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Mersenne Twister: A 623dimensionally equidistributed uniform pseudorandom number generator
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Random number generation
"... Random numbers are the nuts and bolts of simulation. Typically, all the randomness required by the model is simulated by a random number generator whose output is assumed to be a sequence of independent and identically distributed (IID) U(0, 1) random variables (i.e., continuous random variables dis ..."
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Cited by 136 (30 self)
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Random numbers are the nuts and bolts of simulation. Typically, all the randomness required by the model is simulated by a random number generator whose output is assumed to be a sequence of independent and identically distributed (IID) U(0, 1) random variables (i.e., continuous random variables distributed uniformly over the interval
Maximally Equidistributed Combined Tausworthe Generators
, 1996
"... Tausworthe random number generators based on a primitive trinomial allow an easy and fast implementation when their parameters obey certain restrictions. However, such generators, with those restrictions, have bad statistical properties unless we combine them. A generator is called maximally equidis ..."
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Cited by 75 (21 self)
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Tausworthe random number generators based on a primitive trinomial allow an easy and fast implementation when their parameters obey certain restrictions. However, such generators, with those restrictions, have bad statistical properties unless we combine them. A generator is called maximally equidistributed if its vectors of successive values have the best possible equidistribution in all dimensions. This paper shows how to find maximally equidistributed combinations in an efficient manner, and gives a list of generators with that property. Such generators have a strong theoretical support and lend themselves to very fast software implementations.
Improved longperiod generators based on linear recurrences modulo 2
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 2006
"... Fast uniform random number generators with extremely long periods have been defined and implemented based on linear recurrences modulo 2. The twisted GFSR and the Mersenne twister are famous recent examples. Besides the period length, the statistical quality of these generators is usually assessed v ..."
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Cited by 38 (7 self)
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Fast uniform random number generators with extremely long periods have been defined and implemented based on linear recurrences modulo 2. The twisted GFSR and the Mersenne twister are famous recent examples. Besides the period length, the statistical quality of these generators is usually assessed via their equidistribution properties. The hugeperiod generators proposed so far are not quite optimal in that respect. In this paper, we propose new generators of that form, with better equidistribution and “bitmixing ” properties for equivalent period length and speed. The state of our new generators evolves in a more chaotic way than for the Mersenne twister. We illustrate how this can reduce the impact of persistent dependencies among successive output values, which can be observed in certain parts of the period of gigantic generators such as the Mersenne twister.
TestU01: A Software Library in ANSI C for Empirical Testing of Random Number Generators
, 2007
"... This document describes the software library TestU01, implemented in the ANSI C language, and offering a collection of utilities for the (empirical) statistical testing of uniform random number generators (RNG). The library implements several types of generators in generic form, as well as many spec ..."
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Cited by 18 (2 self)
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This document describes the software library TestU01, implemented in the ANSI C language, and offering a collection of utilities for the (empirical) statistical testing of uniform random number generators (RNG). The library implements several types of generators in generic form, as well as many specific generators proposed in the literature or found in widelyused software. It provides general implementations of the classical statistical tests for random number generators, as well as several others proposed in the literature, and some original ones. These tests can be applied to the generators predefined in the library and to userdefined generators. Specific tests suites for either sequences of uniform random numbers in [0, 1] or bit sequences are also available. Basic tools for plotting vectors of points produced by generators are provided as well. Additional software permits one to perform systematic studies of the interaction between a specific test and the structure of the point sets produced by a given family of RNGs. That is, for a given kind of test and a given class of RNGs, to determine how large should be the sample size of the test, as a function of the generator’s period length, before the generator starts to fail the test systematically.
Random Number Generators: Selection Criteria and Testing
, 1998
"... this paper, we shall assume that the sequence is purely periodic, in the sense that the initial state s 0 is always revisited. In other words, the sequence has no transient part. The goal is to make it hard to distinguish between the output of the generator and a typical realization of an i.i.d. uni ..."
