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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.
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