Scholarly record
A SUCCESSIVE MULTI-EXTREMUM APPROXIMATION ALGORITHMS BASED ON SPECIAL FUNCTIONS IN THE ENVIRONMENTAL IMPACTS RESEARCHES ON TECHNOGENIC SYSTEMS
Abstract
Approximation of multi-extremum functions problems arise in a wide range of fields including deterministic and stochastic technics, multi-parameter optimization. The main focus of this thesis is to consider the different principle of approximation problem. Experimental definition of external impacts on complex technogenic systems is related to technical difficulties. This area of research arises from the fact that many problems of multi-extremum optimization are known to be computationally difficult (NP-hard). We propose a new approach to approximation based on the special (in particular, spherically symmetric infinite differentiable) functions. We design new approximation algorithms on structured and unstructured meshes which can be used as a tool for multi-extremum optimization. These algorithms are simple to implement and they are stable. The freedom choice of a basic function provides an opportunity to create the analytical expression for several practical models. The theoretical formulas of the proposed algorithm are derived, and the simulations results are presented. A problem of the environmental factors impacts on complex technogenic systems is used to demonstrate the possibilities of computational tools developed. The results computed for pilot studies are presented with the usage of various components of multi-extremum approximation. Furthermore, these algorithms are suitable for applying approximation techniques for implementation on parallel computers.
Publication Impact Profile
Publication details
References12
Xiablo Li, Yonglin Lei, Weiping Wang, Wenguang Wang, Yifan Yiu, A DSM-based multy-paradigm simulation modeling approach for complex systems, In Proceedings of the 2013 Winter Simulation Conference, pp 1179-1190, 2013.
Shiqian, W., Meng Joo E., Dynamic fuzzy neural networks-a novel approach to function approximation, Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on Neural Network, 30(2), pp 358-364, 2000.
Nicolaos B. Karayiannis, Mary M. Randolph-Gips, The Construction and Training of Reformulated Radial Basis Function Neural Networks, IEEE Transactions on Neural Networks, vol.4, pp 835-844, 2003
Deep, K., Das K.N. , Quadratic approximation based hybrid genetic algorithm for function optimization, Applied Mathematics and Computation, 203(1), pp 86-98, 2008.
Baqais A., Genetic algorithm for function approximation: an experimental investigation, International Journal of Artificial Intelligence and Applications, vol. 7, 2016.
Solovieva E.V., Selenko B.P., Koshev A.N., Method of express analysis the environmental impact, Measuring and computing devices in technological processes, International scientific-technical magazine, Khmelnitsky, vol. 1, pp 175-179, 2002.
Pechersky D.K., Petrunina E.V., Special functions in approximation technique for telemetric medical tasks. II international conference intelligent technologies and means of rehabilitation of people with disabilities, Russia, vol.1, pp 101-105, 2017.
Erohin A.T., Approximation technique for random processes based on special functions, Geophysics methods for environment monitoring, Russia, pp 115-125, 1991.
Joel A Tropp, Greed is good: algorithmic results for sparse approximation, IEEE Transactions on Information Theory, 50(10), pp 2231–2242, 2004.
Liu B., Practice of Uncertain Programming, Physica-Verlag, Heidelberg, 2002.
Gillis N., Luce. R., A fast gradient method for nonnegative sparse regression with self dictionary, arXiv preprint arXiv:1610.01349, 2016.
Ankenbrandt C., An Extension To the Theory of Convergence and A Proof of the Time Complexity of Genetic Algorithms, Foundations of Genetic Algorithms, Morgan Kaufman, pp 53-68, 1991.
View or Download full articleAccess options
SWS access login
Login as SWS Scientific CommitteeLogin as SWS Scientific PartnerLogin as SWS AuthorAuthors and approved SWS contributors will read and export their own linked papers after identity matching by SWS profile, email and SGEM GlobalID.
For librarian assistance: [email protected]
Purchase Instant Access
- Article can be downloaded after successful payment.
- Article may be used according to SWS library access terms.
- Article cannot be redistributed.
