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Test Functions For Optimization
In applied mathematics, test functions, known as artificial landscapes, are useful to evaluate characteristics of optimization algorithms, such as Rate of convergence, convergence rate, precision, robustness and general performance. Here some test functions are presented with the aim of giving an idea about the different situations that optimization algorithms have to face when coping with these kinds of problems. In the first part, some objective functions for single-objective optimization cases are presented. In the second part, test functions with their respective Pareto front, Pareto fronts for multi-objective optimization problems (MOP) are given. The artificial landscapes presented herein for single-objective optimization problems are taken from Bäck, Haupt et al. and from Rody Oldenhuis software. Given the number of problems (55 in total), just a few are presented here. The test functions used to evaluate the algorithms for MOP were taken from Deb,Deb, Kalyanmoy (2002) Mul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rate Of Convergence
In mathematical analysis, particularly numerical analysis, the rate of convergence and order of convergence of a sequence that converges to a limit are any of several characterizations of how quickly that sequence approaches its limit. These are broadly divided into rates and orders of convergence that describe how quickly a sequence further approaches its limit once it is already close to it, called asymptotic rates and orders of convergence, and those that describe how quickly sequences approach their limits from starting points that are not necessarily close to their limits, called non-asymptotic rates and orders of convergence. Asymptotic behavior is particularly useful for deciding when to stop a sequence of numerical computations, for instance once a target precision has been reached with an iterative root-finding algorithm, but pre-asymptotic behavior is often crucial for determining whether to begin a sequence of computations at all, since it may be impossible or imprac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matyas Function
Matyas may refer to: * Mátyás Mátyás () is a Hungarian given name meaning Matthias. Notable people with the given name Mátyás: * Mátyás Bél, Hungarian scientist * Mátyás Cseszneky, Hungarian magnate and cavalry commander * Mátyás Rákosi, Hungarian communist poli ..., Hungarian name * Matyáš, Czech name {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hölder Table Function
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Hölder: * ''Hölder, Hoelder'' as surname * Hölder condition * Hölder's inequality * Hölder mean * Jordan–Hölder theorem In abstract algebra, a composition series provides a way to break up an algebraic structure, such as a group or a module, into simple pieces. The need for considering composition series in the context of modules arises from the fact that many na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Himmelblau Contour Plot
Himmelblau is a German language surname, which means " skyblue".''Behind the Name''"Surname Blau" Retrieved on 26 January 2016. Notable people with the surname include: * David Himmelblau (1924–2011), American scientist * Fabian Himmelblau (1860–1931), Polish bookseller and publisher See also *Coop Himmelb(l)au, an architectural firm *Himmelblau's function, in mathematical optimization *PerfektBreitHimmelblau "PerfektBreitHimmelblau" ("Perfect Stoned Sky-blue") are three songs and a triple A-side-single by the German rock band Die Ärzte. The songs are tracks 8, 3 and 1 of their 2007 album ''Jazz ist anders''. Track listings The track listing ..., a set of songs References {{surname German-language surnames German words and phrases Surnames of Jewish origin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Himmelblau's Function
In mathematical optimization, Himmelblau's function is a multi-modal function, used to test the performance of optimization algorithms. The function is defined by: : f(x, y) = (x^2+y-11)^2 + (x+y^2-7)^2.\quad It has one local maximum at x = -0.270845 and y = -0.923039 where f(x,y) = 181.617 , and four identical local minima: * f(3.0, 2.0) = 0.0, \quad * f(-2.805118, 3.131312) = 0.0, \quad * f(-3.779310, -3.283186) = 0.0, \quad * f(3.584428, -1.848126) = 0.0. \quad The locations of all the minima can be found analytically. However, because they are roots of quartic polynomials, when written in terms of radicals, the expressions are somewhat complicated. The function is named after David Mautner Himmelblau (1924–2011), who introduced it. See also *Test functions for optimization In applied mathematics, test functions, known as artificial landscapes, are useful to evaluate characteristics of optimization algorithms, such as Rate of convergence, convergence rate, precis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
