On probabilistic bounds inspired by interval arithmetic

• Autorzy: Zilinskas A. , Zilinskas J.
• Języki publikacji: EN

Abstrakty

EN

A randomized method aimed at evaluation of probabilistic bounds for function values is considered. Stochastic intervals tightly covering ranges of function values with probability close to one are modelled by a randomized method inspired by interval arithmetic. Statistical properties of the modelled intervals are investigated experimentally. The experimental results are discussed with respect to application of this method in the construction of a branch and bound type randomized algorithm for global optimization.

Słowa kluczowe

EN

global optimization; branch and bound method; randomized computing; interval arithmetic

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2010
• Tom: Vol. 39, no 2
• Strony: 507--525
• Opis fizyczny: Bibliogr. 23 poz., rys., wykr.

Twórcy

autor

Zilinskas A.

autor

Zilinskas J.

• Institute of Mathematics and Informatics, Akademijos 4, LT-08663 Vilnius, Lithuania,

Bibliografia

• ALT, R. and LAMOTTE, J.L. (2001) Experiments on the evaluation of functional ranges using random interval arithmetic. Mathematics and Computers in Simulation, 56 (1), 17-34.
• ALT, R., LAMOTTE, J.L. and MARKOV, S. (2006) On the numerical solution to linear problems using stochastic arithmetic. Proc. ACM Symposium on Applied Computing, 3, Dijon, France, 1055-1059.
• BASAK, P., BASAK, I. and BALAKRISHNAN, N. (2009) Estimation for three-parameter lognormal distribution based on progressively censored data. Computational Statistics and Data Analysis, 53 (10), 3580-3592.
• CSENDES, T. (1998) Optimization methods for process network synthesis - a case study. In: C. Carlsson and I. Eriksson, eds., Global & Multiple Criteria Optimization and Information Systems Quality. Abo Academy, Turku, 113-132.
• FLOUDAS, C.A., AKROTIRIANAKIS, I.G., CARATZOULAS, S., MEYER, C.A. and KALLRATH, J. (2005) Global optimization in the 21st century: Advances and challenges. Computers & Chemical Engineering, 29(6), 1185-1202.
• HANSEN, E. and WALSTER, G.W. (2003) Global Optimization Using Interval Analysis, 2nd. edn. Marcel Dekker, New York.
• HORST, R., PARDALOS, P. and THOAI, N. (1995) Introduction to Global Optimization. Kluwer, Dodrecht.
• KREINOVICH, V., NESTEROV, V.M. and ZHELUDEVA, N.A. (1996) Interval methods that are guaranteed to underestimate (and the resulting new justification of Kaucher arithmetic). Reliable Computing, 2(2), 119-124.
• LEONE, P., NELSON, L. and NOTINGHAM, R. (1961) The folded normal distribution. Technometrics, 3(4), 543-550.
• LERCH, M., TISCHLER, G., VON GUDENBERG, J.W., HOFSCHUSTER, W. and KRAMER, W. (2001) The Interval Library filib++2.0 - Design, Features and Sample Programs. Preprint 2001/4, Universitat Wuppertal.
• MARKOT, M.C., FERNANDEZ, J., CASADO, L.G. and CSENDES, T. (2006) New interval methods for constrained global optimization. Math. Programming, Ser. A, 106, 287-318.
• MARKOV, S., ALT, R. and LAMOTTE, J. (2004) Stochastic arithmetic: s-spaces and some applications. Numerical Algorithms, 37, 275-284.
• RAJASEKARAN, S., PARDALOS, P.M., REIF, J.H. and ROLIM, J.D. (2001) Handbook of Randomized Computing, 1 and 2. Kluwer, Dodrecht.
• SUN, M., and JOHNSON, A.W. (2005) Interval branch and bound with local sampling for constrained global optimization. Journal of Global Optimization, 33, 61-82.
• WINGO, D. (1984) Fitting three-parameter lognormal models by numerical global optimization - an improved algorithm. Computational Statistics and Data Analysis, 2, 13-25.
• ZHIGLJAVSKY, A. (1990) Branch and probability bound methods for global optimization. Informatica, 1, 125-140.
• ZHIGLJAVSKY, A. and ZILINSKAS, A. (2008) Stochastic Global Optimization. Springer, New York.
• ZILINSKAS, A. and ZILINSKAS, J. (2006) On efficiency of tightening bounds in interval global optimization. LNCS 3732. Springer, 197-205.
• ZILINSKAS, A. and ZILINSKAS, J. (2005) On underestimating in interval com-putations. BIT Numerical Mathematics, 45(2), 415-427.
• ZILINSKAS, J. and BOGLE, I.D.L. (2003) Evaluation ranges of functions using balanced random interval arithmetic. Informatica, 14(3), 403-416.
• ZILINSKAS, J. and BOGLE, I.D.L. (2004) Balanced random interval arithmetic. Computers & Chemical Engineering, 28(5), 839-851.
• ZILINSKAS, J. (2005) Comparison of packages for interval arithmetic. Informatica, 16(1), 145-154.
• ZILINSKAS, J. (2006) Estimation of functional ranges using standard and inner interval arithmetic. Informatica, 17(1), 125-136.