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Adaptive Coordinate Descent
Adaptive coordinate descent is an improvement of the coordinate descent algorithm to non-separable optimization by the use of adaptive encoding. The adaptive coordinate descent approach gradually builds a transformation of the coordinate system such that the new coordinates are as decorrelated as possible with respect to the objective function. The adaptive coordinate descent was shown to be competitive to the state-of-the-art evolutionary algorithms and has the following invariance properties: # Invariance with respect to monotonous transformations of the function (scaling) # Invariance with respect to orthogonal transformations of the search space (rotation). CMA-like Adaptive Encoding Update (b) mostly based on principal component analysis (a) is used to extend the coordinate descent method (c) to the optimization of non-separable problems (d). The adaptation of an appropriate coordinate system allows adaptive coordinate descent to outperform coordinate descent on non-separab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordinate Descent
Coordinate descent is an optimization algorithm that successively minimizes along coordinate directions to find the minimum of a function. At each iteration, the algorithm determines a coordinate or coordinate block via a coordinate selection rule, then exactly or inexactly minimizes over the corresponding coordinate hyperplane while fixing all other coordinates or coordinate blocks. A line search along the coordinate direction can be performed at the current iterate to determine the appropriate step size. Coordinate descent is applicable in both differentiable and derivative-free contexts. Description Coordinate descent is based on the idea that the minimization of a multivariable function F(\mathbf) can be achieved by minimizing it along one direction at a time, i.e., solving univariate (or at least much simpler) optimization problems in a loop. In the simplest case of ''cyclic coordinate descent'', one cyclically iterates through the directions, one at a time, minimizing the objec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can perform automated deductions (referred to as automated reasoning) and use mathematical and logical tests to divert the code execution through various routes (referred to as automated decision-making). Using human characteristics as descriptors of machines in metaphorical ways was already practiced by Alan Turing with terms such as "memory", "search" and "stimulus". In contrast, a Heuristic (computer science), heuristic is an approach to problem solving that may not be fully specified or may not guarantee correct or optimal results, especially in problem domains where there is no well-defined correct or optimal result. As an effective method, an algorithm ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maxima and minima, maximizing or minimizing a Function of a real variable, real function by systematically choosing Argument of a function, input values from within an allowed set and computing the Value (mathematics), value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, opti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adaptive Encoding
Adaptation, in biology, is the process or trait by which organisms or population better match their environment Adaptation may also refer to: Arts * Adaptation (arts), a transfer of a work of art from one medium to another ** Film adaptation, a story from another work, adapted into a film ** Literary adaptation, a story from a literary source, adapted into another work ** ** Theatrical adaptation, a story from another work, adapted into a play * ''Adaptation'' (film), a 2002 film by Spike Jonze * "Adaptation" (''The Walking Dead''), a television episode *''Adaptation'', a 2012 novel by Malinda Lo Biology and medicine * Adaptation (eye), the eye's adjustment to light ** Chromatic adaptation, visual systems' adjustments to changes in illumination for preservation of colors ** Prism adaptation, sensory-motor adjustments after the visual field has been artificially shifted * Cellular adaptation, changes by cells/tissues in response to changed microenvironments * High-altitude ad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallel Problem Solving From Nature
Parallel Problem Solving from Nature, or PPSN, is a research conference focusing on the topic of natural computing. Other conferences in the area include the ACM Genetic and Evolutionary Computation Conference (GECCO), the IEEE Congress on Evolutionary Computation (CEC) and EvoStar (Evo*). In 2020 PPSN got a CORE rank of A, corresponding to an ''"excellent conference, and highly respected in a discipline area"''. History The idea behind PPSN emerged around 1989-1990 when Bernard Manderick, Reinhard Männer, Heinz Mühlenbein, and Hans-Paul Schwefel, realised they shared a common field of study that was not covered by the conferences on Operations Research, Physics, or Computer Science they attended regularly. The field of Genetic Algorithms had already been established in the form of the ICGA conference in 1985, but the "fathers" of PPSN wanted a wider focus, with algorithms that included problem solving, parallel computing and the use of natural metaphors (such as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evolutionary Algorithms
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 applications o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonal Transform
