Abstract
The UniCalc solver [3] was designed at the Russian Institute of Artificial Intelligence to solve systems of nonlinear equations and inequalities with possibly inexact data. UniCalc uses the computation techniques based on the subdefinite computations method [13], which can be regarded as an analogue of constraint propagation with interval labels [4]. To implement this method, algorithms of interval mathematics are used, so UniCalc can also be used to solve interval problems. Another feature of UniCalc is its ability to solve different integer problems and problems with mixed data types (integers and reals). The efficiency of UniCalc is confirmed by the results of its successful applications to many problems, from benchmark (test) problems (see, e.g., [8, 10]) to real-life problems. Some optimization problems [11] have also been successfully solved by these techniques.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
G. Alefeld and Ju. Herzberger, Introduction in Interval Computations, Academic Press, N. Y., 1983.
N. S. Asaithambi, Shen Zuhe, and R. E. Moore, “On computing the range of values”, Computing, 1982, Vol. 28, pp. 225–237.
A. B. Babichev, O. B. Kadyrova, T. P. Kashevarova, A. S. Leshchenko, and A. L. Semenov, “UniCalc, A Novel Approach to Solving Systems of Algebraic Equations”, Proceedings of the International Conference on Numerical Analysis with Automatic Result Verifications. Lafayette, Louisiana, USA, February–March, 1993. Interval Computations, 1993, No. 2, pp. 29–47.
E. Davis, “Constraint propagation with interval labels”, Artificial Intelligence, 1987, Vol. 32, pp. 99–118.
E. Hansen, Global Optimization Using Interval Analysis, Marcel Dekker Inc., N. Y., 1992.
H. K. Jacobsen and H.C. Pedersen, An optimization system for teaching purposes, Eksamenproject, IMSOR, DTH, Lyngby, 1976.
T. P. Kashevarova and A. L. Semenov, “Solving Subdefinite Problems for Systems of Ordinary Differential Equations of the First Order in the UniCalc System”, All-Union Scientific-Technical Conference Intelligent Systems in Machine Building, Abstracts, Samara, 1991, pp. 21–24.
R. B. Kearfott, “Some Tests of Generalized Bisection”, ACM Transactions on Mathematical Software, 1987, No. 3, pp. 197–220.
K. Madsen, Parallel Algorithms for Global Optimization Report 91-07, Institute for Numerical Analysis, The Technical University of Denmark, Lyngby, Denmark, 1991.
K. Meintjes and A. P. Morgan, “Chemical Equilibrium Systems as Numerical Test Problems”, ACM Transactions on Mathematical Software, 1990, No. 2, pp. 143–151.
J. J. More, B. S. Garbow, and K. E. Hillstrom, “Testing Unconstrained Optimization Software”, ACM Transactions on Mathematical Software, 1981, No. 1, pp. 17–41.
A. S. Narin’yani, “Active data types for representing and processing of sub-definite information”, In: Actual Problems of the Computer Architecture Development and Computer System Software, Novosibirsk, USSR Acad. of Sciences, Siberian Division, Computer Center, 1983, pp. 128–141.
A. S. Narin’yani, “Subdefiniteness in knowledge representation and processing systems”, Transactions of USSR Acad, of Sciences, Technical Cybernetics, 1986, No. 5, pp. 3–28.
G. L. Nemhauser, A. H. G. Rinnooy Kan, and M. J. Todd (eds.), Handbooks in Operational Research and Management Science, Vol. 1. Optimization, North-Holland, 1989.
C. C. Petersen, “Computational experience with variants of the Balas algorithm applied to the selection of R and D Projects”, Management Science, 1967, Vol. 13, No. 9, pp. 736–750.
A. L. Semenov, Solving Integer/Real Nonlinear Equations by Constraint Propagation, Technical Report No. 12, Institute of Mathematical Modelling, The Technical University of Denmark, Lyngby, Denmark, 1994.
A. L. Semenov and A. S. Leshchenko, “Interval and Symbolic Computations in the UniCalc Solver”, International Conference on Interval and Computer-Algebraic Methods in Science and Engineering INTERVAL-94, Abstracts, St-Petersburg, Russia, March, 1994, pp. 206–208.
A. L. Semenov and D. V. Petunin, “The Use of Multiintervals in the UniCalc Solver”, The International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics SCAN-95. Wuppertal, Germany, September, 1995 (to appear).
V. V. Telerman, Active data types, Preprint 792, USSR Acad. of Sciences, Siberian Division, Computer Center, Novosibirsk, 1988.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Kluwer Academic Publishers
About this chapter
Cite this chapter
Semenov, A.L. (1996). Solving Optimization Problems with Help of the UniCalc Solver. In: Kearfott, R.B., Kreinovich, V. (eds) Applications of Interval Computations. Applied Optimization, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3440-8_9
Download citation
DOI: https://doi.org/10.1007/978-1-4613-3440-8_9
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-3442-2
Online ISBN: 978-1-4613-3440-8
eBook Packages: Springer Book Archive