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Cited by 15 (7 self)
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this paper, we shall assume that the sequence is purely periodic, in the sense that the initial state s 0 is always revisited. In other words, the sequence has no transient part. The goal is to make it hard to distinguish between the output of the generator and a typical realization of an i.i.d. uniform sequence over U . In
Random Number Generators with Period Divisible by a Mersenne Prime
 Proc. ICCSA 2003
, 2003
"... Pseudorandom numbers with long periods and good statistical properties are often required for applications in computational finance. We consider the requirements for good uniform random number generators, and describe a class of generators whose period is a Mersenne prime or a small multiple of ..."
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Cited by 14 (5 self)
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Pseudorandom numbers with long periods and good statistical properties are often required for applications in computational finance. We consider the requirements for good uniform random number generators, and describe a class of generators whose period is a Mersenne prime or a small multiple of a Mersenne prime. These generators are based on "almost primitive" trinomials, that is trinomials having a large primitive factor. They enable very fast vector/parallel implementations with excellent statistical properties.
Construction of Equidistributed Generators based on linear recurrences modulo 2
, 2000
"... Random number generators based on linear recurrences modulo 2 are widely used and appear in dierent forms, such as the simple and combined Tausworthe generators, the GFSR, and the twisted GFSR generators. Lowdiscrepancy point sets for quasiMonte Carlo integration can also be constructed based on t ..."
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Cited by 13 (6 self)
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Random number generators based on linear recurrences modulo 2 are widely used and appear in dierent forms, such as the simple and combined Tausworthe generators, the GFSR, and the twisted GFSR generators. Lowdiscrepancy point sets for quasiMonte Carlo integration can also be constructed based on these linear recurrences. The quality of these generators or point sets is usually measured by certain equidistribution criteria. Combining two or more recurrences and adding linear output transformations can be used to improve the equidistribution properties. In this
A Numerical Comparison of Some Modified Controlled Random Search Algorithms
, 1997
"... In this paper we propose a new version of the Controlled Random Search (CRS) algorithm of Price [13, 14, 15]. The new algorithm has been tested on thirteen global optimization test problems. Numerical experiments indicate that the resulting algorithm performs considerably better than the earlier ver ..."
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Cited by 13 (1 self)
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In this paper we propose a new version of the Controlled Random Search (CRS) algorithm of Price [13, 14, 15]. The new algorithm has been tested on thirteen global optimization test problems. Numerical experiments indicate that the resulting algorithm performs considerably better than the earlier versions of the CRS algorithms. The algorithm, therefore, could offer a reasonable alternative to many currently available stochastic algorithms, especially for problems requiring `direct search' type methods. Also a classification of the CRS algorithms is made based on `global technique'  `local technique' and the relative performance of classes is numerically explored. Keywords: Global optimization, fidistribution, controlled random search 1 Introduction A global optimization algorithm aims at finding a global minimizer or its close approximation of a function f : S ae R n ! R. A point x is said to be a global minimizer of f if f = f(x ) f(x); 8x 2 S. We assume that the func...
Population Set Based Global Optimization Algorithms: Some Modifications and Numerical Studies
, 2003
"... This paper studies the e#ciency and robustness of some recent and well known population set based direct search global optimization methods such as Controlled Random Search, Di#erential Evolution, and the Genetic Algorithm. Some modifications are made to Di#erential Evolution and to the Genetic Algo ..."
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Cited by 13 (2 self)
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This paper studies the e#ciency and robustness of some recent and well known population set based direct search global optimization methods such as Controlled Random Search, Di#erential Evolution, and the Genetic Algorithm. Some modifications are made to Di#erential Evolution and to the Genetic Algorithm to improve their e#ciency and robustness. All methods are tested on two sets of test problems, one composed of easy but commonly used problems and the other of a number of relatively di#cult problems. Keywords: Global Optimization, Direct Search Method, Controlled Random Search, Di#erential Evolution, Genetic Algorithm, Continuous Variable.