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Particle Swarm Optimization
In computational science, particle swarm optimization (PSO) is a computational method that Mathematical optimization, optimizes a problem by iterative method, iteratively trying to improve a candidate solution with regard to a given measure of quality. It solves a problem by having a population of candidate solutions, here dubbed Point particle, particles, and moving these particles around in the Optimization (mathematics)#Concepts and notation, search-space according to simple formula, mathematical formulae over the particle's Position (vector), position and velocity. Each particle's movement is influenced by its local best known position, but is also guided toward the best known positions in the search-space, which are updated as better positions are found by other particles. This is expected to move the swarm toward the best solutions. PSO is originally attributed to James Kennedy (social psychologist), Kennedy, Russell C. Eberhart, Eberhart and Yuhui Shi, Shi and was first int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Swarm Intelligence
Swarm intelligence (SI) is the collective behavior of decentralized, self-organized systems, natural or artificial. The concept is employed in work on artificial intelligence. The expression was introduced by Gerardo Beni and Jing Wang in 1989, in the context of cellular robotic systems. Swarm intelligence systems consist typically of a population of simple agents or boids interacting locally with one another and with their environment.Hu, J.; Turgut, A.; Krajnik, T.; Lennox, B.; Arvin, F.,Occlusion-Based Coordination Protocol Design for Autonomous Robotic Shepherding Tasks IEEE Transactions on Cognitive and Developmental Systems, 2020. The inspiration often comes from nature, especially biological systems. The agents follow very simple rules, and although there is no centralized control structure dictating how individual agents should behave, local, and to a certain degree random, interactions between such agents lead to the emergence of "intelligent" global behavior, unkno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Schools Of Thought
A school of thought, or intellectual tradition, is the perspective of a group of people who share common characteristics of opinion or outlook of a philosophy, discipline, belief, social movement, economics, cultural movement, or art movement. History The phrase has become a common colloquialism which is used to describe those that think alike or those that focus on a common idea. The term's use is common place. Schools are often characterized by their currency, and thus classified into "new" and "old" schools. There is a convention, in political and philosophical fields of thought, to have "modern" and "classical" schools of thought. An example is the modern and classical liberals. This dichotomy is often a component of paradigm shift. However, it is rarely the case that there are only two schools in any given field. Schools are often named after their founders such as the " Rinzai school" of Zen, named after Linji Yixuan; and the Asharite school of early Muslim philoso ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Meta-optimization
Meta-optimization from numerical optimization is the use of one optimization method to tune another optimization method. Meta-optimization is reported to have been used as early as in the late 1970s by Mercer and Sampson for finding optimal parameter settings of a genetic algorithm. Meta-optimization and related concepts are also known in the literature as meta-evolution, super-optimization, automated parameter calibration, hyper-heuristics, etc. Motivation Optimization methods such as genetic algorithm and differential evolution have several parameters that govern their behaviour and efficiency in optimizing a given problem and these parameters must be chosen by the practitioner to achieve satisfactory results. Selecting the behavioural parameters by hand is a laborious task that is susceptible to human misconceptions of what makes the optimizer perform well. The behavioural parameters of an optimizer can be varied and the optimization performance plotted as a landscape. This ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
PSO Meta-Fitness Landscape (12 Benchmark Problems)
PSO may refer to: Orchestras *Pacific Symphony Orchestra *Peoria Symphony Orchestra *Pittsburgh Symphony Orchestra *Plano Symphony Orchestra *Portland Symphony Orchestra * Perth Symphony Orchestra Science and technology * Particle swarm optimization, a swarm intelligence optimization technique * Password Settings Object, used in Windows Active Directory environments * Phase-shift oscillator, an electronic circuit that generates sine waves * Protocol Support Organization, one of the three initial components of ICANN, later disbanded * PSO J318.5-22, a rogue planet discovered in 2013 Other uses * Pakistan State Oil * Patient safety organization * Paysite operator, the operator of a paysite, typically pornographic * Peace Support Operations, a military term used by NATO * Penalty shootout, a method of determining a winner in sports matches which would have otherwise been drawn or tied * ''Phantasy Star Online'', a series of online role-playing video games ** ''Phantasy Star On ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Parameter Selection
A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc. ''Parameter'' has more specific meanings within various disciplines, including mathematics, computer programming, engineering, statistics, logic, linguistics, and electronic musical composition. In addition to its technical uses, there are also extended uses, especially in non-scientific contexts, where it is used to mean defining characteristics or boundaries, as in the phrases 'test parameters' or 'game play parameters'. Modelization When a system is modeled by equations, the values that describe the system are called ''parameters''. For example, in mechanics, the masses, the dimensions and shapes (for solid bodies), the densities and the viscosities ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Uniform Distribution (continuous)
In probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions. Such a distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. The bounds are defined by the parameters, a and b, which are the minimum and maximum values. The interval can either be closed (i.e. ,b/math>) or open (i.e. (a,b)). Therefore, the distribution is often abbreviated U(a,b), where U stands for uniform distribution. The difference between the bounds defines the interval length; all intervals of the same length on the distribution's support are equally probable. It is the maximum entropy probability distribution for a random variable X under no constraint other than that it is contained in the distribution's support. Definitions Probability density function The probability density function of the continuous uniform distribution is f(x) = \begin \dfrac & ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Real Number
In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and in many other branches of mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives. The set of real numbers, sometimes called "the reals", is traditionally denoted by a bold , often using blackboard bold, . The adjective ''real'', used in the 17th century by René Descartes, distinguishes real numbers from imaginary numbers such as the square roots of . The real numbers include the rational numbers, such as the integer and the fraction . The rest of the real numbers are called irrational numbers. Some irrational numbers (as well as all the rationals) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Row Vector
In linear algebra, a column vector with elements is an m \times 1 matrix consisting of a single column of entries, for example, \boldsymbol = \begin x_1 \\ x_2 \\ \vdots \\ x_m \end. Similarly, a row vector is a 1 \times n matrix for some , consisting of a single row of entries, \boldsymbol a = \begin a_1 & a_2 & \dots & a_n \end. (Throughout this article, boldface is used for both row and column vectors.) The transpose (indicated by ) of any row vector is a column vector, and the transpose of any column vector is a row vector: \begin x_1 \; x_2 \; \dots \; x_m \end^ = \begin x_1 \\ x_2 \\ \vdots \\ x_m \end and \begin x_1 \\ x_2 \\ \vdots \\ x_m \end^ = \begin x_1 \; x_2 \; \dots \; x_m \end. The set of all row vectors with entries in a given field (such as the real numbers) forms an -dimensional vector space; similarly, the set of all column vectors with entries forms an -dimensional vector space. The space of row vectors with entries can be regarded as the dual spac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Quasi-newton Methods
In numerical analysis, a quasi-Newton method is an Iterative method, iterative numerical method used either to Root-finding algorithm, find zeroes or to Mathematical optimization, find local maxima and minima of functions via an iterative recurrence formula much like the one for Newton's method, except using approximations of the Derivative, derivatives of the functions in place of exact derivatives. Newton's method requires the Jacobian matrix and determinant, Jacobian matrix of all Partial derivative, partial derivatives of a multivariate function when used to search for zeros or the Hessian matrix when used Newton's method in optimization, for finding extrema. Quasi-Newton methods, on the other hand, can be used when the Jacobian matrices or Hessian matrices are unavailable or are impractical to compute at every iteration. Some Iterative method, iterative methods that reduce to Newton's method, such as sequential quadratic programming, may also be considered quasi-Newton methods ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Gradient Descent
Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for minimizing a differentiable multivariate function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent. Conversely, stepping in the direction of the gradient will lead to a trajectory that maximizes that function; the procedure is then known as ''gradient ascent''. It is particularly useful in machine learning for minimizing the cost or loss function. Gradient descent should not be confused with local search algorithms, although both are iterative methods for optimization. Gradient descent is generally attributed to Augustin-Louis Cauchy, who first suggested it in 1847. Jacques Hadamard independently proposed a similar method in 1907. Its convergence properties for non-linear optimization problems were first studied by Has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Differentiable Function
In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non- vertical tangent line at each interior point in its domain. A differentiable function is smooth (the function is locally well approximated as a linear function at each interior point) and does not contain any break, angle, or cusp. If is an interior point in the domain of a function , then is said to be ''differentiable at'' if the derivative f'(x_0) exists. In other words, the graph of has a non-vertical tangent line at the point . is said to be differentiable on if it is differentiable at every point of . is said to be ''continuously differentiable'' if its derivative is also a continuous function over the domain of the function f. Generally speaking, is said to be of class if its first k derivatives f^(x), f^(x), \ldots, f^(x) exist and are continuous over the domain of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
