Abstract
The results presented in this paper make up the basis for a new way of analyzing extremal problems. A new phenomenon that characterizes an extremal problem has been discovered. The paper tries to reveal fields of application of this phenomenon. The method of animated visual analysis, based on the knowledge discovery in the set of observations of the objective function of the problem interactively, has been developed. The aim of analysis is to find a direction in the definition domain such that maximizes the mean absolute difference between two values of the objective function calculated at randomly selected points in this direction, or (and) maximizes the mean absolute difference per distance unit of the objective function values calculated at two randomly selected points in this direction. The presented approach requires generating many data sets. Sometimes such a generation is very computation-expensive. Therefore, the ideas discussed in this paper may be applied in the case where the investigator wants not only to solve the extremal problem, but also to discover additional knowledge of it.
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Bibliography
Frawley, W. J., Piatetsky-Shapiro, G. and Matheus, C. J.: Knowledge discovery in data-bases: An overview, In: G. Piatetsky-Shapiro and C. J. Matheus (eds), Knowledge Discovery in Databases, AAAI Press/The MIT Press, 1991, pp. 1–27.
Fayyad, U. M., Piatetsky-Shapiro, G., Smyth, P. and Uthurusamay, R. (eds): Advances in Knowledge Discovery and Data Mining, AAAI Press/The MIT Press, 1996.
Dzemyda, G.: Knowledge Discovery Seeking a Higher Optimization Efficiency, Research Report Presented for Habilitation, Mokslo Aidai, Vilnius, 1997. ISBN 9986-479-28-2.
Jones, C. V.: Visualization and optimization, Interactive Transactions of Operations Research and Management Science (ITORMS) 2(1) (1998). http://orcs.bus.okstate.edu/jones98/ and http://www.chesapeake2.com/itorms/.
Leipert, S., Diehl, M., Jünger, M. I. and Kupke, J.: VBCTOOL — a Graphical Interface for Visualization of Branch Cut Algorithms the Tree Interface Version 1.0.1, University of Cologne, 1997. http://www.informatik.uni-koeln.de/ls-juenger/projects/vbctool.html.
Dean, N., Mevenkamp, M. and Monma, C. L.: Netpad: An interactive graphics system for network modeling and optimization, In: O. Balci, R. Sharda and S. A. Zenios (eds), Computer Science and Operations Research: New Developments in Their Interfaces, Pergamon Press, Oxford, 1992, pp. 231–243.
Jones, C. V: Animated sensitivity analysis, In: O. Balci, R. Sharda and S. A. Zenios (eds), Computer Science and Operations Research: New Developments in Their Interfaces, Pergamon Press, Oxford, 1992, pp. 177–196.
Buchanan, I. and McKinnon, K.: An animated interactive modelling system for decision support, European J. Oper. Res. 54 (1991), 306–317.
Carpendale, M. S. T., Cowperthwaite, D. J. and Fracchia, F. D.: 3-dimensional pliable surfaces: For the effective presentation of visual information, In: UIST Proceedings: ACM Symposium on User Interface Software and Technology, ACM Press, New York, 1995, pp. 217–226.
Beshers, C. and Feiner, S.: Auto Visual: Rule-based design of interactive multivariate visualizations, IEEE Comput. Graphics Appl. 13(4) (1993), 41–49.
Chatterjee, A., Das, P. P. and Bhattacharya, S.: Visualization in linear programming using parallel coordinates, Pattern Recognition 26(11) (1993), 1725–1736.
Dzemyda, G.: LP-search with extremal problem structure analysis, In: N. K. Sinha and L. A. Telksnys (eds), Proceedings of the 2nd IFAC Symposium, IFAC Proceedings Series, No. 2, Pergamon Press, 1987, pp. 499–502.
Dzemyda, G.: Visual analysis of a set of function values, In: Proceedings of the 13th International Conference on Pattern Recognition, Vol. 2, Track B, Pattern Recognition and Signal Analysis, IEEE Computer Society Press, Los Alamitos, CA 1996, pp. 700–704.
Dzemyda, G.: On the visual analysis of extremal problems, Informatica (Institute of Mathematics and Informatics, Vilnius) 8(2) (1997), 181–214.
Šaltenis, V. and Dzemyda, G.: The structure analysis of extremal problems using some approximation of characteristics, In: A. Žilinskas (ed.), Teorija Optimaljnych Reshenij, Vol. 8, Inst. Math. Cybern., Vilnius, 1982, pp. 124–138 (in Russian).
Šaltenis, V.: Structure Analysis of Optimization Problems (in Russian), Mokslas, Vilnius, 1989.
Dixon, L. C. W. and Szego, G. P.: The global optimization problem: An introduction, In: L. C. W. Dixon and G. P. Szego (eds), Towards Global Optimization 2, North-Holland, 1978, pp. 1–15.
Dzemyda, G. (ed.): The Package of Applied Programs for Dialogue Solving of Multiextremal Problems MINIMUM: The Description of Using (in Russian), The State Fund of Algorithms and Programs (Reg.No50860000112), Inst. Math. Cybern., Vilnius, 1985.
Dzemyda, G.: Multiextremal problem of computer-aided design, Informatica (Institute of Mathematics and Informatics, Vilnius) 6(3) (1995), 249–263.
Reyment, R. A. and Joreskog, K. G: Applied Factor Analysis in the Natural Sciences, Cambridge University Press, Cambridge, 1993.
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Dzemyda, G. (2002). Animated Visual Analysis of Extremal Problems. In: Dzemyda, G., Šaltenis, V., Žilinskas, A. (eds) Stochastic and Global Optimization. Nonconvex Optimization and Its Applications, vol 59. Springer, Boston, MA. https://doi.org/10.1007/0-306-47648-7_5
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DOI: https://doi.org/10.1007/0-306-47648-7_5
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