Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Random number generators

  • Pierre L'Ecuyer
Reference work entry
First Online:
DOI: https://doi.org/10.1007/1-4020-0611-X_852
How to cite

INTRODUCTION

Several algorithms and heuristics in operations research require a source of random numbers. Such numbers are needed, for example, for Monte Carlo integration, stochastic discrete-event simulation, and probabilistic algorithms (like genetic algorithms or simulated annealing). Typically, the so-called “random numbers” are produced by a deterministic computer program, and are therefore not random at all. The aim of such a program, called a random number generator, is to produce a sequence of values which “look” as if they were a typical sample of i.i.d. (independent and identically distributed) random variables, say from the U(0,1) distribution (the uniform distribution between 0 and 1). Some generators may also produce random integers, or random bits, etc. Since the sequence produced is really deterministic, it is often called a pseudorandom sequence and the generator producing it is then called a pseudorandom number generator. Here, we adopt the well-accepted practice of...

This is a preview of subscription content, log in to check access.

References

  1. [1]
    Blum, L., Blum, M., and Shub, M. (1986). “A Simple Unpredictable Pseudo-Random Number Generator,” SIAM Jl. Comput., 15, 364–383.Google Scholar
  2. [2]
    Bratley, P., Fox, B.L., and Schrage, L.E. (1987). A Guide to Simulation, 2nd ed. Springer-Verlag, New York.Google Scholar
  3. [3]
    Compagner, A. (1991). “Definitions of Randomness,” Amer. Jl. Physics, 59, 700–705.Google Scholar
  4. [4]
    Compagner, A. (1995). “Operational Conditions for Random Number Generation” Physical Review E, 52, 5634–5645.Google Scholar
  5. [5]
    Couture, R. and L'Ecuyer, P. (1994). “On the Lattice Structure of Certain Linear Congruential Sequences Related to AWC/SWB Generators,” Math. of Computation 62, 798–808.Google Scholar
  6. [6]
    Couture, R., L'Ecuyer, P., and Tezuka, S. (1993). “On the Distribution of k-Dimensional Vectors for Simple and Combined Tausworthe Sequences,” Math. of Computation, 60, 749–761 & S11–S16.Google Scholar
  7. [7]
    Devroye, L. (1986). Non-Uniform Random Variate Generation, Springer-Verlag, New York.Google Scholar
  8. [8]
    Eichenauer-Herrmann, J. (1995). “Pseudorandom Number Generation by Nonlinear Methods,” International Statist. Revs., 63, 247–255.Google Scholar
  9. [9]
    Fishman, G. (1996). Monte Carlo: Concepts, Algorithms, and Applications. Springer-Verlag, New York.Google Scholar
  10. [10]
    Fushimi, M. and Tezuka, S. (1983). “The k-Distribution of Generalized Feedback Shift Register Pseudo random Numbers,” Communications of the ACM, 26, 516–523.Google Scholar
  11. [11]
    Hellekalek, P. (1995). Inversive Pseudorandom Number Generators: Concepts, Results, and Links,” in Proc. 1995 Winter Simulation Conference, eds. C. Alexopoulos, K. Kang, W.R., Lilegdon, and D. Goldsman, 255–262, IEEE Press, Piscataway, New Jersey.Google Scholar
  12. [12]
    Knuth, D.E. (1997). The Art of Computer Programming, Vol. 2: Semi numerical Algorithms, 3rd ed. Addison-Wesley, Reading, Massachusetts.Google Scholar
  13. [13]
    L'Ecuyer, P. (1990). “Random Numbers for Simulation,” Communications of the ACM, 33, 85–97.Google Scholar
  14. [14]
    L'Ecuyer, P. (1994). “Uniform Random Number Generation,” Annals Operations Research, 53, 77–120.Google Scholar
  15. [15]
    L'Ecuyer, P. (1996a). “Combined Multiple Recursive Random Number Generators,” Operations Research, 44, 816–822.Google Scholar
  16. [16]
    L'Ecuyer, P. (1996b). “Maximally Equidistributed Combined Tausworthe Generators,” Math. Computation, 65, 203–213.Google Scholar
  17. [17]
    L'Ecuyer, P. (1997). “Bad Lattice Structures for Vectors of Non-Successive Values Produced by Some Linear Recurrences,” INFORMS Jl. Computing, 9, 57–60.Google Scholar
  18. [18]
    L'Ecuyer, P. (1999a). “Good Parameters and Implementations for Combined Multiple Recursive Random Number Generators,” to appear in Operations Research. Google Scholar
  19. [19]
    L'Ecuyer, P. (1999b). “Tables of Maximally Equidistributed Combined LFSR Generators,” to appear in Math. Computation. Google Scholar
  20. [20]
    L'Ecuyer, P. and Andres, T.H. (1997). “A Random Number Generator Based on the Combination of Four LCGs,” Math. and Computers in Simulation, 44, 99–107.Google Scholar
  21. [21]
    L'Ecuyer, P., Blouin, F., and Couture, R. (1993). “A Search for Good Multiple Recursive Random Number Generators,” ACM Trans. Modeling and Computer Simulation, 3(2), 87–98.Google Scholar
  22. [22]
    L'Ecuyer, P. and Côté, S. (1991). “Implementing a Random Number Package with Splitting Facilities,” ACM Trans. Math. Software, 17, 98–111.Google Scholar
  23. [23]
    L'Ecuyer, P., Simard, R., and Wegenkittl, S. (1998). “Sparse Serial tests of Uniformity for Random Number Generation,”submitted. Google Scholar
  24. [24]
    Marsaglia, G. (1985). “A Current View of Random Number Generation,” in Computer Science and Statistics, Proceedings of the Sixteenth Symposium on the Interface, 3–10, Elsevier/North Holland, Amsterdam.Google Scholar
  25. [25]
    Matsumoto, M. and Nishimura, T. (1998). “Mersenne Twister: A 623-dimensionally Equidistributed Uniform Pseudo-Random Number Generator,” ACM Trans. Modeling and Computer Simulation, 8(1), 3–30.Google Scholar
  26. [26]
    Niederreiter, H. (1992). Random Number Generation and Quasi-Monte Carlo Methods, SIAM CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 63, SIAM, Philadelphia. Google Scholar
  27. [27]
    Ripley, B.D. (1990). “Thoughts on Pseudorandom Number Generators,” Jl. Computational and Applied Math., 31, 153–163.Google Scholar
  28. [28]
    Tezuka, S. (1995). Uniform Random Numbers: Theory and Practice. Kluwer Academic, Norwell, Massachusetts.Google Scholar
  29. [29]
    Tezuka, S. and L'Ecuyer, P. (1991). “Efficient and Portable Combined Tausworthe Random Number Generators,” ACM Trans. Modeling and Computer Simulation, 1(2), 99–112.Google Scholar
  30. [30]
    Wang, D. and Compagner, A. (1993). “On the Use of Reducible Polynomials as Random Number Generators,” Math. of Computation, 60, 363–374.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Pierre L'Ecuyer
    • 1
  1. 1.Université de MontréalQueébecCanada