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Differential evolution : A basic variant of the DE algorithm works by having a population of candidate solutions (called agents). These agents are moved around in the search-space by using simple mathematical formulae to combine the positions of existing agents from the population. If the new position of an agent is an... |
Differential evolution : The choice of DE parameters NP , CR and F can have a large impact on optimization performance. Selecting the DE parameters that yield good performance has therefore been the subject of much research. Rules of thumb for parameter selection were devised by Storn et al. and Liu and Lampinen. Ma... |
Differential evolution : Differential evolution can be utilized for constrained optimization as well. A common method involves modifying the target function to include a penalty for any violation of constraints, expressed as: f ( ~ x ) = f ( x ) + ρ × C V ( x ) x)=f(x)+\rho \times \mathrm (x) . Here, C V ( x ) (x) re... |
Differential evolution : Variants of the DE algorithm are continually being developed in an effort to improve optimization performance. The following directions of development can be outlined: New schemes for performing crossover and mutation of agents Various strategies for handling constraints Adaptive strategies tha... |
Differential evolution : Artificial bee colony algorithm CMA-ES Evolution strategy Genetic algorithm == References == |
Dispersive flies optimisation : Dispersive flies optimisation (DFO) is a bare-bones swarm intelligence algorithm which is inspired by the swarming behaviour of flies hovering over food sources. DFO is a simple optimiser which works by iteratively trying to improve a candidate solution with regard to a numerical measure... |
Dispersive flies optimisation : DFO bears many similarities with other existing continuous, population-based optimisers (e.g. particle swarm optimization and differential evolution). In that, the swarming behaviour of the individuals consists of two tightly connected mechanisms, one is the formation of the swarm and th... |
Dispersive flies optimisation : Some of the recent applications of DFO are listed below: Optimising support vector machine kernel to classify imbalanced data Quantifying symmetrical complexity in computational aesthetics Analysing computational autopoiesis and computational creativity Identifying calcifications in medi... |
Effective fitness : In natural evolution and artificial evolution (e.g. artificial life and evolutionary computation) the fitness (or performance or objective measure) of a schema is rescaled to give its effective fitness which takes into account crossover and mutation. Effective fitness is used in Evolutionary Computa... |
Effective fitness : When evolutionary equations of the studied population dynamics are available, one can algorithmically compute the effective fitness of a given population. Though the perfect effective fitness model is yet to be found, it is already known to be a good framework to the better understanding of the movi... |
Effective fitness : Foundations of Genetic Programming |
Evolutionary programming : Evolutionary programming is an evolutionary algorithm, where a share of new population is created by mutation of previous population without crossover. Evolutionary programming differs from evolution strategy ES( μ + λ ) in one detail. All individuals are selected for the new population, whi... |
Evolutionary programming : It was first used by Lawrence J. Fogel in the US in 1960 in order to use simulated evolution as a learning process aiming to generate artificial intelligence. It was used to evolve finite-state machines as predictors. |
Evolutionary programming : Artificial intelligence Genetic algorithm Genetic operator |
Evolutionary programming : The Hitch-Hiker's Guide to Evolutionary Computation: What's Evolutionary Programming (EP)? Evolutionary Programming by Jason Brownlee (PhD) Archived 2013-01-18 at the Wayback Machine |
Fitness approximation : Fitness approximation 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 met... |
Fitness approximation : A complete list of references on Fitness Approximation in Evolutionary Computation, by Yaochu Jin. The cyber shack of Adaptive Fuzzy Fitness Granulation (AFFG) Archived 2021-12-06 at the Wayback Machine That is designed to accelerate the convergence rate of EAs. Inverse reinforcement learning Re... |
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 strateg... |
Fitness function : The quality of the evaluation and calculation of a fitness function is fundamental to the success of an EA optimisation. It implements Darwin's principle of "survival of the fittest". Without fitness-based selection mechanisms for mate selection and offspring acceptance, EA search would be blind and ... |
Fitness function : The fitness function should not only closely align with the designer's goal, but also be computationally efficient. Execution speed is crucial, as a typical evolutionary algorithm must be iterated many times in order to produce a usable result for a non-trivial problem. Fitness approximation may be a... |
Fitness function : Practical applications usually aim at optimizing multiple and at least partially conflicting objectives. Two fundamentally different approaches are often used for this purpose, Pareto optimization and optimization based on fitness calculated using the weighted sum. |
Fitness function : In addition to the primary objectives resulting from the task itself, it may be necessary to include auxiliary objectives in the assessment to support the achievement of one or more primary objectives. An example of a scheduling task is used for illustration purposes. The optimization goals include n... |
Fitness function : Evolutionary computation Inferential programming Test functions for optimization Loss function |
Fitness function : A Nice Introduction to Adaptive Fuzzy Fitness Granulation (AFFG) (PDF), A promising approach to accelerate the convergence rate of EAs. The cyber shack of Adaptive Fuzzy Fitness Granulation (AFFG) That is designed to accelerate the convergence rate of EAs. Fitness functions in evolutionary robotics: ... |
Gaussian adaptation : Gaussian adaptation (GA), also called normal or natural adaptation (NA) is an evolutionary algorithm designed for the maximization of manufacturing yield due to statistical deviation of component values of signal processing systems. In short, GA is a stochastic adaptive process where a number of s... |
Gaussian adaptation : It has also been compared to the natural evolution of populations of living organisms. In this case s(x) is the probability that the individual having an array x of phenotypes will survive by giving offspring to the next generation; a definition of individual fitness given by Hartl 1981. The yield... |
Gaussian adaptation : Mean fitness may be calculated provided that the distribution of parameters and the structure of the landscape is known. The real landscape is not known, but figure below shows a fictitious profile (blue) of a landscape along a line (x) in a room spanned by such parameters. The red curve is the me... |
Gaussian adaptation : Thus far the theory only considers mean values of continuous distributions corresponding to an infinite number of individuals. In reality however, the number of individuals is always limited, which gives rise to an uncertainty in the estimation of m and M (the moment matrix of the Gaussian). And t... |
Gaussian adaptation : In the brain the evolution of DNA-messages is supposed to be replaced by an evolution of signal patterns and the phenotypic landscape is replaced by a mental landscape, the complexity of which will hardly be second to the former. The metaphor with the mental landscape is based on the assumption th... |
Gaussian adaptation : Gaussian adaptation as an evolutionary model of the brain obeying the Hebbian theory of associative learning offers an alternative view of free will due to the ability of the process to maximize the mean fitness of signal patterns in the brain by climbing a mental landscape in analogy with phenoty... |
Gaussian adaptation : The efficiency of Gaussian adaptation relies on the theory of information due to Claude E. Shannon (see information content). When an event occurs with probability P, then the information −log(P) may be achieved. For instance, if the mean fitness is P, the information gained for each individual se... |
Gaussian adaptation : Gaussian adaptation has also been used for other purposes as for instance shadow removal by "The Stauffer-Grimson algorithm" which is equivalent to Gaussian adaptation as used in the section "Computer simulation of Gaussian adaptation" above. In both cases the maximum likelihood method is used for... |
Gaussian adaptation : Entropy in thermodynamics and information theory Fisher's fundamental theorem of natural selection Free will Genetic algorithm Hebbian learning Information content Simulated annealing Stochastic optimization Covariance matrix adaptation evolution strategy (CMA-ES) Unit of selection |
Gaussian adaptation : Bergström, R. M. An Entropy Model of the Developing Brain. Developmental Psychobiology, 2(3): 139–152, 1969. Brooks, D. R. & Wiley, E. O. Evolution as Entropy, Towards a unified theory of Biology. The University of Chicago Press, 1986. Brooks, D. R. Evolution in the Information Age: Rediscovering ... |
Genetic representation : In computer programming, genetic representation is a way of presenting solutions/individuals in evolutionary computation methods. The term encompasses both the concrete data structures and data types used to realize the genetic material of the candidate solutions in the form of a genome, and th... |
Genetic representation : Genetic algorithms (GAs) are typically linear representations; these are often, but not always, binary. Holland's original description of GA used arrays of bits. Arrays of other types and structures can be used in essentially the same way. The main property that makes these genetic representati... |
Genetic representation : Analogous to biology, EAs distinguish between problem space (corresponds to phenotype) and search space (corresponds to genotype). The problem space contains concrete solutions to the problem being addressed, while the search space contains the encoded solutions. The mapping from search space t... |
Genetic representation : The importance of an appropriate choice of search space for the success of an EA application was recognized early on. The following requirements can be placed on a suitable search space and thus on a suitable genotype-phenotype mapping: |
Genetic representation : When mapping the genotype to the phenotype being evaluated, domain-specific knowledge can be used to improve the phenotype and/or ensure that constraints are met. This is a commonly used method to improve EA performance in terms of runtime and solution quality. It is illustrated below by two of... |
Genotypic and phenotypic repair : Genotypic and phenotypic repair are optional components of an evolutionary algorithm (EA). An EA reproduces essential elements of biological evolution as a computer algorithm in order to solve demanding optimization or planning tasks, at least approximately. A candidate solution is rep... |
Genotypic and phenotypic repair : Genotypic repair, also known as genetic repair, is the removal or correction of impermissible entries in the chromosome that violate restrictions. In phenotypic repair, the corrections are only made in the genotype-phenotype mapping and the chromosome remains unchanged. Michalewicz wro... |
Learning classifier system : Learning classifier systems, or LCS, are a paradigm of rule-based machine learning methods that combine a discovery component (e.g. typically a genetic algorithm in evolutionary computation) with a learning component (performing either supervised learning, reinforcement learning, or unsuper... |
Learning classifier system : The architecture and components of a given learning classifier system can be quite variable. It is useful to think of an LCS as a machine consisting of several interacting components. Components may be added or removed, or existing components modified/exchanged to suit the demands of a give... |
Learning classifier system : Adaptive: They can acclimate to a changing environment in the case of online learning. Model free: They make limited assumptions about the environment, or the patterns of association within the data. They can model complex, epistatic, heterogeneous, or distributed underlying patterns withou... |
Learning classifier system : Limited Software Availability: There are a limited number of open source, accessible LCS implementations, and even fewer that are designed to be user friendly or accessible to machine learning practitioners. Interpretation: While LCS algorithms are certainly more interpretable than some adv... |
Learning classifier system : Adaptive-control Data Mining Engineering Design Feature Selection Function Approximation Game-Play Image Classification Knowledge Handling Medical Diagnosis Modeling Navigation Optimization Prediction Querying Robotics Routing Rule-Induction Scheduling Strategy |
Learning classifier system : The name, "Learning Classifier System (LCS)", is a bit misleading since there are many machine learning algorithms that 'learn to classify' (e.g. decision trees, artificial neural networks), but are not LCSs. The term 'rule-based machine learning (RBML)' is useful, as it more clearly captur... |
Learning classifier system : Rule-based machine learning Production system Expert system Genetic algorithm Association rule learning Artificial immune system Population-based Incremental Learning Machine learning |
Mating pool : Mating pool is a concept used in evolutionary algorithms and means a population of parents for the next population. The mating pool is formed by candidate solutions that the selection operators deem to have the highest fitness in the current population. Solutions that are included in the mating pool are r... |
Mating pool : Several methods can be applied to create a mating pool. All of these processes involve the selective breeding of a particular number of individuals within a population. There are multiple criteria that can be employed to determine which individuals make it into the mating pool and which are left behind. T... |
Memetic algorithm : In computer science and operations research, a memetic algorithm (MA) is an extension of an evolutionary algorithm (EA) that aims to accelerate the evolutionary search for the optimum. An EA is a metaheuristic that reproduces the basic principles of biological evolution as a computer algorithm in or... |
Memetic algorithm : Inspired by both Darwinian principles of natural evolution and Dawkins' notion of a meme, the term memetic algorithm (MA) was introduced by Pablo Moscato in his technical report in 1989 where he viewed MA as being close to a form of population-based hybrid genetic algorithm (GA) coupled with an indi... |
Memetic algorithm : The no-free-lunch theorems of optimization and search state that all optimization strategies are equally effective with respect to the set of all optimization problems. Conversely, this means that one can expect the following: The more efficiently an algorithm solves a problem or class of problems, ... |
Memetic algorithm : The learning method/meme used has a significant impact on the improvement results, so care must be taken in deciding which meme or memes to use for a particular optimization problem. The frequency and intensity of individual learning directly define the degree of evolution (exploration) against indi... |
Memetic algorithm : Memetic algorithms have been successfully applied to a multitude of real-world problems. Although many people employ techniques closely related to memetic algorithms, alternative names such as hybrid genetic algorithms are also employed. Researchers have used memetic algorithms to tackle many classi... |
Memetic algorithm : IEEE Workshop on Memetic Algorithms (WOMA 2009). Program Chairs: Jim Smith, University of the West of England, U.K.; Yew-Soon Ong, Nanyang Technological University, Singapore; Gustafson Steven, University of Nottingham; U.K.; Meng Hiot Lim, Nanyang Technological University, Singapore; Natalio Krasno... |
Minimum Population Search : In evolutionary computation, Minimum Population Search (MPS) is a computational method that optimizes a problem by iteratively trying to improve a set of candidate solutions with regard to a given measure of quality. It solves a problem by evolving a small population of candidate solutions b... |
Minimum Population Search : In a similar way to Differential evolution, MPS uses difference vectors between the members of the population in order to generate new solutions. It attempts to provide an efficient use of function evaluations by maintaining a small population size. If the population size is smaller than the... |
Minimum Population Search : A basic variant of the MPS algorithm works by having a population of size equal to the dimension of the problem. New solutions are generated by exploring the hyperplane defined by the current solutions (by means of difference vectors) and performing an additional orthogonal step in order to ... |
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 t... |
Population model (evolutionary algorithm) : In the island model, also called the migration model or coarse grained model, evolution takes place in strictly divided subpopulations. These can be organised panmictically, but do not have to be. From time to time an exchange of individuals takes place, which is called migra... |
Population model (evolutionary algorithm) : The neighbourhood model, also called diffusion model or fine grained model, defines a topological neighbouhood relation between the individuals of a population that is independent of their phenotypic properties. The fundamental idea of this model is to provide the EA populati... |
Population model (evolutionary algorithm) : When applying both population models to genetic algorithms, evolutionary strategy and other EAs, the splitting of a total population into subpopulations usually reduces the risk of premature convergence and leads to better results overall more reliably and faster than would b... |
Population model (evolutionary algorithm) : Since both population models imply population partitioning, they are well suited as a basis for parallelizing an EA. This applies even more to cellular EAs, since they rely only on locally available information about the members of their respective demes. Thus, in the extreme... |
Population model (evolutionary algorithm) : Erick Cantú-Paz (2001): Efficient and Accurate Parallel Genetic Algorithms (PhD thesis, University of Illinois, Urbana-Champaign, USA). Springer, New York, NY. ISBN 978-1-4613-6964-6 doi:10.1007/978-1-4615-4369-5 Martina Gorges-Schleuter (1990): Genetic Algorithms and Populat... |
Population model (evolutionary algorithm) : Cellular automaton Dual-phase evolution Evolutionary algorithm Metaheuristic == References == |
Premature convergence : Premature convergence is an unwanted effect in evolutionary algorithms (EA), a metaheuristic that mimics the basic principles of biological evolution as a computer algorithm for solving an optimization problem. The effect means that the population of an EA has converged too early, resulting in b... |
Premature convergence : Strategies to regain genetic variation can be: a mating strategy called incest prevention, uniform crossover, mimicking sexual selection, favored replacement of similar individuals (preselection or crowding), segmentation of individuals of similar fitness (fitness sharing), increasing population... |
Premature convergence : It is hard to determine when premature convergence has occurred, and it is equally hard to predict its presence in the future. One measure is to use the difference between the average and maximum fitness values, as used by Patnaik & Srinivas, to then vary the crossover and mutation probabilities... |
Premature convergence : There are a number of presumed or hypothesized causes for the occurrence of premature convergence. |
Premature convergence : Evolutionary computation Evolution == References == |
Ensemble learning : In statistics and machine learning, ensemble methods use multiple learning algorithms to obtain better predictive performance than could be obtained from any of the constituent learning algorithms alone. Unlike a statistical ensemble in statistical mechanics, which is usually infinite, a machine lea... |
Ensemble learning : Supervised learning algorithms search through a hypothesis space to find a suitable hypothesis that will make good predictions with a particular problem. Even if this space contains hypotheses that are very well-suited for a particular problem, it may be very difficult to find a good one. Ensembles ... |
Ensemble learning : Empirically, ensembles tend to yield better results when there is a significant diversity among the models. Many ensemble methods, therefore, seek to promote diversity among the models they combine. Although perhaps non-intuitive, more random algorithms (like random decision trees) can be used to pr... |
Ensemble learning : While the number of component classifiers of an ensemble has a great impact on the accuracy of prediction, there is a limited number of studies addressing this problem. A priori determining of ensemble size and the volume and velocity of big data streams make this even more crucial for online ensemb... |
Ensemble learning : R: at least three packages offer Bayesian model averaging tools, including the BMS (an acronym for Bayesian Model Selection) package, the BAS (an acronym for Bayesian Adaptive Sampling) package, and the BMA package. Python: scikit-learn, a package for machine learning in Python offers packages for e... |
Ensemble learning : In recent years, due to growing computational power, which allows for training in large ensemble learning in a reasonable time frame, the number of ensemble learning applications has grown increasingly. Some of the applications of ensemble classifiers include: |
Ensemble learning : Ensemble averaging (machine learning) Bayesian structural time series (BSTS) Mixture of experts |
Ensemble learning : Zhou Zhihua (2012). Ensemble Methods: Foundations and Algorithms. Chapman and Hall/CRC. ISBN 978-1-439-83003-1. Robert Schapire; Yoav Freund (2012). Boosting: Foundations and Algorithms. MIT. ISBN 978-0-262-01718-3. |
Ensemble learning : Robi Polikar (ed.). "Ensemble learning". Scholarpedia. The Waffles (machine learning) toolkit contains implementations of Bagging, Boosting, Bayesian Model Averaging, Bayesian Model Combination, Bucket-of-models, and other ensemble techniques |
AdaBoost : AdaBoost (short for Adaptive Boosting) is a statistical classification meta-algorithm formulated by Yoav Freund and Robert Schapire in 1995, who won the 2003 Gödel Prize for their work. It can be used in conjunction with many types of learning algorithm to improve performance. The output of multiple weak lea... |
AdaBoost : AdaBoost refers to a particular method of training a boosted classifier. A boosted classifier is a classifier of the form F T ( x ) = ∑ t = 1 T f t ( x ) (x)=\sum _^f_(x) where each f t is a weak learner that takes an object x as input and returns a value indicating the class of the object. For example, in... |