In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express this is Q^\mathrm Q = Q Q^\mathrm = I, where is the transpose of and is the identity matrix. This leads to the equivalent characterization: a matrix is orthogonal if its transpose is equal to its inverse: Q^\mathrm=Q^, where is the inverse of . An orthogonal matrix is necessarily invertible (with inverse ), unitary (), where is the Hermitian adjoint (conjugate transpose) of , and therefore normal () over the real numbers. The determinant of any orthogonal matrix is either +1 or −1. As a linear transformation, an orthogonal matrix preserves the inner product of vectors, and therefore acts as an isometry of Euclidean space, such as a rotation, reflection or rotoreflection. In other words, it is a unitary transformation. The set of orthogonal matrices, under multiplication, forms the group , known as the orthogonal gr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CMA-ES
Covariance matrix adaptation evolution strategy (CMA-ES) is a particular kind of strategy for numerical optimization. Evolution strategies (ES) are stochastic, derivative-free methods for numerical optimization of non-linear or non-convex continuous optimization problems. They belong to the class of evolutionary algorithms and evolutionary computation. An evolutionary algorithm is broadly based on the principle of biological evolution, namely the repeated interplay of variation (via recombination and mutation) and selection: in each generation (iteration) new individuals (candidate solutions, denoted as x) are generated by variation, usually in a stochastic way, of the current parental individuals. Then, some individuals are selected to become the parents in the next generation based on their fitness or objective function value f(x). Like this, over the generation sequence, individuals with better and better f-values are generated. In an evolution strategy, new candidate solutions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principal Component Analysis
Principal component analysis (PCA) is a popular technique for analyzing large datasets containing a high number of dimensions/features per observation, increasing the interpretability of data while preserving the maximum amount of information, and enabling the visualization of multidimensional data. Formally, PCA is a statistical technique for reducing the dimensionality of a dataset. This is accomplished by linearly transforming the data into a new coordinate system where (most of) the variation in the data can be described with fewer dimensions than the initial data. Many studies use the first two principal components in order to plot the data in two dimensions and to visually identify clusters of closely related data points. Principal component analysis has applications in many fields such as population genetics, microbiome studies, and atmospheric science. The principal components of a collection of points in a real coordinate space are a sequence of p unit vectors, where th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adaptive Coordinate Descent Illustration
Adaptation, in biology, is the process or trait by which organisms or population better match their environment Adaptation may also refer to: Arts * Adaptation (arts), a transfer of a work of art from one medium to another ** Film adaptation, a story from another work, adapted into a film ** Literary adaptation, a story from a literary source, adapted into another work ** ** Theatrical adaptation, a story from another work, adapted into a play * ''Adaptation'' (film), a 2002 film by Spike Jonze * "Adaptation" (''The Walking Dead''), a television episode *''Adaptation'', a 2012 novel by Malinda Lo Biology and medicine * Adaptation (eye), the eye's adjustment to light ** Chromatic adaptation, visual systems' adjustments to changes in illumination for preservation of colors ** Prism adaptation, sensory-motor adjustments after the visual field has been artificially shifted * Cellular adaptation, changes by cells/tissues in response to changed microenvironments * High-altitude ad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rosenbrock Function
In mathematical optimization, the Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is used as a performance test problem for optimization algorithms. It is also known as Rosenbrock's valley or Rosenbrock's banana function. The global minimum is inside a long, narrow, parabolic shaped flat valley. To find the valley is trivial. To converge to the global minimum, however, is difficult. The function is defined by f(x, y) = (a-x)^2 + b(y-x^2)^2 It has a global minimum at (x, y)=(a, a^2), where f(x, y)=0. Usually, these parameters are set such that a = 1 and b = 100. Only in the trivial case where a=0 the function is symmetric and the minimum is at the origin. Multidimensional generalisations Two variants are commonly encountered. One is the sum of N/2 uncoupled 2D Rosenbrock problems, and is defined only for even Ns: : f(\mathbf) = f(x_1, x_2, \dots, x_N) = \sum_^ \left 00(x_^2 - x_)^2 + (x_ - 1)^2 \right This variant has p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rosenbrock2D
Rosenbrock is a surname. Notable people with the surname include: *Eddie Rosenbrock (1908–1978), Australian rules footballer *Howard Harry Rosenbrock Howard Harry Rosenbrock (16 December 1920 – 21 October 2010) was a leading figure in control theory and control engineering. He was born in Ilford, England in 1920, graduated in 1941 from University College London with a 1st class honors degree ... (1920–2010), English control theorist and engineer * Peter Rosenbrock (1939–2005), Australian rules footballer {{surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
