Test Functions For Optimization

picture info	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]
picture info	Pareto Front In multi-objective optimization, the Pareto front (also called Pareto frontier or Pareto curve) is the set of all Pareto efficient solutions. The concept is widely used in engineering. It allows the designer to restrict attention to the set of efficient choices, and to make tradeoffs within this set, rather than considering the full range of every parameter. Definition The Pareto frontier, ''P''(''Y''), may be more formally described as follows. Consider a system with function f: X \rightarrow \mathbb^m, where ''X'' is a compact set of feasible decisions in the metric space \mathbb^n, and ''Y'' is the feasible set of criterion vectors in \mathbb^m, such that Y = \. We assume that the preferred directions of criteria values are known. A point y^ \in \mathbb^m is preferred to (strictly dominates) another point y^ \in \mathbb^m, written as y^ \succ y^. The Pareto frontier is thus written as: : P(Y) = \. Marginal rate of substitution A significant aspect of the Pareto frontie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Matyas Contour Matyas may refer to: * Mátyás, Hungarian name * Matyáš Matyáš is a Czech masculine given name, cognate to Matthew. Notable people with the name include: * Matyáš Bělohradský (born 2001), Czech figure skater * Matyáš Démar (born 1991), Czech volleyball player * Matyáš Hanč (born 2004), Cze ... , Czech name {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	McCormick Contour McCormick may refer to: Business * McCormick & Company, an American food company specializing in spices and flavorings * McCormick & Schmick's, an American restaurant chain specializing in seafood * McCormick Harvesting Machine Company, a manufacturer of the first mechanical reaper * McCormick Distilling Company, an American distillery * McCormick Tractors, a manufacturer of tractors, headquartered in Fabbrico, Italy Education * McCormick Observatory, at the University of Virginia * McCormick Theological Seminary, a Presbyterian school of theology in Chicago, Illinois * Robert R. McCormick School of Engineering and Applied Science, at Northwestern University, Evanston, Illinois Places in the United States * McCormick, Illinois * McCormick, South Carolina * McCormick, Washington * McCormick Gap, a windgap in Virginia Sports * McCormick Place, an exposition complex in Chicago, Illinois * McCormick Field, a Minor League Baseball park in Asheville, North Carolina Other uses ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	McCormick Function McCormick may refer to: Business * McCormick & Company, an American food company specializing in spices and flavorings * McCormick & Schmick's, an American restaurant chain specializing in seafood * McCormick Harvesting Machine Company, a manufacturer of the first mechanical reaper * McCormick Distilling Company, an American distillery * McCormick Tractors, a manufacturer of tractors, headquartered in Fabbrico, Italy Education * McCormick Observatory, at the University of Virginia * McCormick Theological Seminary, a Presbyterian school of theology in Chicago, Illinois * Robert R. McCormick School of Engineering and Applied Science, at Northwestern University, Evanston, Illinois Places in the United States * McCormick, Illinois * McCormick, South Carolina * McCormick, Washington * McCormick Gap, a windgap in Virginia Sports * McCormick Place, an exposition complex in Chicago, Illinois * McCormick Field, a Minor League Baseball park in Asheville, North Carolina Other uses ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Hölder Table Function Hölder: * ''Hölder, Hoelder'' as surname * Hölder condition * Hölder's inequality In mathematical analysis, Hölder's inequality, named after Otto Hölder, is a fundamental inequality between integrals and an indispensable tool for the study of spaces. :Theorem (Hölder's inequality). Let be a measure space and let with . ... * Hölder mean * Jordan–Hölder theorem {{Disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]