mathbf x) subject to : c_i(\mathbf x) \le 0 ~\forall i \in I. This problem can be solved as a series of unconstrained minimization problems : \min f_p (\mathbf x) := f (\mathbf x) + p ~ \sum_ ~ g(c_i(\mathbf x)) where : g(c_i(\mathbf x))=\max(0,c_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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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 what 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Weight Function
A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is a weighted sum or weighted average. Weight functions occur frequently in statistics and analysis, and are closely related to the concept of a measure. Weight functions can be employed in both discrete and continuous settings. They can be used to construct systems of calculus called "weighted calculus" and "meta-calculus".Jane Grossma''Meta-Calculus: Differential and Integral'' , 1981. Discrete weights General definition In the discrete setting, a weight function w \colon A \to \R^+ is a positive function defined on a discrete set A, which is typically finite or countable. The weight function w(a) := 1 corresponds to the ''unweighted'' situation in which all elements have equal weight. One can then apply this weight to various con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Population Model (evolutionary Algorithm)
The population model of an evolutionary algorithm (EA) describes the structural properties of its population to which its members are subject. A population is the set of all proposed solutions of an EA considered in one iteration, which are also called ''individuals'' according to the biological role model. The individuals of a population can generate further individuals as offspring with the help of the genetic operators of the procedure. The simplest and widely used population model in EAs is the ''global'' or ''Panmixia, panmictic model'', which corresponds to an unstructured population. It allows each individual to choose any other individual of the population as a partner for the production of offspring by Crossover (genetic algorithm), crossover, whereby the details of the Selection (genetic algorithm), selection are irrelevant as long as the Fitness function, fitness of the individuals plays a significant role. Due to global mate selection, the genetic information of even sl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Fitness Approximation
Fitness approximationY. JinA comprehensive survey of fitness approximation in evolutionary computation ''Soft Computing'', 9:3–12, 2005 aims to approximate the objective or fitness functions in evolutionary optimization by building up machine learning models based on data collected from numerical simulations or physical experiments. The machine learning models for fitness approximation are also known as meta-models or surrogates, and evolutionary optimization based on approximated fitness evaluations are also known as surrogate-assisted evolutionary approximation.Surrogate-assisted evolutionary computation: Recent advances and future challenges Swarm and Evolutionary Computation, 1(2):61–70, 2011 Fitness approximation in evolutionary optimiz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Interactive Genetic Algorithms
Interactive evolutionary computation (IEC) or aesthetic selection is a general term for methods of evolutionary computation that use human evaluation. Usually human evaluation is necessary when the form of fitness function is not known (for example, visual appeal or attractiveness; as in Dawkins, 1986) or the result of optimization should fit a particular user preference (for example, taste of coffee or color set of the user interface). IEC design issues The number of evaluations that IEC can receive from one human user is limited by user fatigue which was reported by many researchers as a major problem. In addition, human evaluations are slow and expensive as compared to fitness function computation. Hence, one-user IEC methods should be designed to converge using a small number of evaluations, which necessarily implies very small populations. Several methods were proposed by researchers to speed up convergence, like interactive constrain evolutionary search (user intervention) or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Auxiliary Objectives
Auxiliary may refer to: In language * Auxiliary language (other) * Auxiliary verb In military and law enforcement * Auxiliary police * Auxiliaries, civilians or quasi-military personnel who provide support of some kind to a military service ** Auxiliaries (Roman military) In religion * Auxiliary bishop, in the Roman Catholic Church * Auxiliary organization (LDS Church) In technology * Auxiliary input jack and auxiliary cable, generally for audio ** frequently associated with mobile device audio * Aux-send of a mixing console * An auxiliary port is a common port found on many Cisco routers for CLI access. * A backup site or system Other uses * Auxiliary route, also known as "special route", in road transportation ** An auxiliary route of the Interstate Highway System in the United States * Auxiliary ship is a naval vessel designed to operate in support of combat ships and other naval operations * Auxiliary (fraternity or sorority) * A marching band color guard * Auxili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Monte Carlo Method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. The name comes from the Monte Carlo Casino in Monaco, where the primary developer of the method, mathematician Stanisław Ulam, was inspired by his uncle's gambling habits. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution. They can also be used to model phenomena with significant uncertainty in inputs, such as calculating the risk of a nuclear power plant failure. Monte Carlo methods are often implemented using computer simulations, and they can provide approximate solutions to problems that are otherwise intractable or too complex to analyze mathematically. Monte Carlo methods are widely used in va ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Selection (evolutionary Algorithm)
Selection is a genetic operator in an evolutionary algorithm (EA). An EA is a metaheuristic inspired by biological evolution and aims to solve challenging problems at least approximately. Selection has a dual purpose: on the one hand, it can choose individual genomes from a population for subsequent breeding (e.g., using the crossover operator). In addition, selection mechanisms are also used to choose candidate solutions (individuals) for the next generation. The biological model is natural selection. Retaining the best individual(s) of one generation unchanged in the next generation is called ''elitism'' or ''elitist selection''. It is a successful (slight) variant of the general process of constructing a new population. The basis for selection is the quality of an individual, which is determined by the fitness function. In memetic algorithms, an extension of EA, selection also takes place in the selection of those offspring that are to be improved with the help of a meme ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |