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The function is commonly used as a minimization function with global minimum value 0 at 0,.., 0 in the form due to Thomas Bäck. While Ackley gives the function as an example of "fine-textured broadly unimodal space" his thesis does not actually use the function as a test. For dimensions, is defined as [2]
A class diagram exemplifying the singleton pattern.. In object-oriented programming, the singleton pattern is a software design pattern that restricts the instantiation of a class to a singular instance.
The test functions used to evaluate the algorithms for MOP were taken from Deb, [4] Binh et al. [5] and Binh. [6] The software developed by Deb can be downloaded, [ 7 ] which implements the NSGA-II procedure with GAs, or the program posted on Internet, [ 8 ] which implements the NSGA-II procedure with ES.
A set such as {{,,}} is a singleton as it contains a single element (which itself is a set, but not a singleton). A set is a singleton if and only if its cardinality is 1. In von Neumann's set-theoretic construction of the natural numbers, the number 1 is defined as the singleton {}.
For example, the factory interface is commonly implemented as a singleton to provide global access for creating flyweights. Generally speaking, the retrieval algorithm begins with a request for a new object via the factory interface. The request is typically forwarded to an appropriate cache based on what kind of object it is. If the request is ...
A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector (that is, the dimension of the domain could be 1 or greater than 1); the ...
A function : is monotone in this topological sense if and only if it is non-increasing or non-decreasing, which is the usual meaning of "monotone function" in real analysis. A function between topological spaces is (sometimes) called a proper map if every fiber is a compact subspace of its domain. However, many authors use other non-equivalent ...
In mathematical optimization, the Rastrigin function is a non-convex function used as a performance test problem for optimization algorithms. It is a typical example of non-linear multimodal function. It was first proposed in 1974 by Rastrigin [1] as a 2-dimensional function and has been generalized by Rudolph. [2]