Polynomial Optimization in Mathematical Models Defining Experimental Data Dependencies

摘要

In this paper, the algorithm to mathematically model fragments, which are extracted from non-linear experimental dependencies, is developed, and represents the key steps within the Cut-Glue approximation method. The hybrid search algorithm is based on the classical regression analysis, which takes into account the polynomial structures implemented through the combinatorial laws, and low dimensionality. In the case when the direct search is resource-impossible, the modified evolutionary-genetic algorithm (EGA) is applied. The advantage of the developed algorithm is the guarantee that the optimal polynomial structure exists and can be found. The proposed approach carries out the structural-parametric optimization for each of the studied fragments to define its experimental data dependence. The validation of the polynomial structural-optimization is performed by applying a specially developed software tool, which, in theory, makes possible to approximate fragments of any dimension.