AdaBoost : This derivation follows Rojas (2009): Suppose we have a data set ,y_),\ldots ,(x_,y_)\ where each item x i has an associated class y i ∈ \in \ , and a set of weak classifiers ,\ldots ,k_\ each of which outputs a classification k j ( x i ) ∈ (x_)\in \ for each item. After the ( m − 1 ) -th iteration our... |
AdaBoost : Boosting is a form of linear regression in which the features of each sample x i are the outputs of some weak learner h applied to x i . While regression tries to fit F ( x ) to y ( x ) as precisely as possible without loss of generalization, typically using least square error E ( f ) = ( y ( x ) − f ( ... |
AdaBoost : Boosting can be seen as minimization of a convex loss function over a convex set of functions. Specifically, the loss being minimized by AdaBoost is the exponential loss ∑ i ϕ ( i , y , f ) = ∑ i e − y i f ( x i ) , \phi (i,y,f)=\sum _e^f(x_), whereas LogitBoost performs logistic regression, minimizing ∑ i ϕ... |
AdaBoost : With: Samples x 1 … x n \dots x_ Desired outputs y 1 … y n , y ∈ \dots y_,y\in \ Initial weights w 1 , 1 … w n , 1 \dots w_ set to 1 n Error function E ( f ( x ) , y i ) = e − y i f ( x i ) )=e^f(x_) Weak learners h : x → For t in 1 … T : Choose h t ( x ) (x) : Find weak learner h t ( x ) (x) that mini... |
AdaBoost : Bootstrap aggregating CoBoosting BrownBoost Gradient boosting Multiplicative weight update method § AdaBoost algorithm |
AdaBoost : == Further reading == |
BrownBoost : BrownBoost is a boosting algorithm that may be robust to noisy datasets. BrownBoost is an adaptive version of the boost by majority algorithm. As is the case for all boosting algorithms, BrownBoost is used in conjunction with other machine learning methods. BrownBoost was introduced by Yoav Freund in 2001. |
BrownBoost : AdaBoost performs well on a variety of datasets; however, it can be shown that AdaBoost does not perform well on noisy data sets. This is a result of AdaBoost's focus on examples that are repeatedly misclassified. In contrast, BrownBoost effectively "gives up" on examples that are repeatedly misclassified.... |
BrownBoost : BrownBoost uses a non-convex potential loss function, thus it does not fit into the AdaBoost framework. The non-convex optimization provides a method to avoid overfitting noisy data sets. However, in contrast to boosting algorithms that analytically minimize a convex loss function (e.g. AdaBoost and LogitB... |
BrownBoost : Input: m training examples ( x 1 , y 1 ) , … , ( x m , y m ) ,y_),\ldots ,(x_,y_) where x j ∈ X , y j ∈ Y = \in X,\,y_\in Y=\ The parameter c Initialise: s = c . (The value of s is the amount of time remaining in the game) r i ( x j ) = 0 (x_)=0 ∀ j . The value of r i ( x j ) (x_) is the margin at it... |
BrownBoost : In preliminary experimental results with noisy datasets, BrownBoost outperformed AdaBoost's generalization error; however, LogitBoost performed as well as BrownBoost. An implementation of BrownBoost can be found in the open source software JBoost. |
BrownBoost : Boosting AdaBoost Alternating decision trees |
Cascading classifiers : Cascading is a particular case of ensemble learning based on the concatenation of several classifiers, using all information collected from the output from a given classifier as additional information for the next classifier in the cascade. Unlike voting or stacking ensembles, which are multiexp... |
Cascading classifiers : The term is also used in statistics to describe a model that is staged. For example, a classifier (for example k-means), takes a vector of features (decision variables) and outputs for each possible classification result the probability that the vector belongs to the class. This is usually used ... |
Cascading classifiers : Boosting (meta-algorithm) Bootstrap aggregating |
Cascading classifiers : Gama, J.; Brazdil, P. (2000). "Cascade Generalization". Machine Learning. 41 (3): 315–343. CiteSeerX 10.1.1.46.635. doi:10.1023/a:1007652114878. S2CID 36907021. Minguillón, J. (2002). On Cascading Small Decision Trees (PhD thesis). Universitat Autònoma de Barcelona. Zhao, H.; Ram, S. (2004). "Co... |
Gaussian process emulator : In statistics, Gaussian process emulator is one name for a general type of statistical model that has been used in contexts where the problem is to make maximum use of the outputs of a complicated (often non-random) computer-based simulation model. Each run of the simulation model is computa... |
Gaussian process emulator : Kriging Computer experiment |
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