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Shekel Function
The Shekel function or also Shekel's foxholes is a multidimensional, multimodal, continuous, deterministic function commonly used as a test function for testing optimization techniques. The mathematical form of a function in n dimensions with m maxima is: f(\vec) = \sum_^ \; \left( c_ + \sum\limits_^ (x_ - a_)^2 \right)^ or, similarly, f(x_1,x_2,...,x_,x_n) = \sum_^ \; \left( c_ + \sum\limits_^ (x_ - a_)^2 \right)^ Global minima Numerically certified global minima and the corresponding solutions were obtained using interval methods for up to n = 10.Vanaret C. (2015Hybridization of interval methods and evolutionary algorithms for solving difficult optimization problems.PhD thesis. Ecole Nationale de l'Aviation Civile. Institut National Polytechnique de Toulouse, France. 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: * Convergenc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shekel 2D
Shekel or sheqel ( akk, 𒅆𒅗𒇻 ''šiqlu'' or ''siqlu,'' he, שקל, plural he, שקלים or shekels, Phoenician: ) is an ancient Mesopotamian coin, usually of silver. A shekel was first a unit of weight—very roughly —and became currency in ancient Tyre and ancient Carthage and then in ancient Israel under the Maccabees. Name The word is based on the Semitic verbal root for "weighing" (''Š-Q-L''), cognate to the Akkadian or , a unit of weight equivalent to the Sumerian . Use of the word was first attested in during the Akkadian Empire under the reign of Naram-Sin, and later in in the Code of Hammurabi. The ''Š-Q-L'' root is found in the Hebrew words for "to weigh" (), "weight" () and "consideration" (). It is cognate to the Aramaic root ''T-Q-L'' and the Arabic ''root Θ-Q-L'' ''ثقل'', in words such as (the weight), (heavy) or (unit of weight). The famous writing on the wall in the Biblical Book of Daniel includes a cryptic use of the word in Aram ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the function and the set is called the codomain of the function.Codomain ''Encyclopedia of Mathematics'Codomain. ''Encyclopedia of Mathematics''/ref> The earliest known approach to the notion of function can be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimization (mathematics)
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 maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Test Functions For Optimization
In applied mathematics, test functions, known as artificial landscapes, are useful to evaluate characteristics of optimization algorithms, such as: * Convergence rate. * Precision. * Robustness. * 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 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) Multiobjective optimization us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
