Extraction of optimization models from data: an application of neural networks

This paper continues the research within the paradigm of extracting or building optimization models from data (BOMD) for intelligent control systems. The obtained results are devoted to nonlinear models with real variables, generally speaking, of any functional complexity in the class of functions of arbitrary degree of smoothness and constraints represented by piecewise linear approximation. This is achieved through the use of neural networks as the main used mathematical apparatus.

If the initial training information presents the precedents of both the objective function and the characteristic function of constraints, it is proposed to use an approach based on the training of two neural networks: NN1 — for the synthesis of the objective function and NN2 — for the synthesis of the approximating characteristic function of constraints.

Unfortunately, the solution of the problem presented by such the synthesized 2-neural model may end up finding, generally speaking, a local conditional extremum. In order to find the global extremum of the multiextremal objective function, a heuristic algorithm based on a preliminary classification of the search area by using the decision tree is developed.

The presented in the paper approach to an extraction of conditionally optimization model from the data for the case when there is no information on the points not belonging to the set of admissible solutions is fundamentally novel. For this case, a heuristic algorithm for approximating the region of admissible solutions based on the allocation of regular (non-random) empty segments of the search area is developed. When using this approach in practice in intelligent control systems, it is necessary to additionally apply human-machine procedures for verification and correction of synthesized models.