MATHEMATICAL MODELS AND APPROACHES TO SOLVING OPTIMIZATION PROBLEMS OF ARTIFICIAL INTELLIGENCE

Abstract

The optimization problems of artificial intelligence include the problems of recognition (images, speech), the problems of clinical diagnosis, comparison of texts on plagiarism, automatic translation of texts from one language to another, classification and more. To implement problems in an automated way, it is necessary to adequately formulate their mathematical model. Although many papers have been devoted to this problem, a precise mathematical formulation that would allow algorithms to be developed that are effective in solving them has not yet been developed. Also, the objective function is not simulated explicitly for them. In addition, the resulting global solution for the modeled objective function does not always coincide with the purpose of the study. This is due to the fact that characteristic feature these problems is the presence of a situation of uncertainty, which complicates both their modeling and resolution. Various approaches are used to model problems of this class, in particular stochastic, logical-linguistic methods, Markov models, linear integer programming, pattern recognition theory, neural networks. To solve them, a fast method of spreading constraints and heuristic methods are used. Heuristic algorithms are usually understood as ways of making decisions similar to how a person does it, and built on intuitive reasoning based on previous experience. The use of heuristic algorithms is widespread in problems of recognition of different nature. For many practical problems, these algorithms are almost the only possible way to obtain a satisfactory solution in real time. Much of the applied problems of artificial intelligence in the process of solving them require a search for options, which indicates their combinatorial nature. Therefore, these problems are reduced to the problems of combinatorial optimization. Known modeling methods do not always explain combinatorial nature of artificial intelligence problems. In this paper, mathematical models using combinatorial optimization theory are constructed for some problems of this class. It is shown that the argument of the objective function are combinatorial configurations of various types.